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Infinite Powers: How Calculus Reveals the Secrets of the Universe: Strogatz, Steven: 9780358299288: Amazon.com: Books
2020-04-14
Steven H Strogatz
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 Infinite Powers: How Calculus Reveals the Secrets of the Universe Paperback – April 14, 2020

 by Steven Strogatz (Author)
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 From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better.

 Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

 Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

 Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.

 As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

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 1. Print length
 400 pages
 2. Language
 English
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 Mariner Books
 4. Publication date
 April 14, 2020
 5. Dimensions
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 6. ISBN-10
 0358299284
 7. ISBN-13
 978-0358299288
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 1. Three mysteries above all have spurred its development: the mystery of curves, the mystery of motion, and the mystery of change.
 Highlighted by 1,468 Kindle readers
 2. That’s the big idea behind calculus. Everything becomes simpler at infinity.
 Highlighted by 1,418 Kindle readers
 3. The breakthrough came from insisting that curves were actually made of straight pieces. It wasn’t true, but one could pretend that it was.
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 Editorial Reviews

 Review

 A New York Times Bestseller Featured on NPR's Science Friday Shortlisted for the 2019 Royal Society Science Book Prize Named one of 10 Best Books to Read this Spring by Amazon's Chris Schluep “Marvelous . . . an array of witty and astonishing stories . . . to illuminate how calculus has helped bring into being our contemporary world and so many of the instruments whose role we now blithely assume.” —The Washington Post “Fortunately, we live in an era when a top mathematician can write a book about calculus that is accessible to the mathematically challenged...it is the historical detail in the book that not only allows me to follow the math by taking me through how it was discovered, but also sticks in my mind. [Strogatz] makes me want to get out a textbook and start studying calculus.” —Five Books “Wonderful . . . bringing the insights of calculus — among the most important of all developments in the history of mathematics — to everyone.” —Brian Greene, on Twitter “I've never read a clearer explanation of calculus or the significant powers we gained by harnessing infinity. Michael and I highly recommend it!” —Vsauce, on Twitter “Fascinating anecdotes abound in Infinite Powers . . . Strogatz uses the right amount of technical detail to convey complex concepts with clarity . . . evocatively conveys how calculus illuminates the patterns of the Universe, large and small.” — Nature “A brilliant, appealing explanation of how calculus works and why it makes our lives so much better.” —Amazon's Chris Schluep, for the Saturday Evening Post “Strogatz does a great job of explaining a difficult subject . . . he lays out the case that calculus is fundamental to the way we live today . . . a solid choice for readers who want to know what calculus is all about, and for teachers who wish to improve their presentation.” — Library Journal “An energetic effort that successfully communicates the author’s love of mathematics.” — Kirkus Reviews “Far-ranging survey . . . clear and accessible . . . Strogatz successfully illuminates a notoriously complex topic and this work should enhance appreciation for the history behind its innovations." — Publishers Weekly “A tale of how mathematics has changed all of our lives… Strogatz is a terrific storyteller and patient teacher…. By bringing infinity down to earth… and coupling those stories with some periodic excursions back out to the stars, Infinite Powers does a marvelous job of bringing calculus to life.” —Dan Rockmore, LitHub “Are you one of those people who always said you’d someday learn calculus? Well, someday is here, thanks to Steven Strogatz’s wide-ranging, humane, thoroughly readable take on one of the greatest ideas our species has ever produced.” —Jordan Ellenberg, author of How Not to Be Wrong “This is a glorious book. Steven Strogatz manages to unmask the true hidden wonder and delightful simplicity of calculus. Infinite Powers is a master class in accessible math writing and a perfect read for anyone who feels like they never quite understood what all the fuss was about. It had me leaping for joy.”  —

 About the Author

 STEVEN STROGATZ is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and The New Yorker and has been a frequent guest on Radiolab and Science Friday . He is the author of Sync and The Joy of x . He lives in Ithaca, New York.

 Product details

 * Publisher ‏ : ‎ Mariner Books; Reprint edition (April 14, 2020)
 * Language ‏ : ‎ English
 * Paperback ‏ : ‎ 400 pages
 * ISBN-10 ‏ : ‎ 0358299284
 * ISBN-13 ‏ : ‎ 978-0358299288
 * Item Weight ‏ : ‎ 2.31 pounds
 * Dimensions ‏ : ‎ 5.31 x 1.1 x 8 inches
 * Best Sellers Rank: #18,750 in Books ( See Top 100 in Books )
 + #8 in Calculus (Books)
 + #22 in Expeditions & Discoveries World History (Books)
 + #25 in Applied Mathematics (Books)
 * Customer Reviews:
 4.7 4.7 out of 5 stars 2,240 ratings
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 Steven H. Strogatz

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 STEVEN STROGATZ is the Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and The New Yorker and has been a frequent guest on Radiolab and Science Friday. He lives in Ithaca, New York.

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  5 Stars
  Calculus--The big ideas behind it and how to think about it.
  This book is a great primer for calculus. Most classes teach calculus algebraically, all symbols, no meaning. Infinite powers guides the reader through the development of algebra and its relation to geometry, and provides the why and how of how we got to calculus. With this methodology (and some light proofs) Strogatz is able to guide the reader into asking questions, and seeing the limitations of the math developed by calculus' founding fathers. This is followed by a solid introduction to calculus itself in the time of Newton and Leibniz. Before you know it, you too will have a chill run down your spine as you slowly look up from the book and realize that you understand the meaning of a derivative, not just how to find one.
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  Mark B Gerstein
  5.0 out of 5 stars Thoughts on Strogatz's Infinite Powers: Great intuition on calculus, from a master teacher
  Reviewed in the United States on January 29, 2020
  Verified Purchase
  I enjoyed Steven Strogatz's new work, Infinite Powers: How Calculus Reveals the Secrets of the Universe. The book gives an excellent overview of calculus, which permeates all branches of mathematics and so much of life. I should say at the outset that I had the great opportunity of being taught calculus in college by Dr. Strogatz. After reading this book, I feel even more fortunate for this experience because he's such a gifted communicator.

  What I liked mainly about the book was the intuitive way Strogatz describes differentials and the development of calculus from Newton and Leibniz onwards. He introduces these concepts in several ways. My favorite was the way he demonstrated simply cubing the number 2 and contrasting it with cubing 2.01, where the latter can be expressed as the cube of a sum (2 + .01) and then expanded out with Pascal's triangle. From merely looking at the multiplication of these numbers, one can immediately get a sense of which terms can be neglected in this specific sum and in the whole process of differentiation.

  Strogatz also clearly explains many classic equations in mathematics and physics, such as the heat and the wave equations. I particularly liked the way he described the development of the Fourier series and how this series converts differentiation of sine and cosine into a simple multiplication by minus one, making it easy to deal with. I also liked how he explained how one can easily express even very angular shapes such as a triangular waveform in terms of Fourier series.

  I enjoyed many of the practical examples of how we can see calculus in everyday life, ranging from the oscillations of HIV in people, as tracked by Alan Perelson and David Ho, to the development of CT scans by Hounsfield and Cormack. Strogatz gives an especially hands-on understanding of the fundamental theorem of calculus by describing it in terms of a well-known paint roller analogy and how it can link together the disparate ideas of the slope of a function and the area under a curve.

  Finally, I enjoyed the discussion of many of the personalities in mathematics, such as Descartes and Fermat. I hadn't appreciated the famous feud between these two until I read the book.

  Overall, a great read. I'd highly recommend it, especially for anyone studying or using calculus.
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  Welsh Guy
  5.0 out of 5 stars Pedestrian view of calculus - accessible to all
  Reviewed in the United States on April 22, 2022
  Verified Purchase
  I wasn't sure what to expect when I picked this book and after the first 100 pages I was somewhat disappointed. It seemed to be more of a history book full of anecdotes and stories. I'm still on the fence about my view since I was wanting a deeper analytical book into calculus and newer hypotheses, how complex geometry, multi dimensional calculus, etc all work and what their inner mechanisms are. What little tricks or insights I could get from someone more enlightened than myself. But that was maybe my 'knee jerk' buy a book and see where it takes me attitude that set me up for disappointment!!

  However, from a journey perspective this book is very enjoyable. It shows the layperson what math is and how it basically works without scaring the reader out of their wits with symbols and mathematical posturing. This is where I give this book a big applause. I really think this book should be read before studying mathematics/science/engineering so that one has a context on what has happened and why. This will then allow one to see the forest for the trees and understand that there are other forests and they too have navigational complexities. The author has done a wonderful job of being a guide through the mathematical calculus world and showing how the great minds spring-boarded off the last set of great minds. You get to see that intellect itself is non-linear. Maybe there is a partial differential equation that could compute that too !!! ;-)
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  Gary Moreau, Author
  4.0 out of 5 stars Infinite indeed, but what is infinity?
  Reviewed in the United States on October 20, 2019
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  This is not intended to be a textbook on calculus. And, like a lot of calculus itself, it is and it isn’t - quite. It is, however, a book about the history of calculus, which is fascinating, and the degree to which the universe seems to have been coded in a way that calculus seems to have an uncanny ability to explain is, well, somewhat inexplicable.

  But as the author notes in the beginning, “For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it’s the only way a universe with us in it could be, because nonmathematical universes can’t harbor life intelligent enough to ask the question.” How often do you hear a Professor of Applied Mathematics, at an Ivy League school no less, say something even remotely so self-reflective?

  Steven Strogatz is a great communicator who is both a great mathematician and who, it is easy to tell, gets goose bumps every time he thinks about the wonders of calculus. I am not a professional mathematician but have always found mathematics to be both fascinating and, well, not easy, but very relatable. It’s predictable, and that’s comforting once you can see the pattern.

  If you don’t feel quite that way you may – spoiler alert – find this book to be a bit more like a textbook than advertised. There are plenty of equations and symbols and the like. That is, after all, the alphabet of calculus. But here’s the thing. Unless you are also a math professor, you can ignore all of that. Just go with the prose. It tells the same story, but in a far more relatable form to the average lover of the written word. Just ignore the symbols. If you do you will miss nothing and you will find the professor’s enthusiasm to be quite contagious.

  The beauty of the book is that it is written from a perspective of humility. Both in terms of the enormity of calculus (Most people will relate to the subject matter simply as science.), and in terms of how far we have yet to go in terms of truly understanding the universe and the reality that defines it. We’ve only explained the tip of the iceberg.

  Math is a human convention. It’s not hydrogen or oxygen. It’s not even dark matter, which we “know” makes up most of the universe but which no one has ever isolated, although the Chinese are close. It is very accurate at deciphering reality if getting close to the “real” explanation is close enough. But close is only close. It isn’t reality itself. Reality is, after all, by definition, real.

  That is, ultimately, the problem with the promise of AI. Because AI is ultimately dependent on calculus and other disciplines of mathematics, it will get very smart, but it will never be human. What it will do, however, if we let it, is dumb down what it means to be smart to a standard perfectly suited to its abilities but ignorant of its shortcomings.

  That’s why, despite the promises of the silicon gods, we are very unlikely to see fully autonomous vehicles for decades to come. The only way that could happen is if we take all human drivers off the road overnight (The AI isn’t the problem; it’s us. We are unpredictable.), switch every vehicle to an autonomous vehicle all at the same time, and rebuild our infrastructure to accommodate the vulnerabilities of the various disciplines of mathematics on which the technology is based. And that’s obviously not going to happen. Nor do we want it to.

  Pi, as but one example, despite what you were taught in school, is not a number; it’s a range. It’s a small range, to be sure, but it’s a range nonetheless. In other words, it is precise enough for most things, but it is NOT the fabric of the universe.

  Science is a methodology for understanding reality; it is not, in the most literal sense, reality itself. Reality is not “waiting” to be discovered. It is. And just as an artist can draw a landscape, science can draw reality. Neither, however, IS reality.

  The history of calculus is truly fascinating. And that, to me, as a reader, makes it entertaining. Newton and Galileo and all the rest were truly amazing people. It boggles the mind to think of what they concluded when they did.

  Perhaps the book’s greatest contribution, however, is that it will put Silicon Valley in perspective. You may think your smart phone has changed your life in ways that nothing else possibly could. You’re wrong. I am a great admirer of Steve Jobs but James Clerk Maxwell (a Scot in the 1860s) changed your life in ways that Steve did not come close to.

  And that is why this book is so timely. Calculus is changing our world, and not entirely in good ways. If ever we needed perspective we need it now. Math is elegant. It was designed that way. (Remember that it is not of the universe, like rain or sunshine.) And it does have an uncanny reliability that helps us to understand the world around us.

  Take GPS. We all use it. We all rely on it. But did you know that GPS is all about time, not navigation. Those GPS satellites don’t “see” you; they time you. It only works because scientists came to understand the mathematics of what we call time at a very precise level. That’s not reality, of course, because time is a concept (time, even as we understand it, varies with altitude), but it is close enough to give us GPS. And isn’t that an amazing thing.

  I think so. And that’s why I found this to be such an enjoyable book, beyond the fact that I am simply stimulated by really enthusiastic people and Professor Strogatz is one of the most enthusiastic people I have had the privilege to read in a really long time.

  If, on the other hand, you prefer a good murder mystery, or something with a little romance, at least, you won’t find it in this book. But that’s just my opinion. A little like pi, if you will. Pretty accurate, but not reality itself.

  Decide for yourself. You won’t be wasting your time.
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  5.0 out of 5 stars Nice writing
  Reviewed in the United States on February 13, 2024
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  Alex M. S.
  5.0 out of 5 stars Mucho mejor explicado que cuando estudié la carrera
  Reviewed in Spain on May 1, 2022
  Verified Purchase
  El autor de este libro te explica cálculo diferencial e integral de una manera mucho más clara que mi profesor de primero de carrera en ingeniería.

  Te deja claro su historia, de donde vienen los conceptos, su utilidad, todo sin usar muchas fórmulas.

  Este libro no es para aprobar un examen sino para entender de verdad de que va ésta útil herramienta de las matemáticas.

  Lo recomiendo para cualquiera que quiera comprender de verdad sus bases y no solo memorizar una serie de fórmulas y gráficas, como pasó en mi curso.
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  ADELMAR DE M TORRES
  5.0 out of 5 stars Importance of knowing the value of infinite's conception
  Reviewed in Brazil on July 25, 2020
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  It is a delicious narrative about the origin of calculus and its importance in our daily life. It is a great book for those not familiar with mathematics.
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  Akshay Dhawan
  5.0 out of 5 stars Fantastic
  Reviewed in Canada on May 28, 2020
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  A fantastic book to read about the history and impact of mathematics in our world. I was a bit disappointed to not see any reference of Ramanujan throughout the book as that was one of the reasons I started reading this book. But, otherwise a great book.
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  Roger
  5.0 out of 5 stars Entender la parte fina del cálculo Diferencial Integral
  Reviewed in Mexico on January 2, 2020
  Verified Purchase
  Me gusta mucho el enfoque del libro donde se tratan los aspectos del cálculo a partir del concepto matemático del infinito, de una manera amena y hasta divertida. Creo que para personas que desean consolidar sus conocimientos en el tema puede ser muy útil, también a los docentes de nivel medio y superior les puede ayudar a dar enfoques más interesantes a sus clases. No soy hablante nativo del inglés, por lo que tuve que recurrir continuamente al diccionario, me parece que al autor le gusta utilizar un inglés elegante con términos no muy frecuentes. Eso puede ser un plus lingüístico, aunque puede hacer perder la continuidad en la lectura. Vale la pena de todas maneras. Muy recomendable
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  Utsabraj Sarkar
  5.0 out of 5 stars Great book and nice delivery by Amazon !!
  Reviewed in India on August 16, 2019
  Verified Purchase
  This book is a must for them who find calculus difficult and not interesting. I am teaching Analysis/Calculus for a while now. I will suggest this book to my students. If you belong to that group then you should give it a read too. This book is very well written with motivations coming from Shrek like animations, not joking, it's true. It's a must buy. As for Amazon's end their delivery is wondeful. Thanks Amazon !
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 Infinite Powers: How Calculus Reveals the Secrets of the Universe Paperback – April 14, 2020
 by Steven Strogatz (Author)
 4.7 4.7 out of 5 stars 2,240 ratings
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 From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better.
 Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.
 Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.
 Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.
 As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.
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 400 pages
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 English
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 Mariner Books
 4. Publication date
 April 14, 2020
 5. Dimensions
 5.31 x 1.1 x 8 inches
 6. ISBN-10
 0358299284
 7. ISBN-13
 978-0358299288
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 1. Three mysteries above all have spurred its development: the mystery of curves, the mystery of motion, and the mystery of change.
 Highlighted by 1,468 Kindle readers
 2. That’s the big idea behind calculus. Everything becomes simpler at infinity.
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 3. The breakthrough came from insisting that curves were actually made of straight pieces. It wasn’t true, but one could pretend that it was.
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 A New York Times Bestseller Featured on NPR's Science Friday Shortlisted for the 2019 Royal Society Science Book Prize Named one of 10 Best Books to Read this Spring by Amazon's Chris Schluep “Marvelous . . . an array of witty and astonishing stories . . . to illuminate how calculus has helped bring into being our contemporary world and so many of the instruments whose role we now blithely assume.” —The Washington Post “Fortunately, we live in an era when a top mathematician can write a book about calculus that is accessible to the mathematically challenged...it is the historical detail in the book that not only allows me to follow the math by taking me through how it was discovered, but also sticks in my mind. [Strogatz] makes me want to get out a textbook and start studying calculus.” —Five Books “Wonderful . . . bringing the insights of calculus — among the most important of all developments in the history of mathematics — to everyone.” —Brian Greene, on Twitter “I've never read a clearer explanation of calculus or the significant powers we gained by harnessing infinity. Michael and I highly recommend it!” —Vsauce, on Twitter “Fascinating anecdotes abound in Infinite Powers . . . Strogatz uses the right amount of technical detail to convey complex concepts with clarity . . . evocatively conveys how calculus illuminates the patterns of the Universe, large and small.” — Nature “A brilliant, appealing explanation of how calculus works and why it makes our lives so much better.” —Amazon's Chris Schluep, for the Saturday Evening Post “Strogatz does a great job of explaining a difficult subject . . . he lays out the case that calculus is fundamental to the way we live today . . . a solid choice for readers who want to know what calculus is all about, and for teachers who wish to improve their presentation.” — Library Journal “An energetic effort that successfully communicates the author’s love of mathematics.” — Kirkus Reviews “Far-ranging survey . . . clear and accessible . . . Strogatz successfully illuminates a notoriously complex topic and this work should enhance appreciation for the history behind its innovations." — Publishers Weekly “A tale of how mathematics has changed all of our lives… Strogatz is a terrific storyteller and patient teacher…. By bringing infinity down to earth… and coupling those stories with some periodic excursions back out to the stars, Infinite Powers does a marvelous job of bringing calculus to life.” —Dan Rockmore, LitHub “Are you one of those people who always said you’d someday learn calculus? Well, someday is here, thanks to Steven Strogatz’s wide-ranging, humane, thoroughly readable take on one of the greatest ideas our species has ever produced.” —Jordan Ellenberg, author of How Not to Be Wrong “This is a glorious book. Steven Strogatz manages to unmask the true hidden wonder and delightful simplicity of calculus. Infinite Powers is a master class in accessible math writing and a perfect read for anyone who feels like they never quite understood what all the fuss was about. It had me leaping for joy.”  —
 About the Author
 STEVEN STROGATZ is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and The New Yorker and has been a frequent guest on Radiolab and Science Friday . He is the author of Sync and The Joy of x . He lives in Ithaca, New York.
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 * Publisher ‏ : ‎ Mariner Books; Reprint edition (April 14, 2020)
 * Language ‏ : ‎ English
 * Paperback ‏ : ‎ 400 pages
 * ISBN-10 ‏ : ‎ 0358299284
 * ISBN-13 ‏ : ‎ 978-0358299288
 * Item Weight ‏ : ‎ 2.31 pounds
 * Dimensions ‏ : ‎ 5.31 x 1.1 x 8 inches
 * Best Sellers Rank: #18,750 in Books ( See Top 100 in Books )
 + #8 in Calculus (Books)
 + #22 in Expeditions & Discoveries World History (Books)
 + #25 in Applied Mathematics (Books)
 * Customer Reviews:
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 STEVEN STROGATZ is the Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has blogged about math for the New York Times and The New Yorker and has been a frequent guest on Radiolab and Science Friday. He lives in Ithaca, New York.
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  5 Stars
  Calculus--The big ideas behind it and how to think about it.
  This book is a great primer for calculus. Most classes teach calculus algebraically, all symbols, no meaning. Infinite powers guides the reader through the development of algebra and its relation to geometry, and provides the why and how of how we got to calculus. With this methodology (and some light proofs) Strogatz is able to guide the reader into asking questions, and seeing the limitations of the math developed by calculus' founding fathers. This is followed by a solid introduction to calculus itself in the time of Newton and Leibniz. Before you know it, you too will have a chill run down your spine as you slowly look up from the book and realize that you understand the meaning of a derivative, not just how to find one.
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  Mark B Gerstein
  5.0 out of 5 stars Thoughts on Strogatz's Infinite Powers: Great intuition on calculus, from a master teacher
  Reviewed in the United States on January 29, 2020
  Verified Purchase
  I enjoyed Steven Strogatz's new work, Infinite Powers: How Calculus Reveals the Secrets of the Universe. The book gives an excellent overview of calculus, which permeates all branches of mathematics and so much of life. I should say at the outset that I had the great opportunity of being taught calculus in college by Dr. Strogatz. After reading this book, I feel even more fortunate for this experience because he's such a gifted communicator.
  What I liked mainly about the book was the intuitive way Strogatz describes differentials and the development of calculus from Newton and Leibniz onwards. He introduces these concepts in several ways. My favorite was the way he demonstrated simply cubing the number 2 and contrasting it with cubing 2.01, where the latter can be expressed as the cube of a sum (2 + .01) and then expanded out with Pascal's triangle. From merely looking at the multiplication of these numbers, one can immediately get a sense of which terms can be neglected in this specific sum and in the whole process of differentiation.
  Strogatz also clearly explains many classic equations in mathematics and physics, such as the heat and the wave equations. I particularly liked the way he described the development of the Fourier series and how this series converts differentiation of sine and cosine into a simple multiplication by minus one, making it easy to deal with. I also liked how he explained how one can easily express even very angular shapes such as a triangular waveform in terms of Fourier series.
  I enjoyed many of the practical examples of how we can see calculus in everyday life, ranging from the oscillations of HIV in people, as tracked by Alan Perelson and David Ho, to the development of CT scans by Hounsfield and Cormack. Strogatz gives an especially hands-on understanding of the fundamental theorem of calculus by describing it in terms of a well-known paint roller analogy and how it can link together the disparate ideas of the slope of a function and the area under a curve.
  Finally, I enjoyed the discussion of many of the personalities in mathematics, such as Descartes and Fermat. I hadn't appreciated the famous feud between these two until I read the book.
  Overall, a great read. I'd highly recommend it, especially for anyone studying or using calculus.
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  Welsh Guy
  5.0 out of 5 stars Pedestrian view of calculus - accessible to all
  Reviewed in the United States on April 22, 2022
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  I wasn't sure what to expect when I picked this book and after the first 100 pages I was somewhat disappointed. It seemed to be more of a history book full of anecdotes and stories. I'm still on the fence about my view since I was wanting a deeper analytical book into calculus and newer hypotheses, how complex geometry, multi dimensional calculus, etc all work and what their inner mechanisms are. What little tricks or insights I could get from someone more enlightened than myself. But that was maybe my 'knee jerk' buy a book and see where it takes me attitude that set me up for disappointment!!
  However, from a journey perspective this book is very enjoyable. It shows the layperson what math is and how it basically works without scaring the reader out of their wits with symbols and mathematical posturing. This is where I give this book a big applause. I really think this book should be read before studying mathematics/science/engineering so that one has a context on what has happened and why. This will then allow one to see the forest for the trees and understand that there are other forests and they too have navigational complexities. The author has done a wonderful job of being a guide through the mathematical calculus world and showing how the great minds spring-boarded off the last set of great minds. You get to see that intellect itself is non-linear. Maybe there is a partial differential equation that could compute that too !!! ;-)
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  Gary Moreau, Author
  4.0 out of 5 stars Infinite indeed, but what is infinity?
  Reviewed in the United States on October 20, 2019
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  This is not intended to be a textbook on calculus. And, like a lot of calculus itself, it is and it isn’t - quite. It is, however, a book about the history of calculus, which is fascinating, and the degree to which the universe seems to have been coded in a way that calculus seems to have an uncanny ability to explain is, well, somewhat inexplicable.
  But as the author notes in the beginning, “For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it’s the only way a universe with us in it could be, because nonmathematical universes can’t harbor life intelligent enough to ask the question.” How often do you hear a Professor of Applied Mathematics, at an Ivy League school no less, say something even remotely so self-reflective?
  Steven Strogatz is a great communicator who is both a great mathematician and who, it is easy to tell, gets goose bumps every time he thinks about the wonders of calculus. I am not a professional mathematician but have always found mathematics to be both fascinating and, well, not easy, but very relatable. It’s predictable, and that’s comforting once you can see the pattern.
  If you don’t feel quite that way you may – spoiler alert – find this book to be a bit more like a textbook than advertised. There are plenty of equations and symbols and the like. That is, after all, the alphabet of calculus. But here’s the thing. Unless you are also a math professor, you can ignore all of that. Just go with the prose. It tells the same story, but in a far more relatable form to the average lover of the written word. Just ignore the symbols. If you do you will miss nothing and you will find the professor’s enthusiasm to be quite contagious.
  The beauty of the book is that it is written from a perspective of humility. Both in terms of the enormity of calculus (Most people will relate to the subject matter simply as science.), and in terms of how far we have yet to go in terms of truly understanding the universe and the reality that defines it. We’ve only explained the tip of the iceberg.
  Math is a human convention. It’s not hydrogen or oxygen. It’s not even dark matter, which we “know” makes up most of the universe but which no one has ever isolated, although the Chinese are close. It is very accurate at deciphering reality if getting close to the “real” explanation is close enough. But close is only close. It isn’t reality itself. Reality is, after all, by definition, real.
  That is, ultimately, the problem with the promise of AI. Because AI is ultimately dependent on calculus and other disciplines of mathematics, it will get very smart, but it will never be human. What it will do, however, if we let it, is dumb down what it means to be smart to a standard perfectly suited to its abilities but ignorant of its shortcomings.
  That’s why, despite the promises of the silicon gods, we are very unlikely to see fully autonomous vehicles for decades to come. The only way that could happen is if we take all human drivers off the road overnight (The AI isn’t the problem; it’s us. We are unpredictable.), switch every vehicle to an autonomous vehicle all at the same time, and rebuild our infrastructure to accommodate the vulnerabilities of the various disciplines of mathematics on which the technology is based. And that’s obviously not going to happen. Nor do we want it to.
  Pi, as but one example, despite what you were taught in school, is not a number; it’s a range. It’s a small range, to be sure, but it’s a range nonetheless. In other words, it is precise enough for most things, but it is NOT the fabric of the universe.
  Science is a methodology for understanding reality; it is not, in the most literal sense, reality itself. Reality is not “waiting” to be discovered. It is. And just as an artist can draw a landscape, science can draw reality. Neither, however, IS reality.
  The history of calculus is truly fascinating. And that, to me, as a reader, makes it entertaining. Newton and Galileo and all the rest were truly amazing people. It boggles the mind to think of what they concluded when they did.
  Perhaps the book’s greatest contribution, however, is that it will put Silicon Valley in perspective. You may think your smart phone has changed your life in ways that nothing else possibly could. You’re wrong. I am a great admirer of Steve Jobs but James Clerk Maxwell (a Scot in the 1860s) changed your life in ways that Steve did not come close to.
  And that is why this book is so timely. Calculus is changing our world, and not entirely in good ways. If ever we needed perspective we need it now. Math is elegant. It was designed that way. (Remember that it is not of the universe, like rain or sunshine.) And it does have an uncanny reliability that helps us to understand the world around us.
  Take GPS. We all use it. We all rely on it. But did you know that GPS is all about time, not navigation. Those GPS satellites don’t “see” you; they time you. It only works because scientists came to understand the mathematics of what we call time at a very precise level. That’s not reality, of course, because time is a concept (time, even as we understand it, varies with altitude), but it is close enough to give us GPS. And isn’t that an amazing thing.
  I think so. And that’s why I found this to be such an enjoyable book, beyond the fact that I am simply stimulated by really enthusiastic people and Professor Strogatz is one of the most enthusiastic people I have had the privilege to read in a really long time.
  If, on the other hand, you prefer a good murder mystery, or something with a little romance, at least, you won’t find it in this book. But that’s just my opinion. A little like pi, if you will. Pretty accurate, but not reality itself.
  Decide for yourself. You won’t be wasting your time.
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  prime holders badminton
  5.0 out of 5 stars Nice writing
  Reviewed in the United States on February 13, 2024
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  Great
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  Alex M. S.
  5.0 out of 5 stars Mucho mejor explicado que cuando estudié la carrera
  Reviewed in Spain on May 1, 2022
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  El autor de este libro te explica cálculo diferencial e integral de una manera mucho más clara que mi profesor de primero de carrera en ingeniería.
  Te deja claro su historia, de donde vienen los conceptos, su utilidad, todo sin usar muchas fórmulas.
  Este libro no es para aprobar un examen sino para entender de verdad de que va ésta útil herramienta de las matemáticas.
  Lo recomiendo para cualquiera que quiera comprender de verdad sus bases y no solo memorizar una serie de fórmulas y gráficas, como pasó en mi curso.
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  ADELMAR DE M TORRES
  5.0 out of 5 stars Importance of knowing the value of infinite's conception
  Reviewed in Brazil on July 25, 2020
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  It is a delicious narrative about the origin of calculus and its importance in our daily life. It is a great book for those not familiar with mathematics.
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  Akshay Dhawan
  5.0 out of 5 stars Fantastic
  Reviewed in Canada on May 28, 2020
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  A fantastic book to read about the history and impact of mathematics in our world. I was a bit disappointed to not see any reference of Ramanujan throughout the book as that was one of the reasons I started reading this book. But, otherwise a great book.
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  Roger
  5.0 out of 5 stars Entender la parte fina del cálculo Diferencial Integral
  Reviewed in Mexico on January 2, 2020
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  Me gusta mucho el enfoque del libro donde se tratan los aspectos del cálculo a partir del concepto matemático del infinito, de una manera amena y hasta divertida. Creo que para personas que desean consolidar sus conocimientos en el tema puede ser muy útil, también a los docentes de nivel medio y superior les puede ayudar a dar enfoques más interesantes a sus clases. No soy hablante nativo del inglés, por lo que tuve que recurrir continuamente al diccionario, me parece que al autor le gusta utilizar un inglés elegante con términos no muy frecuentes. Eso puede ser un plus lingüístico, aunque puede hacer perder la continuidad en la lectura. Vale la pena de todas maneras. Muy recomendable
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  Utsabraj Sarkar
  5.0 out of 5 stars Great book and nice delivery by Amazon !!
  Reviewed in India on August 16, 2019
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  This book is a must for them who find calculus difficult and not interesting. I am teaching Analysis/Calculus for a while now. I will suggest this book to my students. If you belong to that group then you should give it a read too. This book is very well written with motivations coming from Shrek like animations, not joking, it's true. It's a must buy. As for Amazon's end their delivery is wondeful. Thanks Amazon !
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Infinite Powers: How Calculus Reveals the Secrets of the Universe: Strogatz, Steven: 9780358299288: Amazon.com: Books
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https://www.goodreads.com/book/show/38412.Fermat_s_Enigma
Fermat's Enigma
1997-04-12
Author
<div><div><div><article><div><section><a href="https://www.goodreads.com/user/show/155663-david-rubenstein"></a></section><section><p>801 reviews2,502 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/79147458">October 8, 2014</a></section><div><p>Simon Singh has the ability to present a story about a mathematics problem, and tell it like a detective story. He makes the subject exciting, even though the outcome is well known. Singh intersperses history with discussions about the mathematics, and makes it quite understandable. <p>Singh starts with the roots of the famous Fermat's Last Theorem, by recounting the stories and mathematics of Pythagoras, Euclid, and Euler. Other, less well-known mathematicians are also given credit, for example Sophie Germain, Daniel Bernoulli, Augustin Cauchy, and Evariste Galois. </p><p>Three hundred fifty years ago, Fermat wrote the following theorem in the margin of a mathematics book: And, Fermat wrote that he had a marvelous proof, but no room in the margin for it. For centuries, mathematicians have attempted to prove the theorem, without success. It had been sort of a "holy grail" of mathematicians to prove the theorem, and many brilliant minds spent years on it. Perhaps in was unprovable, and worst of all, Kurt Godel showed that some theorems are actually <i>undecidable</i>--that is to say, it is impossible even to decide whether or not a theorem is true.</p><p>Singh recounts a fascinating story of the gifted mathematician, Paul Wolfskehl. He was very depressed, and decided to commit suicide on a particular night, at midnight. While waiting for that time to arrive, he started to read about the failed attempts to prove Fermat's Last Theorem. He became so engrossed in the subject, that he worked well past midnight. He found a gap in the logic of a predecessor, and was so proud of himself that he gained a new desire for life. And, in his will he established a fund of 100,000 marks to be given to the mathematician who first completes the proof of the theorem!</p><p>Much of the book describes how Andrew Wiles developed a growing interest in the theorem. He worked in almost total isolation for seven years, in order not to be distracted. He occasionally published little tidbits unrelated to his real endeavor, in order to dispel suspicions about what his real work entailed.</p><p>The central piece of the proof entailed proving the Taniyama-Shimura conjecture, that linked modular forms with elliptic equations. This was a linkage between two far-flung branches of mathematics that seemed to be totally unrelated. To prove the conjecture would allow incredible advances to be made. And then, Ken Ribet showed that a proof of the Taniyama-Shimura conjecture would, in effect, be a direct proof of Fermat's Last Theorem. But many people tried and failed to develop the proof. But that is exactly what Andrew Wiles worked on for so many years.</p><p>I had previously read that during Andrew Wiles' famous lecture, he just casually let the unsuspecting audience know, "and that is a proof of Fermat's Last Theorem." Well, this book tells a somewhat different story. Most of the audience had heard rumors that the third of Wiles' lectures would be of historical significance. They came prepared with cameras, and took photographs during the lecture. So, it was a surprise, but not a total surprise.</p><p>After Wiles' manuscript of the proof was sent to a publisher, six mathematicians reviewed it, and a crucial gap was found in it. Wiles worked furiously for a nightmarish year, and with the help of Richard Taylor, finally closed the gap. Today, Wiles is recognized as the one who developed the proof. But it is clear, that Wiles "stood on the shoulders of giants"; he used--and developed--mathematical techniques that had not existed just a few decades previously.</p><p>Simon Singh writes with a wonderful style. It is clear, not too jargon-heavy but contains enough mathematical "meat" to seem satisfying. The book is followed by ten appendixes that contain more details about some of the mathematics; they are not overly technical, and give the reader a better understanding of some of the issues. I highly recommend this book to everyone interested in math.<br /></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/155663?shelf=history">history</a> <a href="https://www.goodreads.com/review/list/155663?shelf=mathematics">mathematics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/123549343-moeen-sahraei"></a></section><section><p>29 reviews23 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4191089052">September 2, 2021</a></section><div><p>This book is endowed with all elements of a perfect story, which are curiosity, surprising events, tragedy, ambition, alternating defeat / triumph and finally an astonishing success. <br />The “Fermat’s enigma” is a tremendously inspiring narrative of one of the most important and most difficult conundrums of mathematics. It was devised by the reverend Pierre de Fermat who was called “The prince of amateurs” because he had neither had any formal education in mathematics nor he had any known tutor. He learned maths by some copies of ancient books written by Euclid’s disciple named Diophantus. <br />When mathematicians scrutinized margins of his books they saw a short note which baffled the brightest minds for more than 350 years. Fermat claimed a groundbreaking conjecture in the margin of Diophantus book without any proof, but the line next to the proof made the case much worse for other mathematicians. he wrote beside the conjecture:<br />“I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain” .This showed the fact that the formula had indeed a proof but it was lost. If you want to know what that theory is you can search on google because it can’t be properly explained in this review.<br />Since the last 350 years the formula had been attacked by the most eminent mathematicians including Leonhard Euler but none of them could prove it thoroughly.<br />After so many years of fruitless endeavor Andrew wiles managed to prove it. For Andrew the Fermat’s last theorem was personally and emotionally significant because he had been in love with the theorem since he first encountered it when he was just ten years old. After thirty years he used so many new mathematical techniques and finally he put more than 8 years on proving this conjecture in order to firmly prove it and finally he did.<br />This book is only recommended for those who appreciate the true value of mathematics. </p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/70459127-tara"></a></section><section><p>347 reviews19 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2212987189">January 3, 2018</a></section><div><p>Before delving into the book itself, I thought I’d start things off by introducing the problem it’s concerned with, just in case you aren’t already familiar with it.<p><b>So, what exactly <i>is</i> Fermat’s Last Theorem?</b></p><p>Well, basically, this is it:<br /> <br />As you can see, the conjecture is quite easy to understand, and yet, believe it or not, it was so remarkably difficult to prove that it took over 350 years to accomplish! The fact that Fermat (teasingly?) scribbled this rather infuriating note in the margin only added to the frustration felt by the scores of mathematicians who did battle with it over the centuries: <i>“I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.”</i></p><p>No doubt the cheeky bastard would’ve enjoyed Twitter:</p><p></p><p>Okay, now that that’s been taken care of, it’s time to look at the actual book.</p><p><b>What Kind of Book is <i>Fermat’s Enigma</i>?</b></p><p>Simply put, <i>Fermat’s Enigma</i> is a history book. It is most definitely NOT a math book, so don’t expect to find any degree of mathematical rigor or complexity here. There are a handful of fairly simple proofs included in the appendices, but overall, the concepts under discussion are glossed over in a superficial manner, never examined in any kind of detail. If you want something that fleshes out how the proof actually works, I’m afraid you’ll have to look elsewhere. (Singh was kind enough to include quite a few “further reading suggestions” at the end of this book. While I’ve not looked into any of the titles he recommended, I assume many of those might prove more to your liking if you prefer a “math book” on the subject.)</p><p>In any case, while Singh did not pursue the actual mathematics in any real sense, he did positively <i>excel</i> at telling the story of an utterly fascinating struggle, one which spanned hundreds of years and ensnared countless brilliant, talented minds. Readers make the acquaintance of such notable mathematicians as Pythagoras (whose work paved the way for Fermat), Leonhard Euler, Paul Wolfskehl, Sophie Germain, Daniel Bernoulli, Augustin-Louis Cauchy, Evariste Galois, Yutaka Taniyama, Goro Shimura, and of course Andrew Wiles, the man, the myth, the legend who finally proved the damn thing.</p><p> Overall, I was surprised and delighted by just how compelling the story actually was. For me, this book quickly became a veritable page-turner, one I was loathe to put aside. Some may argue that in order to accomplish this, he omitted too much relevant information, that he sacrificed depth for readability. Perhaps this is true to an extent, but in my opinion, while it was admittedly easy to read and follow, it still managed to include a fair amount of pertinent, interesting material. More importantly, it never got bogged down with unnecessary details or lost in minutiae, and never meandered down exasperating tangents, as many otherwise outstanding history books are wont to do. </p><p>And ultimately, what made this book so very stimulating was that the manner in which the story was told really made it come <i>alive.</i> Singh bestowed a truly suspenseful, exciting quest upon the reader, one full of twists and turns, and even *gasp* its fair share of drama. He enthusiastically demonstrated just how action-packed and exhilarating the life of the mind can be. And for accomplishing this tremendous feat, I heartily recommend the book, warts and all.</p><p><b>And Now, For a Few Words on the Star of the Show</b></p><p>Andrew Wiles is an extraordinary human being. Fascinated by Fermat’s Last Theorem since he was ten years old, he vowed to conquer that most impossible of proofs. This was <b>at the age of ten</b>, mind you. I seriously can’t get past that. And then, true to his word, the little rascal grew up to become an eminent mathematician, one who finally went into seclusion for seven years in order to hack away at this tremendous proof. While a not insignificant error marred the first release of said proof, he didn’t let that deter him, but persevered and managed to rectify the error, and, within a couple of years, came out with THE proof. Holy goddamn shit. </p><p>To me, Wiles’ story was completely and utterly inspiring. I was frankly amazed by what the human mind can achieve; I think I will always be in awe of Wiles’ fierce determination and incredible tenacity. Mad respect. </p><p>Anyway, as you can probably tell, Andrew Wiles is a personal hero of mine. He is an undeniable, ultimate badass. Wayne and Garth said it best:</p><p></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/70459127?shelf=stem-shelf-research">stem-shelf-research</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/64969574-barry-cunningham"></a></section><section><p>Author <i></i>1 book179 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2069290193">July 23, 2017</a></section><div><p>Being a scientist of long standing and loving all aspects of science and maths, Fermat's Last Theorem in itself was a wonderful mystery, what I would give to see Fermat's note book with a note in the margin about cubic numbers as opposed to squares. A very trite remark, too lengthy to write in the margin so it is elsewhere, and no one has ever found it or managed to prove his statement, until - - - this book is a brilliant read, you would think it would be as dry as dust, but no! It is a superb account of the proof of the last theorem from Fermat's notebook to be proven. The only thing that still niggles at me, although the mathematical proof is fabulous, it uses modern techniques not available to Fermat, so it is proven but how the hell did Fermat do it??????<br />A brilliant book, beautifully written a tremendous historical question answered in a very modern way, fabulous, well done for readability.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/7733394-muhammad"></a></section><section><p>141 reviews18 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1103553974">February 28, 2016</a></section><div><p>“সমকোণী ত্রিভুজের অতিভুজের ওপর অঙ্কিত বর্গক্ষেত্রের ক্ষেত্রফল অপর দুই বাহুর ওপর অঙ্কিত বর্গক্ষেত্রদ্বয়ের ক্ষেত্রফলের সমষ্টির সমান”-বাংলা মধ্যম শিক্ষা ব্যবস্থার ছাত্র-ছাত্রীরা বিজ্ঞান, ব্যবসা, মানবিক ইত্যাদি ‘শ্রেণীগত পার্থক্য’ভেদে সকলেই নবম শ্রেণীতে ‘পীথাগোরাসের উপপাদ্য’ নামে পরিচিত উপপাদ্য-২৩ পড়ে এসেছেন।<br /><p>চিত্রের সমকোণী ত্রিভুজের (অর্থা��� যে ত্রিভুজের একটি বাহু অপর বাহুর সাথে ৯০ ডিগ্রী কোণে অবস্থিত) অতিভুজ c, লম্ব a এবং ভূমি b। পীথাগোরাসের উপপাদ্য অনুসারে a^2 + b^2 = c^2। a, b এবং c এর কিছু মান বসিয়ে সমীকরণের দু পাশ সমান করে ফেলা যায়, সবচেয়ে সহজ একটি উদাহরণ হলো: </p><p>৩^২ + ৪^২ = ৫^২<br />বা, ৯ + ১৬ = ২৫</p><p>দু হাজার বছরেরও বেশী পুরনো এই উপপাদ্যটি আজ আমাদের প্রতিদিনের জীবনে অসংখ্যবার ব্যবহৃত হচ্ছে। এই উপপাদ্য দিয়ে টিভিস্��্রীন/ কম্পিউটার মনিটর নির্মাতা পর্দার আকার মাপছেন, জ্যোতির্বিদ তারার মাঝের দূরত্ব গুনছেন, ইলেক্ট্রিক্যাল ইঞ্জিনিয়ার ফেজর কারেন্ট হি��েব করছেন, সিভিল ইঞ্জিনিয়ার লোড পরিমাপ করছেন, অর্থনীতিবিদ যোগান আর চাহিদার হিসেব মেলাচ্ছেন......মোট কথা, আমাদের আজকের সভ্যতা যে বিন্দুতে দাঁড়িয়ে আছে তার পেছনে আছে a^2 +b^2 = c^2 জাদুকাঠিসরূপ এই সমীকরণটির অকল্পনীয় অবদান। এই উপপাদ্যটি ছাড়া প্রকৌশলবিদ্যার কোন একটি শাখাও সচল নয়! এ লেখার উদ্দেশ্য পীথাগোরাসের বা তাঁর উপপাদ্যের জয়গান গাওয়া নয় (উপপাদ্যটি আদৌ পীথাগোরাসের নিজস্ব উদ্ভাবিত কিছুও নয়! তাঁর জন্মের বহু আগে থেকেই একাধিক সভ্যতা এই উপপাদ্যটির ব্যবহার করে আসছিলো)। পীথাগোরাসের উপপাদ্য বিভিন্ন প্রকৌশল বিদ্যার অপরিহার্য অঙ্গ হিসেবে এমনিই গরীয়ান, কিন্তু আরো একটি বিষয় উপপাদ্যের সমীকরণটিকে অনন্য করে তুলেছে। ৩৭৭ বছর আগে, ১৬৩৭ সালে ফরাসী গণিতবিদ পিয়ে দ্যা ফার্মা একটি উপপাদ্য দাঁড় করালেন। “নিম্নোক্ত সমীকরণটির কোন সমাধান পূর্ন সংখ্যায় কখনোই পাওয়া যাবেনাঃ </p><p>a^n + b^n = c^n যেখানে a, b, c ও n পূর্ণ সংখ্যা ও n এর মান ২ এর চেয়ে বড় যে কোন সংখ্যা"</p><p>অর্থাৎ, a^3 + b^3 কখনোই c^3 এর সমান হবেনা, a^4 + b^4 কখনোই c^4 এর সমান হবেনা……a^100 + b^100 কখনই c^100 এর সমান হবেনা……a^9999999999999…….(অসীম) + b^9999999999999…….(অসীম) কখনোই c^9999999999999…….(অসীম) এর সমান হবেনা; n এর মান ২ এর ওপর যে কোন পূর্ণ সংখ্যার জন্যই সমীকরণটির কোন সমাধান নেই। “সংখ্যার সংখ্যা কত” এমনটা কেউ বলতে পারবেনা কখনোই। সবচেয়ে বড় শেষ সংখ্যাটির সাথে এক যোগ করে দিলেই আরেকটি নতুন সংখ্যা তৈরী হয়ে যায়। অসীম সংখ্যক সংখ্যার একটি দিয়েও a^n + b^n = c^n সমীকরণটির সমাধান করা যাবেনা? বেশ তো, পরখ করে দেখলেই হয়! a, b, c ও n এর বিভিন্ন মান (অবশ্যই পূর্ন সংখ্যায়) নিয়ে একটার পর একটা হিসেব করেই দেখা যাক। কিছুদূর এগোলেই অবশ্য বোঝা যায় কি ভয়ানক দুঃসাধ্য একটি কাজ এটি! চলক বা ভ্যারিয়েবল গুলোর মান বাড়াবার সাথে সাথে হিসেবটাও ভীষণ বড় ও কঠিন হয়ে পড়ে। আজকের দিনে না হয় কম্পিউটার আছে, সেকেন্ডের মাঝে যা লক্ষ লক্ষ হিসেব করে দেবে, ৩৫০ বছর আগে ফার্মা কিভাবে এমন একটি দাবী জানালেন? ফার্মা কি একের পর এক মান হাতে বসিয়ে হিসেব করে দেখেছেন? সেটি বাস্তব সম্মত কোন উপায় নয়। বাকী থাকলো যুক্তির প্রয়োগে উপপাদ্যটি প্রমাণ করা। ফার্মা অত্যন্ত খেয়ালী একজন গণিতবিদ ছিলেন। তিনি ডায়োফেন্টাস এর অ্যারিথমেটিকা বইটি সবসময় বগলদাবা করে রাখতেন এবং কোন থিওরেম তাঁর মাথায় এলে সেটা এই বইয়ের মার্জিন এ লিখে রাখতেন। ফার্মা প্রায় ৩০০ এর মতো সমস্যা লিখে গেছেন এই মার্জিন এ। আলোচ্য সমস্যাটিকে তাঁর শেষ উপপাদ্য বলা হয়ে থাকে। ফার্মা তাঁর অ্যারিথমেটিকা বইয়ের মার্জিনে সমস্যাটি লিখে নিচে লিখেছিলেন, “<i>এই উপপাদ্যটির একটি দারুণ সমাধান আমার জানা আছে, কিন্তু এই মার্জিনটি তা লেখার জন্য যথেষ্ট চওড়া নয়</i>”! <br />একটি অঙ্ক করতে সর্বোচ্চ কত সময় লাগতে পারে? ১ ঘন্টা? ১ দিন? ১ বছর? ১ যুগ? ফার্মার শেষ এই উপপাদ্যটি ৩৫৮ বছর ধরে পৃথিবীর বড় বড় গণিতবিদদের মুখ ভেংচিয়ে গেছে। ৩৫৮ বছরেও কেউ উপপাদ্যটি প্রমান করতে পারেননি! মাত্রই ১৯ বছর আগে ১৯৯৫ সালে প্রিন্সটন বিশ্ববিদ্যালয়ের অধ্যাপক অ্যান্ড্রু উইলস অবশেষ�� উপপাদ্যটির সমাধান করলেন, দীর্ঘ ৮ বছর যুদ্ধ করবার পর। যে বিপুল গবেষণা ও পড়ালেখা এই সমাধানটির পেছনে বিনিয়োগ করতে হয়েছে উইলস কে, তাকে যুদ্ধ বলাটাই মানায়। “<b>Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem</b>"-বইয়ে সাইমন সিং বিবৃত করেছেন উইলস এর সেই ৮ বছর ব্যাপী সংগ্রাম এর গল্প। সিং এর লেখায় এই বইটি উইলস এর অসাধারণ ধৈর্য্য ও অধ্যবসায় এর চমৎকার একটি ডকুমেন্টারি হয়ে থাকলো। </p><p> মুহম্মদ জাফর ইকবাল এর ‘<a href="https://goodreads.com/book/show/17664068.___________________">নিউরনে আবারো অনুরণন</a>’ যাঁরা পড়েছেন, তাঁরা ফার্মা সংক্রান্ত এ তথ্যগুলো আগেই জানেন। জাফর ইকবাল লিখেছিলেন অ্যান্ড্রু উইলস গণিতের খুব আধুনিক কিছু বিষয়ের ব্যবহার করে ফার্মার উপপাদ্যটি প্রমাণ করেছেন, যা ফার্মার সময়ে উদ্ভাবিতই হয়নি। সাইমন সিং খুব সহজ ভাষায় বর্ণনা করেছেন গণিতের নতুন সেই সংযোজনগুলোর কথা। ১০ বছর বয়েসে অ্যান্ড্রু উইলস প্রথম ফার্মার সমস্যার সাথে পরিচিত হন, তখনি তিনি এটি সমাধান করাকে জীবনের একমাত্র লক্ষ্য হিসেবে দাঁড় করিয়ে ফেলেছিলেন। ৩৯ বছর বয়েসে এসে প্রমাণ সম্পন্ন করতে উইলসকে প্রচুর নতুন বিষয় শিখতে হয়েছে। বিষয়গুলো এত চমৎকার যে কিছু প্রাথমিক ধারণা এখানে জুড়ে দেয়ার লোভ সামলাতে পারছিনা! উইলস এর প্রমাণটি মূলত দাঁড়িয়ে আছে তানিইয়ামা-শিমুরা ধারণা (কঞ্জেকচার) এর ওপর। তানিইয়ামা-শিমুরা কঞ্জেকচার বলে সকল এলিপ্টিক্ ইকুয়েশন ই মডিউলার ফর্ম! খুব কঠিন হয়ে গেলো কি? </p><p>গণিতে x^3 – x^2 = y^2 + y এ ধরণের সমীকরণকে বলা হয় <b>এলিপ্টিক্ ইকুয়েশন</b>। একটি সমীকরণের অসীম সংখ্যক সমাধান থাকতে পারে, প্রত্যেকটি নিয়ে আলাদা ভাবে কাজ করতে যাওয়াটা নিতান্ত বোকামী। সমীকরণের সম্ভাব্য সকল সমাধানকে সসীম একটি ছোট্ট স্পেসে প্রকাশ করতে পারলে কাজটা এক্কেবারেই সহজ হয়ে পড়ে। মানুষ ঘড়ি আবিষ্কার করেছে সময়কে একটা ছকে ফেলে কাজ সহজ করে ফেলবার জন্য। ঘড়ি না থাকলে বিশাল বিস্তৃত সময়ের কোন বিন্দুতে আমরা আছি তা কখনো বুঝতেও পারতাম না (এখনও যে খুব পারি তাও নয়, তবু একটা ধারণা অন্তত করতে পারি)। অমুক কাজটা রাতে করে দেবো বললে তা খুব বিভ্রান্তিকর শোনায়, কারণ রাত অনেকগুলো অন্ধকার সময়ের যোগফল; রাতে কখন কাজটা হবে তা নিশ্চিত হওয়া যায়না। রাত ন’টায় করে দেবো বললে মাথাটা পরিষ্কার হয়ে যায়। সময়ের এই সঠিক পরিমাপের জন্যই মানুষ ঘড়িতে সময়কে ১২ টা ভাগে ভাগ করে নিয়েছে। সমীকরণ সমাধানের ক্ষেত্রেও এই বুদ্ধি খাটানো যায়। </p><p></p><p>চিত্রের ঘড়িটি ফাইভ-ক্লক অ্যারিথমেটিক সিস্টেম। ৪ থেকে ১ ঘর সামনে আগালে আমরা ০ এ পৌঁছাই, অর্থাৎ, সাধারণ গাণিতিক হিসেবে যেখানে ৪ + ১ = ৫, ফাইভ-ক্লক অ্যারিথমেটিক সিস্টেমে ৪ + ১ = ০। ৪ থেকে ২ ঘর সামনে আগালে পৌঁছাই ১ এ। সাধারণ গাণিতিক হিসেবে ৪ + ২ = ৬, ৫-ঘড়ি পদ্ধতিতে ৪ + ২ = ১…ইত্যাদি। <br />ওপরে উল্লেখিত x^3 – x^2 = y^2 + y সমীকরণটির সমাধান ৪টিঃ</p><blockquote>
<br />x = 0, y = 0<br />x = 0, y = 4<br />x = 1, y = 0<br />x = 1, y = 4<br />
</blockquote><br />শেষ সমাধানটি (x = 1, y = 4) সাধারণ গাণিতিক হিসেবে ঠিক গ্রহণযোগ্য না হলেও ৫-ঘড়ি পদ্ধতিতে মাপে মাপে মিলে যায়ঃ <br />x^3 – x^2 = y^2 + y<br />1^3 -1^2 = 4^2 + 4<br />1-1	= 16 + 4<br />0 = 20<br />যেহেতু ৫-ঘড়ি পদ্ধতিতে ৫ = ০, ৫ এর সকল গুণিতকও (৫, ১০, ১৫, ২০……) তাই ০ ই হবে। ৫-ঘড়ি পদ্ধতিতে সংখ্যা ছিলো ৫টি (০,১,২,৩,৪), আর সমাধান ছিলো ৪টি, তাই একে E5 = 4 লেখা হয়। যদি ৭ ঘড়ি পদ্ধতি ব্যবহার করা হতো (অর্থাৎ ঘড়িতে দেয়া সংখ্যাগুলো হতো ০,১,২,৩,৪,৫,৬) তাহলে সমাধান হতো ৯টি। এটাকে এখন একটা সিরিজ আকারে লিখে ফেলা যেতে পারেঃ (E সিরিজ) <p><br />ইত্যাদি। </p><p>এবার আসা যাক মডিউলার ফর্ম এ।<br /></p><p> চিত্রের x ও y অক্ষের মাঝে আটকে পড়া বর্গটির <b>রোটেশনাল</b> ও <b>রিফ্লেকশনাল সিমেট্রি</b> বিদ্যমান, অর্থাৎ বর্গটিকে একই অবস্থানে রেখে উল্টে দিলেও এটি দেখতে একইরকম লাগবে, কোন পরিবর্তন ধরা পড়বেনা, এটি হল রোটেশনাল সিমেট্রি। যদি x এবং y অক্ষ বরাবর দুটি আয়না রেখে বর্গটিকে উল্টে পাল্টে ঘোরানো হয়, তাহলেও মনে হবে বর্গের প্রথম অবস্থার কোন পরিবর্তন হয়নি, এটাই রিফ্লেকশনাল সিমেট্রি। যদি এখন বর্গটিকে ধাক্কা দিয়ে সামনের দিকে সরিয়ে দেয়া হয়, তা হলে x এবং y অক্ষের সাপেক্ষে বর্গের অবস্থানের পরিবর্তনটি স্পষ্ট ধরা পড়বে চোখে, অর্থাৎ এর ট্রান্সলেশনাল সিমেট্রি নে��। </p><p></p><p>এই চিত্রে এবার অসীম সংখ্যক বর্গ আঁকা হলো, x ও y অক্ষের সাপেক্ষে। এই বর্গগুলোর রোটেশনাল ও রিফ্লেকশনাল সিমেট্রি তো আছেই, এদের <b>ট্রান্সলেশনাল সিমেট্রি</b>ও বিদ্যমান। কারণ, বর্গগুলো কোনভাবে চলতে শুরু করলে অক্ষদুটির সাপেক্ষে কোন বর্গটি কোথায় গেল বা তাদের অবস্থানের আদৌ কোন পরিবর্তন হলো কিনা তা আর বোঝার উপায় থাকবেনা। সবদিক থেকেই অসীম সংখ্যক বর্গগুলোর সিমেট্রি বা সমতা একইরকম থাকবে। এটিকে ঠিক মডিউলার ফর্ম বলা চলেনা, কারণ মডিউলার ফর্ম পাওয়া যায় চার ডিমেনশন এর স্পেসে, আমরা আমাদের তিন ডিমেনশন (দৈর্ঘ্য, প্রস্থ ও উচ্চতা) এর জগতের অভিজ্ঞতা দিয়ে চার ডিমেনশন এর বস্তুর ধারণা করতে পারবোনা। মডিউলার ফর্মের সাথে সিমেট্রির সম্পর্কের বিষয়টি ইঙ্গিত করবার জন্যই বর্গক্ষেত্র সংক্রান্ত আলোচনা এখানে! চার ডিমেনশন এ বাস করা আশ্চর্য সিমেট্রিক মডিউলার ফর্মেরা নির্দিষ্ট কিছু উপকরণ (ইনগ্রেডিয়েন্টস) দিয়ে গঠিত। প্রত্যেকটি মডিউলার ফর্ম ই একে অন্যের চেয়ে আলাদা এই উপকরণের বেশকমের কারণে। উপকরণের সংখ্যানুসারে সাজালে মডিউলার ফর্মের জন্যও একটি সিরিজ পাওয়া যায়, এলিপ্টিক কার্ভের E সিরিজের মতো, একে বলা হয় M সিরিজ। ১৯৫০ এর দশকে দুই জাপানী গণিতবিদ বন্ধু ইয়ুতাকা তানিইয়ামা ও গোরো শিমুরা লক্ষ্য করেন এলিপ্টিক কার্ভের E সিরিজ আর মডিউলার ফর্মের M সিরিজ একেবারে হুবহু মিলে যাচ্ছে, এ থেকে তাঁরা ধারণা করলেন সকল এলিপ্টিক সমীকরণ ই আসলে মডিউলার ফর্ম। তবে এটির পক্ষে কোন প্রমাণ তাঁরা করে যেতে পারেননি, তানিইয়ামা’র অকস্মাৎ আত্নহত্যার দরুন। </p><p>তানিইয়ামা-শিমুরা কঞ্জেকচার দিয়েই যে ফার্মার উপপাদ্য প্রমাণিত করা যাবে এ ধারণা দিয়েছিলেন জার্মান গণিতবিদ <b>গেরহার্ড ফ্রে</b>। “<i>মনে করা যাক ফার্মার সমস্যাটির একটি সমাধান আছে</i>”-এই অনুমানের পথে হেঁটে ফ্রে এক নতুন ধরণের এলিপ্টিক কার্ভ আবিষ্কার করলেন যা মডিউলার নয়, তানিইয়ামা-শিমুরার কঞ্জেকচারের সরাসরি বিরোধী। অ্যান্ড্রু উইলস যখন আট বছরের দীর্ঘ সংগ্রাম শেষে উপপাদ্যটি প্রমাণ করলেন, তাঁর প্রমাণটি শুধু ফার্মার সমস্যাটির সমাধানের কাজেই আসেনি, বরং তা গণিত ও নাম্বার থিওরির একাধিক শাখার বিস্তারেও বড় ভূমিকা রেখেছে। তানিইয়ামা-শিমুরা কঞ্জেকচার এখন আর শুধুই একটি কঞ্জেকচার বা অনুমান নয়, এটি একটি স্থাপিত সত্য। গাণিতিক এই তত্ত্বগুলো পরস্পরের সাথে এত দৃঢ়ভাবে সম্পর্কিত, যে শুধু একটির প্রমাণ-ই বাকিগুলোর প্রমাণের জন্য যথেষ্ট, অনেকটা যেন ডমিনো এফেক্টঃ <br /></p><p>অ্যান্ড্রু উইলস বেশ কিছু আধুনিক গাণিতিক হাতিয়ারে নিজেকে সজ্জিত করে ফার্মার উপপাদ্যটি প্রমাণ করেন। এর মধ্যে প্রধান দুটি হলো <i>আইওয়াসাওয়া থিওরী</i> ও <i>কোলিভাগিন-ফ্ল্যাখ মেথড</i>। সদ্য রপ্ত এই বিদ্যাগুলোর প্রয়োগের বেলায় উইলসকে প্রায়ই প্রচন্ড হতাশাজনক পরিস্থিতির ভেতর দিয়ে যেতে হয়েছে। এই টেকনিকগুলো কত কঠিন সে বিষয়ে উইলস বলেছেন সর্বোচ্চ শিক্ষা প্রাপ্ত একজন পেশাদার গণিতবিদেরও এই বিষয়গুলো আয়ত্তে আনতে অন্তত দু-তিন মাস লাগবেই! ফার্মার সমস্যাটির জটিলতার আরেকটি নির্দেশক এটি। </p><p>১৬৩৭ সালে তানিইয়ামা-শিমুরা কঞ্জেকচারের অস্তিত্ব ছিলোনা। ছিলোনা কোলিভাগিন-ফ্ল্যাখ মেথড, আইওয়াসাওয়া থিওরী, মডিউলার ফর্ম, মিয়াওকা অসমতা-এসবের কিছুই। মাত্র ১টি গাণিতিক সমস্যার প্রমাণে ১৫০ পৃষ্ঠা জুড়ে এতগুলো টেকনিকের ব্যবহার ইতিহাস আগে কখনো দেখেনি। উইলস এর এই প্রমাণটি ফার্মার আসল প্রমাণ নয়। ফার্মা কি আদৌ তাঁর সমস্যাটির সমাধান বের করেছিলেন? এক সময় হয়তো এই রহস্যেরও সমাধান হবে, হয়তো আরো অনেক সহজ কোন পদ্ধতি আবিষ্কৃত হবে, তবু অ্যান্ড্রু উইলস এর ১টিই অঙ্ক কষার পেছনে ৮ বছরের পরিশ্রমের গল্প চির অম্লান থাকবে। গণিতের সাথে মোটেই সম্পৃক্ত নয় এমন অনেকেই ৮ বছর লাগিয়ে একটি অঙ্ক করার হাস্যকর দিকটি বের করে উইলসকে নিয়ে নিয়মিত তামাশা করেছে। যে পরিমাণ পরিশ্রম ও লেখাপড়া উইলসকে করতে হয়েছে তার সম্পর্কে কোন ধারণাই হয়তো এই মানুষগুলোর কখনোই হবেনা। মানুষ হিসেবে অন্য মানুষের এ আচরণগুলো মেনে নেয়াটা প্রচণ্ড কষ্টকর ও হতাশাদায়ক এবং ক্ষেত্রবিশেষে মানুষকে সম্মান করার ব্যাপারে মনকে সন্দিহান করে তোলে, সন্দেহ নেই, তবু উইলস এর গল্প শেষ পর্যন্ত মনে করিয়ে দেয়, মানুষ ই তো পারে! </p></p></div><section><ul><a href="https://www.goodreads.com/review/list/7733394?shelf=english">english</a> <a href="https://www.goodreads.com/review/list/7733394?shelf=favorites">favorites</a> <a href="https://www.goodreads.com/review/list/7733394?shelf=mathematics">mathematics</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1713956-manny"></a></section><section><p>Author <i></i>28 books13.4k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/48785490">March 10, 2009</a></section><div><p>I guess the author does a reasonable job. But when I reached the end, I still didn't feel I understood at all how the proof worked. Probably that's just because it's so bloody hard. I got a lot more though out of <i>Prime Obsession</i>, Derbyshire's book on the Riemann Hypothesis, where the author opens up the box and shows you some of the actual math...<br /></p></div><section><ul><a href="https://www.goodreads.com/review/list/1713956?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/117399210-lu-s"></a></section><section><p>1,792 reviews431 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4239090098">March 31, 2022</a></section><div><p>That's an excellent history of mathematics from antiquity to the present day. The author skillfully captures the pedagogical trick of the Last Theorem. This <i>"mathematical siren, ..., which attracted geniuses to destroy their hopes"</i> better is a common thread that compellingly guides us through anecdotes, concepts very well explained in the maze of mathematics. The author manages to give both a technical and societal dimension to his story and, thereby, maintain the reader's attention from start to finish.<p>Very successful.<br />Good reading!</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/117399210?shelf=brit-and-related">brit-and-related</a> <a href="https://www.goodreads.com/review/list/117399210?shelf=e-5-favourites">e-5-favourites</a> <a href="https://www.goodreads.com/review/list/117399210?shelf=g-biography">g-biography</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/2309246-cassandra-kay-silva"></a></section><section><p>704 reviews277 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/178182957">June 20, 2011</a></section><div><p>This is the kind of book that we non mathematical minds can easily digest and love. It gives you an epic scope of the number of minds that it takes to build new ideas. I doubt if Fermat had actually solved this theorem correctly, but this is impossible to prove. Fermat's theorem however was not impossible to prove! It was solved! Thanks to the efforts of many men (and women!) over many lifetimes and one final man who had the determination and persistence to finish the unthinkable. This book has a lot of wonderful elements, and really exemplifies a love of mathematics. Although if you want to actually understand the theorem this book may not be for you! I can honestly say reading it did not put the theorem in any more digestible light than it started out with. Perhaps it was to the authors advantage to skip the technicalities and focus on the enjoyment of the journey. I personally loved this approach, but it may not be for everyone, especially if you are actually looking to understand the theorem (a massive undertaking that is really not in my repertoire to comment on). </p></div><section><ul><a href="https://www.goodreads.com/review/list/2309246?shelf=mathematics">mathematics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1651956-riku-sayuj"></a></section><section><p>653 reviews6,927 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/208542960">December 3, 2011</a></section><div><p>Simon converts what could have been a dry chronicle of proofs into an ode full of excitement, inspiration and intrigue worthy of a gothic love affair. Full review to follow.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/897874-bruce"></a></section><section><p>438 reviews72 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/24852281">April 3, 2009</a></section><div><p>What a fun book this was (thanks, Trevor, for the recommendation)! There are many reasons I think I like (good) nonfiction -- a sense of direct relevance, gravitas, frequent insights into the workings of the universe (and people), but mostly for knowledge narcs -- high levels of information density served up into an intriguing package by someone else who has undertaken the heavy lifting (research, organization, thinking). So, here in Singh's work I get a solid lay understanding not only of the proof to Fermat's Last Theorem, but of much of mathematics (and the lives of mathematicians) since the seventeenth century.<p>I've been thinking also about what attracts me to books on mathematical topics -- the works by Martin Gardner, William Poundstone, and the various other authors in the company of whose thoughts I've had pleasure to spend a week or more. What I've come away with, is that the best of them feed off surprises, those bits of counterintuitive anecdotes that leave you blurting out, "Huh. How about that," and then looking madly around for someone to tell. Like a book of jokes, riddles, or puzzles that provides immediate gratification in the back of the book, </p><u>Fermat's Enigma</u> plugs at least ten conundrums (and their easy-to-understand, logical solutions) into its appendices. For example -- say you're unlucky enough to be forced into a three-way duel. If everyone gets to take turns in order of their skill such that worst shoots first, what should the worst do? Aim at the best in the hopes of getting lucky and eliminating the most dangerous gunsel? Nope, the correct answer is to pass up the turn in the hopes that your first shot will get to be expended against only one remaining combatant. That way, even if you miss, you at least had a chance to take aim at the only person able to shoot back.<p>Pierre Fermat turns out to have been quite the prankster, often tweaking professional mathematicians and academics by mailing them problems they knew full well he had already solved. For those who don't keep this type of trivia at the forefront of their brains, Fermat's the French recluse (and hanging circuit jurist) who once famously scribbled in a copy of Diophantus' </p><u>Arithmetica</u> that x^n + y^n ≠ z^n for any number <i>n</i> greater than 2, a propostion for which he had "a truly marvelous demonstration… which this margin is too narrow to contain." This gets to be Fermat's Last Theorem, simply because it ends up being the last of his conundrums to be proven (not necessarily the last one he wrote). Just think, were it not for the scrupulous care taken by Fermat's son to go through and publish all of Fermat, Sr.'s writings, the world would not have been tantalized by this particular gem for <u>
 <i>over 350 YEARS</i>
</u>.<p>Andrew Wiles published the first (and only?) proof in 1994, and </p><u>Enigma</u> does a tremendous job of walking the reader through not only the stunning depth of his intellectual achievement, but its significance as well. Suffice it to say that I was happy here to read that Taniyama-Shimura get their well-earned due and that modular and elliptical equations can finally be understood to be mathematically analogous (whether or not I have any idea what modular equations actually are). Still, all of this leads to what I think is an even more tantalizing problem. We now know that all of Fermat's conjectures ultimately proved to be solvable and that Fermat's own notes would seem to indicate that he had indeed apparently found ways to solve each of them. But there is no doubt that Fermat's solution could not have relied on the up-to-the-minute maths Wiles employs over 200 pages. So if it was really the limitations of the margin and not of Fermat that inhibited publication… what was Fermat's proof?<br /></p></div><section><ul><a href="https://www.goodreads.com/review/list/897874?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/175635-trevor"></a></section><section><p>1,279 reviews21.3k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/10153784">December 9, 2007</a></section><div><p>This book is as interesting as a detective story while being about quite advanced mathematics - as such it is quite a book showing the remarkable skill of its writer to explain complex ideas in ways that are always readable and enjoyable.<p>A mathematician finds a simple proof to what seems like a deceptively simple problem of mathematics - that pythagoras's theorem only works if the terms are squared, and not if they are any other power up to infinity. Sounds dull. Except that the mathematician jots down that he has found this proof, but not what the proof is. And for hundredsd of years the greatest minds in mathematics have tried to find this simple proof and been beaten by the problem time and again.</p><p>This really is a delightful book and one that gives an insight into how mathematicians think about the world. The proof of Pythagoras's theorem given in this book is so simple that the beauty of mathematical proof is made plain to everyone. Just a little knowledge of algebra is needed for this part of the book - the rest requires no maths at all.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/175635?shelf=biography">biography</a> <a href="https://www.goodreads.com/review/list/175635?shelf=maths">maths</a> <a href="https://www.goodreads.com/review/list/175635?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/38036772-annie"></a></section><section><p>891 reviews300 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2074547154">April 25, 2019</a></section><div><p>Strap in, guys. I’m going to walk you through the history of how Fermat’s Last Theorum was proved, all in one little (okay, big) review. And I can do this because of this awesome, semi-accessible, frequently tangent-taking, but mostly, this <i>deeply fascinating</i> book.<p><b>----------STEP ONE: THE THEORUM----------</b></p><p>For the unenlightened, Fermat’s Last Theorum is this: you probably know the Pythagorean theorum, a² + b² = c², which explains that if you square the shorter two sides of a right-angled triangle and add them together, you get the value of third side squared. This is easily proved (that is, demonstrated to be completely, utterly, logically true via a mathematical proof, using axioms known to be true, which is just like a logic proof if you’ve done philosophy. Or a geometry proof, if you went to 9th grade). Take any triangle, and this will be true. There are infinite solutions to this equation—literally infinite values of A, B, and C which will render this solution true. </p><p>However, Fermat discovered that the formula an + bn = cn where n &gt; 2 has NO whole number solutions. (Go ahead, give it a whirl. I’ll wait).</p><p>Then he challenged the mathematical community to create a mathematical proof demonstrating this must be true. While tantalizing them with the knowledge he’d already created a proof for this with a scribbled note in the margin of his notebook: “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.” </p><p><i>Asshole.</i></p><p>So sparked centuries of people trying to write this proof, to no avail. Until Professor Andrew Wiles (who has the most apropos name ever—he has wiles indeed) of Cambridge, in 1993.</p><p>***</p><p>For clarity, this is Fermat’s Equation (which I’ll refer to as FE): an + bn = cn where n &gt; 2</p><p>And THIS is Fermat’s Last Theorum (which I’ll refer to as FLT): “There are no solutions to Fermat’s Equation”</p><p>***</p><p><b>----------TANGENT: GODEL----------</b></p><p>At this point, it’s been assumed that math is logically perfect—that if you correctly build a proof using axioms (like m + n = n + m), it must be true (and if it’s proven to be true, nothing can prove it to be false). This is known as “axiomatic set theory.” </p><p>Along came Godel (who is analyzed to death by my beloved, Doug Hofstadter- see <a href="https://www.goodreads.com/review/show/1445026327?book_show_action=false&amp;from_review_page=1">here</a> and <a href="https://www.goodreads.com/review/show/1319377019?book_show_action=false&amp;from_review_page=1">here</a>). His ideas are as follows: </p><p>1. If axiomatic set theory is consistent, then there have to be theorems that can’t be proved or disproved. Why? Because of paradoxes. Godel translated the following statement into mathematical notation: “This statement has no proof.” If that’s false, then you COULD create a proof for that statement—however, that would make the statement false, so how could you have a proof for that? So it has to be true. But if it’s true, it can’t be proved because that’s what it literally says. It’s a mathematical statement that is true, but could never be proved to be true (an “undecidable statement”). </p><p>2. There’s no way to prove that axiomatic set theory is consistent; in a way, it’s one of those “undecidable statement” that’s true but can’t be proved to be true. </p><p>Interestingly, this parallels the physicist Heisenberg’s discovery of the uncertainty principle, but we won’t get into that. </p><p>Now, there aren’t very many of those undecidable statements. Godel couldn’t really point to any other undecidable statements besides the one above, so people assumed they were found only in the most extreme math and would probably never even be encountered. </p><p>Welp. A young student named Paul Cohen at Stanford discovered a way to test whether a question is undecidable, and in doing so, discovered several more.</p><p>Which sparked some fear in mathematicians. What if Fermat’s Last Theorum was undecidable?! What if they were wasting their time trying to prove the unprovable?</p><p>Interestingly, if it were an undecidable statement, it couldn’t be proved—yet it would <i>have</i> to be true. The theorum says “there are no whole numbers to the equation an + bn = cn where n &gt; 2.” If this were false, then it would be possible to prove this by offering a solution to this—by finding a whole number N that’s greater than 2 that allows the equation to be solved. Which would make it a decidable statement, which is a contradiction. So it can’t be false and also be an undecidable statement. In other words, Fermat’s Last Theorum might be totally true but there might be no way to prove it. </p><p><b>----------STEP TWO: TANIYAMA-SHIMURA CONJECTURE----------</b></p><p>Modular forms are a mathematical tool, sort of like impossible forms or shapes, that reveal a lot about how numbers are related. </p><p>The Taniyama-Shimura Conjecture (TSC), created by two Japanese mathematicians (one of whom tragically and abruptly killed himself quite young) says every modular form is related to a specific elliptic equation (elliptic equations were Andrew Wiles’s main area of study; they’re a type of equation, not super important that you understand them). </p><p>The fact that these were unified meant there’s a kind of Rosetta stone that’s been discovered: <i>“Simple intuitions in the modular world translate into deep truths in the elliptic world, and vice versa. Very profound problems in the elliptic world can get solved sometimes by translating them using this Rosetta stone into the modular world, and discovering that we have the insights and tools in the modular world to treat the translated problem. Back in the elliptic world we would have been at a loss.”</i></p><p>Beyond that awesomeness, the TSC suggests something even more interesting: that possibly all of mathematics, all the different worlds of mathematics, might have parallels in other worlds, as with the elliptic world and the modular world. All of mathematics might be unified—arguably the absolute ultimate goal of abstract mathematics, because this would give us the most complete picture, and the biggest arsenal of tools to solve mathematical problems. </p><p><b>----------STEP THREE: RIBET’S THEORUM----------</b></p><p>This is all important for FLT because of something called Ribet’s Theorum (Ribet was a colleague of Wiles). Ribet’s Theorum goes like this: the imagined solution to FE can be translated into an elliptic equation. And that elliptic equation doesn’t seem to have a modular world equivalent. But the TSC claims that every elliptic equation must be related to a modular form. </p><p>So if you can PROVE that the elliptic form of the solution to FE has no modular form (which we can! The proof was done in 1986), the following is true: if the TSC is true (i.e. all elliptic equations have modular forms), and the elliptic form of the imagined solution to FE has no modular form, then the imagined solution cannot exist, proving FLT. </p><p>So now, all we have to do is prove that the TSC is true, and FLT is automatically proven to be true. </p><p>And this—THIS—is what Andrew Wiles focused on. Proving the TSC (Taniyama-Shimura Conjecture).</p><p><b>----------STEP FOUR: PROVING THE THEORUM----------</b></p><p>Wiles finally succeeded when he applied a new method called the Kolyvagin-Flach method, which groups elliptic equations into families and then proves that an elliptic equation in that family has a modular form; if that elliptic equation has a modular form, then all other elliptic equations in that family also has a modular form. </p><p>However, the Kolyvagin-Flach method has to be adapted for each family of elliptic equations. Wiles successfully adapted the method for all families of elliptic equations, thereby proving that all elliptic equations have modular forms (which, as a reminder, is basis of the Taniyama-Shimura Conjecture, and proving the TSC proves FLT). </p><p>Two months before I was born, in 1993, he proved FLT in a series of 3 lectures. </p><p>Kinda. Actually, there was a minor flaw in his proof (essentially, he might have failed to properly adapt the Kolyvagin-Flach method for some of the families of equations) but it doesn’t really matter because a year later, Wiles published a work-around to that flaw, so he proved FLT once and for all. </p><p><b>----------CONCLUSION----------</b></p><p>All I can think about is: maybe if math looked like this, if THIS had been our material in high school—maybe then I wouldn’t have disliked it. Maybe other people wouldn’t, either. What a shoddy job we do teaching our children the wonder of learning.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/38036772?shelf=microhistories">microhistories</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/15956368-roberto"></a></section><section><p>627 reviews1 follower</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1789360211">August 25, 2017</a></section><div><p><br /><b>Un teorema è per sempre</b><p>Un tale Fermat, che nel diciassettesimo secolo si dilettava di matematica ed era un po' buontempone, enunciò un teorema all'apparenza banale e lasciò scritto sul margine di una pagina di un libro:</p><p><i>“Dispongo di una meravigliosa dimostrazione di questo teorema, che non può essere contenuta nel margine stretto della pagina”</i></p><p>Il teorema era banale, come pure l'affermazione. Non poteva che scaturirne una dimostrazione banale. </p><p>Eppure... </p><p>La dimostrazione di quell'equazione banale fece perdere il sonno alle maggiori menti matematiche di tutto il mondo, che per 350 anni si arrovellarono per trovare una soluzione. Risultati: zero.</p><p>Cos'è una dimostrazione? In matematica si ritiene che un teorema sia dimostrato quando con un procedimento logico se ne fornisce inequivocabilmente e incontestabilmente la correttezza. </p><p><i>"La ricerca di una dimostrazione matematica è la ricerca di una conoscenza che è più assoluta della conoscenza accumulata da ogni altra disciplina. Il desiderio di una verità definitiva ottenuta attraverso il metodo della dimostrazione è ciò che ha guidato i matematici negli ultimi duemilacinquecento anni."</i></p><p>Solo nel 1993 un matematico inglese, Andrew Wiles, dopo sette anni di sforzi, ossessioni, notti insonni, incubi, entusiasmi e delusioni riuscì a completare la dimostrazione.</p><p>Possibile che Fermat avesse trovato una dimostrazione a questo teorema? No, impossibile crederlo; la dimostrazione di Wiles è composta da 200 pagine di matematica estremamente complessa che non poteva assolutamente essere disponibile al tempo di Fermat e che alla fine però è servita anche ad approfondire intere branche della matematica.</p><p>Ecco, il libro spiega la storia di questa dimostrazione e dei grandi matematici che ci hanno lavorato, spiega la bellezza delle sfide matematiche, l'ostinazione e la determinazione richiesta, l'inventiva necessaria e la potenza di un risultato che diventa "eterno".</p><p>La storia di questa dimostrazione è decisamente interessante; per me l'unica carenza nel libro è l'autore, che è "solo" un giornalista e che, poraccio, di matematica ci capisce come io di taglio e cucito. E trasforma la storia in una telecronaca; per consentire ai profani di capire gli aspetti legati alla successione degli eventi dà per scontate parecchie cose (pur riportandole) rinunciando a spiegare con semplicità, forse perché nemmeno lui ci ha capito un granché.</p><p>Cartesio disse: <i>"quando sono in discussione questioni trascendentali, siate chiari in modo trascendentale". </i></p><p>Ecco Singh chiaro non è. Inutile per me riportare frasi come "Tutto quello che devi fare è aggiungere qualche gamma-zero di struttura (M) e poi ti basta ripercorrere la tua argomentazione ed ecco che funziona" se non se ne spiega il significato. O si omette la frase, o la si spiega. </p><p>Riesce pure a mettere errori di matematica nelle definizioni che, mi dispiace, in un libro di matematica noooooo, proprio non accetto!.</p><p>In ogni caso la storia è affascinante e il libro riesce a trasmettere interesse e curiosità per la matematica e per queste persone meravigliose che si sono prodigate per trovare soluzioni a problemi veramente complessi.<br />Fermat era un buontempone e ci ha preso in giro per 350 anni. Ma senza di lui, oggi le nostre conoscenze matematiche sarebbero certamente inferiori...</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/15956368?shelf=saggi">saggi</a> <a href="https://www.goodreads.com/review/list/15956368?shelf=scienza">scienza</a> <a href="https://www.goodreads.com/review/list/15956368?shelf=uk">uk</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/2964113-rise"></a></section><section><p>298 reviews30 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/121252833">January 17, 2016</a></section><div><p>From my reading journal:<blockquote>May 31, 2009. <br />Yesterday I finished reading <i>Fermat's Last Theorem</i>. I plan to write a glowing book review but this space is too limited to contain it.</blockquote><br /></p></div><section><ul><a href="https://www.goodreads.com/review/list/2964113?shelf=shelfari-favorite">shelfari-favorite</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/50297885-joy-d"></a></section><section><p>1,686 reviews203 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2611419681">September 26, 2022</a></section><div><p><i>“The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.”</i><p>Fermat's Last Theorem states that: xⁿ + yⁿ = zⁿ has no whole number solutions for any integer n greater than 2. Simon Singh fashions the quest to solve this 350-year-old mathematical enigma into a compelling story. In the 1630s, when Pierre de Fermat scribbled a note on a page of his copy of Diophantus’s Arithmetica, stating (in Latin) his theorem and indicating “I have a truly marvelous demonstration of this proposition, which this margin is too narrow to contain.” Singh takes the reader through a series of minibiographies of past mathematicians, ultimately arriving at Andrew Wiles, who spent over eight years developing the 130-page proof. </p><p>Along the way, the reader will learn a great deal about number theory, logic, and the rigorous standards required to achieve an absolute proof. This book covers a wide variety of people and their contributions over the years, such as Pythagoras, Leonhard Euler, Sophie Germain, Gabriel Lame’, Augustin Cauchy, Ernst Kummer, David Hilbert, Kurt Godel, Alan Turing, Goro Shimura, and Yutaka Taniyama.</p><p>The highlight of the book is, of course, Andrew Wiles who discovered Fermat’s Last Theorem at the age of ten, and dedicated himself to figuring out a proof, no matter how long it took. Wiles decided to keep his work secret and work alone in his attic. <i>“You might ask how could I devote an unlimited amount of time to a problem that might simply not be soluble. The answer is that I just loved working on this problem and I was obsessed. I enjoyed pitting my wits against it.” </i></p><p>We learn about the Shimura-Taniyama conjecture, and the relationship between elliptic curves and modular forms. Singh never gets bogged down with calculations – they are instead included in the Appendices. I have a background in mathematics, so this type of subject matter appeals to me, but I daresay it is not required to enjoy this story of challenge, perseverance, and discovery.</p><p>4.5</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/50297885?shelf=2022-top-50">2022-top-50</a> <a href="https://www.goodreads.com/review/list/50297885?shelf=biography">biography</a> <a href="https://www.goodreads.com/review/list/50297885?shelf=history">history</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/98713629-raquel"></a></section><section><p>376 reviews</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3888015256">March 13, 2021</a></section><div><p>Belas histórias de amor. Do amor dos homens por um teorema: o último Teorema de Fermat. <br />Uma odisseia matemática cheia de beleza, frustração e triunfo. Não é apenas a história do genial Andrew Wiles; esta é a história dos homens que amam a matemática. Sem fins utilitários, sem pretensões. De Pitágoras a Wiles, de 1637 a 1994. <br />A Fermat faltou espaço naquela página para fazer a sua brilhante demonstração, mas às posteriores gerações de matemáticos não faltou coragem. Será que Fermat estava, mais uma vez, certo?<br />Esta obra, embora aborde conceitos matemáticos [alguns com um elevado grau de complexidade como a conjectura Taniyama-Shimura] e apresente reflexões que exigem um apurado raciocínio abstracto [sobretudo nesta área de matemática pura] não pretende excluir aqueles que não se encontram entre os poucos eleitos que compreendem perfeitamente a linguagem dos números. A leitura, às vezes, apresenta algumas dificuldades (ultrapassáveis) mas vale muito a pena. Uma obra muito bela e que nos encanta. <p>Para saber um bocadinho mais: <a href="https://seromoluntdeorummolae.blogspot.com/2021/03/o-ultimo-teorema-de-fermat.html">https://seromoluntdeorummolae.blogspo...</a></p><p>*<br />"El recuerdo de Arquímedes persistirá cuando Esquilo esté ya olvidado, porque las lenguas mueren y los conceptos matemáticos no. Inmortalidad es tal vez un término estúpido, pero quizá un matemático posea las mayores probabilidades de alcanzarla, sea cual sea su significado." [G.H.Hardy]</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/42731007-shivam-chaturvedi"></a></section><section><p>40 reviews97 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1294657372">March 22, 2019</a></section><div><p>I never watched any documentaries before going to college (and this was about a century and a half ago.. I am getting old -_-. But yeah, 2009 to be precise). I was always interested in NatGeo and History Channel - but they never showed the real deal on television. The documentaries would be mostly half assed, and at worst, total crap. That's also how Indian television landscape can be broadly categorized too, give or take a few exceptions ofcourse. And so I grew up loving the sciences based on what was taught in school curriculum, and elsewhere what I read on the slow 64-bit internet connection.<p>And then college happened. Parents got me my own laptop - and the college intranet had a ton of stuff that other students shared. That place and that time - was where my love for documentaries was born. I had never been so fascinated with anything before. And the first two that I watched - in a long line of them - were <i>Einstein's Biggest Blunder</i> and BBC's <i>Fermat's Last Theorem</i>. The memory of that sunday afternoon is still pretty fresh. </p><p>Back then, I only had a casual interest in astronomy and cosmology, and Einstein's theories were still something exotic. And so I basically understood jackshit from the first documentary. Even more intrigued than before, I started the second one. <i>Fermat's Last Theorem</i> was much more relatable - I had known the theorem, and understood the concept too. </p><p>Years later when I joined goodreads, I found out that there was a book too. Keeping in with the tradition of firsts, it became the first book on my TBR pile too. Where it stayed until a few days ago - and I finally marked it as read last night. </p><p>To be honest, this isn't the greatest book ever. It isnt even Simon Singh's best, who delivered the goods the much better in <a href="https://www.goodreads.com/review/show/2743827705">Big Bang</a>. But it surely captures the essence of all mathematical and scientific endeavor very well - <b>That every once in a while, in the middle of an ordinary life, <i>science</i> gives us a fairytale</b></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/42731007?shelf=gorgeous-covers">gorgeous-covers</a> <a href="https://www.goodreads.com/review/list/42731007?shelf=history">history</a> <a href="https://www.goodreads.com/review/list/42731007?shelf=my-library">my-library</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/36464297-gorab"></a></section><section><p>599 reviews92 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4972899953">September 23, 2022</a></section><div><p>The best mathematical nonfiction thriller I've ever read!<p></p><p>Consider this equation: x^n + y^n = z^n (where x,y,z,n are natural numbers with n&gt;2)<br />Fermat stated that the above equation has no solutions.<br />It’s the simplicity of this theorem which is elusive of the nature of its difficulty to be proved!</p><p>Stated around 1637, Fermat had scribbled this theorem with a note in the margin - "I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain."<br />This theorem and other notes were published posthumously by his son. Till date, nobody is aware of the proof that Fermat would have concocted in his mind!</p><p>With modern mathematical tools and researches, this theorem which remained unsolved for more than 350 years was finally proved in 1995 by Andrew Wiles.<br />This book is a tale of how this theorem was pursued for centuries and finally how it was proved.</p><p><b>Loved:</b><br />The context setting and remarkable background stories.<br />Fun trivia on numbers - and how mathematics is the language of nature.<br />The depth into which many great minds delved and devoted their entire life.</p><p><b>Recommended:</b><br />If you've ever been intrigued by Mathematics, this is a must read.<br />You don't necessarily need to have a grip on Maths to enjoy this book. Explained in layman terms, detailed mathematical proofs and footnotes are all confined to the Appendix section, for the curious minds.</p><p><b>Notes:</b><br />How I picked this book - A friend sent greetings at 5:29PM mentioning special time. Though I knew about the magic number, but somehow this message helped me traverse down the rabbit hole.<br />Ramanujan -&gt; Magic Number -&gt; Taxicab Number -&gt; Fermat near misses -&gt; Fermat's last Theorem... and from thereon it was a different world altogether!</p><p>Then last month, I went shopping books on behalf of friends. Someone picked these, which I ended up reading before sending :) [thank you!]</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/36464297?shelf=2022">2022</a> <a href="https://www.goodreads.com/review/list/36464297?shelf=non-fiction">non-fiction</a> <a href="https://www.goodreads.com/review/list/36464297?shelf=owned-paperbacks">owned-paperbacks</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/5979619-boudewijn"></a></section><section><p>621 reviews69 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/522358610">June 2, 2022</a></section><div><p>This is a very interesting book. Don't be scared about the contents, it's an enjoyable read even if you don't know anything about mathematics.</p></div><section><ul><a href="https://www.goodreads.com/review/list/5979619?shelf=audio">audio</a> <a href="https://www.goodreads.com/review/list/5979619?shelf=downloaded">downloaded</a> <a href="https://www.goodreads.com/review/list/5979619?shelf=english">english</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/4029126-sol-gonz-lez"></a></section><section><p>Author <i></i>17 books26 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/418050691">September 19, 2012</a></section><div><p>Lectura en 2012<p>Este año tomé nuevamente el libro del Enigma de Fermat, símplemente porque me gustó bastante</p><p>Las matemáticas fueron una de esas cosas con las que siempre tuve un romance eterno. Leyendo nuevamente pude recordar esos episodios en clases en que el maestro en turno llegó un día y anotó este mismo teorema en la pizarra. Nos dejó toda la clase tratando de solucionarlo y obviamente al final nos informó que el mismo no estaba resuelto (o al menos eso recuerdo, porque en ese año ya debería de haber estado). </p><p>Mas detalladamente me hizo recordar a varios amigos que hacían las demostraciones de distintas fórmulas y me las entregaban como si fueran cartas románticas (todavía las guardo).</p><p>La forma en que esta escrita, en ningún momento te hace sentir tedio. Agus dice que son mas bien chismorreos alrededor de la vida de los matemáticos (según como se lo iba contando), y precisamente eso es lo que lo hace interesante. Es la vida de personas que significaron algo para que este teorema existiera y para que finalmente fuera solucionado.</p><p>El gran enigma matemático ha muerto.</p><p>(en serio, leanlo)</p><p>................................................<br />Lectura en 2006</p><p>Finalmente llegamos a lo que fué mi último libro del año (2006 para los despistados). Durante las fiestas me encontré en casa de mis abuelos, y el apartado en donde vive mi hermana, actuaria y fanática de las matemáticas. Lo lamentable es que la mayor parte de los libros que lee yo se los recomiendo, así que la mayoría de los que encontré en su librero ya los había leído.</p><p>Encontré tres libros entre los cuales elegir, sin embargo este brillo llamando mi atención debido a una anécdota. Cuando mi hermana todavía estudiaba, viajaba a casa en autobús cada dos o tres meses. Entre sus compañeras hubo una que le presto este libro y en una ocasión el libro viajó con ella… sin embargo hay que añadir que mi hermana es algo despistada así que en esa ocasión el libro quedó en el autobús. No sé qué fué lo que le ha dado más coraje en esa ocasión, perder un libro prestado o no poder seguirlo leyendo. Tuvo que comprarlo para devolverlo y además se compró su propia edición (que todavía le tengo que devolver).</p><p>El enigma de Fermat es una novela de matemáticas. Mediante un poco de historia Singh nos va narrando la evolución de las matemáticas como un arte, muy lejos de aquellas matemáticas aplicadas. Las matemáticas como algo abstracto que es hermoso por sí mismo, porque tiene un orden y una lógica, porque en sí misma engloba misterios y permite que los descubras mediante una relación con ella.</p><p>Declaro que de niña me gustaba leer el Baldor y en mi último año de preparatoria acabé con todas las operaciones integrales en todos mis libros (y no tenía sólo dos) y este libro ha sido recordar las horas que le dediqué.</p><p>Que hermosas eran para mí las matemáticas.<br />Fue un hermoso fin de año.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/4029126?shelf=2006">2006</a> <a href="https://www.goodreads.com/review/list/4029126?shelf=2012">2012</a> <a href="https://www.goodreads.com/review/list/4029126?shelf=no-ficci%C3%B3n">no-ficción</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/82365956-veronica"></a></section><section><p>101 reviews63 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2418873155">June 29, 2021</a></section><div><p>Why do variables love mathematics? <br />y₀<p>(My head says rationally: Veronica, Goodreads is not a place for the corny wisecracks that you come up with during the day. My heart says differently.)</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/82365956?shelf=mathematics">mathematics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/28901516-arelis-uribe"></a></section><section><p>Author <i></i>7 books1,208 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1911288449">February 19, 2017</a></section><div><p>Había leído parte de este libro cuando estudiaba periodismo, gracias a Alejandra Carmona, una profe muy inquieta que daba el ramo de Antropología y que siempre llegaba con lecturas nuevas y actuales. Por ella descubrí no sólo a autores “académicos”, como Lévi-Strauss y Ángel Rama, sino a escritores que cruzan el periodismo con la etnografía y la literatura, como Martín Caparrós y Simon Singh, autor de El Último Teorema de Fermat. Es un libro hermoso, como hermosas son las matemáticas y como hermoso es el problema que heredó Fermat a sus colegas por más de 300 años y como hermosa es la historia de traiciones, desafíos y sueños que están ligados a este acertijo matemático.<br />Este es un libro que mezcla la investigación científica, el periodismo y la literatura. Aprendí un montón leyéndolo. Está escrito (y traducido) con una prosa limpia, liviana y sencilla, algo muy difícil de lograr, sobre todo cuando se explican temas intrincados, como las matemáticas. Salvo por el exceso de adverbios de mente (que, ay, me ponen medio mal) es un placer leer las explicaciones complejas de manera tan amable.<br />Pienso que la matemática son un universo de lógica, absolutismos y armonía de un nivel superior. Como toda disciplina y todo arte, aspira a la belleza y los matemáticos lo saben, persiguen la belleza de la perfección de los números y le achacan a este universo propiedades como la bondad o la amistad, todo a partir de patrones numéricos. Se me ocurre que mucha de la filosofía matemática refleja la moral de sus autores y, al mismo tiempo, describen también las relaciones humanas y la vida.<br />Me gustó mucho que el autor se hiciera cargo, en un apartado, del sesgo histórico de género que han acompañado las matemáticas. “A través de los siglos las mujeres han sido desanimadas a estudiar matemáticas, pero a pesar de la discriminación, ha habido varias matemáticas que lucharon contra esa costumbre institucionalizada e inscribieron sus nombres en forma indeleble en los anales de las matemáticas”. Y nombra a Hipatia de Alejandría o Sophie Germain, que tuvo que usar el pseudónimo de Monsieur Le Blanc para que tomaran en serio su trabajo. Cuando ella debió revelar su identidad, un destacado matemático (que fue su maestro sin saber que ella no era hombre) escribió: “Cuando una persona del sexo que, de acuerdo con nuestras costumbres y prejuicios, debe encontrar infinitamente más dificultades para familiarizarse con estas espinosas investigaciones, tiene éxito en superar estos obstáculos y penetrar las partes más oscuras de ellas, entonces sin ninguna duda debe tener el más noble coraje, talentos verdaderamente extraordinarios y una genialidad superior”.<br />Cuando yo estaba en octavo básico era muy porra. Me iba mal en el colegio. No estudiaba demasiado. Ese mismo año me puse a pololear con un chico dos años mayor que yo, que era escandalosamente estudioso. Me acuerdo cuando me explicó las potencias. Yo me había sacado un rojo en la prueba y él, con mucha paciencia y amor, me explicó esta materia que en realidad es súper fácil y entretenida. De ahí en adelante me puse igual de odiosa y matea que él. Salí de cuarto medio con promedio 6,9 en matemática. Después estudié periodismo y olvidé los números, pero al leer este libro recordé por qué me gustaban tanto, por qué disfrutaba más resolviendo facsímiles de la PSU de matemáticas que viendo Los Simpsons. Hay tanta perfección en los números, tantos juegos posibles. <br />El libro se trata de cómo se resolvió el problema matemático más famoso de la historia: el teorema de Fermat, que sostiene que no hay soluciones posibles al teorema de Pitágoras cuando la potencia es mayor a 2. El libro explica, también, porque esa demostración es tan endemoniada y difícil. La belleza del problema es que Fermat dijo tener una demostración, pero que no la podía escribir en el margen de un libro, ya que ese espacio era muy pequeño. En rigor, no existía la demostración (no existe, nadie ha visto jamás la demostración de Fermat). Era y es una especie de eslabón perdido de las matemáticas. 350 años después, Andrew Wiles plantearía su propia solución, una muy compleja y elegante, que unifica las matemáticas y que se sirve de todas las etapas de esta ciencia para lograrlo. Al final, el libro cuenta esa historia y también repasa miles de años de epistemología de las matemáticas.<br />Algunas cosas bellísimas que se leen en este libro:<br />—“Pitágoras había descubierto que unas proporciones numéricas simples eran responsables de la armonía de la música”.<br />—“La razón entre la longitud real de los ríos desde su nacimiento hasta su desembocadura y su longitud en línea recta (…) es aproximadamente 3,14: número cercano al valor de π”.<br />—“Las matemáticas son el lenguaje que permite describir la naturaleza del universo”.<br />—“La razón por la cual se le atribuye el teorema a Pitágoras es porque fue él quien primero demostró su validez universal”.<br />—“La llamada demostración científica depende de la observación y la percepción, las cuales son falibles y sólo suministran aproximaciones (…) [la demostración matemática] tiene una verdad más profunda que cualquier otra verdad, porque es el resultado de un proceso lógico. Las matemáticas son una materia de estudio no subjetiva (…) independiente de la opinión”. Es decir, una demostración matemática es una verdad absoluta y se aplica para un caso específico como para todos los de su serie hasta el infinito. Es loca esa hueá, ojalá las ciencias sociales funcionaran así.<br />—“Fermat y Pascal habrían de descubrir las primeras demostraciones y certezas absolutas de la teoría de la probabilidad, una materia que es, en esencia, incierta��.<br />— “[Pascal] sostuvo que ‘la emoción que un apostador siente cuando hace una apuesta es igual a la cantidad que puede ganar multiplicada por la probabilidad de que gane”.<br />—“El primer director del departamento de matemáticas (de la Universidad de Alejandría) fue, ni más ni menos, Euclides”.<br />—Sobre la destrucción de la biblioteca de Alejandría: “En el año 642, un ataque musulmán culminó con éxito aquello en lo que los cristianos habían fracasado”. Quemaron todo por fanatismo dogmático. Maldita religión.<br />— “El crecimiento de cualquier disciplina depende de su capacidad para comunicar y desarrollar ideas”.<br />—“Los números amigos son parejas de números tales que cada uno de ellos es igual a la suma de los divisores del otro”.<br />—“[En matemática] las ideas no corroboradas son infinitamente menos valiosas y se conocen como conjeturas”.<br />—“Es impensable para los matemáticos no poder, al menos en teoría, contestar todas las preguntas, y esta necesidad se llama completud”.<br />—“Los teóricos de los números consideran a los números primos como los más importantes de todos, porque son los átomos de las matemáticas”.<br />—“Dios existe puesto que las matemáticas son consistentes, y el diablo existe puesto que no podemos demostrarlo”, André Weil.<br />—Sobre Galois, un maestro escribió: “la locura matemática domina a este muchacho”. <br />—“Cuando se discuten cuestiones trascendentales, hay que ser trascendentalmente claro”.<br />— Y la frase que escribió Wiles cuando terminó su demostración del teorema de Fermat frente a la comunidad matemática más importante: “Creo que me detendré aquí” &lt;3</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6548739-campbell-mcaulay"></a></section><section><p>47 reviews4 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/218941572">October 4, 2011</a></section><div><p>If you buy the latest Jilly Cooper instead of this you WILL go to hell!<p>This one languished on my bookshelf for the best part of a year as I was too scared to pick it up &amp; start it. What held me back is what will probably put a lot of other potential readers off trying it - the boring old "I'm no good at maths" argument. Although my maths education is probably little above average (a good O Level and a terrible A Level, after which I rallied somewhat to obtain a reasonable HNC maths module) it's //very// many years out of use and it's all I can do to add two numbers up in my head. Given that this book is about a problem that flummoxed the best mathematical minds in the world for over 350 years you'd be forgiven for putting this back on the shelf and choosing something a little simpler. Well, don't even try that... </p><p>YOU DON'T NEED ANY MATHS TO READ THIS! </p><p>What Singh has done here is to present a hugely complex subject in a hugely entertaining way. The search for the answer to Fermat's riddle reads like a detective story and not a matehematical treatise and it includes a truly absorbing potted history of the development of maths over the years and, from Pythagoras to Fermat to Godel to Wiles, each part has a fascinating human side to it. </p><p>Budding mathematicians needn't feel left out as the mechanics of the maths is also included, but it's treated in a gentle way: each step of the problem (and it's solution) is described in a simplified (but certainly not dumbed down) manner and some simple exercises are included in several short appendices. However, take heart! There are several places where elements of the maths are obviously too complex for us mortals and Singh is not afraid to say soo and then gloss over them completely. That may be a disappointment to some, but it's not at all unreasonable in my opinion. </p><p>All in all, the net result is a book that is sensitive to its readers, intelligent, interesting and important. It's literally unputdownable and it had the added bonus of tricking me into thinking that I'm a little cleverer than I really am. </p><p>I notice there's an inevitable Wills and Kate bio on the bestseller list at the moment. Put your hard earned cash into Andrew Morton's pockets or read something that will make you feel like a genius. The choice is yours.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/64022363"></a></section><section><p>50 reviews4 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2415213462">June 13, 2018</a></section><div><p>Αρχικά να πούμε ότι δεν είναι λογοτεχνία. Μου το είχαν προτείνει μαζί με κάποια βιβλία επιστημονικής φαντασίας και συνεπώς περίμενα κάτι αντίστοιχο. Αυτός ήταν και ο λόγος που το παράτησα στην πρώτη απόπειρα.<p>Όμως, είναι μια εξαιρετική και απλοϊκή ιστορία των μαθηματικών σε σχεδόν λογοτεχνική απόδοση. Σίγουρα δεν μαθαίνει κάποιος μαθηματικά με αυτό το βιβλίο, <br />αλλά μπορεί να έρθει σε επαφή με τις πλέον σύγχρονες μορφές τους χωρίς ιδιαίτερες γνώσεις.<br />Σε τελική ανάλυση η ιστορία με συνεπήρε και το βιβλίο σίγουρα άξιζε την δεύτερη ευκαιρία που του έδωσα.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/104765258-david"></a></section><section><p>537 reviews122 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3039819639">July 13, 2022</a></section><div><p>Its a simple problem: x^n + y^n = z^n has no positive integer solutions (xyz) for n&gt;2. So why is it so hard to prove? (or disprove). I'm a math/physics nerd so this book has great appeal. I also like Simon Singh's technical writing. He stayed 100% on track as he traced Pythagoras in 6 BC to Andrew Wiles proof in 1994.<p>We all remember 3-4-5 triangles from geometry/trig, right? Pythagorean Theorem says 3^2 + 4^2 = 5^2. Other famous right triangle uses of these are the 5-12-13 or the 7-24-25, or how about 99-4900 - 4901. So why can't a version of this with cubes, or ^4 or ^5 work?</p><p>Andrew Wiles read <a href="https://goodreads.com/book/show/5954566.The_Last_Problem">The Last Problem</a> by Eric Bell when he was 10. He ultimately left Cambridge, England became a math professor at Princeton.</p><p>The text kept moving at a strong pace. The greatest minds in math all came into play, with their own focus and contribution to solving this problem. Pierre de Fermat lived 1607-1665. The mathematicians before him that get mentioned all contributed to number theory that had direct bearing on this ultimate math problem. Fermat has scribbled in the margins that he knew the proof, but it simply wouldn't fit in the margins.</p><p>Even as computers came into being, the 'brute force' method of MANY trials (with none working) could solve this problem. For even if a million numbers were tried, maybe the next one could work. What was needed was a full mathematical logical proof.</p><p>Solid 4.5*. If you like math/physics, then easy 5. If not, then round down to a very readable 4.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/104765258?shelf=_own">_own</a> <a href="https://www.goodreads.com/review/list/104765258?shelf=math">math</a> <a href="https://www.goodreads.com/review/list/104765258?shelf=z-2022">z-2022</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/106068396-amy"></a></section><section><p>51 reviews9 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3065896612">January 19, 2022</a></section><div><p>✩ <b>5.0 stars</b> ✩<br />In telling the story of one of the most famous problems in mathematics, Simon Singh reveals the beauty of number theory, hidden in the simplicity of the problem that Andrew Wiles fell in love with all those years ago. He maps out a tree of mathematics with Fermat’s Last Theorem as the trunk, the central piece, paying tribute to the countless mathematicians that paved the way for Wiles’ proof. And of course, he describes the sheer tenacity of the mathematical genius as he grapples with the problem for 7 years. I loved the detail with which Singh explored the history of mathematics — he maps out intricate branches of time, delving into the history of Pythagoras, Euler, Turing, Taniyama and Shimura, and so many others, as he attributes to each their own contributions towards Fermat’s Last Theorem.<p>This is a must-read for anyone interested in maths, but perfectly accessible for laymen of any sort.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/106068396?shelf=favorites">favorites</a> <a href="https://www.goodreads.com/review/list/106068396?shelf=library">library</a> <a href="https://www.goodreads.com/review/list/106068396?shelf=non-fic">non-fic</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1325473-jimmy"></a></section><section><p>511 reviews686 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/160574072">June 23, 2016</a></section><div><p>A fantastically entertaining and educational book about the quest to solve the oldest math problem: Fermat's Last Theorem. The intrigue, mystery, and drama surrounding the famous theorem without a proof (but that Fermat had said he had a proof for, just not enough space to write it in the margins) is exciting enough. All the math greats who have attempted to solve it but come up a little short, or a lot short.<p>But it's much more than that, since the final proof of Fermat's Theorem involves so many other math concepts. This book starts and ends with Fermat, but in the middle it is more like a grand tour of all the mathematical developments that make the proof even possible. It's interesting to read about all the different dead ends and other productive findings (that had tangentially made it a little more possible to solve Fermat, but whose main contribution was in some other area). Also, reading about Galois's amazing life always makes me giddy. I mean, I've read about him before, but his story is just so crazy--math genius turned revolutionary thrown in jail involved in affair ends in duel, scribbles out his last thoughts the night before he dies... amazing.</p><p>But don't expect to understand how the proof actually works by the end. The proof itself is over 100 pages, so there is no way a normal non-math genius can understand it. But you will get a general <i>idea</i> of the approach/trajectory/style of the final beast. Also, some of the math concepts leading up to it are quite easily comprehensible. I wouldn't recommend this book to a math whiz... it's more of a fun read for the layperson.</p><p>It would ultimately be more satisfying if the proof were a short elegant thing that didn't involve latest groundbreaking discoveries in math. But maybe the bright side is that we can still wonder about Fermat's original (alleged) proof that was never written down. It had to be different from Andrew Wile's proof; does it exist? Or was Fermat bluffing? Or did he make an error in his proof?</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1325473?shelf=male">male</a> <a href="https://www.goodreads.com/review/list/1325473?shelf=non-fiction">non-fiction</a> <a href="https://www.goodreads.com/review/list/1325473?shelf=poc">poc</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/4962158-rakesh-m"></a></section><section><p>32 reviews29 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1804092963">February 17, 2017</a></section><div><p>This book is a biography of the epic quest to solve the eluding Fermat's last theorem. It chronicles the life and works of not just Fermat, but most of the mathematicians having even a tiny bit to do with the conjecture/theorem. <p>Curious and strange revelations into the lives of many of the princes and princesses of mathematics are presented. It presents the case of lives, pursuits and the times that they lived in. The problems that they face (mathematical and others), how these affect the progress/decline of the field. </p><p>Simon Singh writes brilliantly mixing accounts of math behind the problem along with the lives of these mathematicians. We get to see accounts of love, suicides, suicide averted by fixating on a proof, duels and revolutionaries. For me it was shocking to know, that it was not just the kings and religious fellows destroying these geniuses and their sanctuaries, but Pythagoras also committed a grave mistake once, sentencing Hippasus to death for arguing that sqrt(2) cannot be expressed as a fraction!</p><p>A must read for those interested in history behind the problem.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/4962158?shelf=biography">biography</a> <a href="https://www.goodreads.com/review/list/4962158?shelf=library_reads">library_reads</a> <a href="https://www.goodreads.com/review/list/4962158?shelf=like-to-own">like-to-own</a> </ul></section><hr /></section></article></div><div><article><section><section><a href="https://www.goodreads.com/review/show/1356411307">August 6, 2015</a></section><div><p>Simon Singh gives an excellent account of the quest for the solution to Fermat's puzzle. Starting off with ancient Greeks and arriving at the proof using modern mathematics, he explains the struggles of generations of mathematicians. The author never tries to overwhelm us with the mathematics, but tells us about the people who were involved in proving the theorem. Having said that, all the mathematics in the book can be understood with a background in high school mathematics. <p>This book is a great read simply because of the intellectual achievement that it talks about. Strongly recommended if you're remotely interested in mathematics.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/13421080-maricarmen-estrada-m"></a></section><section><p>282 reviews69 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2048922439">January 11, 2020</a></section><div><p>I have a special love for words. I think I always have. They’re fascinating. The words in this book were used for telling a story about numbers, which made me realize I also love numbers so much, I just didn’t know. Math had always been the “easy subject” at school for me, the one which did not require long hours of study, because it was so logical, the one you could check before turning in an exam and know you had the right answers precisely because it matched so perfectly. “Proof is what lies at the heart of maths.”, indeed, so simple, so beautiful. <br />Well, this story is, as the title describes, a true quest to solve one of the most difficult problems in Mathematics which Fermat’s Last Theorem used to be. Simon Singh did this superbly. He is absolutely great at explaining from whole numbers and 1+1 to elliptical equations and modular forms. But the best was to learn about some of the greatest minds that worked so hard in the last century solving problems and doing the maths that have been the basis and tool for proving this theorem and thus, their great contribution to science: Pythagoras and his controversial Pythagorean Brotherhood, Mersenne, Euclid, Diophantus and his most remarkable “Arithmetica”, of course Pierre de Fermat, Pascal, brilliant Euler, Cantor, Sophie Germain, Theano, Hypatia, Maria Agnesi, Emmy Noether, Gauss, Cauchy, Lamè, Kummer, Wolfskehl, Gödel, Turing, Shimura, Taniyama, and Andrew Wiles. These are not the only ones, of course, but the most outstanding for me from this book. <p>I want to make a special mention to the part where Singh talks about the work of women that were mathematicians. Even as of today, there aren’t many of us women dedicated to numbers or number theory, but we have come to a time when we can actually pursue this career, despite the struggles and obstacles that still exist in our societies. But being a mathematician a few centuries ago was completely outrageous and out of this world! Sophie Germain had to study secretly at night and keep a secret stock of candles to do so, because her dad used to confiscate them to prevent her from studying. Or Agnesi who was referred to as the “witch of Agnesi”. And the most extreme of these was Hypatia of Alexandria who suffered the most tragic and brutal death to the hands of the exulted mob led by the patriarch of Alexandria because she was considered a heretic. These stories really moved me and I’m very glad that their names are remembered and admired although they did not have a voice in their own time. Their only voice was their endless curiosity and passion for trying to understand the Universe and their brilliant work pervaded through history and remained printed in our books and forever in our memories, a greatly deserved honor to inspire all of us. </p><p>And back to Fermat’s Theorem, Wiles amazing work on his childhood’s dream inspired this book and will hopefully inspire many more that see the beauty of numbers to keep working and pushing the frontiers on this science field which Singh perfectly describes as the “language of nature”.</p></p></div><section><ul></ul></section></section></article></div></div>||||I|||| * Home
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 Fermat's Enigma

 Simon Singh

 4.28
 29,267 ratings 1,472 reviews
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 xn + yn = zn, where n represents 3, 4, 5, ...no solution

 "I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

 With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma --based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.
 Genres Science Nonfiction Mathematics History Popular Science Biography Historical
 ...more

 315 pages, Paperback

 First published April 12, 1997

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 About the author

 Simon Singh

 18 books 1,320 followers
 Simon Lehna Singh, MBE is a British author who has specialised in writing about mathematical and scientific topics in an accessible manner. He is the maiden winner of the Lilavati Award.

 His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem ), The Code Book (about cryptography and its history), Big Bang (about the Big Bang theory and the origins of the universe) and Trick or Treatment? Alternative Medicine on Trial (about complementary and alternative medicine).

 He has also produced documentaries and works for television to accompany his books, is a trustee of NESTA, the National Museum of Science and Industry and co-founded the Undergraduate Ambassadors Scheme.

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 4.28
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 David Rubenstein
 801 reviews 2,502 followers
 October 8, 2014
 Simon Singh has the ability to present a story about a mathematics problem, and tell it like a detective story. He makes the subject exciting, even though the outcome is well known. Singh intersperses history with discussions about the mathematics, and makes it quite understandable.

 Singh starts with the roots of the famous Fermat's Last Theorem, by recounting the stories and mathematics of Pythagoras, Euclid, and Euler. Other, less well-known mathematicians are also given credit, for example Sophie Germain, Daniel Bernoulli, Augustin Cauchy, and Evariste Galois.

 Three hundred fifty years ago, Fermat wrote the following theorem in the margin of a mathematics book: And, Fermat wrote that he had a marvelous proof, but no room in the margin for it. For centuries, mathematicians have attempted to prove the theorem, without success. It had been sort of a "holy grail" of mathematicians to prove the theorem, and many brilliant minds spent years on it. Perhaps in was unprovable, and worst of all, Kurt Godel showed that some theorems are actually undecidable --that is to say, it is impossible even to decide whether or not a theorem is true.

 Singh recounts a fascinating story of the gifted mathematician, Paul Wolfskehl. He was very depressed, and decided to commit suicide on a particular night, at midnight. While waiting for that time to arrive, he started to read about the failed attempts to prove Fermat's Last Theorem. He became so engrossed in the subject, that he worked well past midnight. He found a gap in the logic of a predecessor, and was so proud of himself that he gained a new desire for life. And, in his will he established a fund of 100,000 marks to be given to the mathematician who first completes the proof of the theorem!

 Much of the book describes how Andrew Wiles developed a growing interest in the theorem. He worked in almost total isolation for seven years, in order not to be distracted. He occasionally published little tidbits unrelated to his real endeavor, in order to dispel suspicions about what his real work entailed.

 The central piece of the proof entailed proving the Taniyama-Shimura conjecture, that linked modular forms with elliptic equations. This was a linkage between two far-flung branches of mathematics that seemed to be totally unrelated. To prove the conjecture would allow incredible advances to be made. And then, Ken Ribet showed that a proof of the Taniyama-Shimura conjecture would, in effect, be a direct proof of Fermat's Last Theorem. But many people tried and failed to develop the proof. But that is exactly what Andrew Wiles worked on for so many years.

 I had previously read that during Andrew Wiles' famous lecture, he just casually let the unsuspecting audience know, "and that is a proof of Fermat's Last Theorem." Well, this book tells a somewhat different story. Most of the audience had heard rumors that the third of Wiles' lectures would be of historical significance. They came prepared with cameras, and took photographs during the lecture. So, it was a surprise, but not a total surprise.

 After Wiles' manuscript of the proof was sent to a publisher, six mathematicians reviewed it, and a crucial gap was found in it. Wiles worked furiously for a nightmarish year, and with the help of Richard Taylor, finally closed the gap. Today, Wiles is recognized as the one who developed the proof. But it is clear, that Wiles "stood on the shoulders of giants"; he used--and developed--mathematical techniques that had not existed just a few decades previously.

 Simon Singh writes with a wonderful style. It is clear, not too jargon-heavy but contains enough mathematical "meat" to seem satisfying. The book is followed by ten appendixes that contain more details about some of the mathematics; they are not overly technical, and give the reader a better understanding of some of the issues. I highly recommend this book to everyone interested in math.
 history mathematics
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 Moeen Sahraei
 29 reviews 23 followers
 September 2, 2021
 This book is endowed with all elements of a perfect story, which are curiosity, surprising events, tragedy, ambition, alternating defeat / triumph and finally an astonishing success.
 The “Fermat’s enigma” is a tremendously inspiring narrative of one of the most important and most difficult conundrums of mathematics. It was devised by the reverend Pierre de Fermat who was called “The prince of amateurs” because he had neither had any formal education in mathematics nor he had any known tutor. He learned maths by some copies of ancient books written by Euclid’s disciple named Diophantus.
 When mathematicians scrutinized margins of his books they saw a short note which baffled the brightest minds for more than 350 years. Fermat claimed a groundbreaking conjecture in the margin of Diophantus book without any proof, but the line next to the proof made the case much worse for other mathematicians. he wrote beside the conjecture:
 “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain” .This showed the fact that the formula had indeed a proof but it was lost. If you want to know what that theory is you can search on google because it can’t be properly explained in this review.
 Since the last 350 years the formula had been attacked by the most eminent mathematicians including Leonhard Euler but none of them could prove it thoroughly.
 After so many years of fruitless endeavor Andrew wiles managed to prove it. For Andrew the Fermat’s last theorem was personally and emotionally significant because he had been in love with the theorem since he first encountered it when he was just ten years old. After thirty years he used so many new mathematical techniques and finally he put more than 8 years on proving this conjecture in order to firmly prove it and finally he did.
 This book is only recommended for those who appreciate the true value of mathematics.
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 Tara
 347 reviews 19 followers
 January 3, 2018
 Before delving into the book itself, I thought I’d start things off by introducing the problem it’s concerned with, just in case you aren’t already familiar with it.

 So, what exactly is Fermat’s Last Theorem?

 Well, basically, this is it:

 As you can see, the conjecture is quite easy to understand, and yet, believe it or not, it was so remarkably difficult to prove that it took over 350 years to accomplish! The fact that Fermat (teasingly?) scribbled this rather infuriating note in the margin only added to the frustration felt by the scores of mathematicians who did battle with it over the centuries: “I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.”

 No doubt the cheeky bastard would’ve enjoyed Twitter:



 Okay, now that that’s been taken care of, it’s time to look at the actual book.

 What Kind of Book is Fermat’s Enigma?

 Simply put, Fermat’s Enigma is a history book. It is most definitely NOT a math book, so don’t expect to find any degree of mathematical rigor or complexity here. There are a handful of fairly simple proofs included in the appendices, but overall, the concepts under discussion are glossed over in a superficial manner, never examined in any kind of detail. If you want something that fleshes out how the proof actually works, I’m afraid you’ll have to look elsewhere. (Singh was kind enough to include quite a few “further reading suggestions” at the end of this book. While I’ve not looked into any of the titles he recommended, I assume many of those might prove more to your liking if you prefer a “math book” on the subject.)

 In any case, while Singh did not pursue the actual mathematics in any real sense, he did positively excel at telling the story of an utterly fascinating struggle, one which spanned hundreds of years and ensnared countless brilliant, talented minds. Readers make the acquaintance of such notable mathematicians as Pythagoras (whose work paved the way for Fermat), Leonhard Euler, Paul Wolfskehl, Sophie Germain, Daniel Bernoulli, Augustin-Louis Cauchy, Evariste Galois, Yutaka Taniyama, Goro Shimura, and of course Andrew Wiles, the man, the myth, the legend who finally proved the damn thing.

 Overall, I was surprised and delighted by just how compelling the story actually was. For me, this book quickly became a veritable page-turner, one I was loathe to put aside. Some may argue that in order to accomplish this, he omitted too much relevant information, that he sacrificed depth for readability. Perhaps this is true to an extent, but in my opinion, while it was admittedly easy to read and follow, it still managed to include a fair amount of pertinent, interesting material. More importantly, it never got bogged down with unnecessary details or lost in minutiae, and never meandered down exasperating tangents, as many otherwise outstanding history books are wont to do.

 And ultimately, what made this book so very stimulating was that the manner in which the story was told really made it come alive. Singh bestowed a truly suspenseful, exciting quest upon the reader, one full of twists and turns, and even *gasp* its fair share of drama. He enthusiastically demonstrated just how action-packed and exhilarating the life of the mind can be. And for accomplishing this tremendous feat, I heartily recommend the book, warts and all.

 And Now, For a Few Words on the Star of the Show

 Andrew Wiles is an extraordinary human being. Fascinated by Fermat’s Last Theorem since he was ten years old, he vowed to conquer that most impossible of proofs. This was at the age of ten , mind you. I seriously can’t get past that. And then, true to his word, the little rascal grew up to become an eminent mathematician, one who finally went into seclusion for seven years in order to hack away at this tremendous proof. While a not insignificant error marred the first release of said proof, he didn’t let that deter him, but persevered and managed to rectify the error, and, within a couple of years, came out with THE proof. Holy goddamn shit.

 To me, Wiles’ story was completely and utterly inspiring. I was frankly amazed by what the human mind can achieve; I think I will always be in awe of Wiles’ fierce determination and incredible tenacity. Mad respect.

 Anyway, as you can probably tell, Andrew Wiles is a personal hero of mine. He is an undeniable, ultimate badass. Wayne and Garth said it best:

 stem-shelf-research
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 Barry Cunningham
 Author 1 book 179 followers
 July 23, 2017
 Being a scientist of long standing and loving all aspects of science and maths, Fermat's Last Theorem in itself was a wonderful mystery, what I would give to see Fermat's note book with a note in the margin about cubic numbers as opposed to squares. A very trite remark, too lengthy to write in the margin so it is elsewhere, and no one has ever found it or managed to prove his statement, until - - - this book is a brilliant read, you would think it would be as dry as dust, but no! It is a superb account of the proof of the last theorem from Fermat's notebook to be proven. The only thing that still niggles at me, although the mathematical proof is fabulous, it uses modern techniques not available to Fermat, so it is proven but how the hell did Fermat do it??????
 A brilliant book, beautifully written a tremendous historical question answered in a very modern way, fabulous, well done for readability.
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 Muhammad
 141 reviews 18 followers
 February 28, 2016
 “সমকোণী ত্রিভুজের অতিভুজের ওপর অঙ্কিত বর্গক্ষেত্রের ক্ষেত্রফল অপর দুই বাহুর ওপর অঙ্কিত বর্গক্ষেত্রদ্বয়ের ক্ষেত্রফলের সমষ্টির সমান”-বাংলা মধ্যম শিক্ষা ব্যবস্থার ছাত্র-ছাত্রীরা বিজ্ঞান, ব্যবসা, মানবিক ইত্যাদি ‘শ্রেণীগত পার্থক্য’ভেদে সকলেই নবম শ্রেণীতে ‘পীথাগোরাসের উপপাদ্য’ নামে পরিচিত উপপাদ্য-২৩ পড়ে এসেছেন।


 চিত্রের সমকোণী ত্রিভুজের (অর্থা��� যে ত্রিভুজের একটি বাহু অপর বাহুর সাথে ৯০ ডিগ্রী কোণে অবস্থিত) অতিভুজ c, লম্ব a এবং ভূমি b। পীথাগোরাসের উপপাদ্য অনুসারে a^2 + b^2 = c^2। a, b এবং c এর কিছু মান বসিয়ে সমীকরণের দু পাশ সমান করে ফেলা যায়, সবচেয়ে সহজ একটি উদাহরণ হলো:

 ৩^২ + ৪^২ = ৫^২
 বা, ৯ + ১৬ = ২৫

 দু হাজার বছরেরও বেশী পুরনো এই উপপাদ্যটি আজ আমাদের প্রতিদিনের জীবনে অসংখ্যবার ব্যবহৃত হচ্ছে। এই উপপাদ্য দিয়ে টিভিস্��্রীন/ কম্পিউটার মনিটর নির্মাতা পর্দার আকার মাপছেন, জ্যোতির্বিদ তারার মাঝের দূরত্ব গুনছেন, ইলেক্ট্রিক্যাল ইঞ্জিনিয়ার ফেজর কারেন্ট হি��েব করছেন, সিভিল ইঞ্জিনিয়ার লোড পরিমাপ করছেন, অর্থনীতিবিদ যোগান আর চাহিদার হিসেব মেলাচ্ছেন......মোট কথা, আমাদের আজকের সভ্যতা যে বিন্দুতে দাঁড়িয়ে আছে তার পেছনে আছে a^2 +b^2 = c^2 জাদুকাঠিসরূপ এই সমীকরণটির অকল্পনীয় অবদান। এই উপপাদ্যটি ছাড়া প্রকৌশলবিদ্যার কোন একটি শাখাও সচল নয়! এ লেখার উদ্দেশ্য পীথাগোরাসের বা তাঁর উপপাদ্যের জয়গান গাওয়া নয় (উপপাদ্যটি আদৌ পীথাগোরাসের নিজস্ব উদ্ভাবিত কিছুও নয়! তাঁর জন্মের বহু আগে থেকেই একাধিক সভ্যতা এই উপপাদ্যটির ব্যবহার করে আসছিলো)। পীথাগোরাসের উপপাদ্য বিভিন্ন প্রকৌশল বিদ্যার অপরিহার্য অঙ্গ হিসেবে এমনিই গরীয়ান, কিন্তু আরো একটি বিষয় উপপাদ্যের সমীকরণটিকে অনন্য করে তুলেছে। ৩৭৭ বছর আগে, ১৬৩৭ সালে ফরাসী গণিতবিদ পিয়ে দ্যা ফার্মা একটি উপপাদ্য দাঁড় করালেন। “নিম্নোক্ত সমীকরণটির কোন সমাধান পূর্ন সংখ্যায় কখনোই পাওয়া যাবেনাঃ

 a^n + b^n = c^n যেখানে a, b, c ও n পূর্ণ সংখ্যা ও n এর মান ২ এর চেয়ে বড় যে কোন সংখ্যা"

 অর্থাৎ, a^3 + b^3 কখনোই c^3 এর সমান হবেনা, a^4 + b^4 কখনোই c^4 এর সমান হবেনা……a^100 + b^100 কখনই c^100 এর সমান হবেনা……a^9999999999999…….(অসীম) + b^9999999999999…….(অসীম) কখনোই c^9999999999999…….(অসীম) এর সমান হবেনা; n এর মান ২ এর ওপর যে কোন পূর্ণ সংখ্যার জন্যই সমীকরণটির কোন সমাধান নেই। “সংখ্যার সংখ্যা কত” এমনটা কেউ বলতে পারবেনা কখনোই। সবচেয়ে বড় শেষ সংখ্যাটির সাথে এক যোগ করে দিলেই আরেকটি নতুন সংখ্যা তৈরী হয়ে যায়। অসীম সংখ্যক সংখ্যার একটি দিয়েও a^n + b^n = c^n সমীকরণটির সমাধান করা যাবেনা? বেশ তো, পরখ করে দেখলেই হয়! a, b, c ও n এর বিভিন্ন মান (অবশ্যই পূর্ন সংখ্যায়) নিয়ে একটার পর একটা হিসেব করেই দেখা যাক। কিছুদূর এগোলেই অবশ্য বোঝা যায় কি ভয়ানক দুঃসাধ্য একটি কাজ এটি! চলক বা ভ্যারিয়েবল গুলোর মান বাড়াবার সাথে সাথে হিসেবটাও ভীষণ বড় ও কঠিন হয়ে পড়ে। আজকের দিনে না হয় কম্পিউটার আছে, সেকেন্ডের মাঝে যা লক্ষ লক্ষ হিসেব করে দেবে, ৩৫০ বছর আগে ফার্মা কিভাবে এমন একটি দাবী জানালেন? ফার্মা কি একের পর এক মান হাতে বসিয়ে হিসেব করে দেখেছেন? সেটি বাস্তব সম্মত কোন উপায় নয়। বাকী থাকলো যুক্তির প্রয়োগে উপপাদ্যটি প্রমাণ করা। ফার্মা অত্যন্ত খেয়ালী একজন গণিতবিদ ছিলেন। তিনি ডায়োফেন্টাস এর অ্যারিথমেটিকা বইটি সবসময় বগলদাবা করে রাখতেন এবং কোন থিওরেম তাঁর মাথায় এলে সেটা এই বইয়ের মার্জিন এ লিখে রাখতেন। ফার্মা প্রায় ৩০০ এর মতো সমস্যা লিখে গেছেন এই মার্জিন এ। আলোচ্য সমস্যাটিকে তাঁর শেষ উপপাদ্য বলা হয়ে থাকে। ফার্মা তাঁর অ্যারিথমেটিকা বইয়ের মার্জিনে সমস্যাটি লিখে নিচে লিখেছিলেন, “ এই উপপাদ্যটির একটি দারুণ সমাধান আমার জানা আছে, কিন্তু এই মার্জিনটি তা লেখার জন্য যথেষ্ট চওড়া নয় ”!
 একটি অঙ্ক করতে সর্বোচ্চ কত সময় লাগতে পারে? ১ ঘন্টা? ১ দিন? ১ বছর? ১ যুগ? ফার্মার শেষ এই উপপাদ্যটি ৩৫৮ বছর ধরে পৃথিবীর বড় বড় গণিতবিদদের মুখ ভেংচিয়ে গেছে। ৩৫৮ বছরেও কেউ উপপাদ্যটি প্রমান করতে পারেননি! মাত্রই ১৯ বছর আগে ১৯৯৫ সালে প্রিন্সটন বিশ্ববিদ্যালয়ের অধ্যাপক অ্যান্ড্রু উইলস অবশেষ�� উপপাদ্যটির সমাধান করলেন, দীর্ঘ ৮ বছর যুদ্ধ করবার পর। যে বিপুল গবেষণা ও পড়ালেখা এই সমাধানটির পেছনে বিনিয়োগ করতে হয়েছে উইলস কে, তাকে যুদ্ধ বলাটাই মানায়। “ Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem "-বইয়ে সাইমন সিং বিবৃত করেছেন উইলস এর সেই ৮ বছর ব্যাপী সংগ্রাম এর গল্প। সিং এর লেখায় এই বইটি উইলস এর অসাধারণ ধৈর্য্য ও অধ্যবসায় এর চমৎকার একটি ডকুমেন্টারি হয়ে থাকলো।

 মুহম্মদ জাফর ইকবাল এর ‘ নিউরনে আবারো অনুরণন ’ যাঁরা পড়েছেন, তাঁরা ফার্মা সংক্রান্ত এ তথ্যগুলো আগেই জানেন। জাফর ইকবাল লিখেছিলেন অ্যান্ড্রু উইলস গণিতের খুব আধুনিক কিছু বিষয়ের ব্যবহার করে ফার্মার উপপাদ্যটি প্রমাণ করেছেন, যা ফার্মার সময়ে উদ্ভাবিতই হয়নি। সাইমন সিং খুব সহজ ভাষায় বর্ণনা করেছেন গণিতের নতুন সেই সংযোজনগুলোর কথা। ১০ বছর বয়েসে অ্যান্ড্রু উইলস প্রথম ফার্মার সমস্যার সাথে পরিচিত হন, তখনি তিনি এটি সমাধান করাকে জীবনের একমাত্র লক্ষ্য হিসেবে দাঁড় করিয়ে ফেলেছিলেন। ৩৯ বছর বয়েসে এসে প্রমাণ সম্পন্ন করতে উইলসকে প্রচুর নতুন বিষয় শিখতে হয়েছে। বিষয়গুলো এত চমৎকার যে কিছু প্রাথমিক ধারণা এখানে জুড়ে দেয়ার লোভ সামলাতে পারছিনা! উইলস এর প্রমাণটি মূলত দাঁড়িয়ে আছে তানিইয়ামা-শিমুরা ধারণা (কঞ্জেকচার) এর ওপর। তানিইয়ামা-শিমুরা কঞ্জেকচার বলে সকল এলিপ্টিক্ ইকুয়েশন ই মডিউলার ফর্ম! খুব কঠিন হয়ে গেলো কি?

 গণিতে x^3 – x^2 = y^2 + y এ ধরণের সমীকরণকে বলা হয় এলিপ্টিক্ ইকুয়েশন । একটি সমীকরণের অসীম সংখ্যক সমাধান থাকতে পারে, প্রত্যেকটি নিয়ে আলাদা ভাবে কাজ করতে যাওয়াটা নিতান্ত বোকামী। সমীকরণের সম্ভাব্য সকল সমাধানকে সসীম একটি ছোট্ট স্পেসে প্রকাশ করতে পারলে কাজটা এক্কেবারেই সহজ হয়ে পড়ে। মানুষ ঘড়ি আবিষ্কার করেছে সময়কে একটা ছকে ফেলে কাজ সহজ করে ফেলবার জন্য। ঘড়ি না থাকলে বিশাল বিস্তৃত সময়ের কোন বিন্দুতে আমরা আছি তা কখনো বুঝতেও পারতাম না (এখনও যে খুব পারি তাও নয়, তবু একটা ধারণা অন্তত করতে পারি)। অমুক কাজটা রাতে করে দেবো বললে তা খুব বিভ্রান্তিকর শোনায়, কারণ রাত অনেকগুলো অন্ধকার সময়ের যোগফল; রাতে কখন কাজটা হবে তা নিশ্চিত হওয়া যায়না। রাত ন’টায় করে দেবো বললে মাথাটা পরিষ্কার হয়ে যায়। সময়ের এই সঠিক পরিমাপের জন্যই মানুষ ঘড়িতে সময়কে ১২ টা ভাগে ভাগ করে নিয়েছে। সমীকরণ সমাধানের ক্ষেত্রেও এই বুদ্ধি খাটানো যায়।



 চিত্রের ঘড়িটি ফাইভ-ক্লক অ্যারিথমেটিক সিস্টেম। ৪ থেকে ১ ঘর সামনে আগালে আমরা ০ এ পৌঁছাই, অর্থাৎ, সাধারণ গাণিতিক হিসেবে যেখানে ৪ + ১ = ৫, ফাইভ-ক্লক অ্যারিথমেটিক সিস্টেমে ৪ + ১ = ০। ৪ থেকে ২ ঘর সামনে আগালে পৌঁছাই ১ এ। সাধারণ গাণিতিক হিসেবে ৪ + ২ = ৬, ৫-ঘড়ি পদ্ধতিতে ৪ + ২ = ১…ইত্যাদি।
 ওপরে উল্লেখিত x^3 – x^2 = y^2 + y সমীকরণটির সমাধান ৪টিঃ

 x = 0, y = 0
 x = 0, y = 4
 x = 1, y = 0
 x = 1, y = 4

 শেষ সমাধানটি (x = 1, y = 4) সাধারণ গাণিতিক হিসেবে ঠিক গ্রহণযোগ্য না হলেও ৫-ঘড়ি পদ্ধতিতে মাপে মাপে মিলে যায়ঃ
 x^3 – x^2 = y^2 + y
 1^3 -1^2 = 4^2 + 4
 1-1 = 16 + 4
 0 = 20
 যেহেতু ৫-ঘড়ি পদ্ধতিতে ৫ = ০, ৫ এর সকল গুণিতকও (৫, ১০, ১৫, ২০……) তাই ০ ই হবে। ৫-ঘড়ি পদ্ধতিতে সংখ্যা ছিলো ৫টি (০,১,২,৩,৪), আর সমাধান ছিলো ৪টি, তাই একে E5 = 4 লেখা হয়। যদি ৭ ঘড়ি পদ্ধতি ব্যবহার করা হতো (অর্থাৎ ঘড়িতে দেয়া সংখ্যাগুলো হতো ০,১,২,৩,৪,৫,৬) তাহলে সমাধান হতো ৯টি। এটাকে এখন একটা সিরিজ আকারে লিখে ফেলা যেতে পারেঃ (E সিরিজ)


 ইত্যাদি।

 এবার আসা যাক মডিউলার ফর্ম এ।


 চিত্রের x ও y অক্ষের মাঝে আটকে পড়া বর্গটির রোটেশনাল ও রিফ্লেকশনাল সিমেট্রি বিদ্যমান, অর্থাৎ বর্গটিকে একই অবস্থানে রেখে উল্টে দিলেও এটি দেখতে একইরকম লাগবে, কোন পরিবর্তন ধরা পড়বেনা, এটি হল রোটেশনাল সিমেট্রি। যদি x এবং y অক্ষ বরাবর দুটি আয়না রেখে বর্গটিকে উল্টে পাল্টে ঘোরানো হয়, তাহলেও মনে হবে বর্গের প্রথম অবস্থার কোন পরিবর্তন হয়নি, এটাই রিফ্লেকশনাল সিমেট্রি। যদি এখন বর্গটিকে ধাক্কা দিয়ে সামনের দিকে সরিয়ে দেয়া হয়, তা হলে x এবং y অক্ষের সাপেক্ষে বর্গের অবস্থানের পরিবর্তনটি স্পষ্ট ধরা পড়বে চোখে, অর্থাৎ এর ট্রান্সলেশনাল সিমেট্রি নে��।



 এই চিত্রে এবার অসীম সংখ্যক বর্গ আঁকা হলো, x ও y অক্ষের সাপেক্ষে। এই বর্গগুলোর রোটেশনাল ও রিফ্লেকশনাল সিমেট্রি তো আছেই, এদের ট্রান্সলেশনাল সিমেট্রি ও বিদ্যমান। কারণ, বর্গগুলো কোনভাবে চলতে শুরু করলে অক্ষদুটির সাপেক্ষে কোন বর্গটি কোথায় গেল বা তাদের অবস্থানের আদৌ কোন পরিবর্তন হলো কিনা তা আর বোঝার উপায় থাকবেনা। সবদিক থেকেই অসীম সংখ্যক বর্গগুলোর সিমেট্রি বা সমতা একইরকম থাকবে। এটিকে ঠিক মডিউলার ফর্ম বলা চলেনা, কারণ মডিউলার ফর্ম পাওয়া যায় চার ডিমেনশন এর স্পেসে, আমরা আমাদের তিন ডিমেনশন (দৈর্ঘ্য, প্রস্থ ও উচ্চতা) এর জগতের অভিজ্ঞতা দিয়ে চার ডিমেনশন এর বস্তুর ধারণা করতে পারবোনা। মডিউলার ফর্মের সাথে সিমেট্রির সম্পর্কের বিষয়টি ইঙ্গিত করবার জন্যই বর্গক্ষেত্র সংক্রান্ত আলোচনা এখানে! চার ডিমেনশন এ বাস করা আশ্চর্য সিমেট্রিক মডিউলার ফর্মেরা নির্দিষ্ট কিছু উপকরণ (ইনগ্রেডিয়েন্টস) দিয়ে গঠিত। প্রত্যেকটি মডিউলার ফর্ম ই একে অন্যের চেয়ে আলাদা এই উপকরণের বেশকমের কারণে। উপকরণের সংখ্যানুসারে সাজালে মডিউলার ফর্মের জন্যও একটি সিরিজ পাওয়া যায়, এলিপ্টিক কার্ভের E সিরিজের মতো, একে বলা হয় M সিরিজ। ১৯৫০ এর দশকে দুই জাপানী গণিতবিদ বন্ধু ইয়ুতাকা তানিইয়ামা ও গোরো শিমুরা লক্ষ্য করেন এলিপ্টিক কার্ভের E সিরিজ আর মডিউলার ফর্মের M সিরিজ একেবারে হুবহু মিলে যাচ্ছে, এ থেকে তাঁরা ধারণা করলেন সকল এলিপ্টিক সমীকরণ ই আসলে মডিউলার ফর্ম। তবে এটির পক্ষে কোন প্রমাণ তাঁরা করে যেতে পারেননি, তানিইয়ামা’র অকস্মাৎ আত্নহত্যার দরুন।

 তানিইয়ামা-শিমুরা কঞ্জেকচার দিয়েই যে ফার্মার উপপাদ্য প্রমাণিত করা যাবে এ ধারণা দিয়েছিলেন জার্মান গণিতবিদ গেরহার্ড ফ্রে । “ মনে করা যাক ফার্মার সমস্যাটির একটি সমাধান আছে ”-এই অনুমানের পথে হেঁটে ফ্রে এক নতুন ধরণের এলিপ্টিক কার্ভ আবিষ্কার করলেন যা মডিউলার নয়, তানিইয়ামা-শিমুরার কঞ্জেকচারের সরাসরি বিরোধী। অ্যান্ড্রু উইলস যখন আট বছরের দীর্ঘ সংগ্রাম শেষে উপপাদ্যটি প্রমাণ করলেন, তাঁর প্রমাণটি শুধু ফার্মার সমস্যাটির সমাধানের কাজেই আসেনি, বরং তা গণিত ও নাম্বার থিওরির একাধিক শাখার বিস্তারেও বড় ভূমিকা রেখেছে। তানিইয়ামা-শিমুরা কঞ্জেকচার এখন আর শুধুই একটি কঞ্জেকচার বা অনুমান নয়, এটি একটি স্থাপিত সত্য। গাণিতিক এই তত্ত্বগুলো পরস্পরের সাথে এত দৃঢ়ভাবে সম্পর্কিত, যে শুধু একটির প্রমাণ-ই বাকিগুলোর প্রমাণের জন্য যথেষ্ট, অনেকটা যেন ডমিনো এফেক্টঃ


 অ্যান্ড্রু উইলস বেশ কিছু আধুনিক গাণিতিক হাতিয়ারে নিজেকে সজ্জিত করে ফার্মার উপপাদ্যটি প্রমাণ করেন। এর মধ্যে প্রধান দুটি হলো আইওয়াসাওয়া থিওরী ও কোলিভাগিন-ফ্ল্যাখ মেথড । সদ্য রপ্ত এই বিদ্যাগুলোর প্রয়োগের বেলায় উইলসকে প্রায়ই প্রচন্ড হতাশাজনক পরিস্থিতির ভেতর দিয়ে যেতে হয়েছে। এই টেকনিকগুলো কত কঠিন সে বিষয়ে উইলস বলেছেন সর্বোচ্চ শিক্ষা প্রাপ্ত একজন পেশাদার গণিতবিদেরও এই বিষয়গুলো আয়ত্তে আনতে অন্তত দু-তিন মাস লাগবেই! ফার্মার সমস্যাটির জটিলতার আরেকটি নির্দেশক এটি।

 ১৬৩৭ সালে তানিইয়ামা-শিমুরা কঞ্জেকচারের অস্তিত্ব ছিলোনা। ছিলোনা কোলিভাগিন-ফ্ল্যাখ মেথড, আইওয়াসাওয়া থিওরী, মডিউলার ফর্ম, মিয়াওকা অসমতা-এসবের কিছুই। মাত্র ১টি গাণিতিক সমস্যার প্রমাণে ১৫০ পৃষ্ঠা জুড়ে এতগুলো টেকনিকের ব্যবহার ইতিহাস আগে কখনো দেখেনি। উইলস এর এই প্রমাণটি ফার্মার আসল প্রমাণ নয়। ফার্মা কি আদৌ তাঁর সমস্যাটির সমাধান বের করেছিলেন? এক সময় হয়তো এই রহস্যেরও সমাধান হবে, হয়তো আরো অনেক সহজ কোন পদ্ধতি আবিষ্কৃত হবে, তবু অ্যান্ড্রু উইলস এর ১টিই অঙ্ক কষার পেছনে ৮ বছরের পরিশ্রমের গল্প চির অম্লান থাকবে। গণিতের সাথে মোটেই সম্পৃক্ত নয় এমন অনেকেই ৮ বছর লাগিয়ে একটি অঙ্ক করার হাস্যকর দিকটি বের করে উইলসকে নিয়ে নিয়মিত তামাশা করেছে। যে পরিমাণ পরিশ্রম ও লেখাপড়া উইলসকে করতে হয়েছে তার সম্পর্কে কোন ধারণাই হয়তো এই মানুষগুলোর কখনোই হবেনা। মানুষ হিসেবে অন্য মানুষের এ আচরণগুলো মেনে নেয়াটা প্রচণ্ড কষ্টকর ও হতাশাদায়ক এবং ক্ষেত্রবিশেষে মানুষকে সম্মান করার ব্যাপারে মনকে সন্দিহান করে তোলে, সন্দেহ নেই, তবু উইলস এর গল্প শেষ পর্যন্ত মনে করিয়ে দেয়, মানুষ ই তো পারে!
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 Manny
 Author 28 books 13.4k followers
 March 10, 2009
 I guess the author does a reasonable job. But when I reached the end, I still didn't feel I understood at all how the proof worked. Probably that's just because it's so bloody hard. I got a lot more though out of Prime Obsession , Derbyshire's book on the Riemann Hypothesis, where the author opens up the box and shows you some of the actual math...
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 Luís
 1,792 reviews 431 followers
 March 31, 2022
 That's an excellent history of mathematics from antiquity to the present day. The author skillfully captures the pedagogical trick of the Last Theorem. This "mathematical siren, ..., which attracted geniuses to destroy their hopes" better is a common thread that compellingly guides us through anecdotes, concepts very well explained in the maze of mathematics. The author manages to give both a technical and societal dimension to his story and, thereby, maintain the reader's attention from start to finish.

 Very successful.
 Good reading!
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 Cassandra Kay Silva
 704 reviews 277 followers
 June 20, 2011
 This is the kind of book that we non mathematical minds can easily digest and love. It gives you an epic scope of the number of minds that it takes to build new ideas. I doubt if Fermat had actually solved this theorem correctly, but this is impossible to prove. Fermat's theorem however was not impossible to prove! It was solved! Thanks to the efforts of many men (and women!) over many lifetimes and one final man who had the determination and persistence to finish the unthinkable. This book has a lot of wonderful elements, and really exemplifies a love of mathematics. Although if you want to actually understand the theorem this book may not be for you! I can honestly say reading it did not put the theorem in any more digestible light than it started out with. Perhaps it was to the authors advantage to skip the technicalities and focus on the enjoyment of the journey. I personally loved this approach, but it may not be for everyone, especially if you are actually looking to understand the theorem (a massive undertaking that is really not in my repertoire to comment on).
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 Riku Sayuj
 653 reviews 6,927 followers
 December 3, 2011
 Simon converts what could have been a dry chronicle of proofs into an ode full of excitement, inspiration and intrigue worthy of a gothic love affair. Full review to follow.
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 Bruce
 438 reviews 72 followers
 April 3, 2009
 What a fun book this was (thanks, Trevor, for the recommendation)! There are many reasons I think I like (good) nonfiction -- a sense of direct relevance, gravitas, frequent insights into the workings of the universe (and people), but mostly for knowledge narcs -- high levels of information density served up into an intriguing package by someone else who has undertaken the heavy lifting (research, organization, thinking). So, here in Singh's work I get a solid lay understanding not only of the proof to Fermat's Last Theorem, but of much of mathematics (and the lives of mathematicians) since the seventeenth century.

 I've been thinking also about what attracts me to books on mathematical topics -- the works by Martin Gardner, William Poundstone, and the various other authors in the company of whose thoughts I've had pleasure to spend a week or more. What I've come away with, is that the best of them feed off surprises, those bits of counterintuitive anecdotes that leave you blurting out, "Huh. How about that," and then looking madly around for someone to tell. Like a book of jokes, riddles, or puzzles that provides immediate gratification in the back of the book, Fermat's Enigma plugs at least ten conundrums (and their easy-to-understand, logical solutions) into its appendices. For example -- say you're unlucky enough to be forced into a three-way duel. If everyone gets to take turns in order of their skill such that worst shoots first, what should the worst do? Aim at the best in the hopes of getting lucky and eliminating the most dangerous gunsel? Nope, the correct answer is to pass up the turn in the hopes that your first shot will get to be expended against only one remaining combatant. That way, even if you miss, you at least had a chance to take aim at the only person able to shoot back.

 Pierre Fermat turns out to have been quite the prankster, often tweaking professional mathematicians and academics by mailing them problems they knew full well he had already solved. For those who don't keep this type of trivia at the forefront of their brains, Fermat's the French recluse (and hanging circuit jurist) who once famously scribbled in a copy of Diophantus' Arithmetica that x^n + y^n ≠ z^n for any number n greater than 2, a propostion for which he had "a truly marvelous demonstration… which this margin is too narrow to contain." This gets to be Fermat's Last Theorem, simply because it ends up being the last of his conundrums to be proven (not necessarily the last one he wrote). Just think, were it not for the scrupulous care taken by Fermat's son to go through and publish all of Fermat, Sr.'s writings, the world would not have been tantalized by this particular gem for over 350 YEARS .

 Andrew Wiles published the first (and only?) proof in 1994, and Enigma does a tremendous job of walking the reader through not only the stunning depth of his intellectual achievement, but its significance as well. Suffice it to say that I was happy here to read that Taniyama-Shimura get their well-earned due and that modular and elliptical equations can finally be understood to be mathematically analogous (whether or not I have any idea what modular equations actually are). Still, all of this leads to what I think is an even more tantalizing problem. We now know that all of Fermat's conjectures ultimately proved to be solvable and that Fermat's own notes would seem to indicate that he had indeed apparently found ways to solve each of them. But there is no doubt that Fermat's solution could not have relied on the up-to-the-minute maths Wiles employs over 200 pages. So if it was really the limitations of the margin and not of Fermat that inhibited publication… what was Fermat's proof?
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 Trevor
 1,279 reviews 21.3k followers
 December 9, 2007
 This book is as interesting as a detective story while being about quite advanced mathematics - as such it is quite a book showing the remarkable skill of its writer to explain complex ideas in ways that are always readable and enjoyable.

 A mathematician finds a simple proof to what seems like a deceptively simple problem of mathematics - that pythagoras's theorem only works if the terms are squared, and not if they are any other power up to infinity. Sounds dull. Except that the mathematician jots down that he has found this proof, but not what the proof is. And for hundredsd of years the greatest minds in mathematics have tried to find this simple proof and been beaten by the problem time and again.

 This really is a delightful book and one that gives an insight into how mathematicians think about the world. The proof of Pythagoras's theorem given in this book is so simple that the beauty of mathematical proof is made plain to everyone. Just a little knowledge of algebra is needed for this part of the book - the rest requires no maths at all.
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 Annie
 891 reviews 300 followers
 April 25, 2019
 Strap in, guys. I’m going to walk you through the history of how Fermat’s Last Theorum was proved, all in one little (okay, big) review. And I can do this because of this awesome, semi-accessible, frequently tangent-taking, but mostly, this deeply fascinating book.

 ----------STEP ONE: THE THEORUM----------

 For the unenlightened, Fermat’s Last Theorum is this: you probably know the Pythagorean theorum, a² + b² = c², which explains that if you square the shorter two sides of a right-angled triangle and add them together, you get the value of third side squared. This is easily proved (that is, demonstrated to be completely, utterly, logically true via a mathematical proof, using axioms known to be true, which is just like a logic proof if you’ve done philosophy. Or a geometry proof, if you went to 9th grade). Take any triangle, and this will be true. There are infinite solutions to this equation—literally infinite values of A, B, and C which will render this solution true.

 However, Fermat discovered that the formula an + bn = cn where n > 2 has NO whole number solutions. (Go ahead, give it a whirl. I’ll wait).

 Then he challenged the mathematical community to create a mathematical proof demonstrating this must be true. While tantalizing them with the knowledge he’d already created a proof for this with a scribbled note in the margin of his notebook: “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.”

 Asshole.

 So sparked centuries of people trying to write this proof, to no avail. Until Professor Andrew Wiles (who has the most apropos name ever—he has wiles indeed) of Cambridge, in 1993.

 ***

 For clarity, this is Fermat’s Equation (which I’ll refer to as FE): an + bn = cn where n > 2

 And THIS is Fermat’s Last Theorum (which I’ll refer to as FLT): “There are no solutions to Fermat’s Equation”

 ***

 ----------TANGENT: GODEL----------

 At this point, it’s been assumed that math is logically perfect—that if you correctly build a proof using axioms (like m + n = n + m), it must be true (and if it’s proven to be true, nothing can prove it to be false). This is known as “axiomatic set theory.”

 Along came Godel (who is analyzed to death by my beloved, Doug Hofstadter- see here and here ). His ideas are as follows:

 1. If axiomatic set theory is consistent, then there have to be theorems that can’t be proved or disproved. Why? Because of paradoxes. Godel translated the following statement into mathematical notation: “This statement has no proof.” If that’s false, then you COULD create a proof for that statement—however, that would make the statement false, so how could you have a proof for that? So it has to be true. But if it’s true, it can’t be proved because that’s what it literally says. It’s a mathematical statement that is true, but could never be proved to be true (an “undecidable statement”).

 2. There’s no way to prove that axiomatic set theory is consistent; in a way, it’s one of those “undecidable statement” that’s true but can’t be proved to be true.

 Interestingly, this parallels the physicist Heisenberg’s discovery of the uncertainty principle, but we won’t get into that.

 Now, there aren’t very many of those undecidable statements. Godel couldn’t really point to any other undecidable statements besides the one above, so people assumed they were found only in the most extreme math and would probably never even be encountered.

 Welp. A young student named Paul Cohen at Stanford discovered a way to test whether a question is undecidable, and in doing so, discovered several more.

 Which sparked some fear in mathematicians. What if Fermat’s Last Theorum was undecidable?! What if they were wasting their time trying to prove the unprovable?

 Interestingly, if it were an undecidable statement, it couldn’t be proved—yet it would have to be true. The theorum says “there are no whole numbers to the equation an + bn = cn where n > 2.” If this were false, then it would be possible to prove this by offering a solution to this—by finding a whole number N that’s greater than 2 that allows the equation to be solved. Which would make it a decidable statement, which is a contradiction. So it can’t be false and also be an undecidable statement. In other words, Fermat’s Last Theorum might be totally true but there might be no way to prove it.

 ----------STEP TWO: TANIYAMA-SHIMURA CONJECTURE----------

 Modular forms are a mathematical tool, sort of like impossible forms or shapes, that reveal a lot about how numbers are related.

 The Taniyama-Shimura Conjecture (TSC), created by two Japanese mathematicians (one of whom tragically and abruptly killed himself quite young) says every modular form is related to a specific elliptic equation (elliptic equations were Andrew Wiles’s main area of study; they’re a type of equation, not super important that you understand them).

 The fact that these were unified meant there’s a kind of Rosetta stone that’s been discovered: “Simple intuitions in the modular world translate into deep truths in the elliptic world, and vice versa. Very profound problems in the elliptic world can get solved sometimes by translating them using this Rosetta stone into the modular world, and discovering that we have the insights and tools in the modular world to treat the translated problem. Back in the elliptic world we would have been at a loss.”

 Beyond that awesomeness, the TSC suggests something even more interesting: that possibly all of mathematics, all the different worlds of mathematics, might have parallels in other worlds, as with the elliptic world and the modular world. All of mathematics might be unified—arguably the absolute ultimate goal of abstract mathematics, because this would give us the most complete picture, and the biggest arsenal of tools to solve mathematical problems.

 ----------STEP THREE: RIBET’S THEORUM----------

 This is all important for FLT because of something called Ribet’s Theorum (Ribet was a colleague of Wiles). Ribet’s Theorum goes like this: the imagined solution to FE can be translated into an elliptic equation. And that elliptic equation doesn’t seem to have a modular world equivalent. But the TSC claims that every elliptic equation must be related to a modular form.

 So if you can PROVE that the elliptic form of the solution to FE has no modular form (which we can! The proof was done in 1986), the following is true: if the TSC is true (i.e. all elliptic equations have modular forms), and the elliptic form of the imagined solution to FE has no modular form, then the imagined solution cannot exist, proving FLT.

 So now, all we have to do is prove that the TSC is true, and FLT is automatically proven to be true.

 And this—THIS—is what Andrew Wiles focused on. Proving the TSC (Taniyama-Shimura Conjecture).

 ----------STEP FOUR: PROVING THE THEORUM----------

 Wiles finally succeeded when he applied a new method called the Kolyvagin-Flach method, which groups elliptic equations into families and then proves that an elliptic equation in that family has a modular form; if that elliptic equation has a modular form, then all other elliptic equations in that family also has a modular form.

 However, the Kolyvagin-Flach method has to be adapted for each family of elliptic equations. Wiles successfully adapted the method for all families of elliptic equations, thereby proving that all elliptic equations have modular forms (which, as a reminder, is basis of the Taniyama-Shimura Conjecture, and proving the TSC proves FLT).

 Two months before I was born, in 1993, he proved FLT in a series of 3 lectures.

 Kinda. Actually, there was a minor flaw in his proof (essentially, he might have failed to properly adapt the Kolyvagin-Flach method for some of the families of equations) but it doesn’t really matter because a year later, Wiles published a work-around to that flaw, so he proved FLT once and for all.

 ----------CONCLUSION----------

 All I can think about is: maybe if math looked like this, if THIS had been our material in high school—maybe then I wouldn’t have disliked it. Maybe other people wouldn’t, either. What a shoddy job we do teaching our children the wonder of learning.
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 Roberto
 627 reviews 1 follower
 August 25, 2017

 Un teorema è per sempre

 Un tale Fermat, che nel diciassettesimo secolo si dilettava di matematica ed era un po' buontempone, enunciò un teorema all'apparenza banale e lasciò scritto sul margine di una pagina di un libro:

 “Dispongo di una meravigliosa dimostrazione di questo teorema, che non può essere contenuta nel margine stretto della pagina”

 Il teorema era banale, come pure l'affermazione. Non poteva che scaturirne una dimostrazione banale.

 Eppure...

 La dimostrazione di quell'equazione banale fece perdere il sonno alle maggiori menti matematiche di tutto il mondo, che per 350 anni si arrovellarono per trovare una soluzione. Risultati: zero.

 Cos'è una dimostrazione? In matematica si ritiene che un teorema sia dimostrato quando con un procedimento logico se ne fornisce inequivocabilmente e incontestabilmente la correttezza.

 "La ricerca di una dimostrazione matematica è la ricerca di una conoscenza che è più assoluta della conoscenza accumulata da ogni altra disciplina. Il desiderio di una verità definitiva ottenuta attraverso il metodo della dimostrazione è ciò che ha guidato i matematici negli ultimi duemilacinquecento anni."

 Solo nel 1993 un matematico inglese, Andrew Wiles, dopo sette anni di sforzi, ossessioni, notti insonni, incubi, entusiasmi e delusioni riuscì a completare la dimostrazione.

 Possibile che Fermat avesse trovato una dimostrazione a questo teorema? No, impossibile crederlo; la dimostrazione di Wiles è composta da 200 pagine di matematica estremamente complessa che non poteva assolutamente essere disponibile al tempo di Fermat e che alla fine però è servita anche ad approfondire intere branche della matematica.

 Ecco, il libro spiega la storia di questa dimostrazione e dei grandi matematici che ci hanno lavorato, spiega la bellezza delle sfide matematiche, l'ostinazione e la determinazione richiesta, l'inventiva necessaria e la potenza di un risultato che diventa "eterno".

 La storia di questa dimostrazione è decisamente interessante; per me l'unica carenza nel libro è l'autore, che è "solo" un giornalista e che, poraccio, di matematica ci capisce come io di taglio e cucito. E trasforma la storia in una telecronaca; per consentire ai profani di capire gli aspetti legati alla successione degli eventi dà per scontate parecchie cose (pur riportandole) rinunciando a spiegare con semplicità, forse perché nemmeno lui ci ha capito un granché.

 Cartesio disse: "quando sono in discussione questioni trascendentali, siate chiari in modo trascendentale".

 Ecco Singh chiaro non è. Inutile per me riportare frasi come "Tutto quello che devi fare è aggiungere qualche gamma-zero di struttura (M) e poi ti basta ripercorrere la tua argomentazione ed ecco che funziona" se non se ne spiega il significato. O si omette la frase, o la si spiega.

 Riesce pure a mettere errori di matematica nelle definizioni che, mi dispiace, in un libro di matematica noooooo, proprio non accetto!.

 In ogni caso la storia è affascinante e il libro riesce a trasmettere interesse e curiosità per la matematica e per queste persone meravigliose che si sono prodigate per trovare soluzioni a problemi veramente complessi.
 Fermat era un buontempone e ci ha preso in giro per 350 anni. Ma senza di lui, oggi le nostre conoscenze matematiche sarebbero certamente inferiori...
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 Rise
 298 reviews 30 followers
 January 17, 2016
 From my reading journal:

 May 31, 2009.
 Yesterday I finished reading Fermat's Last Theorem. I plan to write a glowing book review but this space is too limited to contain it.

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 Joy D
 1,686 reviews 203 followers
 September 26, 2022
 “The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.”

 Fermat's Last Theorem states that: xⁿ + yⁿ = zⁿ has no whole number solutions for any integer n greater than 2. Simon Singh fashions the quest to solve this 350-year-old mathematical enigma into a compelling story. In the 1630s, when Pierre de Fermat scribbled a note on a page of his copy of Diophantus’s Arithmetica, stating (in Latin) his theorem and indicating “I have a truly marvelous demonstration of this proposition, which this margin is too narrow to contain.” Singh takes the reader through a series of minibiographies of past mathematicians, ultimately arriving at Andrew Wiles, who spent over eight years developing the 130-page proof.

 Along the way, the reader will learn a great deal about number theory, logic, and the rigorous standards required to achieve an absolute proof. This book covers a wide variety of people and their contributions over the years, such as Pythagoras, Leonhard Euler, Sophie Germain, Gabriel Lame’, Augustin Cauchy, Ernst Kummer, David Hilbert, Kurt Godel, Alan Turing, Goro Shimura, and Yutaka Taniyama.

 The highlight of the book is, of course, Andrew Wiles who discovered Fermat’s Last Theorem at the age of ten, and dedicated himself to figuring out a proof, no matter how long it took. Wiles decided to keep his work secret and work alone in his attic. “You might ask how could I devote an unlimited amount of time to a problem that might simply not be soluble. The answer is that I just loved working on this problem and I was obsessed. I enjoyed pitting my wits against it.”

 We learn about the Shimura-Taniyama conjecture, and the relationship between elliptic curves and modular forms. Singh never gets bogged down with calculations – they are instead included in the Appendices. I have a background in mathematics, so this type of subject matter appeals to me, but I daresay it is not required to enjoy this story of challenge, perseverance, and discovery.

 4.5
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 Raquel
 376 reviews
 March 13, 2021
 Belas histórias de amor. Do amor dos homens por um teorema: o último Teorema de Fermat.
 Uma odisseia matemática cheia de beleza, frustração e triunfo. Não é apenas a história do genial Andrew Wiles; esta é a história dos homens que amam a matemática. Sem fins utilitários, sem pretensões. De Pitágoras a Wiles, de 1637 a 1994.
 A Fermat faltou espaço naquela página para fazer a sua brilhante demonstração, mas às posteriores gerações de matemáticos não faltou coragem. Será que Fermat estava, mais uma vez, certo?
 Esta obra, embora aborde conceitos matemáticos [alguns com um elevado grau de complexidade como a conjectura Taniyama-Shimura] e apresente reflexões que exigem um apurado raciocínio abstracto [sobretudo nesta área de matemática pura] não pretende excluir aqueles que não se encontram entre os poucos eleitos que compreendem perfeitamente a linguagem dos números. A leitura, às vezes, apresenta algumas dificuldades (ultrapassáveis) mas vale muito a pena. Uma obra muito bela e que nos encanta.

 Para saber um bocadinho mais: https://seromoluntdeorummolae.blogspo...


 *
 "El recuerdo de Arquímedes persistirá cuando Esquilo esté ya olvidado, porque las lenguas mueren y los conceptos matemáticos no. Inmortalidad es tal vez un término estúpido, pero quizá un matemático posea las mayores probabilidades de alcanzarla, sea cual sea su significado." [G.H.Hardy]
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 Shivam Chaturvedi
 40 reviews 97 followers
 March 22, 2019
 I never watched any documentaries before going to college (and this was about a century and a half ago.. I am getting old -_-. But yeah, 2009 to be precise). I was always interested in NatGeo and History Channel - but they never showed the real deal on television. The documentaries would be mostly half assed, and at worst, total crap. That's also how Indian television landscape can be broadly categorized too, give or take a few exceptions ofcourse. And so I grew up loving the sciences based on what was taught in school curriculum, and elsewhere what I read on the slow 64-bit internet connection.

 And then college happened. Parents got me my own laptop - and the college intranet had a ton of stuff that other students shared. That place and that time - was where my love for documentaries was born. I had never been so fascinated with anything before. And the first two that I watched - in a long line of them - were Einstein's Biggest Blunder and BBC's Fermat's Last Theorem . The memory of that sunday afternoon is still pretty fresh.

 Back then, I only had a casual interest in astronomy and cosmology, and Einstein's theories were still something exotic. And so I basically understood jackshit from the first documentary. Even more intrigued than before, I started the second one. Fermat's Last Theorem was much more relatable - I had known the theorem, and understood the concept too.

 Years later when I joined goodreads, I found out that there was a book too. Keeping in with the tradition of firsts, it became the first book on my TBR pile too. Where it stayed until a few days ago - and I finally marked it as read last night.

 To be honest, this isn't the greatest book ever. It isnt even Simon Singh's best, who delivered the goods the much better in Big Bang . But it surely captures the essence of all mathematical and scientific endeavor very well - That every once in a while, in the middle of an ordinary life, science gives us a fairytale
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 Gorab
 599 reviews 92 followers
 September 23, 2022
 The best mathematical nonfiction thriller I've ever read!



 Consider this equation: x^n + y^n = z^n (where x,y,z,n are natural numbers with n>2)
 Fermat stated that the above equation has no solutions.
 It’s the simplicity of this theorem which is elusive of the nature of its difficulty to be proved!

 Stated around 1637, Fermat had scribbled this theorem with a note in the margin - "I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain."
 This theorem and other notes were published posthumously by his son. Till date, nobody is aware of the proof that Fermat would have concocted in his mind!

 With modern mathematical tools and researches, this theorem which remained unsolved for more than 350 years was finally proved in 1995 by Andrew Wiles.
 This book is a tale of how this theorem was pursued for centuries and finally how it was proved.

 Loved:
 The context setting and remarkable background stories.
 Fun trivia on numbers - and how mathematics is the language of nature.
 The depth into which many great minds delved and devoted their entire life.

 Recommended:
 If you've ever been intrigued by Mathematics, this is a must read.
 You don't necessarily need to have a grip on Maths to enjoy this book. Explained in layman terms, detailed mathematical proofs and footnotes are all confined to the Appendix section, for the curious minds.

 Notes:
 How I picked this book - A friend sent greetings at 5:29PM mentioning special time. Though I knew about the magic number, but somehow this message helped me traverse down the rabbit hole.
 Ramanujan -> Magic Number -> Taxicab Number -> Fermat near misses -> Fermat's last Theorem... and from thereon it was a different world altogether!

 Then last month, I went shopping books on behalf of friends. Someone picked these, which I ended up reading before sending :) [thank you!]
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 Boudewijn
 621 reviews 69 followers
 June 2, 2022
 This is a very interesting book. Don't be scared about the contents, it's an enjoyable read even if you don't know anything about mathematics.
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 Sol González
 Author 17 books 26 followers
 September 19, 2012
 Lectura en 2012

 Este año tomé nuevamente el libro del Enigma de Fermat, símplemente porque me gustó bastante

 Las matemáticas fueron una de esas cosas con las que siempre tuve un romance eterno. Leyendo nuevamente pude recordar esos episodios en clases en que el maestro en turno llegó un día y anotó este mismo teorema en la pizarra. Nos dejó toda la clase tratando de solucionarlo y obviamente al final nos informó que el mismo no estaba resuelto (o al menos eso recuerdo, porque en ese año ya debería de haber estado).

 Mas detalladamente me hizo recordar a varios amigos que hacían las demostraciones de distintas fórmulas y me las entregaban como si fueran cartas románticas (todavía las guardo).

 La forma en que esta escrita, en ningún momento te hace sentir tedio. Agus dice que son mas bien chismorreos alrededor de la vida de los matemáticos (según como se lo iba contando), y precisamente eso es lo que lo hace interesante. Es la vida de personas que significaron algo para que este teorema existiera y para que finalmente fuera solucionado.

 El gran enigma matemático ha muerto.

 (en serio, leanlo)

 ................................................
 Lectura en 2006

 Finalmente llegamos a lo que fué mi último libro del año (2006 para los despistados). Durante las fiestas me encontré en casa de mis abuelos, y el apartado en donde vive mi hermana, actuaria y fanática de las matemáticas. Lo lamentable es que la mayor parte de los libros que lee yo se los recomiendo, así que la mayoría de los que encontré en su librero ya los había leído.

 Encontré tres libros entre los cuales elegir, sin embargo este brillo llamando mi atención debido a una anécdota. Cuando mi hermana todavía estudiaba, viajaba a casa en autobús cada dos o tres meses. Entre sus compañeras hubo una que le presto este libro y en una ocasión el libro viajó con ella… sin embargo hay que añadir que mi hermana es algo despistada así que en esa ocasión el libro quedó en el autobús. No sé qué fué lo que le ha dado más coraje en esa ocasión, perder un libro prestado o no poder seguirlo leyendo. Tuvo que comprarlo para devolverlo y además se compró su propia edición (que todavía le tengo que devolver).

 El enigma de Fermat es una novela de matemáticas. Mediante un poco de historia Singh nos va narrando la evolución de las matemáticas como un arte, muy lejos de aquellas matemáticas aplicadas. Las matemáticas como algo abstracto que es hermoso por sí mismo, porque tiene un orden y una lógica, porque en sí misma engloba misterios y permite que los descubras mediante una relación con ella.

 Declaro que de niña me gustaba leer el Baldor y en mi último año de preparatoria acabé con todas las operaciones integrales en todos mis libros (y no tenía sólo dos) y este libro ha sido recordar las horas que le dediqué.

 Que hermosas eran para mí las matemáticas.
 Fue un hermoso fin de año.
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 Veronica
 101 reviews 63 followers
 June 29, 2021
 Why do variables love mathematics?
 y₀

 (My head says rationally: Veronica, Goodreads is not a place for the corny wisecracks that you come up with during the day. My heart says differently.)
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 Arelis Uribe
 Author 7 books 1,208 followers
 February 19, 2017
 Había leído parte de este libro cuando estudiaba periodismo, gracias a Alejandra Carmona, una profe muy inquieta que daba el ramo de Antropología y que siempre llegaba con lecturas nuevas y actuales. Por ella descubrí no sólo a autores “académicos”, como Lévi-Strauss y Ángel Rama, sino a escritores que cruzan el periodismo con la etnografía y la literatura, como Martín Caparrós y Simon Singh, autor de El Último Teorema de Fermat. Es un libro hermoso, como hermosas son las matemáticas y como hermoso es el problema que heredó Fermat a sus colegas por más de 300 años y como hermosa es la historia de traiciones, desafíos y sueños que están ligados a este acertijo matemático.
 Este es un libro que mezcla la investigación científica, el periodismo y la literatura. Aprendí un montón leyéndolo. Está escrito (y traducido) con una prosa limpia, liviana y sencilla, algo muy difícil de lograr, sobre todo cuando se explican temas intrincados, como las matemáticas. Salvo por el exceso de adverbios de mente (que, ay, me ponen medio mal) es un placer leer las explicaciones complejas de manera tan amable.
 Pienso que la matemática son un universo de lógica, absolutismos y armonía de un nivel superior. Como toda disciplina y todo arte, aspira a la belleza y los matemáticos lo saben, persiguen la belleza de la perfección de los números y le achacan a este universo propiedades como la bondad o la amistad, todo a partir de patrones numéricos. Se me ocurre que mucha de la filosofía matemática refleja la moral de sus autores y, al mismo tiempo, describen también las relaciones humanas y la vida.
 Me gustó mucho que el autor se hiciera cargo, en un apartado, del sesgo histórico de género que han acompañado las matemáticas. “A través de los siglos las mujeres han sido desanimadas a estudiar matemáticas, pero a pesar de la discriminación, ha habido varias matemáticas que lucharon contra esa costumbre institucionalizada e inscribieron sus nombres en forma indeleble en los anales de las matemáticas”. Y nombra a Hipatia de Alejandría o Sophie Germain, que tuvo que usar el pseudónimo de Monsieur Le Blanc para que tomaran en serio su trabajo. Cuando ella debió revelar su identidad, un destacado matemático (que fue su maestro sin saber que ella no era hombre) escribió: “Cuando una persona del sexo que, de acuerdo con nuestras costumbres y prejuicios, debe encontrar infinitamente más dificultades para familiarizarse con estas espinosas investigaciones, tiene éxito en superar estos obstáculos y penetrar las partes más oscuras de ellas, entonces sin ninguna duda debe tener el más noble coraje, talentos verdaderamente extraordinarios y una genialidad superior”.
 Cuando yo estaba en octavo básico era muy porra. Me iba mal en el colegio. No estudiaba demasiado. Ese mismo año me puse a pololear con un chico dos años mayor que yo, que era escandalosamente estudioso. Me acuerdo cuando me explicó las potencias. Yo me había sacado un rojo en la prueba y él, con mucha paciencia y amor, me explicó esta materia que en realidad es súper fácil y entretenida. De ahí en adelante me puse igual de odiosa y matea que él. Salí de cuarto medio con promedio 6,9 en matemática. Después estudié periodismo y olvidé los números, pero al leer este libro recordé por qué me gustaban tanto, por qué disfrutaba más resolviendo facsímiles de la PSU de matemáticas que viendo Los Simpsons. Hay tanta perfección en los números, tantos juegos posibles.
 El libro se trata de cómo se resolvió el problema matemático más famoso de la historia: el teorema de Fermat, que sostiene que no hay soluciones posibles al teorema de Pitágoras cuando la potencia es mayor a 2. El libro explica, también, porque esa demostración es tan endemoniada y difícil. La belleza del problema es que Fermat dijo tener una demostración, pero que no la podía escribir en el margen de un libro, ya que ese espacio era muy pequeño. En rigor, no existía la demostración (no existe, nadie ha visto jamás la demostración de Fermat). Era y es una especie de eslabón perdido de las matemáticas. 350 años después, Andrew Wiles plantearía su propia solución, una muy compleja y elegante, que unifica las matemáticas y que se sirve de todas las etapas de esta ciencia para lograrlo. Al final, el libro cuenta esa historia y también repasa miles de años de epistemología de las matemáticas.
 Algunas cosas bellísimas que se leen en este libro:
 —“Pitágoras había descubierto que unas proporciones numéricas simples eran responsables de la armonía de la música”.
 —“La razón entre la longitud real de los ríos desde su nacimiento hasta su desembocadura y su longitud en línea recta (…) es aproximadamente 3,14: número cercano al valor de π”.
 —“Las matemáticas son el lenguaje que permite describir la naturaleza del universo”.
 —“La razón por la cual se le atribuye el teorema a Pitágoras es porque fue él quien primero demostró su validez universal”.
 —“La llamada demostración científica depende de la observación y la percepción, las cuales son falibles y sólo suministran aproximaciones (…) [la demostración matemática] tiene una verdad más profunda que cualquier otra verdad, porque es el resultado de un proceso lógico. Las matemáticas son una materia de estudio no subjetiva (…) independiente de la opinión”. Es decir, una demostración matemática es una verdad absoluta y se aplica para un caso específico como para todos los de su serie hasta el infinito. Es loca esa hueá, ojalá las ciencias sociales funcionaran así.
 —“Fermat y Pascal habrían de descubrir las primeras demostraciones y certezas absolutas de la teoría de la probabilidad, una materia que es, en esencia, incierta��.
 — “[Pascal] sostuvo que ‘la emoción que un apostador siente cuando hace una apuesta es igual a la cantidad que puede ganar multiplicada por la probabilidad de que gane”.
 —“El primer director del departamento de matemáticas (de la Universidad de Alejandría) fue, ni más ni menos, Euclides”.
 —Sobre la destrucción de la biblioteca de Alejandría: “En el año 642, un ataque musulmán culminó con éxito aquello en lo que los cristianos habían fracasado”. Quemaron todo por fanatismo dogmático. Maldita religión.
 — “El crecimiento de cualquier disciplina depende de su capacidad para comunicar y desarrollar ideas”.
 —“Los números amigos son parejas de números tales que cada uno de ellos es igual a la suma de los divisores del otro”.
 —“[En matemática] las ideas no corroboradas son infinitamente menos valiosas y se conocen como conjeturas”.
 —“Es impensable para los matemáticos no poder, al menos en teoría, contestar todas las preguntas, y esta necesidad se llama completud”.
 —“Los teóricos de los números consideran a los números primos como los más importantes de todos, porque son los átomos de las matemáticas”.
 —“Dios existe puesto que las matemáticas son consistentes, y el diablo existe puesto que no podemos demostrarlo”, André Weil.
 —Sobre Galois, un maestro escribió: “la locura matemática domina a este muchacho”.
 —“Cuando se discuten cuestiones trascendentales, hay que ser trascendentalmente claro”.
 — Y la frase que escribió Wiles cuando terminó su demostración del teorema de Fermat frente a la comunidad matemática más importante: “Creo que me detendré aquí” <3
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 Campbell Mcaulay
 47 reviews 4 followers
 October 4, 2011
 If you buy the latest Jilly Cooper instead of this you WILL go to hell!


 This one languished on my bookshelf for the best part of a year as I was too scared to pick it up & start it. What held me back is what will probably put a lot of other potential readers off trying it - the boring old "I'm no good at maths" argument. Although my maths education is probably little above average (a good O Level and a terrible A Level, after which I rallied somewhat to obtain a reasonable HNC maths module) it's //very// many years out of use and it's all I can do to add two numbers up in my head. Given that this book is about a problem that flummoxed the best mathematical minds in the world for over 350 years you'd be forgiven for putting this back on the shelf and choosing something a little simpler. Well, don't even try that...

 YOU DON'T NEED ANY MATHS TO READ THIS!

 What Singh has done here is to present a hugely complex subject in a hugely entertaining way. The search for the answer to Fermat's riddle reads like a detective story and not a matehematical treatise and it includes a truly absorbing potted history of the development of maths over the years and, from Pythagoras to Fermat to Godel to Wiles, each part has a fascinating human side to it.

 Budding mathematicians needn't feel left out as the mechanics of the maths is also included, but it's treated in a gentle way: each step of the problem (and it's solution) is described in a simplified (but certainly not dumbed down) manner and some simple exercises are included in several short appendices. However, take heart! There are several places where elements of the maths are obviously too complex for us mortals and Singh is not afraid to say soo and then gloss over them completely. That may be a disappointment to some, but it's not at all unreasonable in my opinion.

 All in all, the net result is a book that is sensitive to its readers, intelligent, interesting and important. It's literally unputdownable and it had the added bonus of tricking me into thinking that I'm a little cleverer than I really am.

 I notice there's an inevitable Wills and Kate bio on the bestseller list at the moment. Put your hard earned cash into Andrew Morton's pockets or read something that will make you feel like a genius. The choice is yours.
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 Γιώργος Πισίνας
 50 reviews 4 followers
 June 13, 2018
 Αρχικά να πούμε ότι δεν είναι λογοτεχνία. Μου το είχαν προτείνει μαζί με κάποια βιβλία επιστημονικής φαντασίας και συνεπώς περίμενα κάτι αντίστοιχο. Αυτός ήταν και ο λόγος που το παράτησα στην πρώτη απόπειρα.

 Όμως, είναι μια εξαιρετική και απλοϊκή ιστορία των μαθηματικών σε σχεδόν λογοτεχνική απόδοση. Σίγουρα δεν μαθαίνει κάποιος μαθηματικά με αυτό το βιβλίο,
 αλλά μπορεί να έρθει σε επαφή με τις πλέον σύγχρονες μορφές τους χωρίς ιδιαίτερες γνώσεις.
 Σε τελική ανάλυση η ιστορία με συνεπήρε και το βιβλίο σίγουρα άξιζε την δεύτερη ευκαιρία που του έδωσα.
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 David
 537 reviews 122 followers
 July 13, 2022
 Its a simple problem: x^n + y^n = z^n has no positive integer solutions (xyz) for n>2. So why is it so hard to prove? (or disprove). I'm a math/physics nerd so this book has great appeal. I also like Simon Singh's technical writing. He stayed 100% on track as he traced Pythagoras in 6 BC to Andrew Wiles proof in 1994.

 We all remember 3-4-5 triangles from geometry/trig, right? Pythagorean Theorem says 3^2 + 4^2 = 5^2. Other famous right triangle uses of these are the 5-12-13 or the 7-24-25, or how about 99-4900 - 4901. So why can't a version of this with cubes, or ^4 or ^5 work?

 Andrew Wiles read The Last Problem by Eric Bell when he was 10. He ultimately left Cambridge, England became a math professor at Princeton.

 The text kept moving at a strong pace. The greatest minds in math all came into play, with their own focus and contribution to solving this problem. Pierre de Fermat lived 1607-1665. The mathematicians before him that get mentioned all contributed to number theory that had direct bearing on this ultimate math problem. Fermat has scribbled in the margins that he knew the proof, but it simply wouldn't fit in the margins.

 Even as computers came into being, the 'brute force' method of MANY trials (with none working) could solve this problem. For even if a million numbers were tried, maybe the next one could work. What was needed was a full mathematical logical proof.

 Solid 4.5*. If you like math/physics, then easy 5. If not, then round down to a very readable 4.
 _own math z-2022
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 amy
 51 reviews 9 followers
 January 19, 2022
 ✩ 5.0 stars ✩
 In telling the story of one of the most famous problems in mathematics, Simon Singh reveals the beauty of number theory, hidden in the simplicity of the problem that Andrew Wiles fell in love with all those years ago. He maps out a tree of mathematics with Fermat’s Last Theorem as the trunk, the central piece, paying tribute to the countless mathematicians that paved the way for Wiles’ proof. And of course, he describes the sheer tenacity of the mathematical genius as he grapples with the problem for 7 years. I loved the detail with which Singh explored the history of mathematics — he maps out intricate branches of time, delving into the history of Pythagoras, Euler, Turing, Taniyama and Shimura, and so many others, as he attributes to each their own contributions towards Fermat’s Last Theorem.

 This is a must-read for anyone interested in maths, but perfectly accessible for laymen of any sort.
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 Jimmy
 511 reviews 686 followers
 June 23, 2016
 A fantastically entertaining and educational book about the quest to solve the oldest math problem: Fermat's Last Theorem. The intrigue, mystery, and drama surrounding the famous theorem without a proof (but that Fermat had said he had a proof for, just not enough space to write it in the margins) is exciting enough. All the math greats who have attempted to solve it but come up a little short, or a lot short.

 But it's much more than that, since the final proof of Fermat's Theorem involves so many other math concepts. This book starts and ends with Fermat, but in the middle it is more like a grand tour of all the mathematical developments that make the proof even possible. It's interesting to read about all the different dead ends and other productive findings (that had tangentially made it a little more possible to solve Fermat, but whose main contribution was in some other area). Also, reading about Galois's amazing life always makes me giddy. I mean, I've read about him before, but his story is just so crazy--math genius turned revolutionary thrown in jail involved in affair ends in duel, scribbles out his last thoughts the night before he dies... amazing.

 But don't expect to understand how the proof actually works by the end. The proof itself is over 100 pages, so there is no way a normal non-math genius can understand it. But you will get a general idea of the approach/trajectory/style of the final beast. Also, some of the math concepts leading up to it are quite easily comprehensible. I wouldn't recommend this book to a math whiz... it's more of a fun read for the layperson.

 It would ultimately be more satisfying if the proof were a short elegant thing that didn't involve latest groundbreaking discoveries in math. But maybe the bright side is that we can still wonder about Fermat's original (alleged) proof that was never written down. It had to be different from Andrew Wile's proof; does it exist? Or was Fermat bluffing? Or did he make an error in his proof?
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 Rakesh M
 32 reviews 29 followers
 February 17, 2017
 This book is a biography of the epic quest to solve the eluding Fermat's last theorem. It chronicles the life and works of not just Fermat, but most of the mathematicians having even a tiny bit to do with the conjecture/theorem.

 Curious and strange revelations into the lives of many of the princes and princesses of mathematics are presented. It presents the case of lives, pursuits and the times that they lived in. The problems that they face (mathematical and others), how these affect the progress/decline of the field.

 Simon Singh writes brilliantly mixing accounts of math behind the problem along with the lives of these mathematicians. We get to see accounts of love, suicides, suicide averted by fixating on a proof, duels and revolutionaries. For me it was shocking to know, that it was not just the kings and religious fellows destroying these geniuses and their sanctuaries, but Pythagoras also committed a grave mistake once, sentencing Hippasus to death for arguing that sqrt(2) cannot be expressed as a fraction!

 A must read for those interested in history behind the problem.
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 Hariprasad
 4 reviews 2 followers
 August 6, 2015
 Simon Singh gives an excellent account of the quest for the solution to Fermat's puzzle. Starting off with ancient Greeks and arriving at the proof using modern mathematics, he explains the struggles of generations of mathematicians. The author never tries to overwhelm us with the mathematics, but tells us about the people who were involved in proving the theorem. Having said that, all the mathematics in the book can be understood with a background in high school mathematics.

 This book is a great read simply because of the intellectual achievement that it talks about. Strongly recommended if you're remotely interested in mathematics.
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 Maricarmen Estrada M
 282 reviews 69 followers
 January 11, 2020
 I have a special love for words. I think I always have. They’re fascinating. The words in this book were used for telling a story about numbers, which made me realize I also love numbers so much, I just didn’t know. Math had always been the “easy subject” at school for me, the one which did not require long hours of study, because it was so logical, the one you could check before turning in an exam and know you had the right answers precisely because it matched so perfectly. “Proof is what lies at the heart of maths.”, indeed, so simple, so beautiful.
 Well, this story is, as the title describes, a true quest to solve one of the most difficult problems in Mathematics which Fermat’s Last Theorem used to be. Simon Singh did this superbly. He is absolutely great at explaining from whole numbers and 1+1 to elliptical equations and modular forms. But the best was to learn about some of the greatest minds that worked so hard in the last century solving problems and doing the maths that have been the basis and tool for proving this theorem and thus, their great contribution to science: Pythagoras and his controversial Pythagorean Brotherhood, Mersenne, Euclid, Diophantus and his most remarkable “Arithmetica”, of course Pierre de Fermat, Pascal, brilliant Euler, Cantor, Sophie Germain, Theano, Hypatia, Maria Agnesi, Emmy Noether, Gauss, Cauchy, Lamè, Kummer, Wolfskehl, Gödel, Turing, Shimura, Taniyama, and Andrew Wiles. These are not the only ones, of course, but the most outstanding for me from this book.

 I want to make a special mention to the part where Singh talks about the work of women that were mathematicians. Even as of today, there aren’t many of us women dedicated to numbers or number theory, but we have come to a time when we can actually pursue this career, despite the struggles and obstacles that still exist in our societies. But being a mathematician a few centuries ago was completely outrageous and out of this world! Sophie Germain had to study secretly at night and keep a secret stock of candles to do so, because her dad used to confiscate them to prevent her from studying. Or Agnesi who was referred to as the “witch of Agnesi”. And the most extreme of these was Hypatia of Alexandria who suffered the most tragic and brutal death to the hands of the exulted mob led by the patriarch of Alexandria because she was considered a heretic. These stories really moved me and I’m very glad that their names are remembered and admired although they did not have a voice in their own time. Their only voice was their endless curiosity and passion for trying to understand the Universe and their brilliant work pervaded through history and remained printed in our books and forever in our memories, a greatly deserved honor to inspire all of us.

 And back to Fermat’s Theorem, Wiles amazing work on his childhood’s dream inspired this book and will hopefully inspire many more that see the beauty of numbers to keep working and pushing the frontiers on this science field which Singh perfectly describes as the “language of nature”.
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801 reviews2,502 followers     October 8, 2014   Simon Singh has the ability to present a story about a mathematics problem, and tell it like a detective story. He makes the subject exciting, even though the outcome is well known. Singh intersperses history with discussions about the mathematics, and makes it quite understandable. Singh starts with the roots of the famous Fermat's Last Theorem, by recounting the stories and mathematics of Pythagoras, Euclid, and Euler. Other, less well-known mathematicians are also given credit, for example Sophie Germain, Daniel Bernoulli, Augustin Cauchy, and Evariste Galois.  Three hundred fifty years ago, Fermat wrote the following theorem in the margin of a mathematics book: And, Fermat wrote that he had a marvelous proof, but no room in the margin for it. For centuries, mathematicians have attempted to prove the theorem, without success. It had been sort of a "holy grail" of mathematicians to prove the theorem, and many brilliant minds spent years on it. Perhaps in was unprovable, and worst of all, Kurt Godel showed that some theorems are actually undecidable--that is to say, it is impossible even to decide whether or not a theorem is true. Singh recounts a fascinating story of the gifted mathematician, Paul Wolfskehl. He was very depressed, and decided to commit suicide on a particular night, at midnight. While waiting for that time to arrive, he started to read about the failed attempts to prove Fermat's Last Theorem. He became so engrossed in the subject, that he worked well past midnight. He found a gap in the logic of a predecessor, and was so proud of himself that he gained a new desire for life. And, in his will he established a fund of 100,000 marks to be given to the mathematician who first completes the proof of the theorem! Much of the book describes how Andrew Wiles developed a growing interest in the theorem. He worked in almost total isolation for seven years, in order not to be distracted. He occasionally published little tidbits unrelated to his real endeavor, in order to dispel suspicions about what his real work entailed. The central piece of the proof entailed proving the Taniyama-Shimura conjecture, that linked modular forms with elliptic equations. This was a linkage between two far-flung branches of mathematics that seemed to be totally unrelated. To prove the conjecture would allow incredible advances to be made. And then, Ken Ribet showed that a proof of the Taniyama-Shimura conjecture would, in effect, be a direct proof of Fermat's Last Theorem. But many people tried and failed to develop the proof. But that is exactly what Andrew Wiles worked on for so many years. I had previously read that during Andrew Wiles' famous lecture, he just casually let the unsuspecting audience know, "and that is a proof of Fermat's Last Theorem." Well, this book tells a somewhat different story. Most of the audience had heard rumors that the third of Wiles' lectures would be of historical significance. They came prepared with cameras, and took photographs during the lecture. So, it was a surprise, but not a total surprise. After Wiles' manuscript of the proof was sent to a publisher, six mathematicians reviewed it, and a crucial gap was found in it. Wiles worked furiously for a nightmarish year, and with the help of Richard Taylor, finally closed the gap. Today, Wiles is recognized as the one who developed the proof. But it is clear, that Wiles "stood on the shoulders of giants"; he used--and developed--mathematical techniques that had not existed just a few decades previously. Simon Singh writes with a wonderful style. It is clear, not too jargon-heavy but contains enough mathematical "meat" to seem satisfying. The book is followed by ten appendixes that contain more details about some of the mathematics; they are not overly technical, and give the reader a better understanding of some of the issues. I highly recommend this book to everyone interested in math.      history mathematics               29 reviews23 followers     September 2, 2021   This book is endowed with all elements of a perfect story, which are curiosity, surprising events, tragedy, ambition, alternating defeat / triumph and finally an astonishing success. The “Fermat’s enigma” is a tremendously inspiring narrative of one of the most important and most difficult conundrums of mathematics. It was devised by the reverend Pierre de Fermat who was called “The prince of amateurs” because he had neither had any formal education in mathematics nor he had any known tutor. He learned maths by some copies of ancient books written by Euclid’s disciple named Diophantus. When mathematicians scrutinized margins of his books they saw a short note which baffled the brightest minds for more than 350 years. Fermat claimed a groundbreaking conjecture in the margin of Diophantus book without any proof, but the line next to the proof made the case much worse for other mathematicians. he wrote beside the conjecture:“I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain” .This showed the fact that the formula had indeed a proof but it was lost. If you want to know what that theory is you can search on google because it can’t be properly explained in this review.Since the last 350 years the formula had been attacked by the most eminent mathematicians including Leonhard Euler but none of them could prove it thoroughly.After so many years of fruitless endeavor Andrew wiles managed to prove it. For Andrew the Fermat’s last theorem was personally and emotionally significant because he had been in love with the theorem since he first encountered it when he was just ten years old. After thirty years he used so many new mathematical techniques and finally he put more than 8 years on proving this conjecture in order to firmly prove it and finally he did.This book is only recommended for those who appreciate the true value of mathematics.                   347 reviews19 followers     January 3, 2018   Before delving into the book itself, I thought I’d start things off by introducing the problem it’s concerned with, just in case you aren’t already familiar with it. So, what exactly is Fermat’s Last Theorem?  Well, basically, this is it: As you can see, the conjecture is quite easy to understand, and yet, believe it or not, it was so remarkably difficult to prove that it took over 350 years to accomplish! The fact that Fermat (teasingly?) scribbled this rather infuriating note in the margin only added to the frustration felt by the scores of mathematicians who did battle with it over the centuries: “I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.”  No doubt the cheeky bastard would’ve enjoyed Twitter:   Okay, now that that’s been taken care of, it’s time to look at the actual book.  What Kind of Book is Fermat’s Enigma?  Simply put, Fermat’s Enigma is a history book. It is most definitely NOT a math book, so don’t expect to find any degree of mathematical rigor or complexity here. There are a handful of fairly simple proofs included in the appendices, but overall, the concepts under discussion are glossed over in a superficial manner, never examined in any kind of detail. If you want something that fleshes out how the proof actually works, I’m afraid you’ll have to look elsewhere. (Singh was kind enough to include quite a few “further reading suggestions” at the end of this book. While I’ve not looked into any of the titles he recommended, I assume many of those might prove more to your liking if you prefer a “math book” on the subject.) In any case, while Singh did not pursue the actual mathematics in any real sense, he did positively excel at telling the story of an utterly fascinating struggle, one which spanned hundreds of years and ensnared countless brilliant, talented minds. Readers make the acquaintance of such notable mathematicians as Pythagoras (whose work paved the way for Fermat), Leonhard Euler, Paul Wolfskehl, Sophie Germain, Daniel Bernoulli, Augustin-Louis Cauchy, Evariste Galois, Yutaka Taniyama, Goro Shimura, and of course Andrew Wiles, the man, the myth, the legend who finally proved the damn thing.  Overall, I was surprised and delighted by just how compelling the story actually was. For me, this book quickly became a veritable page-turner, one I was loathe to put aside. Some may argue that in order to accomplish this, he omitted too much relevant information, that he sacrificed depth for readability. Perhaps this is true to an extent, but in my opinion, while it was admittedly easy to read and follow, it still managed to include a fair amount of pertinent, interesting material. More importantly, it never got bogged down with unnecessary details or lost in minutiae, and never meandered down exasperating tangents, as many otherwise outstanding history books are wont to do.  And ultimately, what made this book so very stimulating was that the manner in which the story was told really made it come alive. Singh bestowed a truly suspenseful, exciting quest upon the reader, one full of twists and turns, and even *gasp* its fair share of drama. He enthusiastically demonstrated just how action-packed and exhilarating the life of the mind can be. And for accomplishing this tremendous feat, I heartily recommend the book, warts and all.  And Now, For a Few Words on the Star of the Show  Andrew Wiles is an extraordinary human being. Fascinated by Fermat’s Last Theorem since he was ten years old, he vowed to conquer that most impossible of proofs. This was at the age of ten, mind you. I seriously can’t get past that. And then, true to his word, the little rascal grew up to become an eminent mathematician, one who finally went into seclusion for seven years in order to hack away at this tremendous proof. While a not insignificant error marred the first release of said proof, he didn’t let that deter him, but persevered and managed to rectify the error, and, within a couple of years, came out with THE proof. Holy goddamn shit.  To me, Wiles’ story was completely and utterly inspiring. I was frankly amazed by what the human mind can achieve; I think I will always be in awe of Wiles’ fierce determination and incredible tenacity. Mad respect.  Anyway, as you can probably tell, Andrew Wiles is a personal hero of mine. He is an undeniable, ultimate badass. Wayne and Garth said it best:       stem-shelf-research               Author  1 book179 followers     July 23, 2017   Being a scientist of long standing and loving all aspects of science and maths, Fermat's Last Theorem in itself was a wonderful mystery, what I would give to see Fermat's note book with a note in the margin about cubic numbers as opposed to squares. A very trite remark, too lengthy to write in the margin so it is elsewhere, and no one has ever found it or managed to prove his statement, until - - - this book is a brilliant read, you would think it would be as dry as dust, but no! It is a superb account of the proof of the last theorem from Fermat's notebook to be proven. The only thing that still niggles at me, although the mathematical proof is fabulous, it uses modern techniques not available to Fermat, so it is proven but how the hell did Fermat do it??????A brilliant book, beautifully written a tremendous historical question answered in a very modern way, fabulous, well done for readability.                  141 reviews18 followers     February 28, 2016   “সমকোণী ত্রিভুজের অতিভুজের ওপর অঙ্কিত বর্গক্ষেত্রের ক্ষেত্রফল অপর দুই বাহুর ওপর অঙ্কিত বর্গক্ষেত্রদ্বয়ের ক্ষেত্রফলের সমষ্টির সমান”-বাংলা মধ্যম শিক্ষা ব্যবস্থার ছাত্র-ছাত্রীরা বিজ্ঞান, ব্যবসা, মানবিক ইত্যাদি ‘শ্রেণীগত পার্থক্য’ভেদে সকলেই নবম শ্রেণীতে ‘পীথাগোরাসের উপপাদ্য’ নামে পরিচিত উপপাদ্য-২৩ পড়ে এসেছেন। চিত্রের সমকোণী ত্রিভুজের (অর্থা��� যে ত্রিভুজের একটি বাহু অপর বাহুর সাথে ৯০ ডিগ্রী কোণে অবস্থিত) অতিভুজ c, লম্ব a এবং ভূমি b। পীথাগোরাসের উপপাদ্য অনুসারে a^2 + b^2 = c^2। a, b এবং c এর কিছু মান বসিয়ে সমীকরণের দু পাশ সমান করে ফেলা যায়, সবচেয়ে সহজ একটি উদাহরণ হলো:  ৩^২ + ৪^২ = ৫^২বা, ৯ + ১৬ = ২৫ দু হাজার বছরেরও বেশী পুরনো এই উপপাদ্যটি আজ আমাদের প্রতিদিনের জীবনে অসংখ্যবার ব্যবহৃত হচ্ছে। এই উপপাদ্য দিয়ে টিভিস্��্রীন/ কম্পিউটার মনিটর নির্মাতা পর্দার আকার মাপছেন, জ্যোতির্বিদ তারার মাঝের দূরত্ব গুনছেন, ইলেক্ট্রিক্যাল ইঞ্জিনিয়ার ফেজর কারেন্ট হি��েব করছেন, সিভিল ইঞ্জিনিয়ার লোড পরিমাপ করছেন, অর্থনীতিবিদ যোগান আর চাহিদার হিসেব মেলাচ্ছেন......মোট কথা, আমাদের আজকের সভ্যতা যে বিন্দুতে দাঁড়িয়ে আছে তার পেছনে আছে a^2 +b^2 = c^2 জাদুকাঠিসরূপ এই সমীকরণটির অকল্পনীয় অবদান। এই উপপাদ্যটি ছাড়া প্রকৌশলবিদ্যার কোন একটি শাখাও সচল নয়! এ লেখার উদ্দেশ্য পীথাগোরাসের বা তাঁর উপপাদ্যের জয়গান গাওয়া নয় (উপপাদ্যটি আদৌ পীথাগোরাসের নিজস্ব উদ্ভাবিত কিছুও নয়! তাঁর জন্মের বহু আগে থেকেই একাধিক সভ্যতা এই উপপাদ্যটির ব্যবহার করে আসছিলো)। পীথাগোরাসের উপপাদ্য বিভিন্ন প্রকৌশল বিদ্যার অপরিহার্য অঙ্গ হিসেবে এমনিই গরীয়ান, কিন্তু আরো একটি বিষয় উপপাদ্যের সমীকরণটিকে অনন্য করে তুলেছে। ৩৭৭ বছর আগে, ১৬৩৭ সালে ফরাসী গণিতবিদ পিয়ে দ্যা ফার্মা একটি উপপাদ্য দাঁড় করালেন। “নিম্নোক্ত সমীকরণটির কোন সমাধান পূর্ন সংখ্যায় কখনোই পাওয়া যাবেনাঃ  a^n + b^n = c^n যেখানে a, b, c ও n পূর্ণ সংখ্যা ও n এর মান ২ এর চেয়ে বড় যে কোন সংখ্যা" অর্থাৎ, a^3 + b^3 কখনোই c^3 এর সমান হবেনা, a^4 + b^4 কখনোই c^4 এর সমান হবেনা……a^100 + b^100 কখনই c^100 এর সমান হবেনা……a^9999999999999…….(অসীম) + b^9999999999999…….(অসীম) কখনোই c^9999999999999…….(অসীম) এর সমান হবেনা; n এর মান ২ এর ওপর যে কোন পূর্ণ সংখ্যার জন্যই সমীকরণটির কোন সমাধান নেই। “সংখ্যার সংখ্যা কত” এমনটা কেউ বলতে পারবেনা কখনোই। সবচেয়ে বড় শেষ সংখ্যাটির সাথে এক যোগ করে দিলেই আরেকটি নতুন সংখ্যা তৈরী হয়ে যায়। অসীম সংখ্যক সংখ্যার একটি দিয়েও a^n + b^n = c^n সমীকরণটির সমাধান করা যাবেনা? বেশ তো, পরখ করে দেখলেই হয়! a, b, c ও n এর বিভিন্ন মান (অবশ্যই পূর্ন সংখ্যায়) নিয়ে একটার পর একটা হিসেব করেই দেখা যাক। কিছুদূর এগোলেই অবশ্য বোঝা যায় কি ভয়ানক দুঃসাধ্য একটি কাজ এটি! চলক বা ভ্যারিয়েবল গুলোর মান বাড়াবার সাথে সাথে হিসেবটাও ভীষণ বড় ও কঠিন হয়ে পড়ে। আজকের দিনে না হয় কম্পিউটার আছে, সেকেন্ডের মাঝে যা লক্ষ লক্ষ হিসেব করে দেবে, ৩৫০ বছর আগে ফার্মা কিভাবে এমন একটি দাবী জানালেন? ফার্মা কি একের পর এক মান হাতে বসিয়ে হিসেব করে দেখেছেন? সেটি বাস্তব সম্মত কোন উপায় নয়। বাকী থাকলো যুক্তির প্রয়োগে উপপাদ্যটি প্রমাণ করা। ফার্মা অত্যন্ত খেয়ালী একজন গণিতবিদ ছিলেন। তিনি ডায়োফেন্টাস এর অ্যারিথমেটিকা বইটি সবসময় বগলদাবা করে রাখতেন এবং কোন থিওরেম তাঁর মাথায় এলে সেটা এই বইয়ের মার্জিন এ লিখে রাখতেন। ফার্মা প্রায় ৩০০ এর মতো সমস্যা লিখে গেছেন এই মার্জিন এ। আলোচ্য সমস্যাটিকে তাঁর শেষ উপপাদ্য বলা হয়ে থাকে। ফার্মা তাঁর অ্যারিথমেটিকা বইয়ের মার্জিনে সমস্যাটি লিখে নিচে লিখেছিলেন, “এই উপপাদ্যটির একটি দারুণ সমাধান আমার জানা আছে, কিন্তু এই মার্জিনটি তা লেখার জন্য যথেষ্ট চওড়া নয়”! একটি অঙ্ক করতে সর্বোচ্চ কত সময় লাগতে পারে? ১ ঘন্টা? ১ দিন? ১ বছর? ১ যুগ? ফার্মার শেষ এই উপপাদ্যটি ৩৫৮ বছর ধরে পৃথিবীর বড় বড় গণিতবিদদের মুখ ভেংচিয়ে গেছে। ৩৫৮ বছরেও কেউ উপপাদ্যটি প্রমান করতে পারেননি! মাত্রই ১৯ বছর আগে ১৯৯৫ সালে প্রিন্সটন বিশ্ববিদ্যালয়ের অধ্যাপক অ্যান্ড্রু উইলস অবশেষ�� উপপাদ্যটির সমাধান করলেন, দীর্ঘ ৮ বছর যুদ্ধ করবার পর। যে বিপুল গবেষণা ও পড়ালেখা এই সমাধানটির পেছনে বিনিয়োগ করতে হয়েছে উইলস কে, তাকে যুদ্ধ বলাটাই মানায়। “Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem"-বইয়ে সাইমন সিং বিবৃত করেছেন উইলস এর সেই ৮ বছর ব্যাপী সংগ্রাম এর গল্প। সিং এর লেখায় এই বইটি উইলস এর অসাধারণ ধৈর্য্য ও অধ্যবসায় এর চমৎকার একটি ডকুমেন্টারি হয়ে থাকলো।   মুহম্মদ জাফর ইকবাল এর ‘নিউরনে আবারো অনুরণন’ যাঁরা পড়েছেন, তাঁরা ফার্মা সংক্রান্ত এ তথ্যগুলো আগেই জানেন। জাফর ইকবাল লিখেছিলেন অ্যান্ড্রু উইলস গণিতের খুব আধুনিক কিছু বিষয়ের ব্যবহার করে ফার্মার উপপাদ্যটি প্রমাণ করেছেন, যা ফার্মার সময়ে উদ্ভাবিতই হয়নি। সাইমন সিং খুব সহজ ভাষায় বর্ণনা করেছেন গণিতের নতুন সেই সংযোজনগুলোর কথা। ১০ বছর বয়েসে অ্যান্ড্রু উইলস প্রথম ফার্মার সমস্যার সাথে পরিচিত হন, তখনি তিনি এটি সমাধান করাকে জীবনের একমাত্র লক্ষ্য হিসেবে দাঁড় করিয়ে ফেলেছিলেন। ৩৯ বছর বয়েসে এসে প্রমাণ সম্পন্ন করতে উইলসকে প্রচুর নতুন বিষয় শিখতে হয়েছে। বিষয়গুলো এত চমৎকার যে কিছু প্রাথমিক ধারণা এখানে জুড়ে দেয়ার লোভ সামলাতে পারছিনা! উইলস এর প্রমাণটি মূলত দাঁড়িয়ে আছে তানিইয়ামা-শিমুরা ধারণা (কঞ্জেকচার) এর ওপর। তানিইয়ামা-শিমুরা কঞ্জেকচার বলে সকল এলিপ্টিক্ ইকুয়েশন ই মডিউলার ফর্ম! খুব কঠিন হয়ে গেলো কি?  গণিতে x^3 – x^2 = y^2 + y এ ধরণের সমীকরণকে বলা হয় এলিপ্টিক্ ইকুয়েশন। একটি সমীকরণের অসীম সংখ্যক সমাধান থাকতে পারে, প্রত্যেকটি নিয়ে আলাদা ভাবে কাজ করতে যাওয়াটা নিতান্ত বোকামী। সমীকরণের সম্ভাব্য সকল সমাধানকে সসীম একটি ছোট্ট স্পেসে প্রকাশ করতে পারলে কাজটা এক্কেবারেই সহজ হয়ে পড়ে। মানুষ ঘড়ি আবিষ্কার করেছে সময়কে একটা ছকে ফেলে কাজ সহজ করে ফেলবার জন্য। ঘড়ি না থাকলে বিশাল বিস্তৃত সময়ের কোন বিন্দুতে আমরা আছি তা কখনো বুঝতেও পারতাম না (এখনও যে খুব পারি তাও নয়, তবু একটা ধারণা অন্তত করতে পারি)। অমুক কাজটা রাতে করে দেবো বললে তা খুব বিভ্রান্তিকর শোনায়, কারণ রাত অনেকগুলো অন্ধকার সময়ের যোগফল; রাতে কখন কাজটা হবে তা নিশ্চিত হওয়া যায়না। রাত ন’টায় করে দেবো বললে মাথাটা পরিষ্কার হয়ে যায়। সময়ের এই সঠিক পরিমাপের জন্যই মানুষ ঘড়িতে সময়কে ১২ টা ভাগে ভাগ করে নিয়েছে। সমীকরণ সমাধানের ক্ষেত্রেও এই বুদ্ধি খাটানো যায়।    চিত্রের ঘড়িটি ফাইভ-ক্লক অ্যারিথমেটিক সিস্টেম। ৪ থেকে ১ ঘর সামনে আগালে আমরা ০ এ পৌঁছাই, অর্থাৎ, সাধারণ গাণিতিক হিসেবে যেখানে ৪ + ১ = ৫, ফাইভ-ক্লক অ্যারিথমেটিক সিস্টেমে ৪ + ১ = ০। ৪ থেকে ২ ঘর সামনে আগালে পৌঁছাই ১ এ। সাধারণ গাণিতিক হিসেবে ৪ + ২ = ৬, ৫-ঘড়ি পদ্ধতিতে ৪ + ২ = ১…ইত্যাদি। ওপরে উল্লেখিত x^3 – x^2 = y^2 + y সমীকরণটির সমাধান ৪টিঃ 
x = 0, y = 0x = 0, y = 4x = 1, y = 0x = 1, y = 4
 শেষ সমাধানটি (x = 1, y = 4) সাধারণ গাণিতিক হিসেবে ঠিক গ্রহণযোগ্য না হলেও ৫-ঘড়ি পদ্ধতিতে মাপে মাপে মিলে যায়ঃ x^3 – x^2 = y^2 + y1^3 -1^2 = 4^2 + 41-1	= 16 + 40 = 20যেহেতু ৫-ঘড়ি পদ্ধতিতে ৫ = ০, ৫ এর সকল গুণিতকও (৫, ১০, ১৫, ২০……) তাই ০ ই হবে। ৫-ঘড়ি পদ্ধতিতে সংখ্যা ছিলো ৫টি (০,১,২,৩,৪), আর সমাধান ছিলো ৪টি, তাই একে E5 = 4 লেখা হয়। যদি ৭ ঘড়ি পদ্ধতি ব্যবহার করা হতো (অর্থাৎ ঘড়িতে দেয়া সংখ্যাগুলো হতো ০,১,২,৩,৪,৫,৬) তাহলে সমাধান হতো ৯টি। এটাকে এখন একটা সিরিজ আকারে লিখে ফেলা যেতে পারেঃ (E সিরিজ)  ইত্যাদি।  এবার আসা যাক মডিউলার ফর্ম এ।   চিত্রের x ও y অক্ষের মাঝে আটকে পড়া বর্গটির রোটেশনাল ও রিফ্লেকশনাল সিমেট্রি বিদ্যমান, অর্থাৎ বর্গটিকে একই অবস্থানে রেখে উল্টে দিলেও এটি দেখতে একইরকম লাগবে, কোন পরিবর্তন ধরা পড়বেনা, এটি হল রোটেশনাল সিমেট্রি। যদি x এবং y অক্ষ বরাবর দুটি আয়না রেখে বর্গটিকে উল্টে পাল্টে ঘোরানো হয়, তাহলেও মনে হবে বর্গের প্রথম অবস্থার কোন পরিবর্তন হয়নি, এটাই রিফ্লেকশনাল সিমেট্রি। যদি এখন বর্গটিকে ধাক্কা দিয়ে সামনের দিকে সরিয়ে দেয়া হয়, তা হলে x এবং y অক্ষের সাপেক্ষে বর্গের অবস্থানের পরিবর্তনটি স্পষ্ট ধরা পড়বে চোখে, অর্থাৎ এর ট্রান্সলেশনাল সিমেট্রি নে��।    এই চিত্রে এবার অসীম সংখ্যক বর্গ আঁকা হলো, x ও y অক্ষের সাপেক্ষে। এই বর্গগুলোর রোটেশনাল ও রিফ্লেকশনাল সিমেট্রি তো আছেই, এদের ট্রান্সলেশনাল সিমেট্রিও বিদ্যমান। কারণ, বর্গগুলো কোনভাবে চলতে শুরু করলে অক্ষদুটির সাপেক্ষে কোন বর্গটি কোথায় গেল বা তাদের অবস্থানের আদৌ কোন পরিবর্তন হলো কিনা তা আর বোঝার উপায় থাকবেনা। সবদিক থেকেই অসীম সংখ্যক বর্গগুলোর সিমেট্রি বা সমতা একইরকম থাকবে। এটিকে ঠিক মডিউলার ফর্ম বলা চলেনা, কারণ মডিউলার ফর্ম পাওয়া যায় চার ডিমেনশন এর স্পেসে, আমরা আমাদের তিন ডিমেনশন (দৈর্ঘ্য, প্রস্থ ও উচ্চতা) এর জগতের অভিজ্ঞতা দিয়ে চার ডিমেনশন এর বস্তুর ধারণা করতে পারবোনা। মডিউলার ফর্মের সাথে সিমেট্রির সম্পর্কের বিষয়টি ইঙ্গিত করবার জন্যই বর্গক্ষেত্র সংক্রান্ত আলোচনা এখানে! চার ডিমেনশন এ বাস করা আশ্চর্য সিমেট্রিক মডিউলার ফর্মেরা নির্দিষ্ট কিছু উপকরণ (ইনগ্রেডিয়েন্টস) দিয়ে গঠিত। প্রত্যেকটি মডিউলার ফর্ম ই একে অন্যের চেয়ে আলাদা এই উপকরণের বেশকমের কারণে। উপকরণের সংখ্যানুসারে সাজালে মডিউলার ফর্মের জন্যও একটি সিরিজ পাওয়া যায়, এলিপ্টিক কার্ভের E সিরিজের মতো, একে বলা হয় M সিরিজ। ১৯৫০ এর দশকে দুই জাপানী গণিতবিদ বন্ধু ইয়ুতাকা তানিইয়ামা ও গোরো শিমুরা লক্ষ্য করেন এলিপ্টিক কার্ভের E সিরিজ আর মডিউলার ফর্মের M সিরিজ একেবারে হুবহু মিলে যাচ্ছে, এ থেকে তাঁরা ধারণা করলেন সকল এলিপ্টিক সমীকরণ ই আসলে মডিউলার ফর্ম। তবে এটির পক্ষে কোন প্রমাণ তাঁরা করে যেতে পারেননি, তানিইয়ামা’র অকস্মাৎ আত্নহত্যার দরুন।  তানিইয়ামা-শিমুরা কঞ্জেকচার দিয়েই যে ফার্মার উপপাদ্য প্রমাণিত করা যাবে এ ধারণা দিয়েছিলেন জার্মান গণিতবিদ গেরহার্ড ফ্রে। “মনে করা যাক ফার্মার সমস্যাটির একটি সমাধান আছে”-এই অনুমানের পথে হেঁটে ফ্রে এক নতুন ধরণের এলিপ্টিক কার্ভ আবিষ্কার করলেন যা মডিউলার নয়, তানিইয়ামা-শিমুরার কঞ্জেকচারের সরাসরি বিরোধী। অ্যান্ড্রু উইলস যখন আট বছরের দীর্ঘ সংগ্রাম শেষে উপপাদ্যটি প্রমাণ করলেন, তাঁর প্রমাণটি শুধু ফার্মার সমস্যাটির সমাধানের কাজেই আসেনি, বরং তা গণিত ও নাম্বার থিওরির একাধিক শাখার বিস্তারেও বড় ভূমিকা রেখেছে। তানিইয়ামা-শিমুরা কঞ্জেকচার এখন আর শুধুই একটি কঞ্জেকচার বা অনুমান নয়, এটি একটি স্থাপিত সত্য। গাণিতিক এই তত্ত্বগুলো পরস্পরের সাথে এত দৃঢ়ভাবে সম্পর্কিত, যে শুধু একটির প্রমাণ-ই বাকিগুলোর প্রমাণের জন্য যথেষ্ট, অনেকটা যেন ডমিনো এফেক্টঃ   অ্যান্ড্রু উইলস বেশ কিছু আধুনিক গাণিতিক হাতিয়ারে নিজেকে সজ্জিত করে ফার্মার উপপাদ্যটি প্রমাণ করেন। এর মধ্যে প্রধান দুটি হলো আইওয়াসাওয়া থিওরী ও কোলিভাগিন-ফ্ল্যাখ মেথড। সদ্য রপ্ত এই বিদ্যাগুলোর প্রয়োগের বেলায় উইলসকে প্রায়ই প্রচন্ড হতাশাজনক পরিস্থিতির ভেতর দিয়ে যেতে হয়েছে। এই টেকনিকগুলো কত কঠিন সে বিষয়ে উইলস বলেছেন সর্বোচ্চ শিক্ষা প্রাপ্ত একজন পেশাদার গণিতবিদেরও এই বিষয়গুলো আয়ত্তে আনতে অন্তত দু-তিন মাস লাগবেই! ফার্মার সমস্যাটির জটিলতার আরেকটি নির্দেশক এটি।  ১৬৩৭ সালে তানিইয়ামা-শিমুরা কঞ্জেকচারের অস্তিত্ব ছিলোনা। ছিলোনা কোলিভাগিন-ফ্ল্যাখ মেথড, আইওয়াসাওয়া থিওরী, মডিউলার ফর্ম, মিয়াওকা অসমতা-এসবের কিছুই। মাত্র ১টি গাণিতিক সমস্যার প্রমাণে ১৫০ পৃষ্ঠা জুড়ে এতগুলো টেকনিকের ব্যবহার ইতিহাস আগে কখনো দেখেনি। উইলস এর এই প্রমাণটি ফার্মার আসল প্রমাণ নয়। ফার্মা কি আদৌ তাঁর সমস্যাটির সমাধান বের করেছিলেন? এক সময় হয়তো এই রহস্যেরও সমাধান হবে, হয়তো আরো অনেক সহজ কোন পদ্ধতি আবিষ্কৃত হবে, তবু অ্যান্ড্রু উইলস এর ১টিই অঙ্ক কষার পেছনে ৮ বছরের পরিশ্রমের গল্প চির অম্লান থাকবে। গণিতের সাথে মোটেই সম্পৃক্ত নয় এমন অনেকেই ৮ বছর লাগিয়ে একটি অঙ্ক করার হাস্যকর দিকটি বের করে উইলসকে নিয়ে নিয়মিত তামাশা করেছে। যে পরিমাণ পরিশ্রম ও লেখাপড়া উইলসকে করতে হয়েছে তার সম্পর্কে কোন ধারণাই হয়তো এই মানুষগুলোর কখনোই হবেনা। মানুষ হিসেবে অন্য মানুষের এ আচরণগুলো মেনে নেয়াটা প্রচণ্ড কষ্টকর ও হতাশাদায়ক এবং ক্ষেত্রবিশেষে মানুষকে সম্মান করার ব্যাপারে মনকে সন্দিহান করে তোলে, সন্দেহ নেই, তবু উইলস এর গল্প শেষ পর্যন্ত মনে করিয়ে দেয়, মানুষ ই তো পারে!      english favorites mathematics               Author  28 books13.4k followers     March 10, 2009   I guess the author does a reasonable job. But when I reached the end, I still didn't feel I understood at all how the proof worked. Probably that's just because it's so bloody hard. I got a lot more though out of Prime Obsession, Derbyshire's book on the Riemann Hypothesis, where the author opens up the box and shows you some of the actual math...     science               1,792 reviews431 followers     March 31, 2022   That's an excellent history of mathematics from antiquity to the present day. The author skillfully captures the pedagogical trick of the Last Theorem. This "mathematical siren, ..., which attracted geniuses to destroy their hopes" better is a common thread that compellingly guides us through anecdotes, concepts very well explained in the maze of mathematics. The author manages to give both a technical and societal dimension to his story and, thereby, maintain the reader's attention from start to finish.Very successful.Good reading!     brit-and-related e-5-favourites g-biography               704 reviews277 followers     June 20, 2011   This is the kind of book that we non mathematical minds can easily digest and love. It gives you an epic scope of the number of minds that it takes to build new ideas. I doubt if Fermat had actually solved this theorem correctly, but this is impossible to prove. Fermat's theorem however was not impossible to prove! It was solved! Thanks to the efforts of many men (and women!) over many lifetimes and one final man who had the determination and persistence to finish the unthinkable. This book has a lot of wonderful elements, and really exemplifies a love of mathematics. Although if you want to actually understand the theorem this book may not be for you! I can honestly say reading it did not put the theorem in any more digestible light than it started out with. Perhaps it was to the authors advantage to skip the technicalities and focus on the enjoyment of the journey. I personally loved this approach, but it may not be for everyone, especially if you are actually looking to understand the theorem (a massive undertaking that is really not in my repertoire to comment on).     mathematics               653 reviews6,927 followers     December 3, 2011   Simon converts what could have been a dry chronicle of proofs into an ode full of excitement, inspiration and intrigue worthy of a gothic love affair. Full review to follow.                  438 reviews72 followers     April 3, 2009   What a fun book this was (thanks, Trevor, for the recommendation)! There are many reasons I think I like (good) nonfiction -- a sense of direct relevance, gravitas, frequent insights into the workings of the universe (and people), but mostly for knowledge narcs -- high levels of information density served up into an intriguing package by someone else who has undertaken the heavy lifting (research, organization, thinking). So, here in Singh's work I get a solid lay understanding not only of the proof to Fermat's Last Theorem, but of much of mathematics (and the lives of mathematicians) since the seventeenth century.I've been thinking also about what attracts me to books on mathematical topics -- the works by Martin Gardner, William Poundstone, and the various other authors in the company of whose thoughts I've had pleasure to spend a week or more. What I've come away with, is that the best of them feed off surprises, those bits of counterintuitive anecdotes that leave you blurting out, "Huh. How about that," and then looking madly around for someone to tell. Like a book of jokes, riddles, or puzzles that provides immediate gratification in the back of the book,  Fermat's Enigma plugs at least ten conundrums (and their easy-to-understand, logical solutions) into its appendices. For example -- say you're unlucky enough to be forced into a three-way duel. If everyone gets to take turns in order of their skill such that worst shoots first, what should the worst do? Aim at the best in the hopes of getting lucky and eliminating the most dangerous gunsel? Nope, the correct answer is to pass up the turn in the hopes that your first shot will get to be expended against only one remaining combatant. That way, even if you miss, you at least had a chance to take aim at the only person able to shoot back.Pierre Fermat turns out to have been quite the prankster, often tweaking professional mathematicians and academics by mailing them problems they knew full well he had already solved. For those who don't keep this type of trivia at the forefront of their brains, Fermat's the French recluse (and hanging circuit jurist) who once famously scribbled in a copy of Diophantus'  Arithmetica that x^n + y^n ≠ z^n for any number n greater than 2, a propostion for which he had "a truly marvelous demonstration… which this margin is too narrow to contain." This gets to be Fermat's Last Theorem, simply because it ends up being the last of his conundrums to be proven (not necessarily the last one he wrote). Just think, were it not for the scrupulous care taken by Fermat's son to go through and publish all of Fermat, Sr.'s writings, the world would not have been tantalized by this particular gem for 
 over 350 YEARS
.Andrew Wiles published the first (and only?) proof in 1994, and  Enigma does a tremendous job of walking the reader through not only the stunning depth of his intellectual achievement, but its significance as well. Suffice it to say that I was happy here to read that Taniyama-Shimura get their well-earned due and that modular and elliptical equations can finally be understood to be mathematically analogous (whether or not I have any idea what modular equations actually are). Still, all of this leads to what I think is an even more tantalizing problem. We now know that all of Fermat's conjectures ultimately proved to be solvable and that Fermat's own notes would seem to indicate that he had indeed apparently found ways to solve each of them. But there is no doubt that Fermat's solution could not have relied on the up-to-the-minute maths Wiles employs over 200 pages. So if it was really the limitations of the margin and not of Fermat that inhibited publication… what was Fermat's proof?     science               1,279 reviews21.3k followers     December 9, 2007   This book is as interesting as a detective story while being about quite advanced mathematics - as such it is quite a book showing the remarkable skill of its writer to explain complex ideas in ways that are always readable and enjoyable.A mathematician finds a simple proof to what seems like a deceptively simple problem of mathematics - that pythagoras's theorem only works if the terms are squared, and not if they are any other power up to infinity. Sounds dull. Except that the mathematician jots down that he has found this proof, but not what the proof is. And for hundredsd of years the greatest minds in mathematics have tried to find this simple proof and been beaten by the problem time and again. This really is a delightful book and one that gives an insight into how mathematicians think about the world. The proof of Pythagoras's theorem given in this book is so simple that the beauty of mathematical proof is made plain to everyone. Just a little knowledge of algebra is needed for this part of the book - the rest requires no maths at all.     biography maths science               891 reviews300 followers     April 25, 2019   Strap in, guys. I’m going to walk you through the history of how Fermat’s Last Theorum was proved, all in one little (okay, big) review. And I can do this because of this awesome, semi-accessible, frequently tangent-taking, but mostly, this deeply fascinating book. ----------STEP ONE: THE THEORUM----------  For the unenlightened, Fermat’s Last Theorum is this: you probably know the Pythagorean theorum, a² + b² = c², which explains that if you square the shorter two sides of a right-angled triangle and add them together, you get the value of third side squared. This is easily proved (that is, demonstrated to be completely, utterly, logically true via a mathematical proof, using axioms known to be true, which is just like a logic proof if you’ve done philosophy. Or a geometry proof, if you went to 9th grade). Take any triangle, and this will be true. There are infinite solutions to this equation—literally infinite values of A, B, and C which will render this solution true.  However, Fermat discovered that the formula an + bn = cn where n &gt; 2 has NO whole number solutions. (Go ahead, give it a whirl. I’ll wait). Then he challenged the mathematical community to create a mathematical proof demonstrating this must be true. While tantalizing them with the knowledge he’d already created a proof for this with a scribbled note in the margin of his notebook: “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.”   Asshole.  So sparked centuries of people trying to write this proof, to no avail. Until Professor Andrew Wiles (who has the most apropos name ever—he has wiles indeed) of Cambridge, in 1993. *** For clarity, this is Fermat’s Equation (which I’ll refer to as FE): an + bn = cn where n &gt; 2 And THIS is Fermat’s Last Theorum (which I’ll refer to as FLT): “There are no solutions to Fermat’s Equation” ***  ----------TANGENT: GODEL----------  At this point, it’s been assumed that math is logically perfect—that if you correctly build a proof using axioms (like m + n = n + m), it must be true (and if it’s proven to be true, nothing can prove it to be false). This is known as “axiomatic set theory.”  Along came Godel (who is analyzed to death by my beloved, Doug Hofstadter- see here and here). His ideas are as follows:  1. If axiomatic set theory is consistent, then there have to be theorems that can’t be proved or disproved. Why? Because of paradoxes. Godel translated the following statement into mathematical notation: “This statement has no proof.” If that’s false, then you COULD create a proof for that statement—however, that would make the statement false, so how could you have a proof for that? So it has to be true. But if it’s true, it can’t be proved because that’s what it literally says. It’s a mathematical statement that is true, but could never be proved to be true (an “undecidable statement”).  2. There’s no way to prove that axiomatic set theory is consistent; in a way, it’s one of those “undecidable statement” that’s true but can’t be proved to be true.  Interestingly, this parallels the physicist Heisenberg’s discovery of the uncertainty principle, but we won’t get into that.  Now, there aren’t very many of those undecidable statements. Godel couldn’t really point to any other undecidable statements besides the one above, so people assumed they were found only in the most extreme math and would probably never even be encountered.  Welp. A young student named Paul Cohen at Stanford discovered a way to test whether a question is undecidable, and in doing so, discovered several more. Which sparked some fear in mathematicians. What if Fermat’s Last Theorum was undecidable?! What if they were wasting their time trying to prove the unprovable? Interestingly, if it were an undecidable statement, it couldn’t be proved—yet it would have to be true. The theorum says “there are no whole numbers to the equation an + bn = cn where n &gt; 2.” If this were false, then it would be possible to prove this by offering a solution to this—by finding a whole number N that’s greater than 2 that allows the equation to be solved. Which would make it a decidable statement, which is a contradiction. So it can’t be false and also be an undecidable statement. In other words, Fermat’s Last Theorum might be totally true but there might be no way to prove it.   ----------STEP TWO: TANIYAMA-SHIMURA CONJECTURE----------  Modular forms are a mathematical tool, sort of like impossible forms or shapes, that reveal a lot about how numbers are related.  The Taniyama-Shimura Conjecture (TSC), created by two Japanese mathematicians (one of whom tragically and abruptly killed himself quite young) says every modular form is related to a specific elliptic equation (elliptic equations were Andrew Wiles’s main area of study; they’re a type of equation, not super important that you understand them).  The fact that these were unified meant there’s a kind of Rosetta stone that’s been discovered: “Simple intuitions in the modular world translate into deep truths in the elliptic world, and vice versa. Very profound problems in the elliptic world can get solved sometimes by translating them using this Rosetta stone into the modular world, and discovering that we have the insights and tools in the modular world to treat the translated problem. Back in the elliptic world we would have been at a loss.”  Beyond that awesomeness, the TSC suggests something even more interesting: that possibly all of mathematics, all the different worlds of mathematics, might have parallels in other worlds, as with the elliptic world and the modular world. All of mathematics might be unified—arguably the absolute ultimate goal of abstract mathematics, because this would give us the most complete picture, and the biggest arsenal of tools to solve mathematical problems.   ----------STEP THREE: RIBET’S THEORUM----------  This is all important for FLT because of something called Ribet’s Theorum (Ribet was a colleague of Wiles). Ribet’s Theorum goes like this: the imagined solution to FE can be translated into an elliptic equation. And that elliptic equation doesn’t seem to have a modular world equivalent. But the TSC claims that every elliptic equation must be related to a modular form.  So if you can PROVE that the elliptic form of the solution to FE has no modular form (which we can! The proof was done in 1986), the following is true: if the TSC is true (i.e. all elliptic equations have modular forms), and the elliptic form of the imagined solution to FE has no modular form, then the imagined solution cannot exist, proving FLT.  So now, all we have to do is prove that the TSC is true, and FLT is automatically proven to be true.  And this—THIS—is what Andrew Wiles focused on. Proving the TSC (Taniyama-Shimura Conjecture).  ----------STEP FOUR: PROVING THE THEORUM----------  Wiles finally succeeded when he applied a new method called the Kolyvagin-Flach method, which groups elliptic equations into families and then proves that an elliptic equation in that family has a modular form; if that elliptic equation has a modular form, then all other elliptic equations in that family also has a modular form.  However, the Kolyvagin-Flach method has to be adapted for each family of elliptic equations. Wiles successfully adapted the method for all families of elliptic equations, thereby proving that all elliptic equations have modular forms (which, as a reminder, is basis of the Taniyama-Shimura Conjecture, and proving the TSC proves FLT).  Two months before I was born, in 1993, he proved FLT in a series of 3 lectures.  Kinda. Actually, there was a minor flaw in his proof (essentially, he might have failed to properly adapt the Kolyvagin-Flach method for some of the families of equations) but it doesn’t really matter because a year later, Wiles published a work-around to that flaw, so he proved FLT once and for all.   ----------CONCLUSION----------  All I can think about is: maybe if math looked like this, if THIS had been our material in high school—maybe then I wouldn’t have disliked it. Maybe other people wouldn’t, either. What a shoddy job we do teaching our children the wonder of learning.     microhistories               627 reviews1 follower     August 25, 2017     Un teorema è per sempre Un tale Fermat, che nel diciassettesimo secolo si dilettava di matematica ed era un po' buontempone, enunciò un teorema all'apparenza banale e lasciò scritto sul margine di una pagina di un libro:  “Dispongo di una meravigliosa dimostrazione di questo teorema, che non può essere contenuta nel margine stretto della pagina”  Il teorema era banale, come pure l'affermazione. Non poteva che scaturirne una dimostrazione banale.  Eppure...  La dimostrazione di quell'equazione banale fece perdere il sonno alle maggiori menti matematiche di tutto il mondo, che per 350 anni si arrovellarono per trovare una soluzione. Risultati: zero. Cos'è una dimostrazione? In matematica si ritiene che un teorema sia dimostrato quando con un procedimento logico se ne fornisce inequivocabilmente e incontestabilmente la correttezza.   "La ricerca di una dimostrazione matematica è la ricerca di una conoscenza che è più assoluta della conoscenza accumulata da ogni altra disciplina. Il desiderio di una verità definitiva ottenuta attraverso il metodo della dimostrazione è ciò che ha guidato i matematici negli ultimi duemilacinquecento anni."  Solo nel 1993 un matematico inglese, Andrew Wiles, dopo sette anni di sforzi, ossessioni, notti insonni, incubi, entusiasmi e delusioni riuscì a completare la dimostrazione. Possibile che Fermat avesse trovato una dimostrazione a questo teorema? No, impossibile crederlo; la dimostrazione di Wiles è composta da 200 pagine di matematica estremamente complessa che non poteva assolutamente essere disponibile al tempo di Fermat e che alla fine però è servita anche ad approfondire intere branche della matematica. Ecco, il libro spiega la storia di questa dimostrazione e dei grandi matematici che ci hanno lavorato, spiega la bellezza delle sfide matematiche, l'ostinazione e la determinazione richiesta, l'inventiva necessaria e la potenza di un risultato che diventa "eterno". La storia di questa dimostrazione è decisamente interessante; per me l'unica carenza nel libro è l'autore, che è "solo" un giornalista e che, poraccio, di matematica ci capisce come io di taglio e cucito. E trasforma la storia in una telecronaca; per consentire ai profani di capire gli aspetti legati alla successione degli eventi dà per scontate parecchie cose (pur riportandole) rinunciando a spiegare con semplicità, forse perché nemmeno lui ci ha capito un granché. Cartesio disse: "quando sono in discussione questioni trascendentali, siate chiari in modo trascendentale".   Ecco Singh chiaro non è. Inutile per me riportare frasi come "Tutto quello che devi fare è aggiungere qualche gamma-zero di struttura (M) e poi ti basta ripercorrere la tua argomentazione ed ecco che funziona" se non se ne spiega il significato. O si omette la frase, o la si spiega.  Riesce pure a mettere errori di matematica nelle definizioni che, mi dispiace, in un libro di matematica noooooo, proprio non accetto!. In ogni caso la storia è affascinante e il libro riesce a trasmettere interesse e curiosità per la matematica e per queste persone meravigliose che si sono prodigate per trovare soluzioni a problemi veramente complessi.Fermat era un buontempone e ci ha preso in giro per 350 anni. Ma senza di lui, oggi le nostre conoscenze matematiche sarebbero certamente inferiori...     saggi scienza uk               298 reviews30 followers     January 17, 2016   From my reading journal:May 31, 2009. Yesterday I finished reading Fermat's Last Theorem. I plan to write a glowing book review but this space is too limited to contain it.      shelfari-favorite               1,686 reviews203 followers     September 26, 2022    “The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.” Fermat's Last Theorem states that: xⁿ + yⁿ = zⁿ has no whole number solutions for any integer n greater than 2. Simon Singh fashions the quest to solve this 350-year-old mathematical enigma into a compelling story. In the 1630s, when Pierre de Fermat scribbled a note on a page of his copy of Diophantus’s Arithmetica, stating (in Latin) his theorem and indicating “I have a truly marvelous demonstration of this proposition, which this margin is too narrow to contain.” Singh takes the reader through a series of minibiographies of past mathematicians, ultimately arriving at Andrew Wiles, who spent over eight years developing the 130-page proof.  Along the way, the reader will learn a great deal about number theory, logic, and the rigorous standards required to achieve an absolute proof. This book covers a wide variety of people and their contributions over the years, such as Pythagoras, Leonhard Euler, Sophie Germain, Gabriel Lame’, Augustin Cauchy, Ernst Kummer, David Hilbert, Kurt Godel, Alan Turing, Goro Shimura, and Yutaka Taniyama. The highlight of the book is, of course, Andrew Wiles who discovered Fermat’s Last Theorem at the age of ten, and dedicated himself to figuring out a proof, no matter how long it took. Wiles decided to keep his work secret and work alone in his attic. “You might ask how could I devote an unlimited amount of time to a problem that might simply not be soluble. The answer is that I just loved working on this problem and I was obsessed. I enjoyed pitting my wits against it.”   We learn about the Shimura-Taniyama conjecture, and the relationship between elliptic curves and modular forms. Singh never gets bogged down with calculations – they are instead included in the Appendices. I have a background in mathematics, so this type of subject matter appeals to me, but I daresay it is not required to enjoy this story of challenge, perseverance, and discovery. 4.5     2022-top-50 biography history               376 reviews     March 13, 2021   Belas histórias de amor. Do amor dos homens por um teorema: o último Teorema de Fermat. Uma odisseia matemática cheia de beleza, frustração e triunfo. Não é apenas a história do genial Andrew Wiles; esta é a história dos homens que amam a matemática. Sem fins utilitários, sem pretensões. De Pitágoras a Wiles, de 1637 a 1994. A Fermat faltou espaço naquela página para fazer a sua brilhante demonstração, mas às posteriores gerações de matemáticos não faltou coragem. Será que Fermat estava, mais uma vez, certo?Esta obra, embora aborde conceitos matemáticos [alguns com um elevado grau de complexidade como a conjectura Taniyama-Shimura] e apresente reflexões que exigem um apurado raciocínio abstracto [sobretudo nesta área de matemática pura] não pretende excluir aqueles que não se encontram entre os poucos eleitos que compreendem perfeitamente a linguagem dos números. A leitura, às vezes, apresenta algumas dificuldades (ultrapassáveis) mas vale muito a pena. Uma obra muito bela e que nos encanta. Para saber um bocadinho mais: https://seromoluntdeorummolae.blogspo...  *"El recuerdo de Arquímedes persistirá cuando Esquilo esté ya olvidado, porque las lenguas mueren y los conceptos matemáticos no. Inmortalidad es tal vez un término estúpido, pero quizá un matemático posea las mayores probabilidades de alcanzarla, sea cual sea su significado." [G.H.Hardy]                   40 reviews97 followers     March 22, 2019   I never watched any documentaries before going to college (and this was about a century and a half ago.. I am getting old -_-. But yeah, 2009 to be precise). I was always interested in NatGeo and History Channel - but they never showed the real deal on television. The documentaries would be mostly half assed, and at worst, total crap. That's also how Indian television landscape can be broadly categorized too, give or take a few exceptions ofcourse. And so I grew up loving the sciences based on what was taught in school curriculum, and elsewhere what I read on the slow 64-bit internet connection.And then college happened. Parents got me my own laptop - and the college intranet had a ton of stuff that other students shared. That place and that time - was where my love for documentaries was born. I had never been so fascinated with anything before. And the first two that I watched - in a long line of them - were Einstein's Biggest Blunder and BBC's Fermat's Last Theorem. The memory of that sunday afternoon is still pretty fresh.  Back then, I only had a casual interest in astronomy and cosmology, and Einstein's theories were still something exotic. And so I basically understood jackshit from the first documentary. Even more intrigued than before, I started the second one. Fermat's Last Theorem was much more relatable - I had known the theorem, and understood the concept too.  Years later when I joined goodreads, I found out that there was a book too. Keeping in with the tradition of firsts, it became the first book on my TBR pile too. Where it stayed until a few days ago - and I finally marked it as read last night.  To be honest, this isn't the greatest book ever. It isnt even Simon Singh's best, who delivered the goods the much better in Big Bang. But it surely captures the essence of all mathematical and scientific endeavor very well - That every once in a while, in the middle of an ordinary life, science gives us a fairytale      gorgeous-covers history my-library               599 reviews92 followers     September 23, 2022   The best mathematical nonfiction thriller I've ever read!  Consider this equation: x^n + y^n = z^n (where x,y,z,n are natural numbers with n&gt;2)Fermat stated that the above equation has no solutions.It’s the simplicity of this theorem which is elusive of the nature of its difficulty to be proved! Stated around 1637, Fermat had scribbled this theorem with a note in the margin - "I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain."This theorem and other notes were published posthumously by his son. Till date, nobody is aware of the proof that Fermat would have concocted in his mind! With modern mathematical tools and researches, this theorem which remained unsolved for more than 350 years was finally proved in 1995 by Andrew Wiles.This book is a tale of how this theorem was pursued for centuries and finally how it was proved.  Loved: The context setting and remarkable background stories.Fun trivia on numbers - and how mathematics is the language of nature.The depth into which many great minds delved and devoted their entire life.  Recommended: If you've ever been intrigued by Mathematics, this is a must read.You don't necessarily need to have a grip on Maths to enjoy this book. Explained in layman terms, detailed mathematical proofs and footnotes are all confined to the Appendix section, for the curious minds.  Notes: How I picked this book - A friend sent greetings at 5:29PM mentioning special time. Though I knew about the magic number, but somehow this message helped me traverse down the rabbit hole.Ramanujan -&gt; Magic Number -&gt; Taxicab Number -&gt; Fermat near misses -&gt; Fermat's last Theorem... and from thereon it was a different world altogether! Then last month, I went shopping books on behalf of friends. Someone picked these, which I ended up reading before sending :) [thank you!]     2022 non-fiction owned-paperbacks               621 reviews69 followers     June 2, 2022   This is a very interesting book. Don't be scared about the contents, it's an enjoyable read even if you don't know anything about mathematics.    audio downloaded english               Author  17 books26 followers     September 19, 2012   Lectura en 2012Este año tomé nuevamente el libro del Enigma de Fermat, símplemente porque me gustó bastante Las matemáticas fueron una de esas cosas con las que siempre tuve un romance eterno. Leyendo nuevamente pude recordar esos episodios en clases en que el maestro en turno llegó un día y anotó este mismo teorema en la pizarra. Nos dejó toda la clase tratando de solucionarlo y obviamente al final nos informó que el mismo no estaba resuelto (o al menos eso recuerdo, porque en ese año ya debería de haber estado).  Mas detalladamente me hizo recordar a varios amigos que hacían las demostraciones de distintas fórmulas y me las entregaban como si fueran cartas románticas (todavía las guardo). La forma en que esta escrita, en ningún momento te hace sentir tedio. Agus dice que son mas bien chismorreos alrededor de la vida de los matemáticos (según como se lo iba contando), y precisamente eso es lo que lo hace interesante. Es la vida de personas que significaron algo para que este teorema existiera y para que finalmente fuera solucionado. El gran enigma matemático ha muerto. (en serio, leanlo) ................................................Lectura en 2006 Finalmente llegamos a lo que fué mi último libro del año (2006 para los despistados). Durante las fiestas me encontré en casa de mis abuelos, y el apartado en donde vive mi hermana, actuaria y fanática de las matemáticas. Lo lamentable es que la mayor parte de los libros que lee yo se los recomiendo, así que la mayoría de los que encontré en su librero ya los había leído. Encontré tres libros entre los cuales elegir, sin embargo este brillo llamando mi atención debido a una anécdota. Cuando mi hermana todavía estudiaba, viajaba a casa en autobús cada dos o tres meses. Entre sus compañeras hubo una que le presto este libro y en una ocasión el libro viajó con ella… sin embargo hay que añadir que mi hermana es algo despistada así que en esa ocasión el libro quedó en el autobús. No sé qué fué lo que le ha dado más coraje en esa ocasión, perder un libro prestado o no poder seguirlo leyendo. Tuvo que comprarlo para devolverlo y además se compró su propia edición (que todavía le tengo que devolver). El enigma de Fermat es una novela de matemáticas. Mediante un poco de historia Singh nos va narrando la evolución de las matemáticas como un arte, muy lejos de aquellas matemáticas aplicadas. Las matemáticas como algo abstracto que es hermoso por sí mismo, porque tiene un orden y una lógica, porque en sí misma engloba misterios y permite que los descubras mediante una relación con ella. Declaro que de niña me gustaba leer el Baldor y en mi último año de preparatoria acabé con todas las operaciones integrales en todos mis libros (y no tenía sólo dos) y este libro ha sido recordar las horas que le dediqué. Que hermosas eran para mí las matemáticas.Fue un hermoso fin de año.     2006 2012 no-ficción               101 reviews63 followers     June 29, 2021   Why do variables love mathematics? y₀(My head says rationally: Veronica, Goodreads is not a place for the corny wisecracks that you come up with during the day. My heart says differently.)     mathematics               Author  7 books1,208 followers     February 19, 2017   Había leído parte de este libro cuando estudiaba periodismo, gracias a Alejandra Carmona, una profe muy inquieta que daba el ramo de Antropología y que siempre llegaba con lecturas nuevas y actuales. Por ella descubrí no sólo a autores “académicos”, como Lévi-Strauss y Ángel Rama, sino a escritores que cruzan el periodismo con la etnografía y la literatura, como Martín Caparrós y Simon Singh, autor de El Último Teorema de Fermat. Es un libro hermoso, como hermosas son las matemáticas y como hermoso es el problema que heredó Fermat a sus colegas por más de 300 años y como hermosa es la historia de traiciones, desafíos y sueños que están ligados a este acertijo matemático.Este es un libro que mezcla la investigación científica, el periodismo y la literatura. Aprendí un montón leyéndolo. Está escrito (y traducido) con una prosa limpia, liviana y sencilla, algo muy difícil de lograr, sobre todo cuando se explican temas intrincados, como las matemáticas. Salvo por el exceso de adverbios de mente (que, ay, me ponen medio mal) es un placer leer las explicaciones complejas de manera tan amable.Pienso que la matemática son un universo de lógica, absolutismos y armonía de un nivel superior. Como toda disciplina y todo arte, aspira a la belleza y los matemáticos lo saben, persiguen la belleza de la perfección de los números y le achacan a este universo propiedades como la bondad o la amistad, todo a partir de patrones numéricos. Se me ocurre que mucha de la filosofía matemática refleja la moral de sus autores y, al mismo tiempo, describen también las relaciones humanas y la vida.Me gustó mucho que el autor se hiciera cargo, en un apartado, del sesgo histórico de género que han acompañado las matemáticas. “A través de los siglos las mujeres han sido desanimadas a estudiar matemáticas, pero a pesar de la discriminación, ha habido varias matemáticas que lucharon contra esa costumbre institucionalizada e inscribieron sus nombres en forma indeleble en los anales de las matemáticas”. Y nombra a Hipatia de Alejandría o Sophie Germain, que tuvo que usar el pseudónimo de Monsieur Le Blanc para que tomaran en serio su trabajo. Cuando ella debió revelar su identidad, un destacado matemático (que fue su maestro sin saber que ella no era hombre) escribió: “Cuando una persona del sexo que, de acuerdo con nuestras costumbres y prejuicios, debe encontrar infinitamente más dificultades para familiarizarse con estas espinosas investigaciones, tiene éxito en superar estos obstáculos y penetrar las partes más oscuras de ellas, entonces sin ninguna duda debe tener el más noble coraje, talentos verdaderamente extraordinarios y una genialidad superior”.Cuando yo estaba en octavo básico era muy porra. Me iba mal en el colegio. No estudiaba demasiado. Ese mismo año me puse a pololear con un chico dos años mayor que yo, que era escandalosamente estudioso. Me acuerdo cuando me explicó las potencias. Yo me había sacado un rojo en la prueba y él, con mucha paciencia y amor, me explicó esta materia que en realidad es súper fácil y entretenida. De ahí en adelante me puse igual de odiosa y matea que él. Salí de cuarto medio con promedio 6,9 en matemática. Después estudié periodismo y olvidé los números, pero al leer este libro recordé por qué me gustaban tanto, por qué disfrutaba más resolviendo facsímiles de la PSU de matemáticas que viendo Los Simpsons. Hay tanta perfección en los números, tantos juegos posibles. El libro se trata de cómo se resolvió el problema matemático más famoso de la historia: el teorema de Fermat, que sostiene que no hay soluciones posibles al teorema de Pitágoras cuando la potencia es mayor a 2. El libro explica, también, porque esa demostración es tan endemoniada y difícil. La belleza del problema es que Fermat dijo tener una demostración, pero que no la podía escribir en el margen de un libro, ya que ese espacio era muy pequeño. En rigor, no existía la demostración (no existe, nadie ha visto jamás la demostración de Fermat). Era y es una especie de eslabón perdido de las matemáticas. 350 años después, Andrew Wiles plantearía su propia solución, una muy compleja y elegante, que unifica las matemáticas y que se sirve de todas las etapas de esta ciencia para lograrlo. Al final, el libro cuenta esa historia y también repasa miles de años de epistemología de las matemáticas.Algunas cosas bellísimas que se leen en este libro:—“Pitágoras había descubierto que unas proporciones numéricas simples eran responsables de la armonía de la música”.—“La razón entre la longitud real de los ríos desde su nacimiento hasta su desembocadura y su longitud en línea recta (…) es aproximadamente 3,14: número cercano al valor de π”.—“Las matemáticas son el lenguaje que permite describir la naturaleza del universo”.—“La razón por la cual se le atribuye el teorema a Pitágoras es porque fue él quien primero demostró su validez universal”.—“La llamada demostración científica depende de la observación y la percepción, las cuales son falibles y sólo suministran aproximaciones (…) [la demostración matemática] tiene una verdad más profunda que cualquier otra verdad, porque es el resultado de un proceso lógico. Las matemáticas son una materia de estudio no subjetiva (…) independiente de la opinión”. Es decir, una demostración matemática es una verdad absoluta y se aplica para un caso específico como para todos los de su serie hasta el infinito. Es loca esa hueá, ojalá las ciencias sociales funcionaran así.—“Fermat y Pascal habrían de descubrir las primeras demostraciones y certezas absolutas de la teoría de la probabilidad, una materia que es, en esencia, incierta��.— “[Pascal] sostuvo que ‘la emoción que un apostador siente cuando hace una apuesta es igual a la cantidad que puede ganar multiplicada por la probabilidad de que gane”.—“El primer director del departamento de matemáticas (de la Universidad de Alejandría) fue, ni más ni menos, Euclides”.—Sobre la destrucción de la biblioteca de Alejandría: “En el año 642, un ataque musulmán culminó con éxito aquello en lo que los cristianos habían fracasado”. Quemaron todo por fanatismo dogmático. Maldita religión.— “El crecimiento de cualquier disciplina depende de su capacidad para comunicar y desarrollar ideas”.—“Los números amigos son parejas de números tales que cada uno de ellos es igual a la suma de los divisores del otro”.—“[En matemática] las ideas no corroboradas son infinitamente menos valiosas y se conocen como conjeturas”.—“Es impensable para los matemáticos no poder, al menos en teoría, contestar todas las preguntas, y esta necesidad se llama completud”.—“Los teóricos de los números consideran a los números primos como los más importantes de todos, porque son los átomos de las matemáticas”.—“Dios existe puesto que las matemáticas son consistentes, y el diablo existe puesto que no podemos demostrarlo”, André Weil.—Sobre Galois, un maestro escribió: “la locura matemática domina a este muchacho”. —“Cuando se discuten cuestiones trascendentales, hay que ser trascendentalmente claro”.— Y la frase que escribió Wiles cuando terminó su demostración del teorema de Fermat frente a la comunidad matemática más importante: “Creo que me detendré aquí” &lt;3                  47 reviews4 followers     October 4, 2011   If you buy the latest Jilly Cooper instead of this you WILL go to hell!This one languished on my bookshelf for the best part of a year as I was too scared to pick it up &amp; start it. What held me back is what will probably put a lot of other potential readers off trying it - the boring old "I'm no good at maths" argument. Although my maths education is probably little above average (a good O Level and a terrible A Level, after which I rallied somewhat to obtain a reasonable HNC maths module) it's //very// many years out of use and it's all I can do to add two numbers up in my head. Given that this book is about a problem that flummoxed the best mathematical minds in the world for over 350 years you'd be forgiven for putting this back on the shelf and choosing something a little simpler. Well, don't even try that...  YOU DON'T NEED ANY MATHS TO READ THIS!  What Singh has done here is to present a hugely complex subject in a hugely entertaining way. The search for the answer to Fermat's riddle reads like a detective story and not a matehematical treatise and it includes a truly absorbing potted history of the development of maths over the years and, from Pythagoras to Fermat to Godel to Wiles, each part has a fascinating human side to it.  Budding mathematicians needn't feel left out as the mechanics of the maths is also included, but it's treated in a gentle way: each step of the problem (and it's solution) is described in a simplified (but certainly not dumbed down) manner and some simple exercises are included in several short appendices. However, take heart! There are several places where elements of the maths are obviously too complex for us mortals and Singh is not afraid to say soo and then gloss over them completely. That may be a disappointment to some, but it's not at all unreasonable in my opinion.  All in all, the net result is a book that is sensitive to its readers, intelligent, interesting and important. It's literally unputdownable and it had the added bonus of tricking me into thinking that I'm a little cleverer than I really am.  I notice there's an inevitable Wills and Kate bio on the bestseller list at the moment. Put your hard earned cash into Andrew Morton's pockets or read something that will make you feel like a genius. The choice is yours.                   50 reviews4 followers     June 13, 2018   Αρχικά να πούμε ότι δεν είναι λογοτεχνία. Μου το είχαν προτείνει μαζί με κάποια βιβλία επιστημονικής φαντασίας και συνεπώς περίμενα κάτι αντίστοιχο. Αυτός ήταν και ο λόγος που το παράτησα στην πρώτη απόπειρα.Όμως, είναι μια εξαιρετική και απλοϊκή ιστορία των μαθηματικών σε σχεδόν λογοτεχνική απόδοση. Σίγουρα δεν μαθαίνει κάποιος μαθηματικά με αυτό το βιβλίο, αλλά μπορεί να έρθει σε επαφή με τις πλέον σύγχρονες μορφές τους χωρίς ιδιαίτερες γνώσεις.Σε τελική ανάλυση η ιστορία με συνεπήρε και το βιβλίο σίγουρα άξιζε την δεύτερη ευκαιρία που του έδωσα.                   537 reviews122 followers     July 13, 2022   Its a simple problem: x^n + y^n = z^n has no positive integer solutions (xyz) for n&gt;2. So why is it so hard to prove? (or disprove). I'm a math/physics nerd so this book has great appeal. I also like Simon Singh's technical writing. He stayed 100% on track as he traced Pythagoras in 6 BC to Andrew Wiles proof in 1994.We all remember 3-4-5 triangles from geometry/trig, right? Pythagorean Theorem says 3^2 + 4^2 = 5^2. Other famous right triangle uses of these are the 5-12-13 or the 7-24-25, or how about 99-4900 - 4901. So why can't a version of this with cubes, or ^4 or ^5 work? Andrew Wiles read The Last Problem by Eric Bell when he was 10. He ultimately left Cambridge, England became a math professor at Princeton. The text kept moving at a strong pace. The greatest minds in math all came into play, with their own focus and contribution to solving this problem. Pierre de Fermat lived 1607-1665. The mathematicians before him that get mentioned all contributed to number theory that had direct bearing on this ultimate math problem. Fermat has scribbled in the margins that he knew the proof, but it simply wouldn't fit in the margins. Even as computers came into being, the 'brute force' method of MANY trials (with none working) could solve this problem. For even if a million numbers were tried, maybe the next one could work. What was needed was a full mathematical logical proof. Solid 4.5*. If you like math/physics, then easy 5. If not, then round down to a very readable 4.     _own math z-2022               51 reviews9 followers     January 19, 2022   ✩ 5.0 stars ✩In telling the story of one of the most famous problems in mathematics, Simon Singh reveals the beauty of number theory, hidden in the simplicity of the problem that Andrew Wiles fell in love with all those years ago. He maps out a tree of mathematics with Fermat’s Last Theorem as the trunk, the central piece, paying tribute to the countless mathematicians that paved the way for Wiles’ proof. And of course, he describes the sheer tenacity of the mathematical genius as he grapples with the problem for 7 years. I loved the detail with which Singh explored the history of mathematics — he maps out intricate branches of time, delving into the history of Pythagoras, Euler, Turing, Taniyama and Shimura, and so many others, as he attributes to each their own contributions towards Fermat’s Last Theorem.This is a must-read for anyone interested in maths, but perfectly accessible for laymen of any sort.     favorites library non-fic               511 reviews686 followers     June 23, 2016   A fantastically entertaining and educational book about the quest to solve the oldest math problem: Fermat's Last Theorem. The intrigue, mystery, and drama surrounding the famous theorem without a proof (but that Fermat had said he had a proof for, just not enough space to write it in the margins) is exciting enough. All the math greats who have attempted to solve it but come up a little short, or a lot short.But it's much more than that, since the final proof of Fermat's Theorem involves so many other math concepts. This book starts and ends with Fermat, but in the middle it is more like a grand tour of all the mathematical developments that make the proof even possible. It's interesting to read about all the different dead ends and other productive findings (that had tangentially made it a little more possible to solve Fermat, but whose main contribution was in some other area). Also, reading about Galois's amazing life always makes me giddy. I mean, I've read about him before, but his story is just so crazy--math genius turned revolutionary thrown in jail involved in affair ends in duel, scribbles out his last thoughts the night before he dies... amazing. But don't expect to understand how the proof actually works by the end. The proof itself is over 100 pages, so there is no way a normal non-math genius can understand it. But you will get a general idea of the approach/trajectory/style of the final beast. Also, some of the math concepts leading up to it are quite easily comprehensible. I wouldn't recommend this book to a math whiz... it's more of a fun read for the layperson. It would ultimately be more satisfying if the proof were a short elegant thing that didn't involve latest groundbreaking discoveries in math. But maybe the bright side is that we can still wonder about Fermat's original (alleged) proof that was never written down. It had to be different from Andrew Wile's proof; does it exist? Or was Fermat bluffing? Or did he make an error in his proof?     male non-fiction poc               32 reviews29 followers     February 17, 2017   This book is a biography of the epic quest to solve the eluding Fermat's last theorem. It chronicles the life and works of not just Fermat, but most of the mathematicians having even a tiny bit to do with the conjecture/theorem. Curious and strange revelations into the lives of many of the princes and princesses of mathematics are presented. It presents the case of lives, pursuits and the times that they lived in. The problems that they face (mathematical and others), how these affect the progress/decline of the field.  Simon Singh writes brilliantly mixing accounts of math behind the problem along with the lives of these mathematicians. We get to see accounts of love, suicides, suicide averted by fixating on a proof, duels and revolutionaries. For me it was shocking to know, that it was not just the kings and religious fellows destroying these geniuses and their sanctuaries, but Pythagoras also committed a grave mistake once, sentencing Hippasus to death for arguing that sqrt(2) cannot be expressed as a fraction! A must read for those interested in history behind the problem.     biography library_reads like-to-own           August 6, 2015   Simon Singh gives an excellent account of the quest for the solution to Fermat's puzzle. Starting off with ancient Greeks and arriving at the proof using modern mathematics, he explains the struggles of generations of mathematicians. The author never tries to overwhelm us with the mathematics, but tells us about the people who were involved in proving the theorem. Having said that, all the mathematics in the book can be understood with a background in high school mathematics. This book is a great read simply because of the intellectual achievement that it talks about. Strongly recommended if you're remotely interested in mathematics.                   282 reviews69 followers     January 11, 2020   I have a special love for words. I think I always have. They’re fascinating. The words in this book were used for telling a story about numbers, which made me realize I also love numbers so much, I just didn’t know. Math had always been the “easy subject” at school for me, the one which did not require long hours of study, because it was so logical, the one you could check before turning in an exam and know you had the right answers precisely because it matched so perfectly. “Proof is what lies at the heart of maths.”, indeed, so simple, so beautiful. Well, this story is, as the title describes, a true quest to solve one of the most difficult problems in Mathematics which Fermat’s Last Theorem used to be. Simon Singh did this superbly. He is absolutely great at explaining from whole numbers and 1+1 to elliptical equations and modular forms. But the best was to learn about some of the greatest minds that worked so hard in the last century solving problems and doing the maths that have been the basis and tool for proving this theorem and thus, their great contribution to science: Pythagoras and his controversial Pythagorean Brotherhood, Mersenne, Euclid, Diophantus and his most remarkable “Arithmetica”, of course Pierre de Fermat, Pascal, brilliant Euler, Cantor, Sophie Germain, Theano, Hypatia, Maria Agnesi, Emmy Noether, Gauss, Cauchy, Lamè, Kummer, Wolfskehl, Gödel, Turing, Shimura, Taniyama, and Andrew Wiles. These are not the only ones, of course, but the most outstanding for me from this book. I want to make a special mention to the part where Singh talks about the work of women that were mathematicians. Even as of today, there aren’t many of us women dedicated to numbers or number theory, but we have come to a time when we can actually pursue this career, despite the struggles and obstacles that still exist in our societies. But being a mathematician a few centuries ago was completely outrageous and out of this world! Sophie Germain had to study secretly at night and keep a secret stock of candles to do so, because her dad used to confiscate them to prevent her from studying. Or Agnesi who was referred to as the “witch of Agnesi”. And the most extreme of these was Hypatia of Alexandria who suffered the most tragic and brutal death to the hands of the exulted mob led by the patriarch of Alexandria because she was considered a heretic. These stories really moved me and I’m very glad that their names are remembered and admired although they did not have a voice in their own time. Their only voice was their endless curiosity and passion for trying to understand the Universe and their brilliant work pervaded through history and remained printed in our books and forever in our memories, a greatly deserved honor to inspire all of us.  And back to Fermat’s Theorem, Wiles amazing work on his childhood’s dream inspired this book and will hopefully inspire many more that see the beauty of numbers to keep working and pushing the frontiers on this science field which Singh perfectly describes as the “language of nature”.
Fermat's Enigma
https://www.goodreads.com/book/show/38412.Fermat_s_Enigma
https://www.goodreads.com/book/show/433567.Flatland
Flatland: A Romance of Many Dimensions
2023-01-01
Author
<div><div><div><article><div><section><a href="https://www.goodreads.com/user/show/538288-robert"></a></section><section><p>Author <i></i>5 books101 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/8288779">March 2, 2009</a></section><div><p>When you read this book, keep two things in mind. First, it was written back in 1880, when relativity had not yet been invented, when quantum theory was not yet discovered, when only a handful of mathematicians had the courage (yet) to challenge Euclid and imagine curved space geometries and geometries with infinite dimensionality. As such, it is an absolutely brilliant work of speculative mathematics deftly hidden in a peculiar but strangely amusing social satire.<p>Second, its point, even about itself, is still as apropos today as it was then. We <i>still</i> do not really know what the true dimensionality of the Universe is. It seems somehow unlikely that it is just "four", even in terms of spacetime dimensions. String theory talks seriously about thousands of dimensions. Quantum theory implements <i>very</i> seriously <i>infinite</i> numbers of dimensions. And yet we are still stuck in our 3 space dimensions mentally, hardly able to visualize the 4 in which we live "properly" unless we study theoretical physics for a decade or three, and utterly unable to mentally imagine those four embedded in a veritable Hilbert's Grand Hotel of dimensions.</p><p>Ultimately, this is a book about keeping an open mind. A <i>really</i> open mind -- avoiding the trap of scientific materialism and the trap of theistic idealism and the trap of any other favorite -ism you might come up with. Our entire visible space-time continuum could be nothing more than a single thin page in an infinitely thick book of similar pages, that book one of an infinite number of similar books on an infinite shelf, that shelf but one such shelf in an infinite bookcase of shelves, that bookcase but one in an infinite library of bookcases, that library but one... but by now you get the idea.</p><p>We have a hard time opening our minds up to the enormous range of possibilities, preferring to live our lives mentally trapped in a single tiny period on just one of those pages, in pointland. We may be quite unable to actually perceive the space in which our tiny point is embedded, but our minds are capable of <i>con</i>ceiving it, and Abbot's lovely parable is a mind-expanding work to those who choose to read it that way.</p><p>rgb</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1413439-stephen"></a></section><section><p>1,517 reviews10.8k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/29775315">April 27, 2012</a></section><div><p>Take a <b>classically styled</b>, 19th century <b>satire</b> about <b>Victorian social mores</b>…dress it up in <b>dimensional geometry</b> involving <b>anthropomorphized shapes</b> (e.g., lines, squares, cubes, etc.)…bathe it in the sweet, scented waters of <b>social commentary</b>…and wrap it all around <b>humble</b>, open-minded <b>Square</b> as protagonist. <p>The result is Flatland, a unique “classic” parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Since I’m recommending the book, I’m really hoping for the former, as I do not want to incur a cyber-flogging (or worse) from my fellow “goodreaders.” </p><p>So...um...math. </p><p>Let’s get this out of the way right now. As I alluded to in my intro, this book contains MATH. Now I hesitate to even mention that, because of the potential angst that subject causes many of my friends. I certainly don’t want people going all <br /><a href="http://s153.photobucket.com/albums/s207/sullypython/Scared%20and%20scary/?action=view&amp;current=screamscream.jpg">
 
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</a><br /><a href="http://s153.photobucket.com/albums/s207/sullypython/Scared%20and%20scary/?action=view&amp;current=Untitled.jpg">
 
</a><br />…and dashing away in a panic. </p><p>Rest easy and increase your calm, the math is very minor. It’s really limited to discussions of geometric figures in the context of how many spatial dimensions they inhabit. <b>Damn</b>, that didn’t sound good either….just trust me, you won’t need a slide rule, an abacus or a lifeline to Stephen Hawking to read the book. </p><p><b>However</b>, with that said, while the math is not tricky, some of the concepts can be a little brain twisty to try and visualize. Thus, I want to caution that when you get to the section where a three dimensional “Sphere” is explaining a universe containing only one dimension to our two-dimensional protagonist, you should….IMMEDIATELY…DISCONTINUE…READING…until you have:</p><p><b>1.</b> burned some incense, <br /><b>2.</b> poured a big tumbler of whiskey, and <br /><b>3.</b> eaten a few “peyote” brownies, </p><u>because</u> the SHIT is about to get…<p><a href="http://s153.photobucket.com/albums/s207/sullypython/Famous%20people/?action=view&amp;current=Busey.jpg">
 
</a></p><p><b><u>PLOT SUMMARY</u>:</b></p><p>Written in 1884, the story is told by “A. Square,” who lives in Flatland, a world of two-dimensions, which means length and width, but no depth (just like the Kardashians). The men of Flatland are multi-sided polygons, and the more sides an individual has, the greater their social standing. On the other hand, women are all simple lines and have no voice in the governing of the society. </p><p>Yep...the Flatlanders are chauvinists. </p><p>The book begins with “A Square” describing his life as part of the “professional class” and providing details on daily life in Flatland. This section serves as a In reality, this is a pretty good satire on Victorian London society, the social caste system and gender inequality. </p><p>Later, “A Square” dreams of a one-dimensional world called Lineland, where the inhabitants exist as simple points along a straight line, as there is no other width or depth. <i>I seriously hope you have that tumbler of whiskey and some brownies close by because you are going to need them</i>. What follows is a fun, but somewhat confusing discussions during which “A Square” tries to explain the two-dimensional world to the king of Lineland. </p><p>Eventually, our protagonist wakes up back in Flatland, only to find that he is now being visited by a Sphere from a three-dimensional universe…<i>whiskey…peyote…now</i>. Sphere takes our flatlander on a mind-expanding, eye opening journey to witness the wonders and mysteries of the higher and higher dimensions (3rd, 4th, 5th, etc.). Afterwards, “A Square” returns to Flatland to teach the wonders of such “enlightened” dimensions to his fellow flatlanders, the result of which is…</p><p>…nope…no spoilers here! </p><p><b><u>THOUGHTS</u>:</b></p><p>As I sit here, sober and “mostly” peyote free, I think I enjoyed the “ideas and concepts” of the story more than the actual plot. The writing was fine, but nothing that struck me as particularly eloquent. However, I’ve the concepts of the story have stayed with me and I have actually become more appreciative of the material as time has gone by. </p><p>Overall, I liked the book. I think it’s worth reading, but more for the interesting ideas and mental gymnastics that the narrative puts you through than for the simply enjoyment of the plot. Still, a worthwhile read, and since it’s actually a novella, you can get through it quickly without a large time commitment. </p><p>3.0 stars. Recommended!</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1413439?shelf=1800s">1800s</a> <a href="https://www.goodreads.com/review/list/1413439?shelf=classics">classics</a> <a href="https://www.goodreads.com/review/list/1413439?shelf=classics-european">classics-european</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/25683251"></a></section><section><p>1,032 reviews1,677 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2390298063">June 18, 2018</a></section><div><p><b>حجمستان</b><br />یادداشتی بر داستان «پختستان» نوشتۀ ادوین ابوت<blockquote><br /><b>معرفی</b><br />ادوین ابوت رمان پختستان را در سال ۱۸۸۴ در انگلستان دوران ویکتوریا منتشر کرد: دوران نظام اجتماعی و اخلاقی خشک، و ازلی‌ابدی.<br />رمان از دو فصل تشکیل شده: در فصل اول راوی که مربعی از اهالی پختستان است سرزمین دو بعدی خود را توصیف می‌کند، شکل و شمایل هندسی و فیزیکی پختستان، این چگونه همدیگر را می‌بینند، همدیگر را می‌شناسند. همچنین از ساختار اجتماعی و سیاسی پختستان می‌گوید، اختلاف طبقاتی و تنش‌های بین اشکال مختلف، انقلاب‌ها و سرکوب‌ها، تبعیض‌های جنسیتی، و... <br />در فصل دوم، مربع برای نخستین بار با دنیاهای جدیدی رو به رو می‌شود، دنیاهایی که حتی تصورشان برای اهالی پختستان ناممکن است و صحبت کردن از آن، جرم. اگر فصل اول انتقاد از وضع کنونی است، فصل دوم را می‌توان نوید امکان تغییر به وضعی جدید دانست، وضعی جدیدی که همه ناممکنش می‌دانند، تنها از آن جهت که هنوز یاد نگرفته‌اند به جهت درست نگاه کنند، و به محض آن که یاد بگیرند، تعجب خواهند کرد که چطور در تمام این مدت از دیدن آن عاجز بودند.<br /></blockquote><p>شبی تابستانی ادوین ابوت در کتابخانه نشسته بود و به مسأله‌ی بغرنجی فکر می‌کرد. مسأله از این قرار بود که آیا می‌توان بعدی مکانی غیر از سه بعد تصور کرد که در جهتی غیر از جهاتی که می‌شناسیم امتداد داشته باشد؟ و اگر چنین جهان چهار بعدی ممکن باشد، در مقایسه با ما چه شکلی خواهد داشت؟</p><p>در همین فکرها بود، که ناگهان اتفاق شگفت‌انگیزی افتاد. در وسط اتاق مطالعه‌اش، نقطه‌ای پدید آمد، در مقابل چشمان حیرت‌زده‌اش به سرعت رشد کرد، به جنینی بدل شد، سپس کودکی شد و نوجوانی و جوانی، و در عرض چند ثانیه، پیرمردی در مقابل او ایستاده بود. </p><p>ادوین ابوت وحشت‌زده فریاد کشید و به قفسه‌ی کتاب‌ها چنگ زد تا خودش را از افتادن نگاه دارد و چند کتاب با سر و صدا زمین ریخت. زنش از این همه داد و فریاد هراسان به اتاق دوید و پرسید: «چه خبر شده؟»<br />ابوت بی آن که بتواند حرف بزند پیرمرد را نشان داد و زن که تازه متوجه حضور پیرمرد محترم و موقری در کتابخانه‌ی شوهرش شده بود، با رعایت آداب چند کلمه‌ای با او خوش و بش کرد و رو به ابوت گفت: «ادوین، نمی‌فهمم سبب این رفتار بدون نزاکت چیست؟ از آقای محترم دعوت کن بنشیند. من هم‌اکنون چای می‌آورم.» و از اتاق خارج شد.</p><p>پیرمرد رو کرد به ابوت، که هنوز به قفسه چنگ زده بود، و گفت: «معذرت می‌خواهم که این طور ظاهر شدم. همیشه وارد شدن به حجمستان دردسر ساز است.»</p><p>ابوت با لکنت گفت: «شما که هستید؟»</p><p>«ببخشید، فراموش کردم خودم را معرفی کنم. من متوازی الانسان هستم. در جهان چهار بعدی که از آن می‌آیم نام من این است.»</p><p>«متوازی الانسان؟»</p><p>«بله، خب این طور تصور کنید که تمام وجود شما در جهان سه بعدی، فقط یکی از اضلاع ما در جهان چهار بعدی است. همان طور که تمام وجود مربع در جهان دو بعدی، فقط یکی از پهلوهای مکعب در جهان سه بعدی است. من هم چون از انسان‌هایی دو به دو متوازی ساخته شده‌ام، متوازی الانسان نامیده می‌شوم.»</p><p>ابوت دهانش را چنان باز کرده بود که انگار در نیمه‌راه یک ناسزا متوقف شده. پیرمرد گفت: «بیایید، بگذارید نشان‌تان دهم.» و قبل از آن که ابوت بتواند کاری بکند، دست او را گرفت و او را در جهتی، نه بالا و پایین، نه چپ و راست، نه درون و بیرون، بلکه در جهتی به کلی متفاوت بلند کرد، از جهان سه بعدی برداشت و بیرون برد. ابوت از وحشت جهان چهار بعدی یک بند فریاد می‌زد، مخصوصاً وقتی چشمش به میهمانش افتاد که به شکلی غیر قابل توصیف، از انسان‌هایی دو به دو متوازی ساخته شده بود و هر انسان با تمام سه بعدش تنها یکی از اضلاع او را تشکیل می‌داد.</p><p>متوازی الانسان صبر کرد تا وحشت ابوت به انس بدل شود، و آن گاه برای او شرح داد که چطور در تمام این مدت جهانی چهار بعدی درست جلوی چشم تمام اهالی حجمستان بود، اما هیچ کس سر را به جهت درست نمی‌گرداند تا آن را ببیند، جهتی غیر از بالا و پایین و چپ و راست. و از ابوت خواست که دیگر اهالی حجمستان را از وجود این جهان عظیم مطلع کند، جهانی که حجمستان با تمام عظمتش در قیاس با آن، همچون نقش روی دیوار است.</p><p>ابوت به جهان سه بعدی نگاه کرد که همچون نقش روی دیوار، بدون حجم به نظر می‌رسید. از آن جا می‌توانست داخل کتابخانه‌اش را ببیند، انگار که سقفی به کار نباشد، با آن که سقف بود، و همسرش که سینی چای به دست سرگردان در میان اتاق ایستاده بود و سر در نمی‌آورد که مردها کجا رفته‌اند. گفت: «اما هیچ کس حرف من را درک نخواهد کرد.»</p><p>متوازی الانسان گفت: «خب چرا یک داستان نمی‌نویسی تا فهمش راحت‌تر شود؟»</p><p>«چه داستانی؟»</p><p>«نمی‌دانم. مثلاً داستان یک مربع ساکن جهان دو بعدی، که روزی کره‌ای از جهان سه بعدی در خانه‌اش ظاهر می‌شود و سعی می‌کند بعد سوم را برای او توضیح دهد.»</p><p>ابوت به تمام چند صد چشم متوازی الانسان نگاه کرد، و به نشان پذیرش سر تکان داد. از همین حالا عنوان داستان را انتخاب کرده بود: «پختستان».</p><p>این یادداشت برای سایت پلاتو نوشته شده، به این آدرس:<br /><a href="http://pelatto.ir/?p=5701">لینک</a></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/25683251?shelf=%D8%AF%D8%A7%D8%B3%D8%AA%D8%A7%D9%86-%D8%AE%D8%A7%D8%B1%D8%AC%DB%8C">داستان-خارجی</a> <a href="https://www.goodreads.com/review/list/25683251?shelf=%D8%B7%D9%86%D8%B2">طنز</a> <a href="https://www.goodreads.com/review/list/25683251?shelf=%D9%81%D8%A7%D9%86%D8%AA%D8%B2%DB%8C">فانتزی</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1199525-cecily"></a></section><section><p>1,095 reviews3,838 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4018708899">May 26, 2022</a></section><div><p><b>Imagine losing or gaining a spatial dimension</b><p>Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute <a href="https://www.youtube.com/watch?v=_4ruHJFsb4g">Action Lab video</a>, explaining what a 4D ball would look like in 3D. I sent it to <a href="https://www.goodreads.com/review/show/1397326385">Apatt</a> who likened it to <b><a href="https://www.goodreads.com/review/show/4030230286">And He Built a Crooked House</a>,</b> which in turn, reminded me of a book I’d heard of, <b>Flatland</b>. </p><p>Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both. </p><p><b>And He Built a Crooked House</b>, by Robert Heinlein</p><p>This is an early short story (1941) by a big name in sci-fi. It's about a 4D construction.</p><p>Quintus Teal is a young architect who thinks of a house as “<i>a machine for living, a vital process, a live dynamic thing</i>”. His big idea is to use the fourth spatial dimension to “<i>put an eight-room house on the land now occupied by a one-room house. Like a tesseract</i>”. He goes on to explain a lot of geometry, and I would have been bemused if I hadn’t already seen illustrations of what a tesseract, aka hypercube, would look like. </p><p>We’re all familiar with a <a href="https://en.wikipedia.org/wiki/Cube">cube</a> and its net:<br /></p><p>Then add a dimension for a <a href="https://en.wikipedia.org/wiki/Tesseract">hypercube</a> and its net:<br /></p><p>For more of an explanation, see video links at the end of this review. </p><p>Teal achieves his dream “<i>by using strong girders and folding money</i>” and takes his friends, Mr and Mrs Bailey to see it.<br />“<i>That's the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation.</i></p><p>But four dimensions don’t fit easily into a three dimensional world, and things become strange. Stranger than any staircases or buildings that <a href="https://mcescher.com/">Escher</a> drew.</p><p><b>Flatland</b>, by Edwin A Abbott</p><p>About a 2D world and published in 1884. </p><p>This short book uses geometry as an analogy for a socio-political satire of Victorian attitudes to class and social mobility; gender (in)equality; biological determinism, evolution, and eugenics; religion and the supernatural. It probably works better for those with more knowledge of and interest in the period than I have. Fortunately, my edition had lots of notes, and Abbot included several illustrations. </p><p>The key concept is that in a two-dimensional world, a three-dimensional figure is observed as a cross-section. If it's moving, it is seen as a series of cross-sections, and can appear to appear and disappear out of nowhere.</p><p>In the first half, the narrator, A Square, explains the very hierarchical social system of the two-dimensional Flatland. The more sides a shape has, and the more regular it is, the higher up the scale it is. “<i>Delicate females</i>” are are mere lines, “<i>wholly devoid of brain-power, and have neither reflection, judgement, nor forethought, and hardly any memory</i>”, but Abbot himself was a priest and headmaster who believed in women’s education, including at university. </p><p>The second half has more of a story: “<i>my initiation into the mysteries of Space</i>” and “<i>the Gospel of Three Dimensions</i>”. A Square develops a theoretical and then practical understanding of other spatial dimensions. The trouble is, that’s unimaginable and heretical in Flatland. </p><p>The progression of understanding of different spatial dimensions is well explained, with a few illustrations: A square is “<i>a Line of Lines</i>” and a sphere is “<i>many Circles in one</i>”. However, Abbott’s love of initial capital letters was a little distracting, and in part of the second section the language becomes overly Biblical and deferential (thee, thou, My Lord etc).</p><p><br /><b>Image</b>: <i>“The Weeping Woman”, in which “Picasso used cubist forms of fragmentation to depict the face in a series of angular planes”.</i> (<a href="https://en.wikipedia.org/wiki/The_Weeping_Woman">Source</a>)</p><p><b>Clearly explained information about 2D and 4D</b></p><p>To understand the fourth dimension, you need a firm grasp of the zeroth, first, second, and third dimensions. Unless you have a mathematical background, I strongly suggest you watch one or two of these videos before reading either story. I found it helpful to see the same ideas explained in slightly different ways.</p><p>•	The fourth dimension explained, via second and third, in six minutes, <a href="https://www.youtube.com/watch?v=Z73uXPBUT7o">HERE</a>. </p><p>•	Hypercubes explained and illustrated, without sound, in five minutes, <a href="https://www.youtube.com/watch?v=AzL091mZQ-E">HERE</a>. </p><p>•	Five-minute TED animation, summarising the story of Flatland and explaining 2D and 4D, <a href="https://www.youtube.com/watch?v=MGv8MMi8QO0">HERE</a>. </p><p>•	Animation of the story of Flatland, narrated by Carl Sagan, in four minutes, <a href="https://www.youtube.com/watch?v=-wv0vxVRGMY">HERE</a>. </p><p>•	Animation of the story of Flatland, made in 1965, eleven minutes, <a href="https://www.youtube.com/watch?v=yBbZmwROv84">HERE</a>. </p><p>•	Carl Sagan <b>explains</b> Flatland and goes on to the fourth dimension, in nine minutes, <a href="https://www.youtube.com/watch?v=N0WjV6MmCyM">HERE</a>. </p><p><b>The two stories</b></p><p>•	You can read Flatland, free, in a variety of digital formats, on Gutenberg, <a href="https://gutenberg.org/ebooks/201">HERE</a>. </p><p>•	You also can find the text of And He Built a Crooked House online. </p><p><br /><b>Image</b>: <i>“Mr Osborne, may I be excused? My brain is full.”</i> (The Far Side, by <a href="https://goodreads.com/author/show/19928.Gary_Larson">Gary Larson</a>)</p><p><b>See also</b></p><p>•	If it’s all too much, there’s Norton Juster’s delightful picture book, <b>The Dot and the Line</b>, which I reviewed <a href="https://www.goodreads.com/review/show/3075710794">HERE</a>. I included illustrations and a link to an Oscar-winning animation.</p><p>•	Malcolm wrote two short stories about very high-tech homes in <b>The Martian Chronicles</b>, which I reviewed <a href="https://www.goodreads.com/review/show/1759520518">HERE</a>. <b>Usher II</b> is a subversive dystopian comedy that's also a tribute to Poe's Fall of the House of Usher. <b>There Will Come Soft Rains</b> starts off almost slapstick, but takes a very tragic turn. </p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1199525?shelf=humour">humour</a> <a href="https://www.goodreads.com/review/list/1199525?shelf=maths">maths</a> <a href="https://www.goodreads.com/review/list/1199525?shelf=politics">politics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/48483884-michael-finocchiaro"></a></section><section><p>Author <i></i>3 books5,415 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1950101151">March 23, 2017</a></section><div><p>A curious little novella about a man a two-dimensional world thinking literally out of the box. First he explains his world in which the angles you have the higher social status you have in Flatland - Circles being the highest rank. He meets someone from Lineland (one-dimensional) who is incapable of understanding Flatland and he meets Sphere from Spaceland (three dimenions) and he is able himself to comprehend the difference between "up" and "North". However, Sphere cannot extrapolate to 4+ dimensions and when the protagonist returns to Flatland and tries to explain Spaceland, he is imprisoned as a heretic. <p>The text is a social criticism on the rigid thinking of hierarchal social ranks, the dogmatism and often anti-scientific bent of religion, and also has a feminist bent to it as well. A fascinating and mind-bending little book that has not aged a day after almost a century and a half.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/48483884?shelf=english-20th-c">english-20th-c</a> <a href="https://www.goodreads.com/review/list/48483884?shelf=fiction">fiction</a> <a href="https://www.goodreads.com/review/list/48483884?shelf=geek-classics">geek-classics</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/70395042-fergus-quondam-happy-face"></a></section><section><p>934 reviews17.6k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4907582510">January 19, 2023</a></section><div><p>I will start my own brief multi-dimensional romance on this book - but dangerously, perhaps, exploring elements of my own experiences out into Spaceland that led me back, like Abbott, to my home-sweet-home of Flatland - with a caveat that I am a rather odd duck.<p>Being born with ASD didn't help at all. </p><p>We Aspies, like Supertramp, always Take the Long Way Home. The prolonged ingenuous Springtime of The Soul. And the soul rejoices in the bright laughter of - as Mallarme says - the Jeu Suprême - as all reality curls up comfortably at its Ironic Edges.</p><p>But the simplicity of higher mathematics in high school soon became in my eyes an overgrown jungle. It was, to me, unworkable, because we Aspies come from a psychological Flatland: to the world, Dullsville.</p><p>So my apologies at the outset to my GR friends who were math majors.</p><p>No, I took this book at a personal EXISTENTIAL level! So please: take this review very much with a grain of salt!<br />***</p><p>As you probably know, I like to often change the subject. My adventures in Spaceland taught me that when my interlocutors dug deep, their interjections were to me like speeding bullets. I dodged them: I knew they would spell my mediocre death-in-life: I didn't want to go there.</p><p>Didn't even want to go to Spaceland - no - but the philosophical skills my teenaged reading skills gave me PUSHED me into a sophisticated outer spaceland. </p><p>That sophistication fed my nascent knowledge.</p><p>So when I went to college, I explored Spaceland heuristically. And of course - that path leads us into the Den of the Minotaur. </p><p>Yikes.</p><p>Anyway, after King Minos' foul beast had thoroughly chewed me up and expectorated me... alone, I found myself back home in Flatland! <br />***</p><p>An awakening refused leads back to simplicity, as Abbott found -</p><p>And it's where I am now writing this:</p><p>In "a state of simplicity (which cost me) not less than EVERYTHING."</p><p>And won me Flatland forever...</p><p>Flatland - AKA God's Peace - a patient, silent witness to an Ugly World.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/614778-ahmad-sharabiani"></a></section><section><p>9,568 reviews55.6k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/526023970">August 18, 2020</a></section><div><p>Flatland: A Romance of Many Dimensions, Edwin A. Abbott<p>Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley &amp; Co. of London. </p><p>Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions. </p><p>The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides. </p><p>The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. </p><p>The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium. </p><p>On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points". </p><p>These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so. </p><p>In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. ...</p><p>عنوانها: «پـَختِستان»؛ «افسانه ی دو بعدی»؛ «سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه»؛ نویسنده: ادوین ابوت؛ تاریخ نخستین خوانش سال 1997میلادی</p><p>عنوان: پـَختِستان؛ نویسنده: ادوین ابوت؛ بازنگری و مقدمه از: یانش هوفمان؛ مترجم منوچهر انور؛ تهران، روشنگران و مطالهات زنان، 1375؛ در 195ص؛ شابک 9645512433؛ چاپ دیگر تهران، کارنامه، 1388؛ در 172ص؛ شابک 9789644310799؛ چاپ دوم 1393؛ موضوع بعد چهارم - از نویسندگان بریتانیایی - سده 19م</p><p>عنوان: افسانه ی دو بعدی؛ نویسنده: ادوین ابوت؛ مترجم: جلال جامعی؛ شیراز، لورا، 1387، در 192ص؛ شابک 9789648851366؛</p><p>عنوان: سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه؛ نویسنده: یک مربع (ادوین ابوت)؛ برگردان: آهنگ کوثر؛ شیراز، نوید شیراز، 1397؛ شابک 9786001927768؛ </p><p>پَختستان: رمان بُعدهای بسیار، رمان کوتاهی از الهی‌دان و استاد دانشگاه انگلیسی، «ادوین ابوت» است، که نخستین‌بار آن‌را در سال 1884میلادی با نام مستعار نویسندگی «یک مربع» منتشر کردند؛ در این کتاب از دنیای خیالی «دوبُعدی پَختستان»، برای نشان دادن فرهنگ سلسله‌ مراتبی «انگلستان» دوره ی «ویکتوریا» استفاده شده‌ است.؛ این نگاره بیشتر یک تمثیل عبرت‌ آموز است، تا یک داستان؛ و نیز نقدی تند و گزنده، از ساختار اجتماعی و سیاسی جامعه ی روزگار خود، و ارزش‌ها، و روابط انسانی در آن است؛ «ابوت» برای اینکه نشان دهد، انسان‌ها در این دنیا از نظر افق دانش و بینش، در چه قفس تنگی گرفتار هستند، از جهانی خیالی با باشندگانی دو بُعدی سود برده است.؛ این باشندگان دارای شکل‌های هندسی «مثلث»، «مربع»، «پنج‌بر»، «شش‌بر» و «بالا و بالاتر» تا «دایره‌» هستند، که ناگزیر در سطح می‌زیند.؛ نویسنده و راوی داستان، یک مربع است، که این دنیا را شرح می‌دهد.؛ «پَختستان» در زمان انتشار خود، مورد توجه قرار نگرفت، پس از انتشار نظریه ی نسبیت عام انیشتین، این کتاب دوباره به یاد همگان افتاد، چرا که در آن به مفهوم «بُعد چهارم» نیز اشاره شده بود.؛ در مقاله‌ ای تحت عنوان «اقلیدس، نیوتن و انیشتین»، که در شمارهٔ دوازدهم ماه فوریه سال 1920میلادی مجله ی «نیچر» منتشر شد، از این کتاب نام برده شد، و «ابوت» را از یک نظر همچون پیامبری دانست، که در آن زمان به درک اهمیت زمان، در شرح یک پدیده، آگاه بوده‌ است.؛ انتشارات «هارپرکالینز» در سال 1983میلادی، نسخه‌ ای از این کتاب را با پیشگفتار «آیزاک آسیموف» منتشر کرد.؛ عنوان «پَختستان» را، مترجم نخست این کتاب، جناب «منوچهر انور»، برای آن برگزیدند، که از واژه ی فارسی «پَخت» به معنای «پهن» و بی‌برجستگی، و پسوند ستان تشکیل شده‌ است.؛</p><p>تاریخ بهنگام رسانی 27/05/1399هجری خورشیدی؛ ا. شربیانی</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/614778?shelf=19th-century">19th-century</a> <a href="https://www.goodreads.com/review/list/614778?shelf=british">british</a> <a href="https://www.goodreads.com/review/list/614778?shelf=classics">classics</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1856758-dan"></a></section><section><p>87 reviews</p></section></div><section><section><a href="https://www.goodreads.com/review/show/41686487">January 4, 2009</a></section><div><p>This book should not be read in hopes of finding an entertaining story. As a novel, it's terrible. It's plot (if you can call it that) is simple and contrived. But, it wasn't written as a novel.<p>Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them.</p><p>The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear.</p><p>In the course of the explanation, the book also describes "Lineland," a one dimensional world where the inhabitants would also have trouble understanding dimensions above their own.</p><p>This book's excellence lies in the way it takes a complex topic and breaks it down into a metaphor that can be more easily understood. It argues quite well that if there is a fourth dimension, it probably isn't "time."</p><p>This book isn't one that will win wide-spread acclaim from the general reading community. For those of us who enjoy higher math, though, it's excellent.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/2457095-apatt"></a></section><section><p>507 reviews752 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1948006444">April 6, 2017</a></section><div><p><i>“I used to be a renegade, I used to fool around <br />But I couldn't take the punishment and had to settle down <br />Now I'm playing it real straight, and yes, I cut my hair <br />You might think I'm crazy, but I don't even care <br />Because I can tell what's going on<br />It's hip to be square”</i><br /><a href="https://www.youtube.com/watch?v=LB5YkmjalDg">Huey Lewis And The News - Hip To Be Square</a><p>According to IMDB, several film adaptations have been made of <i>Flatland</i>, but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can’t imagine a more appropriate theme song than the above Huey Lewis And The News number.</p><p><i>Flatland</i> is set in a two-dimensional world and narrated in the first person by a square (or “A Square” as appears on the original edition’s book cover). In the first half of the book Square gives us a tour of his world where women are straight lines and, if you are symmetrical, the more sides you have the better. This means that circles are the elite of this society because they are really polygons with zillions of super tiny sides. Irregular polygons are abominations and isosceles are plebeians. <br /> <br />Special laws are applied to women because they are capable of accidentally stabbing people to death due to their pointiness. Use of colours is banned because they can be used as disguises. How these geometric persons move around without legs is deliberately left unexplained (with a bit of "lampshading"). The second half of the book tells the remarkable story of Square’s adventures in lands of different dimensions, one, three and even zero (no trip to the fourth dimension, though; no <i>time</i>, probably). Guided by an enigmatic Sphere who seems to have popped up out of nowhere (and who Square initially mistook to be a circle), these trips to other planes of existence enables Square to not only think outside the box but to introduce him to the existence of boxes. This was a steep learning curve for him but he adapts like a champ and becomes a more rounded individual because of it.<br /> <br /><i>Flatland</i> is a very odd novella it is part allegory, part satire, part geometry lessons, part spec fic. I generally avoid reading geometry books because they are full of problems I don’t want to consider (screw the hypotenuse, man!). However, for <i>Flatland</i> I don’t mind making an exception, for once I find the flat characters entirely acceptable and even find the more apparently rounded character to be arrogant and clearly obtuse in their outlook, if not in appearance. The satirical look at the class system makes this all too real issue painfully acute. One thing that blows my mind a bit is that prior to reading the book I visualized it as a story of different geometric shapes moving around going about their business. However, the denizens of the Flatland cannot actually see these different shapes. As the Square (or Edwin Abbott Abbott) mentions early in the book you have to imagine looking at these shapes with your line of sight on the same level as their surface. Mr. Abbott explains it very clearly as follows:</p><p><i>“Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.”</i><br /></p><p>So all they really ever see is straight lines of different lengths, however, they can distinguish the different geometrical shapes by hearing, by touch (done by the working class only), and by sight with the aid of fog for estimating depths (different angles appear to fade differently into fog). In the one-dimensional Lineland everybody looks like a point and sideways movement is impossible; as for the zero-dimensional Pointland, there is only one denizen and he is weird!</p><p>I really enjoyed <i>Flatland</i>, it is bizarre and thought-provoking; it definitely gave me a new perspective on life. The treatment of women may seem a little sexist but E.A. Abbott is perhaps satirizing sexism rather than perpetuating it. I definitely recommend you read <i>Flatland</i> before you flatline.<br /></p><p><b>Notes:</b><br />• Audiobook credit: Wonderfully read for Librovox (i.e. free) by Ruth Golding. <a href="https://librivox.org/flatland-a-romance-of-many-dimensions-by-edwin-abbott-abbott/">(link)</a></p><p>• There are quite a few diagrams scattered over the book, drawn by AbbottX2 himself, they illustrate the geometrical concepts nicely. These should be in all editions as they are intrinsic to the story.</p><p>• There is one error in the book where Square mentions a cellar: <i>“So I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned.”</i>. You can't have a bloody cellar if you only have two dimensions and you can’t “fall through” anything.</p><p>• Another error (I think) is the existence of cupboards in Flatland. If there is no depth or verticality you can't have cupboards!</p><p>• The 3D world is called Spaceland, it is not our world. Their most popular singer is probably Britney Sphere. (͡° ͜ʖ ͡°)</p><p>• I initially thought this book was a collaboration between two abbots.<br /> <br /><b>Quotes:</b><br />Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name.</p><p>In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself. Such at least is the painful teaching of my experience.</p><p>Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life?</p><p>You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions—how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration?<br /> <br />Hipster Square</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/2457095?shelf=classics">classics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/110812-kinga"></a></section><section><p>475 reviews2,123 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/365470072">March 19, 2015</a></section><div><p>This was one crazy, opium fuelled, brilliant book about geometry and different dimensions and I am going to explain it the best way I can but Edwin A Abbott does it so much better.<p>Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off are women who are not even figures; they are just straight lines. They have few rights and no one actually takes their intellect seriously. On the other hand they are dangerous because being straight lines they can easily pierce any figure. A woman from behind looks just like a dot, you might miss her until it’s to late and she has stabbed you. Different parts of Flatland developed different strategies for dealing with the danger, from not allowing women to leave their houses, to forcing them to constantly wiggle their bums, so they are visible from far. They should also sound a ‘peace-cry’ when out and about, in case anyone missed the wiggling bum. Seriously children, don’t do drugs. It makes you write things like that. </p><p>The second part of the book gets more interesting as it delves deeper into the concept of dimensions. As I said, our hero lives in a two-dimension reality. Try to imagine such a world. You probably see it as a piece of paper with various figures drawn on it. Of course, that’s how a creature from 3D world would see it. You’re looking at it from above, i.e from the third dimension. If a 2D world was your entire reality you would only be able to see lines and dots. Your eyes would be on the same level as the figures and you would see everything in one dimension and infer the second dimension because you can move in it and you have learnt it through experience.</p><p>The same way we can’t actually see the third dimension but we can tell it’s there. We know we can move in three dimensions and we know about perspective, light, shadow, etc. It is easier for us to understand a two-dimension reality than it is to imagine a four-dimension one. We can see it perfectly when our Square visits a one dimensional land and he laughs at it and tries to explain to the King that there is more to life than just looking at a dot in front of you. There is another dimension where there are not only dots but lines as well. The King of course laughs him off. Yet, when Square is confronted by Sphere who tells him about the third dimension and shows him ‘tricks’ that the third dimension allows him to do, Square is just as incredulous.</p><p>Even though the mathematics tells him there must be another dimension (and another, and another), he can’t quite believe it until Sphere shows him a little bit of a 3D world. Then he is a convert, and he quickly assumes there must be more dimensions. Fourth and fifth and ad infinitum. I think while reading this I got as close as I would ever get to understanding and imagining a 4D world. If in a 3D world we can see the insides of everything of a 2D world, then I suppose a in 4D world we would be able to actually SEE all three dimensions, all the insides of everything. My brains hurts. Am I making any sense? I thought I could see it but now it’s been a week after I finished reading the book and had those vivid dreams about the fourth dimension. The vision pales. I still believe in it but I can no longer grasp it. Just like the poor Square, back in his 2D-Land, thrown in prison for preaching revolution, still believes in the third dimension, but can no longer conjure the image of a Sphere in his head. Sometimes he feels he can almost see it again for half a second, and then it’s gone.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/110812?shelf=gutenberg-project-project">gutenberg-project-project</a> <a href="https://www.goodreads.com/review/list/110812?shelf=pub-1880s">pub-1880s</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/50009464-julie-demar"></a></section><section><p>5 reviews4,020 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1776648197">October 6, 2016</a></section><div><p>Un racconto fantastico a più dimensioni con una velata (neanche poi troppo) critica alla chiusura mentale. Geniale.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6237864-nandakishore-mridula"></a></section><section><p>1,238 reviews2,207 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/260034031">January 3, 2016</a></section><div><p>At the outset... the 5 stars are <i>entirely subjective</i>. I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did.<p>I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: <i>Flatland</i> by Edwin A. Abbot and <i>An Episode of Flatland</i> by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.) </p><p>We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm.</p><p>Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic.</p><p>There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits.</p><p>Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious.</p><p>In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension).</p><p>Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story.</p><p>Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life.</p><p>Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it. </p><p>Since it is available online free from Gutenberg, I suggest everyone to give it a try.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/6237864?shelf=general-fiction">general-fiction</a> <a href="https://www.goodreads.com/review/list/6237864?shelf=mathematics">mathematics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/58774673-jon-nakapalau"></a></section><section><p>4,753 reviews635 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1741641409">December 18, 2021</a></section><div><p>I have to be honest...did not get as much from this book as I could have because of my decayed math skills (not that there was ever much there to decay). But it was a "bucket-list" book that I thought was quite inventive. Think this would be a really good STEM book for 8th graders; if they can understand the concepts here then I think they are ready for high school math. </p></div><section><ul><a href="https://www.goodreads.com/review/list/58774673?shelf=classics">classics</a> <a href="https://www.goodreads.com/review/list/58774673?shelf=math">math</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/62223917-coffee-quasars"></a></section><section><p>49 reviews5 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2139668386">November 8, 2018</a></section><div><p>3.5 stars.<p>This is a very personal rating. I think I would’ve enjoyed this far more if I’d read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew. </p><p>This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry and higher dimensions. It simply came a little too late for me.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/25867535-carol-she-s-so-novel"></a></section><section><p>773 reviews552 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3702810517">February 19, 2021</a></section><div><p>For the most part I <b>hate</b> maths, other than stats &amp; arithmetic, but I <b>loved</b> this absolutely mad book!<p>My copy didn't come with the line drawings, but they are available on <a href="http://www.geom.uiuc.edu/~banchoff/Flatland/">http://www.geom.uiuc.edu/~banchoff/Fl...</a> I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe!</p><p>I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may have made me try harder with maths - although I don't think anything could have made me &amp; trig friends!</p><p>Knocked off a star for an often patronising attitude to women. Abbott may have thought he was being funny.</p><p>I didn't.</p><blockquote>
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</blockquote></p></div><section><ul><a href="https://www.goodreads.com/review/list/25867535?shelf=classics">classics</a> <a href="https://www.goodreads.com/review/list/25867535?shelf=how-bizarre">how-bizarre</a> <a href="https://www.goodreads.com/review/list/25867535?shelf=victoriana">victoriana</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/44824883-paul"></a></section><section><p>2,306 reviews20 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1558980626">August 16, 2017</a></section><div><p>What a fantastic little thought-experiment, only really half-disguised as a story. Through his witty little parable, Abbott manages to explore the physical, mathematical, societal, philosophical and theological without once spoon-feeding his readers (OK, maybe there's a little bit of spoon-feeding in the earlier chapters).<p>It's only a shame, then, that this is without a doubt the most misogynist book I've ever read in my forty-odd years... Oh, well; I suppose nothing's perfect...</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/44824883?shelf=books-read-in-2017">books-read-in-2017</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/47208326-charles-van-buren"></a></section><section><p>1,674 reviews170 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2980347078">September 17, 2019</a></section><div><p>Very strange<p>Review of free Kindle edition<br />ASIN: B0083ZRQR4<br />124 pages</p><p>I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage about FLATLAND from THE POT THIEF WHO STUDIED EDWARD ABBEY by J. Michael Orenduff. Orenduff, a former college professor with his PhD in Mathematical Logic, a former university president and chancellor is now a full-time author known mainly for writing the Pot Thief Mystery Series. He should understand FLATLAND as a mathematician and as an author. Here is what his characters say about FLATLAND:</p><p>“All work is 3-D,” said Martin. <br />We stared at him. <br />He looked at me. “Remember that book Flatland you made me read?”<br />“I didn’t make you read it.”<br />“When a white college student visits a fourteen-year-old dropout on the rez and suggests a book, that’s the same as making me read it.”<br />“But you liked it, right?”<br />“Yeah, because it made me feel smarter than the guy who wrote it.”<br />“How so?” asked Sharice. <br />“He says the men who live in Flatland are polygons. The fewer sides a man has, the lower he is on the social scale. So triangles are the lowest level, squares are higher, pentagons higher and so on. But he also says they can see each other and interact, which is impossible. Because if they were truly two-dimensional, they would have no sides, so there would be nothing to see.”<br />“You could see them from the top,” said Susannah, “and from that vantage point, you could also see how many sides they have.”<br />“No. To see them from on top, you’d have to be above them. But there is no up in Flatland. And there is no down. There is only north, south, east and west. So they wouldn’t even know other men existed.”<br />“They would when they bumped into them,” she said. <br />He shook his head and placed two pennies on the table, sliding them until they touched. “These pennies can bump into each other because they have sides. But imagine them without sides. I don’t mean just really flat. I mean no side dimension at all. The men in Flatland can’t bump into each other because they have no sides.”<br />“Why do you keep calling them men? Aren’t there women in Flatland?”<br />“Sure. The author says they are straight lines.<br />”She shook her head. “Sheesh. I might have guessed. The women are the lowest life-forms because they have only one dimension.”<br />“Right. And he makes the same sort of mistake in describing them, saying that seen from straight-on they look like a point. But you can’t see the end of a line because that would require that it have some height. Lines have only length. You could see them from below or above but not in a world that has only two dimensions.”<br />“He says something else about women,” I noted. “Because of their lack of intelligence, they accidentally pierce and kill people without even knowing it. But ten minutes later they can’t remember it happening.”<br />Sharice stared at me. “And you made him read that?”<br />“For the math part. I knew he was smart enough not to believe the stuff about women.”<br />“He was also smart enough not to believe the stuff about math. A guy who thinks you can see something that doesn’t have sides …wait, they can’t see anything anyway. If they had eyes, they would have to be on their surface, because they have no sides. So the only direction their eyes could look would be up. But there is no up.”<br />“See,”I said, trying to move beyond my having forced a misogynist book on Martin, “You’re also smarter than the author.”</p><p>I agree with Mr. Orenduff and his fictional characters. That's my position and I'm sticking to it.</p><p>No illustrations in the free Kindle edition. However, Amazon offers the Distinguished Chiron Edition with illustrations by the author. This is supposed to be some kind of improvement of the original 1884 edition. The illustrations which I examined seem to confirm Mr. Orenduff's opinions by depicting a very flat three dimensional world instead of a two dimensional one.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/53179837-george-kaslov"></a></section><section><p>96 reviews129 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2273875786">August 19, 2018</a></section><div><p>Quite a charming allegory for the English society of the time, and boy does it show it's age. This is basically covered by everyone who reviewed this book, so I am not going to talk about that. What I noticed and I haven't seen anybody mention this yet, is the fact that at the time when this book was written Darwinian evolution has already grasped popular imagination. Just look how he talked about careful pairings between men and women to produce an equilateral triangle and then how each generation after that is achieved gets more sides until it reaches their version of perfection that is the circle. As I am aware people looked towards evolution with quite an optimism at the time and started envisioning utopias that will come to existence with careful work, selection and patience. Just look at the squares enlightenment at the prospect of 3 then 4 and as many dimensions it can possibly go. <p>Now this book, by it's writing style would get 3 stars, but no one can write something that after reading it makes me spend a night thinking about tesseracts (4 dimensional cubes) and glomes (4 dimensional spheres) and not be rewarded. Both mindfuckery and awesomeness.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/53179837?shelf=sci-fi">sci-fi</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/102547271-wee-lassie"></a></section><section><p>97 reviews50 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3220529943">March 7, 2020</a></section><div><p>This is without a doubt, the weirdest book I've ever read. Took me a little while to get into but once I did, I couldn't put the thing down. I would heartely recomend this to anyone not put off by the idea of shapes being the main characters.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/4879879-luana"></a></section><section><p>99 reviews296 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/230636861">November 16, 2011</a></section><div><p><b> Questo libricino è talmente matto e bello che dovete andare a comprarlo, e siccome so che le mie maniere dispotiche, e poco convincenti (purtroppo non ho le doti dei venditori di cose inutili che riescono a farti comprare di tutti convincendoti che siano utili)forse non vi indurranno all'acquisto, armatevi di convincitudine vostra, e andate a comprarvelo, o a rubarlo, o a prenderlo in prestito dalla biblioteca.<br />Perché? Leggete quanto segue </b><p>Se come me siete sempre stati delle perfette </p><u> schiappe in matematica e geometria </u> questo è il libro che vi illuminerà di sapienza, una volta finito di leggerlo vorrete andare dai vostri vecchi professori/maestri, sbattere loro Flatlandia in testa e urlare <b> MA CHE ACCIDENTI TI COSTAVA SPIEGARMELO COSì SEMPLICE?? </b>. Purtroppo però temo si tratti di un provvedimento anticostituzionale, dunque, anziché prendervela con vecchi pedagoghi incapaci, potrete gentilmente ringraziare Abbott che nel 1882 ha scritto questo libro non so con quali intenti (devo ancora leggere saggi/articoli/, ma era troppo forte la voglia di parlarvene), ma di sicuro aveva capito che nel 1991 sarebbe nata una asina matematica come me, quindi ha voluto far parlare figure geometriche.<p>Se <b> al contrario </b> siete divini, comprendete la matematica e la geometria, avete l'occulto dono del far di conto e del comprendere combinazioni di lati, angoli, e quant'altro, tranquilli, a Flatlandia ce n'è anche per voi. <br />Per quanto siate saccenti, dubito infatti che in uno dei vostri compiti perfetti delle superiori o esami da 30/30 con lode dell'Università, le figure geometriche abbiano mai preso a muoversi o a parlare.</p><p>Ma non è tutto qui. Se pensavate che Geometria e Politica e Filosofia potessero difficilmente incastrarsi tra loro, vi sbagliavate. Perché nella Geometria di Flatlandia la Politica sessista e razzista discrimina le Donne, gli Isosceli, gli Irregolari e assurge a razza perfetta i Circoli. Quando poi qualcuno vede o sente, anche per sua non colpa, qualcosa che non andava visto o sentito, viene fatto sparire. Che cosa assurda, si potrebbe pensare. E invece no. Succede anche da noi. Quindi tranquilli, a Flatlandia ci ritroverete molto.</p><p>Non incazzatevi troppo con Abbott se ce l'aveva con le donne.<br />Insomma, Dante ha reagito bene. Ma a volte gli approcci sessuali non vanno a finire in Commedie, sopratutto non in Divine.</p><p>La mia cartolina da Flatlandia smette qui di essere priva di raziocinio, scusate, ma sono ancora troppo esaltata.<br />Se decidete di farci un salto, tuttavia, chiedetemi l'indirizzo, perché colleziono cartoline, e da Flatlandia le ricevo ben volentieri.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/39340211-liam-o-leary"></a></section><section><p>468 reviews113 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3289686613">June 1, 2021</a></section><div><p><a href="https://www.youtube.com/watch?v=w59SbGR9xUE">My 4th best read of 2020.</a><br />An incredible, timeless book. <p>Flatland should be prescribed reading for mathematics in secondary school, because it teaches so much conceptually using basic mathematics that everyone can understand. My interpretation below might clarify what I mean.</p><p>It demonstrates the utility of mathematics is abstraction, not measurement. It's what the units 'represent' that enables and motivates quantitative calculations. By counting something we bring a perception into existence, and we count when we care about and can demonstrate that it can be counted by more than one observer. Counting is also a subject decision insofar as we attribute a value to the variable counted, and a meaning to what its counting could mean. 'What counts has been counted'... in a nutshell?</p><p>It also demonstrates that mathematical models can model social systems. The strength of mathematical models of social systems is that they avoid any obvious sociocultural bias and so enables things that would normally be socially censored to be claimed as theoretical propositions. In short, it enables discourse about stereotypes and demonstrates the possibility of universal social or moral values. I feel a lot of the social norms of Flatland still apply today, in a way.</p><p>The importance of Spaceland I think is to demonstrate how it is nearly impossible to mathematically, or universally, demonstrate evidence of realities outside of measurable reality, because they begin and end in the subjective experience of the individual. Which is used as an argument both for and against religion. I think Flatland as a theological text favours spiritual belief in its lowly depiction of atheism or 'man as God' in Pointland as a less diverse system, geometrically speaking. I guess in a way it's calling existentialists navel-gazers insofar as they take their perception to solipsistic levels that is perhaps theologically speaking commits the blasphemy of 'self-as-a-God'. This shows why Flatland is so brilliant — it can simply, concisely and thoroughly show a complex understanding of human nature — such as how theists fail to explain their conviction, and atheists fail not to reject any conviction that conflicts with their original sense of perception. Most people don't get get that far in a debate in an hour let alone in less than 100 pages! </p><p>Ok... I think I've made my point. I think most people read this as some 'goofy maths' essay, but I see it as a social commentary that somehow covers the archetypes of society and the perception of reality in less than 100 pages and is somehow still ahead of its time a century later.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/39340211?shelf=on-philosophy">on-philosophy</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/95425278-carlo-mascellani"></a></section><section><p>Author <i></i>16 books247 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/5313905320">February 3, 2023</a></section><div><p>Trama originale. Un po' lenta la prima parte, sin troppo veloce quella finale, ma non importa. Esclusione, pregiudizio, chiusura mentale e conseguente condanna di tutte e tre la fanno da padrone in questa storia godibile. Non sono in sé nuove le tematiche (basti pensare a Swift), ma il modo in cui sono trattate e la profondità con la quale vengono sviscerate le ragioni che sostengono la necessità di un fecondo relativismo culturale in luogo di una sterile dittatura assolutistica. Consigliato.</p></div><section><ul><a href="https://www.goodreads.com/review/list/95425278?shelf=narrativa">narrativa</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/14046996-roy-lotz"></a></section><section><p>Author <i></i>1 book8,092 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1035361667">June 15, 2016</a></section><div><p><blockquote>
 <i>For why should you praise, for example, the integrity of a Square who faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of his right angles? Or again, why blame a lying Isosceles, when you ought rather to deplore the incurable inequality of his sides?</i>
</blockquote>	<br />This is one of those delightful little books, so difficult to review because its charms require no toil to appreciate, and also because the book is so short you might as well read it and skip the reviews. So I’ll keep my remarks brief.<p>	The charm of the book lies in its conceit, rather than its execution. Indeed, though certainly able, Abbott is not an expert writer; nor does he pretend to be. The genius of this book is in the simple beauty of its premise: What would life be like for a square living in a two-dimensional world? </p><p>	Abbott wrings a remarkable amount out of this simple question. First, he gives us a satire of Victorian culture—perhaps the less enduring part of this work, though certainly keen and ruthless in its modest way. To me, the most interesting point Abbott makes in his satire has to do with education. The residents of Flatland spend all their time learning various methods to identify the shapes of others. For if you are living on a two-dimensional plane, telling a square from a circle is no easy matter, as they all appear to you as flat lines. And this question of shapes is important in Flatland, as one’s status depends on one’s shape, with irregulars being the lowest and circles the highest. So was Abbott implying that, when we educate our own youngsters, most of this “education” consists in merely teaching them to navigate our own social hierarchy?</p><p>But of course, the more fascinating part of the work has to do with dimensions. How would the possibility of two dimensions appear to a one-dimensional creature? Incomprehensible. And how would the prospect of three dimensions seem to a two-dimensional creature? Nonsense. To the residents of Flatland, tales of cubes and spheres appear like so much absurd metaphysics. Abbott uses this point to show how narrow is our mental framework, how completely blind we are to realities outside our everyday, commonsense world. Doing so, Abbott elevates this work from novelty to true art. For after satirizing the world we know, he gives us a glimpse of a world beyond.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/14046996?shelf=novels-novellas-short-stories">novels-novellas-short-stories</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/67934812-alice"></a></section><section><p>229 reviews43 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2151720198">January 16, 2018</a></section><div><p>5*<br /><b>A world where every character is a shape, but only seen on a side view so everybody looks like a straight line. That's why the would is called flatland because everything is in 2 dimensions.</b><p><b>THIS IS THE BEST BOOK I HAVE EVER READ!</b> It's so trippy and it's really funny too. I can't just give funny quotes though because you need to know the context from the beginning of the chapter and then the context of the chapter before that to get the humor.</p><p><b>Some quotes to give an idea of what the book is like:</b><br />"Place a penny on the middle of one of your tables in Space, and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander), the penny will then have ceased to appear oval at all and will have become, so far as you can see, a Straight Line."</p><p>"Our Women are Straight Lines. Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed, when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight Lines or Women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles, and by this name I shall refer to them in the following pages. Our Middle Class consists of Equilateral or Equal-Sided Triangles."</p><p>"The thought flashed across me that I might have before me a burglar or cutthroat, some monstrous Irregular Isosceles, who, by feigning the voice of a Circle, had obtained admission somehow into the house and was now preparing to stab me with his acute angle."</p><p>HERE'S A FREE LEGAL LINK FOR THIS BOOK SO YOU DON'T GET A VIRUS: (The author has been dead for 100 years of course it's legal.)<br /><a href="https://www.gutenberg.org/ebooks/97">https://www.gutenberg.org/ebooks/97</a></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/67934812?shelf=4-star-5-star">4-star-5-star</a> <a href="https://www.goodreads.com/review/list/67934812?shelf=5-star">5-star</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/17943496-daria"></a></section><section><p>30 reviews41 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1731246728">August 20, 2016</a></section><div><p>Unico, inclassificabile, geniale. Come dice Giorgio Manganelli nella postfazione "un capolavoro di illusionismo prospettico". Questa lettura è stata uno stimolante esercizio mentale e di immaginazione, un invito al ragionamento come non ne apprezzavo da tanto, tanto tempo. Si sente che Abbott era un insegnante, perchè il linguaggio è didattico e la struttura metodica. Tuttavia, per le sue implicazioni profonde, mi ha commossa e fatto venire la pelle d'oca. Consigliato a chiunque. Leggetelo, assaporatelo, regalatelo ai ragazzi. Questi sono libri speciali.</p></div><section><ul><a href="https://www.goodreads.com/review/list/17943496?shelf=preferiti">preferiti</a> <a href="https://www.goodreads.com/review/list/17943496?shelf=racconti-e-storie-brevi">racconti-e-storie-brevi</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6551496-jennycash"></a></section><section><p>590 reviews8 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4591690635">March 21, 2022</a></section><div><p>Published in 1884, this is meant to be a satire on Victorian culture but it's also just a math nerd's dream. Very cleverly done. The first half is the history and explanation of Flatland. The second half is the opening of the mind of A Square to understand a third or even fourth dimension.</p></div><section><ul><a href="https://www.goodreads.com/review/list/6551496?shelf=mustich">mustich</a> <a href="https://www.goodreads.com/review/list/6551496?shelf=novella">novella</a> <a href="https://www.goodreads.com/review/list/6551496?shelf=read-in-2022">read-in-2022</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/5617661-jan-maat"></a></section><section><p>1,525 reviews1,772 followers</p></section></div><section><section><p><b>Read</b></p><a href="https://www.goodreads.com/review/show/177447165">April 2, 2017</a></section><div><p>The narrator, a shape living in a two-dimensional universe, has his thought-world turned upside down went he meets a mysterious being from a three-dimensional world. 3D creature proceeds to blow 2D creature's mind by exposing him to 1 dimensional world, who however in turn refuses to accept the possibility of 4, or more D , world (s). This notion of perspective and liberation from one's own perspective gives the work a transcendent slyness and power as it offers a freedom beyond whatever the limited conceptions of the author were.<p>Comes with illustrations showing the exciting worlds of triangles and such.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/5617661?shelf=19th-century">19th-century</a> <a href="https://www.goodreads.com/review/list/5617661?shelf=british-isles">british-isles</a> <a href="https://www.goodreads.com/review/list/5617661?shelf=humour">humour</a> </ul></section></section></article></div></div>||||I|||| * Home
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 Flatland: A Romance of Many Dimensions

 Edwin A. Abbott , Banesh Hoffmann ( Introduction) , Giorgio Manganelli ( Contributor)
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 3.81
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 This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.] , a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.
 Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher .
 Genres Fiction Science Fiction Classics Mathematics Fantasy Philosophy Literature
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 96 pages, Paperback

 First published January 1, 1884

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 Edwin A. Abbott

 285 books 476 followers
 From Biography Base:

 Edwin Abbott Abbott, English schoolmaster and theologian, is best known as the author of the mathematical satire Flatland (1884).

 He was educated at the City of London School and at St John's College, Cambridge, where he took the highest honours in classics, mathematics and theology, and became fellow of his college. In 1862 he took orders. After holding masterships at King Edward's School, Birmingham, and at Clifton College, he succeeded G. F. Mortimer as headmaster of the City of London School in 1865 at the early age of twenty-six. He was Hulsean lecturer in 1876.

 He retired in 1889, and devoted himself to literary and theological pursuits. Dr. Abbott's liberal inclinations in theology were prominent both in his educational views and in his books. His Shakespearian Grammar (1870) is a permanent contribution to English philology. In 1885 he published a life of Francis Bacon. His theological writings include three anonymously published religious romances - Philochristus (1878), Onesimus (1882), and Sitanus (1906).

 More weighty contributions are the anonymous theological discussion The Kernel and the Husk (1886), Philomythus (1891), his book The Anglican Career of Cardinal Newman (1892), and his article "The Gospels" in the ninth edition of the Encyclopædia Britannica, embodying a critical view which caused considerable stir in the English theological world. He also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine Vocabulary (1905), Johannine Grammar (1906). Flatland was published in 1884.

 Sources that say he is the brother of Evelyn Abbott (1843 - 1901), who was a well-known tutor of Balliol College, Oxford, and author of a scholarly history of Greece, are in error.

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 Robert
 Author 5 books 101 followers
 March 2, 2009
 When you read this book, keep two things in mind. First, it was written back in 1880, when relativity had not yet been invented, when quantum theory was not yet discovered, when only a handful of mathematicians had the courage (yet) to challenge Euclid and imagine curved space geometries and geometries with infinite dimensionality. As such, it is an absolutely brilliant work of speculative mathematics deftly hidden in a peculiar but strangely amusing social satire.

 Second, its point, even about itself, is still as apropos today as it was then. We still do not really know what the true dimensionality of the Universe is. It seems somehow unlikely that it is just "four", even in terms of spacetime dimensions. String theory talks seriously about thousands of dimensions. Quantum theory implements very seriously infinite numbers of dimensions. And yet we are still stuck in our 3 space dimensions mentally, hardly able to visualize the 4 in which we live "properly" unless we study theoretical physics for a decade or three, and utterly unable to mentally imagine those four embedded in a veritable Hilbert's Grand Hotel of dimensions.

 Ultimately, this is a book about keeping an open mind. A really open mind -- avoiding the trap of scientific materialism and the trap of theistic idealism and the trap of any other favorite -ism you might come up with. Our entire visible space-time continuum could be nothing more than a single thin page in an infinitely thick book of similar pages, that book one of an infinite number of similar books on an infinite shelf, that shelf but one such shelf in an infinite bookcase of shelves, that bookcase but one in an infinite library of bookcases, that library but one... but by now you get the idea.

 We have a hard time opening our minds up to the enormous range of possibilities, preferring to live our lives mentally trapped in a single tiny period on just one of those pages, in pointland. We may be quite unable to actually perceive the space in which our tiny point is embedded, but our minds are capable of con ceiving it, and Abbot's lovely parable is a mind-expanding work to those who choose to read it that way.

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 Stephen
 1,517 reviews 10.8k followers
 April 27, 2012
 Take a classically styled , 19th century satire about Victorian social mores …dress it up in dimensional geometry involving anthropomorphized shapes (e.g., lines, squares, cubes, etc.)…bathe it in the sweet, scented waters of social commentary …and wrap it all around humble , open-minded Square as protagonist.

 The result is Flatland, a unique “classic” parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Since I’m recommending the book, I’m really hoping for the former, as I do not want to incur a cyber-flogging (or worse) from my fellow “goodreaders.”

 So...um...math.

 Let’s get this out of the way right now. As I alluded to in my intro, this book contains MATH. Now I hesitate to even mention that, because of the potential angst that subject causes many of my friends. I certainly don’t want people going all



 …and dashing away in a panic.

 Rest easy and increase your calm, the math is very minor. It’s really limited to discussions of geometric figures in the context of how many spatial dimensions they inhabit. Damn , that didn’t sound good either….just trust me, you won’t need a slide rule, an abacus or a lifeline to Stephen Hawking to read the book.

 However , with that said, while the math is not tricky, some of the concepts can be a little brain twisty to try and visualize. Thus, I want to caution that when you get to the section where a three dimensional “Sphere” is explaining a universe containing only one dimension to our two-dimensional protagonist, you should….IMMEDIATELY…DISCONTINUE…READING…until you have:

 1. burned some incense,
 2. poured a big tumbler of whiskey, and
 3. eaten a few “peyote” brownies, because the SHIT is about to get…



 PLOT SUMMARY:

 Written in 1884, the story is told by “A. Square,” who lives in Flatland, a world of two-dimensions, which means length and width, but no depth (just like the Kardashians). The men of Flatland are multi-sided polygons, and the more sides an individual has, the greater their social standing. On the other hand, women are all simple lines and have no voice in the governing of the society.

 Yep...the Flatlanders are chauvinists.

 The book begins with “A Square” describing his life as part of the “professional class” and providing details on daily life in Flatland. This section serves as a In reality, this is a pretty good satire on Victorian London society, the social caste system and gender inequality.

 Later, “A Square” dreams of a one-dimensional world called Lineland, where the inhabitants exist as simple points along a straight line, as there is no other width or depth. I seriously hope you have that tumbler of whiskey and some brownies close by because you are going to need them . What follows is a fun, but somewhat confusing discussions during which “A Square” tries to explain the two-dimensional world to the king of Lineland.

 Eventually, our protagonist wakes up back in Flatland, only to find that he is now being visited by a Sphere from a three-dimensional universe… whiskey…peyote…now . Sphere takes our flatlander on a mind-expanding, eye opening journey to witness the wonders and mysteries of the higher and higher dimensions (3rd, 4th, 5th, etc.). Afterwards, “A Square” returns to Flatland to teach the wonders of such “enlightened” dimensions to his fellow flatlanders, the result of which is…

 …nope…no spoilers here!

 THOUGHTS:

 As I sit here, sober and “mostly” peyote free, I think I enjoyed the “ideas and concepts” of the story more than the actual plot. The writing was fine, but nothing that struck me as particularly eloquent. However, I’ve the concepts of the story have stayed with me and I have actually become more appreciative of the material as time has gone by.

 Overall, I liked the book. I think it’s worth reading, but more for the interesting ideas and mental gymnastics that the narrative puts you through than for the simply enjoyment of the plot. Still, a worthwhile read, and since it’s actually a novella, you can get through it quickly without a large time commitment.

 3.0 stars. Recommended!
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 فؤاد
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 June 18, 2018
 حجمستان
 یادداشتی بر داستان «پختستان» نوشتۀ ادوین ابوت


 معرفی
 ادوین ابوت رمان پختستان را در سال ۱۸۸۴ در انگلستان دوران ویکتوریا منتشر کرد: دوران نظام اجتماعی و اخلاقی خشک، و ازلی‌ابدی.
 رمان از دو فصل تشکیل شده: در فصل اول راوی که مربعی از اهالی پختستان است سرزمین دو بعدی خود را توصیف می‌کند، شکل و شمایل هندسی و فیزیکی پختستان، این چگونه همدیگر را می‌بینند، همدیگر را می‌شناسند. همچنین از ساختار اجتماعی و سیاسی پختستان می‌گوید، اختلاف طبقاتی و تنش‌های بین اشکال مختلف، انقلاب‌ها و سرکوب‌ها، تبعیض‌های جنسیتی، و...
 در فصل دوم، مربع برای نخستین بار با دنیاهای جدیدی رو به رو می‌شود، دنیاهایی که حتی تصورشان برای اهالی پختستان ناممکن است و صحبت کردن از آن، جرم. اگر فصل اول انتقاد از وضع کنونی است، فصل دوم را می‌توان نوید امکان تغییر به وضعی جدید دانست، وضعی جدیدی که همه ناممکنش می‌دانند، تنها از آن جهت که هنوز یاد نگرفته‌اند به جهت درست نگاه کنند، و به محض آن که یاد بگیرند، تعجب خواهند کرد که چطور در تمام این مدت از دیدن آن عاجز بودند.



 شبی تابستانی ادوین ابوت در کتابخانه نشسته بود و به مسأله‌ی بغرنجی فکر می‌کرد. مسأله از این قرار بود که آیا می‌توان بعدی مکانی غیر از سه بعد تصور کرد که در جهتی غیر از جهاتی که می‌شناسیم امتداد داشته باشد؟ و اگر چنین جهان چهار بعدی ممکن باشد، در مقایسه با ما چه شکلی خواهد داشت؟

 در همین فکرها بود، که ناگهان اتفاق شگفت‌انگیزی افتاد. در وسط اتاق مطالعه‌اش، نقطه‌ای پدید آمد، در مقابل چشمان حیرت‌زده‌اش به سرعت رشد کرد، به جنینی بدل شد، سپس کودکی شد و نوجوانی و جوانی، و در عرض چند ثانیه، پیرمردی در مقابل او ایستاده بود.

 ادوین ابوت وحشت‌زده فریاد کشید و به قفسه‌ی کتاب‌ها چنگ زد تا خودش را از افتادن نگاه دارد و چند کتاب با سر و صدا زمین ریخت. زنش از این همه داد و فریاد هراسان به اتاق دوید و پرسید: «چه خبر شده؟»
 ابوت بی آن که بتواند حرف بزند پیرمرد را نشان داد و زن که تازه متوجه حضور پیرمرد محترم و موقری در کتابخانه‌ی شوهرش شده بود، با رعایت آداب چند کلمه‌ای با او خوش و بش کرد و رو به ابوت گفت: «ادوین، نمی‌فهمم سبب این رفتار بدون نزاکت چیست؟ از آقای محترم دعوت کن بنشیند. من هم‌اکنون چای می‌آورم.» و از اتاق خارج شد.

 پیرمرد رو کرد به ابوت، که هنوز به قفسه چنگ زده بود، و گفت: «معذرت می‌خواهم که این طور ظاهر شدم. همیشه وارد شدن به حجمستان دردسر ساز است.»

 ابوت با لکنت گفت: «شما که هستید؟»

 «ببخشید، فراموش کردم خودم را معرفی کنم. من متوازی الانسان هستم. در جهان چهار بعدی که از آن می‌آیم نام من این است.»

 «متوازی الانسان؟»

 «بله، خب این طور تصور کنید که تمام وجود شما در جهان سه بعدی، فقط یکی از اضلاع ما در جهان چهار بعدی است. همان طور که تمام وجود مربع در جهان دو بعدی، فقط یکی از پهلوهای مکعب در جهان سه بعدی است. من هم چون از انسان‌هایی دو به دو متوازی ساخته شده‌ام، متوازی الانسان نامیده می‌شوم.»

 ابوت دهانش را چنان باز کرده بود که انگار در نیمه‌راه یک ناسزا متوقف شده. پیرمرد گفت: «بیایید، بگذارید نشان‌تان دهم.» و قبل از آن که ابوت بتواند کاری بکند، دست او را گرفت و او را در جهتی، نه بالا و پایین، نه چپ و راست، نه درون و بیرون، بلکه در جهتی به کلی متفاوت بلند کرد، از جهان سه بعدی برداشت و بیرون برد. ابوت از وحشت جهان چهار بعدی یک بند فریاد می‌زد، مخصوصاً وقتی چشمش به میهمانش افتاد که به شکلی غیر قابل توصیف، از انسان‌هایی دو به دو متوازی ساخته شده بود و هر انسان با تمام سه بعدش تنها یکی از اضلاع او را تشکیل می‌داد.

 متوازی الانسان صبر کرد تا وحشت ابوت به انس بدل شود، و آن گاه برای او شرح داد که چطور در تمام این مدت جهانی چهار بعدی درست جلوی چشم تمام اهالی حجمستان بود، اما هیچ کس سر را به جهت درست نمی‌گرداند تا آن را ببیند، جهتی غیر از بالا و پایین و چپ و راست. و از ابوت خواست که دیگر اهالی حجمستان را از وجود این جهان عظیم مطلع کند، جهانی که حجمستان با تمام عظمتش در قیاس با آن، همچون نقش روی دیوار است.

 ابوت به جهان سه بعدی نگاه کرد که همچون نقش روی دیوار، بدون حجم به نظر می‌رسید. از آن جا می‌توانست داخل کتابخانه‌اش را ببیند، انگار که سقفی به کار نباشد، با آن که سقف بود، و همسرش که سینی چای به دست سرگردان در میان اتاق ایستاده بود و سر در نمی‌آورد که مردها کجا رفته‌اند. گفت: «اما هیچ کس حرف من را درک نخواهد کرد.»

 متوازی الانسان گفت: «خب چرا یک داستان نمی‌نویسی تا فهمش راحت‌تر شود؟»

 «چه داستانی؟»

 «نمی‌دانم. مثلاً داستان یک مربع ساکن جهان دو بعدی، که روزی کره‌ای از جهان سه بعدی در خانه‌اش ظاهر می‌شود و سعی می‌کند بعد سوم را برای او توضیح دهد.»

 ابوت به تمام چند صد چشم متوازی الانسان نگاه کرد، و به نشان پذیرش سر تکان داد. از همین حالا عنوان داستان را انتخاب کرده بود: «پختستان».






 این یادداشت برای سایت پلاتو نوشته شده، به این آدرس:
 لینک
 داستان-خارجی طنز فانتزی
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 Cecily
 1,095 reviews 3,838 followers
 May 26, 2022
 Imagine losing or gaining a spatial dimension

 Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute Action Lab video , explaining what a 4D ball would look like in 3D. I sent it to Apatt who likened it to And He Built a Crooked House, which in turn, reminded me of a book I’d heard of, Flatland .

 Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both.

 And He Built a Crooked House , by Robert Heinlein

 This is an early short story (1941) by a big name in sci-fi. It's about a 4D construction.

 Quintus Teal is a young architect who thinks of a house as “ a machine for living, a vital process, a live dynamic thing ”. His big idea is to use the fourth spatial dimension to “ put an eight-room house on the land now occupied by a one-room house. Like a tesseract ”. He goes on to explain a lot of geometry, and I would have been bemused if I hadn’t already seen illustrations of what a tesseract, aka hypercube, would look like.

 We’re all familiar with a cube and its net:


 Then add a dimension for a hypercube and its net:


 For more of an explanation, see video links at the end of this review.

 Teal achieves his dream “ by using strong girders and folding money ” and takes his friends, Mr and Mrs Bailey to see it.
 “ That's the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation.

 But four dimensions don’t fit easily into a three dimensional world, and things become strange. Stranger than any staircases or buildings that Escher drew.

 Flatland , by Edwin A Abbott

 About a 2D world and published in 1884.

 This short book uses geometry as an analogy for a socio-political satire of Victorian attitudes to class and social mobility; gender (in)equality; biological determinism, evolution, and eugenics; religion and the supernatural. It probably works better for those with more knowledge of and interest in the period than I have. Fortunately, my edition had lots of notes, and Abbot included several illustrations.

 The key concept is that in a two-dimensional world, a three-dimensional figure is observed as a cross-section. If it's moving, it is seen as a series of cross-sections, and can appear to appear and disappear out of nowhere.

 In the first half, the narrator, A Square, explains the very hierarchical social system of the two-dimensional Flatland. The more sides a shape has, and the more regular it is, the higher up the scale it is. “ Delicate females ” are are mere lines, “ wholly devoid of brain-power, and have neither reflection, judgement, nor forethought, and hardly any memory ”, but Abbot himself was a priest and headmaster who believed in women’s education, including at university.

 The second half has more of a story: “ my initiation into the mysteries of Space ” and “ the Gospel of Three Dimensions ”. A Square develops a theoretical and then practical understanding of other spatial dimensions. The trouble is, that’s unimaginable and heretical in Flatland.

 The progression of understanding of different spatial dimensions is well explained, with a few illustrations: A square is “ a Line of Lines ” and a sphere is “ many Circles in one ”. However, Abbott’s love of initial capital letters was a little distracting, and in part of the second section the language becomes overly Biblical and deferential (thee, thou, My Lord etc).


 Image : “The Weeping Woman”, in which “Picasso used cubist forms of fragmentation to depict the face in a series of angular planes”. ( Source )

 Clearly explained information about 2D and 4D

 To understand the fourth dimension, you need a firm grasp of the zeroth, first, second, and third dimensions. Unless you have a mathematical background, I strongly suggest you watch one or two of these videos before reading either story. I found it helpful to see the same ideas explained in slightly different ways.

 • The fourth dimension explained, via second and third, in six minutes, HERE .

 • Hypercubes explained and illustrated, without sound, in five minutes, HERE .

 • Five-minute TED animation, summarising the story of Flatland and explaining 2D and 4D, HERE .

 • Animation of the story of Flatland, narrated by Carl Sagan, in four minutes, HERE .

 • Animation of the story of Flatland, made in 1965, eleven minutes, HERE .

 • Carl Sagan explains Flatland and goes on to the fourth dimension, in nine minutes, HERE .

 The two stories

 • You can read Flatland, free, in a variety of digital formats, on Gutenberg, HERE .

 • You also can find the text of And He Built a Crooked House online.


 Image : “Mr Osborne, may I be excused? My brain is full.” (The Far Side, by Gary Larson )

 See also

 • If it’s all too much, there’s Norton Juster’s delightful picture book, The Dot and the Line , which I reviewed HERE . I included illustrations and a link to an Oscar-winning animation.

 • Malcolm wrote two short stories about very high-tech homes in The Martian Chronicles , which I reviewed HERE . Usher II is a subversive dystopian comedy that's also a tribute to Poe's Fall of the House of Usher. There Will Come Soft Rains starts off almost slapstick, but takes a very tragic turn.
 humour maths politics
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 Michael Finocchiaro
 Author 3 books 5,415 followers
 March 23, 2017
 A curious little novella about a man a two-dimensional world thinking literally out of the box. First he explains his world in which the angles you have the higher social status you have in Flatland - Circles being the highest rank. He meets someone from Lineland (one-dimensional) who is incapable of understanding Flatland and he meets Sphere from Spaceland (three dimenions) and he is able himself to comprehend the difference between "up" and "North". However, Sphere cannot extrapolate to 4+ dimensions and when the protagonist returns to Flatland and tries to explain Spaceland, he is imprisoned as a heretic.

 The text is a social criticism on the rigid thinking of hierarchal social ranks, the dogmatism and often anti-scientific bent of religion, and also has a feminist bent to it as well. A fascinating and mind-bending little book that has not aged a day after almost a century and a half.
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 Fergus, Quondam Happy Face
 934 reviews 17.6k followers
 January 19, 2023
 I will start my own brief multi-dimensional romance on this book - but dangerously, perhaps, exploring elements of my own experiences out into Spaceland that led me back, like Abbott, to my home-sweet-home of Flatland - with a caveat that I am a rather odd duck.

 Being born with ASD didn't help at all.

 We Aspies, like Supertramp, always Take the Long Way Home. The prolonged ingenuous Springtime of The Soul. And the soul rejoices in the bright laughter of - as Mallarme says - the Jeu Suprême - as all reality curls up comfortably at its Ironic Edges.

 But the simplicity of higher mathematics in high school soon became in my eyes an overgrown jungle. It was, to me, unworkable, because we Aspies come from a psychological Flatland: to the world, Dullsville.

 So my apologies at the outset to my GR friends who were math majors.

 No, I took this book at a personal EXISTENTIAL level! So please: take this review very much with a grain of salt!
 ***

 As you probably know, I like to often change the subject. My adventures in Spaceland taught me that when my interlocutors dug deep, their interjections were to me like speeding bullets. I dodged them: I knew they would spell my mediocre death-in-life: I didn't want to go there.

 Didn't even want to go to Spaceland - no - but the philosophical skills my teenaged reading skills gave me PUSHED me into a sophisticated outer spaceland.

 That sophistication fed my nascent knowledge.

 So when I went to college, I explored Spaceland heuristically. And of course - that path leads us into the Den of the Minotaur.

 Yikes.

 Anyway, after King Minos' foul beast had thoroughly chewed me up and expectorated me... alone, I found myself back home in Flatland!
 ***

 An awakening refused leads back to simplicity, as Abbott found -

 And it's where I am now writing this:

 In "a state of simplicity (which cost me) not less than EVERYTHING."

 And won me Flatland forever...

 Flatland - AKA God's Peace - a patient, silent witness to an Ugly World.
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 Ahmad Sharabiani
 9,568 reviews 55.6k followers
 August 18, 2020
 Flatland: A Romance of Many Dimensions, Edwin A. Abbott

 Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley & Co. of London.

 Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.

 The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides.

 The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions.

 The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium.

 On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points".

 These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so.

 In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. ...

 عنوانها: «پـَختِستان»؛ «افسانه ی دو بعدی»؛ «سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه»؛ نویسنده: ادوین ابوت؛ تاریخ نخستین خوانش سال 1997میلادی

 عنوان: پـَختِستان؛ نویسنده: ادوین ابوت؛ بازنگری و مقدمه از: یانش هوفمان؛ مترجم منوچهر انور؛ تهران، روشنگران و مطالهات زنان، 1375؛ در 195ص؛ شابک 9645512433؛ چاپ دیگر تهران، کارنامه، 1388؛ در 172ص؛ شابک 9789644310799؛ چاپ دوم 1393؛ موضوع بعد چهارم - از نویسندگان بریتانیایی - سده 19م

 عنوان: افسانه ی دو بعدی؛ نویسنده: ادوین ابوت؛ مترجم: جلال جامعی؛ شیراز، لورا، 1387، در 192ص؛ شابک 9789648851366؛

 عنوان: سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه؛ نویسنده: یک مربع (ادوین ابوت)؛ برگردان: آهنگ کوثر؛ شیراز، نوید شیراز، 1397؛ شابک 9786001927768؛

 پَختستان: رمان بُعدهای بسیار، رمان کوتاهی از الهی‌دان و استاد دانشگاه انگلیسی، «ادوین ابوت» است، که نخستین‌بار آن‌را در سال 1884میلادی با نام مستعار نویسندگی «یک مربع» منتشر کردند؛ در این کتاب از دنیای خیالی «دوبُعدی پَختستان»، برای نشان دادن فرهنگ سلسله‌ مراتبی «انگلستان» دوره ی «ویکتوریا» استفاده شده‌ است.؛ این نگاره بیشتر یک تمثیل عبرت‌ آموز است، تا یک داستان؛ و نیز نقدی تند و گزنده، از ساختار اجتماعی و سیاسی جامعه ی روزگار خود، و ارزش‌ها، و روابط انسانی در آن است؛ «ابوت» برای اینکه نشان دهد، انسان‌ها در این دنیا از نظر افق دانش و بینش، در چه قفس تنگی گرفتار هستند، از جهانی خیالی با باشندگانی دو بُعدی سود برده است.؛ این باشندگان دارای شکل‌های هندسی «مثلث»، «مربع»، «پنج‌بر»، «شش‌بر» و «بالا و بالاتر» تا «دایره‌» هستند، که ناگزیر در سطح می‌زیند.؛ نویسنده و راوی داستان، یک مربع است، که این دنیا را شرح می‌دهد.؛ «پَختستان» در زمان انتشار خود، مورد توجه قرار نگرفت، پس از انتشار نظریه ی نسبیت عام انیشتین، این کتاب دوباره به یاد همگان افتاد، چرا که در آن به مفهوم «بُعد چهارم» نیز اشاره شده بود.؛ در مقاله‌ ای تحت عنوان «اقلیدس، نیوتن و انیشتین»، که در شمارهٔ دوازدهم ماه فوریه سال 1920میلادی مجله ی «نیچر» منتشر شد، از این کتاب نام برده شد، و «ابوت» را از یک نظر همچون پیامبری دانست، که در آن زمان به درک اهمیت زمان، در شرح یک پدیده، آگاه بوده‌ است.؛ انتشارات «هارپرکالینز» در سال 1983میلادی، نسخه‌ ای از این کتاب را با پیشگفتار «آیزاک آسیموف» منتشر کرد.؛ عنوان «پَختستان» را، مترجم نخست این کتاب، جناب «منوچهر انور»، برای آن برگزیدند، که از واژه ی فارسی «پَخت» به معنای «پهن» و بی‌برجستگی، و پسوند ستان تشکیل شده‌ است.؛

 تاریخ بهنگام رسانی 27/05/1399هجری خورشیدی؛ ا. شربیانی
 19th-century british classics
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 Dan
 87 reviews
 January 4, 2009
 This book should not be read in hopes of finding an entertaining story. As a novel, it's terrible. It's plot (if you can call it that) is simple and contrived. But, it wasn't written as a novel.

 Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them.

 The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear.

 In the course of the explanation, the book also describes "Lineland," a one dimensional world where the inhabitants would also have trouble understanding dimensions above their own.

 This book's excellence lies in the way it takes a complex topic and breaks it down into a metaphor that can be more easily understood. It argues quite well that if there is a fourth dimension, it probably isn't "time."

 This book isn't one that will win wide-spread acclaim from the general reading community. For those of us who enjoy higher math, though, it's excellent.
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 Apatt
 507 reviews 752 followers
 April 6, 2017
 “I used to be a renegade, I used to fool around
 But I couldn't take the punishment and had to settle down
 Now I'm playing it real straight, and yes, I cut my hair
 You might think I'm crazy, but I don't even care
 Because I can tell what's going on
 It's hip to be square”
 Huey Lewis And The News - Hip To Be Square

 According to IMDB, several film adaptations have been made of Flatland , but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can’t imagine a more appropriate theme song than the above Huey Lewis And The News number.

 Flatland is set in a two-dimensional world and narrated in the first person by a square (or “A Square” as appears on the original edition’s book cover). In the first half of the book Square gives us a tour of his world where women are straight lines and, if you are symmetrical, the more sides you have the better. This means that circles are the elite of this society because they are really polygons with zillions of super tiny sides. Irregular polygons are abominations and isosceles are plebeians.

 Special laws are applied to women because they are capable of accidentally stabbing people to death due to their pointiness. Use of colours is banned because they can be used as disguises. How these geometric persons move around without legs is deliberately left unexplained (with a bit of "lampshading"). The second half of the book tells the remarkable story of Square’s adventures in lands of different dimensions, one, three and even zero (no trip to the fourth dimension, though; no time , probably). Guided by an enigmatic Sphere who seems to have popped up out of nowhere (and who Square initially mistook to be a circle), these trips to other planes of existence enables Square to not only think outside the box but to introduce him to the existence of boxes. This was a steep learning curve for him but he adapts like a champ and becomes a more rounded individual because of it.

 Flatland is a very odd novella it is part allegory, part satire, part geometry lessons, part spec fic. I generally avoid reading geometry books because they are full of problems I don’t want to consider (screw the hypotenuse, man!). However, for Flatland I don’t mind making an exception, for once I find the flat characters entirely acceptable and even find the more apparently rounded character to be arrogant and clearly obtuse in their outlook, if not in appearance. The satirical look at the class system makes this all too real issue painfully acute. One thing that blows my mind a bit is that prior to reading the book I visualized it as a story of different geometric shapes moving around going about their business. However, the denizens of the Flatland cannot actually see these different shapes. As the Square (or Edwin Abbott Abbott) mentions early in the book you have to imagine looking at these shapes with your line of sight on the same level as their surface. Mr. Abbott explains it very clearly as follows:

 “Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.”


 So all they really ever see is straight lines of different lengths, however, they can distinguish the different geometrical shapes by hearing, by touch (done by the working class only), and by sight with the aid of fog for estimating depths (different angles appear to fade differently into fog). In the one-dimensional Lineland everybody looks like a point and sideways movement is impossible; as for the zero-dimensional Pointland, there is only one denizen and he is weird!

 I really enjoyed Flatland , it is bizarre and thought-provoking; it definitely gave me a new perspective on life. The treatment of women may seem a little sexist but E.A. Abbott is perhaps satirizing sexism rather than perpetuating it. I definitely recommend you read Flatland before you flatline.


 Notes:
 • Audiobook credit: Wonderfully read for Librovox (i.e. free) by Ruth Golding. (link)

 • There are quite a few diagrams scattered over the book, drawn by AbbottX2 himself, they illustrate the geometrical concepts nicely. These should be in all editions as they are intrinsic to the story.

 • There is one error in the book where Square mentions a cellar: “So I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned.” . You can't have a bloody cellar if you only have two dimensions and you can’t “fall through” anything.

 • Another error (I think) is the existence of cupboards in Flatland. If there is no depth or verticality you can't have cupboards!

 • The 3D world is called Spaceland, it is not our world. Their most popular singer is probably Britney Sphere. (͡° ͜ʖ ͡°)

 • I initially thought this book was a collaboration between two abbots.

 Quotes:
 Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name.

 In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself. Such at least is the painful teaching of my experience.

 Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life?

 You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions—how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration?

 Hipster Square
 classics
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 Duane
 828 reviews 388 followers
 June 9, 2017
 I give it an extra star for it's originality, it's uniqueness. The concept was genius, Abbott was probably a math genius himself. However, as a work of literature it does not hold up well. It has a shadowy similarity to Gulliver's Travels , but falls well short of that Swift classic.
 2017-book-challenge english-calssics rated-books
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 Kinga
 475 reviews 2,123 followers
 March 19, 2015
 This was one crazy, opium fuelled, brilliant book about geometry and different dimensions and I am going to explain it the best way I can but Edwin A Abbott does it so much better.

 Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off are women who are not even figures; they are just straight lines. They have few rights and no one actually takes their intellect seriously. On the other hand they are dangerous because being straight lines they can easily pierce any figure. A woman from behind looks just like a dot, you might miss her until it’s to late and she has stabbed you. Different parts of Flatland developed different strategies for dealing with the danger, from not allowing women to leave their houses, to forcing them to constantly wiggle their bums, so they are visible from far. They should also sound a ‘peace-cry’ when out and about, in case anyone missed the wiggling bum. Seriously children, don’t do drugs. It makes you write things like that.

 The second part of the book gets more interesting as it delves deeper into the concept of dimensions. As I said, our hero lives in a two-dimension reality. Try to imagine such a world. You probably see it as a piece of paper with various figures drawn on it. Of course, that’s how a creature from 3D world would see it. You’re looking at it from above, i.e from the third dimension. If a 2D world was your entire reality you would only be able to see lines and dots. Your eyes would be on the same level as the figures and you would see everything in one dimension and infer the second dimension because you can move in it and you have learnt it through experience.

 The same way we can’t actually see the third dimension but we can tell it’s there. We know we can move in three dimensions and we know about perspective, light, shadow, etc. It is easier for us to understand a two-dimension reality than it is to imagine a four-dimension one. We can see it perfectly when our Square visits a one dimensional land and he laughs at it and tries to explain to the King that there is more to life than just looking at a dot in front of you. There is another dimension where there are not only dots but lines as well. The King of course laughs him off. Yet, when Square is confronted by Sphere who tells him about the third dimension and shows him ‘tricks’ that the third dimension allows him to do, Square is just as incredulous.

 Even though the mathematics tells him there must be another dimension (and another, and another), he can’t quite believe it until Sphere shows him a little bit of a 3D world. Then he is a convert, and he quickly assumes there must be more dimensions. Fourth and fifth and ad infinitum. I think while reading this I got as close as I would ever get to understanding and imagining a 4D world. If in a 3D world we can see the insides of everything of a 2D world, then I suppose a in 4D world we would be able to actually SEE all three dimensions, all the insides of everything. My brains hurts. Am I making any sense? I thought I could see it but now it’s been a week after I finished reading the book and had those vivid dreams about the fourth dimension. The vision pales. I still believe in it but I can no longer grasp it. Just like the poor Square, back in his 2D-Land, thrown in prison for preaching revolution, still believes in the third dimension, but can no longer conjure the image of a Sphere in his head. Sometimes he feels he can almost see it again for half a second, and then it’s gone.
 gutenberg-project-project pub-1880s
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 Djali ❀
 112 reviews 93 followers
 April 7, 2022
 5 per la seconda parte e 3 per la prima, che a tratti risulta un po’ noiosa essendo una sorta di elenco delle regole di Flatlandia.
 In ogni caso, geniale!
 biblioteca classici con-recensione
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 Julie Demar
 5 reviews 4,020 followers
 October 6, 2016
 Un racconto fantastico a più dimensioni con una velata (neanche poi troppo) critica alla chiusura mentale. Geniale.
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 Nandakishore Mridula
 1,238 reviews 2,207 followers
 January 3, 2016
 At the outset... the 5 stars are entirely subjective . I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did.

 I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland by Edwin A. Abbot and An Episode of Flatland by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.)

 We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm.

 Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic.

 There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits.

 Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious.

 In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension).

 Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story.

 Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life.

 Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it.

 Since it is available online free from Gutenberg, I suggest everyone to give it a try.
 general-fiction mathematics
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 Jon Nakapalau
 4,753 reviews 635 followers
 December 18, 2021
 I have to be honest...did not get as much from this book as I could have because of my decayed math skills (not that there was ever much there to decay). But it was a "bucket-list" book that I thought was quite inventive. Think this would be a really good STEM book for 8th graders; if they can understand the concepts here then I think they are ready for high school math.
 classics math
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 Coffee&Quasars
 49 reviews 5 followers
 November 8, 2018
 3.5 stars.

 This is a very personal rating. I think I would’ve enjoyed this far more if I’d read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew.

 This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry and higher dimensions. It simply came a little too late for me.
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 Carol She's So Novel꧁꧂
 773 reviews 552 followers
 February 19, 2021
 For the most part I hate maths, other than stats & arithmetic, but I loved this absolutely mad book!

 My copy didn't come with the line drawings, but they are available on http://www.geom.uiuc.edu/~banchoff/Fl... I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe!

 I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may have made me try harder with maths - although I don't think anything could have made me & trig friends!

 Knocked off a star for an often patronising attitude to women. Abbott may have thought he was being funny.

 I didn't.

 classics how-bizarre victoriana
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 Paul
 2,306 reviews 20 followers
 August 16, 2017
 What a fantastic little thought-experiment, only really half-disguised as a story. Through his witty little parable, Abbott manages to explore the physical, mathematical, societal, philosophical and theological without once spoon-feeding his readers (OK, maybe there's a little bit of spoon-feeding in the earlier chapters).

 It's only a shame, then, that this is without a doubt the most misogynist book I've ever read in my forty-odd years... Oh, well; I suppose nothing's perfect...
 books-read-in-2017
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 Charles van Buren
 1,674 reviews 170 followers
 September 17, 2019
 Very strange

 Review of free Kindle edition
 ASIN: B0083ZRQR4
 124 pages

 I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage about FLATLAND from THE POT THIEF WHO STUDIED EDWARD ABBEY by J. Michael Orenduff. Orenduff, a former college professor with his PhD in Mathematical Logic, a former university president and chancellor is now a full-time author known mainly for writing the Pot Thief Mystery Series. He should understand FLATLAND as a mathematician and as an author. Here is what his characters say about FLATLAND:

 “All work is 3-D,” said Martin.
 We stared at him.
 He looked at me. “Remember that book Flatland you made me read?”
 “I didn’t make you read it.”
 “When a white college student visits a fourteen-year-old dropout on the rez and suggests a book, that’s the same as making me read it.”
 “But you liked it, right?”
 “Yeah, because it made me feel smarter than the guy who wrote it.”
 “How so?” asked Sharice.
 “He says the men who live in Flatland are polygons. The fewer sides a man has, the lower he is on the social scale. So triangles are the lowest level, squares are higher, pentagons higher and so on. But he also says they can see each other and interact, which is impossible. Because if they were truly two-dimensional, they would have no sides, so there would be nothing to see.”
 “You could see them from the top,” said Susannah, “and from that vantage point, you could also see how many sides they have.”
 “No. To see them from on top, you’d have to be above them. But there is no up in Flatland. And there is no down. There is only north, south, east and west. So they wouldn’t even know other men existed.”
 “They would when they bumped into them,” she said.
 He shook his head and placed two pennies on the table, sliding them until they touched. “These pennies can bump into each other because they have sides. But imagine them without sides. I don’t mean just really flat. I mean no side dimension at all. The men in Flatland can’t bump into each other because they have no sides.”
 “Why do you keep calling them men? Aren’t there women in Flatland?”
 “Sure. The author says they are straight lines.
 ”She shook her head. “Sheesh. I might have guessed. The women are the lowest life-forms because they have only one dimension.”
 “Right. And he makes the same sort of mistake in describing them, saying that seen from straight-on they look like a point. But you can’t see the end of a line because that would require that it have some height. Lines have only length. You could see them from below or above but not in a world that has only two dimensions.”
 “He says something else about women,” I noted. “Because of their lack of intelligence, they accidentally pierce and kill people without even knowing it. But ten minutes later they can’t remember it happening.”
 Sharice stared at me. “And you made him read that?”
 “For the math part. I knew he was smart enough not to believe the stuff about women.”
 “He was also smart enough not to believe the stuff about math. A guy who thinks you can see something that doesn’t have sides …wait, they can’t see anything anyway. If they had eyes, they would have to be on their surface, because they have no sides. So the only direction their eyes could look would be up. But there is no up.”
 “See,”I said, trying to move beyond my having forced a misogynist book on Martin, “You’re also smarter than the author.”

 I agree with Mr. Orenduff and his fictional characters. That's my position and I'm sticking to it.

 No illustrations in the free Kindle edition. However, Amazon offers the Distinguished Chiron Edition with illustrations by the author. This is supposed to be some kind of improvement of the original 1884 edition. The illustrations which I examined seem to confirm Mr. Orenduff's opinions by depicting a very flat three dimensional world instead of a two dimensional one.
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 George Kaslov
 96 reviews 129 followers
 August 19, 2018
 Quite a charming allegory for the English society of the time, and boy does it show it's age. This is basically covered by everyone who reviewed this book, so I am not going to talk about that. What I noticed and I haven't seen anybody mention this yet, is the fact that at the time when this book was written Darwinian evolution has already grasped popular imagination. Just look how he talked about careful pairings between men and women to produce an equilateral triangle and then how each generation after that is achieved gets more sides until it reaches their version of perfection that is the circle. As I am aware people looked towards evolution with quite an optimism at the time and started envisioning utopias that will come to existence with careful work, selection and patience. Just look at the squares enlightenment at the prospect of 3 then 4 and as many dimensions it can possibly go.

 Now this book, by it's writing style would get 3 stars, but no one can write something that after reading it makes me spend a night thinking about tesseracts (4 dimensional cubes) and glomes (4 dimensional spheres) and not be rewarded. Both mindfuckery and awesomeness.
 sci-fi
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 Wee Lassie
 97 reviews 50 followers
 March 7, 2020
 This is without a doubt, the weirdest book I've ever read. Took me a little while to get into but once I did, I couldn't put the thing down. I would heartely recomend this to anyone not put off by the idea of shapes being the main characters.
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 Luana
 99 reviews 296 followers
 November 16, 2011
 Questo libricino è talmente matto e bello che dovete andare a comprarlo, e siccome so che le mie maniere dispotiche, e poco convincenti (purtroppo non ho le doti dei venditori di cose inutili che riescono a farti comprare di tutti convincendoti che siano utili)forse non vi indurranno all'acquisto, armatevi di convincitudine vostra, e andate a comprarvelo, o a rubarlo, o a prenderlo in prestito dalla biblioteca.
 Perché? Leggete quanto segue

 Se come me siete sempre stati delle perfette schiappe in matematica e geometria questo è il libro che vi illuminerà di sapienza, una volta finito di leggerlo vorrete andare dai vostri vecchi professori/maestri, sbattere loro Flatlandia in testa e urlare MA CHE ACCIDENTI TI COSTAVA SPIEGARMELO COSì SEMPLICE?? . Purtroppo però temo si tratti di un provvedimento anticostituzionale, dunque, anziché prendervela con vecchi pedagoghi incapaci, potrete gentilmente ringraziare Abbott che nel 1882 ha scritto questo libro non so con quali intenti (devo ancora leggere saggi/articoli/, ma era troppo forte la voglia di parlarvene), ma di sicuro aveva capito che nel 1991 sarebbe nata una asina matematica come me, quindi ha voluto far parlare figure geometriche.

 Se al contrario siete divini, comprendete la matematica e la geometria, avete l'occulto dono del far di conto e del comprendere combinazioni di lati, angoli, e quant'altro, tranquilli, a Flatlandia ce n'è anche per voi.
 Per quanto siate saccenti, dubito infatti che in uno dei vostri compiti perfetti delle superiori o esami da 30/30 con lode dell'Università, le figure geometriche abbiano mai preso a muoversi o a parlare.

 Ma non è tutto qui. Se pensavate che Geometria e Politica e Filosofia potessero difficilmente incastrarsi tra loro, vi sbagliavate. Perché nella Geometria di Flatlandia la Politica sessista e razzista discrimina le Donne, gli Isosceli, gli Irregolari e assurge a razza perfetta i Circoli. Quando poi qualcuno vede o sente, anche per sua non colpa, qualcosa che non andava visto o sentito, viene fatto sparire. Che cosa assurda, si potrebbe pensare. E invece no. Succede anche da noi. Quindi tranquilli, a Flatlandia ci ritroverete molto.

 Non incazzatevi troppo con Abbott se ce l'aveva con le donne.
 Insomma, Dante ha reagito bene. Ma a volte gli approcci sessuali non vanno a finire in Commedie, sopratutto non in Divine.

 La mia cartolina da Flatlandia smette qui di essere priva di raziocinio, scusate, ma sono ancora troppo esaltata.
 Se decidete di farci un salto, tuttavia, chiedetemi l'indirizzo, perché colleziono cartoline, e da Flatlandia le ricevo ben volentieri.
 27 likes
 4 comments
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 Matteo Fumagalli
 Author 1 book 7,599 followers
 September 10, 2017
 Videorecensione: https://www.youtube.com/watch?v=i-UCR...
 adelphi letteratura-inglese
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 Liam O'Leary
 468 reviews 113 followers
 June 1, 2021
 My 4th best read of 2020.
 An incredible, timeless book.

 Flatland should be prescribed reading for mathematics in secondary school, because it teaches so much conceptually using basic mathematics that everyone can understand. My interpretation below might clarify what I mean.

 It demonstrates the utility of mathematics is abstraction, not measurement. It's what the units 'represent' that enables and motivates quantitative calculations. By counting something we bring a perception into existence, and we count when we care about and can demonstrate that it can be counted by more than one observer. Counting is also a subject decision insofar as we attribute a value to the variable counted, and a meaning to what its counting could mean. 'What counts has been counted'... in a nutshell?

 It also demonstrates that mathematical models can model social systems. The strength of mathematical models of social systems is that they avoid any obvious sociocultural bias and so enables things that would normally be socially censored to be claimed as theoretical propositions. In short, it enables discourse about stereotypes and demonstrates the possibility of universal social or moral values. I feel a lot of the social norms of Flatland still apply today, in a way.

 The importance of Spaceland I think is to demonstrate how it is nearly impossible to mathematically, or universally, demonstrate evidence of realities outside of measurable reality, because they begin and end in the subjective experience of the individual. Which is used as an argument both for and against religion. I think Flatland as a theological text favours spiritual belief in its lowly depiction of atheism or 'man as God' in Pointland as a less diverse system, geometrically speaking. I guess in a way it's calling existentialists navel-gazers insofar as they take their perception to solipsistic levels that is perhaps theologically speaking commits the blasphemy of 'self-as-a-God'. This shows why Flatland is so brilliant — it can simply, concisely and thoroughly show a complex understanding of human nature — such as how theists fail to explain their conviction, and atheists fail not to reject any conviction that conflicts with their original sense of perception. Most people don't get get that far in a debate in an hour let alone in less than 100 pages!

 Ok... I think I've made my point. I think most people read this as some 'goofy maths' essay, but I see it as a social commentary that somehow covers the archetypes of society and the perception of reality in less than 100 pages and is somehow still ahead of its time a century later.
 on-philosophy
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 Carlo Mascellani
 Author 16 books 247 followers
 February 3, 2023
 Trama originale. Un po' lenta la prima parte, sin troppo veloce quella finale, ma non importa. Esclusione, pregiudizio, chiusura mentale e conseguente condanna di tutte e tre la fanno da padrone in questa storia godibile. Non sono in sé nuove le tematiche (basti pensare a Swift), ma il modo in cui sono trattate e la profondità con la quale vengono sviscerate le ragioni che sostengono la necessità di un fecondo relativismo culturale in luogo di una sterile dittatura assolutistica. Consigliato.
 narrativa
 25 likes
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 Roy Lotz
 Author 1 book 8,092 followers
 June 15, 2016
 For why should you praise, for example, the integrity of a Square who faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of his right angles? Or again, why blame a lying Isosceles, when you ought rather to deplore the incurable inequality of his sides?

 This is one of those delightful little books, so difficult to review because its charms require no toil to appreciate, and also because the book is so short you might as well read it and skip the reviews. So I’ll keep my remarks brief.

 The charm of the book lies in its conceit, rather than its execution. Indeed, though certainly able, Abbott is not an expert writer; nor does he pretend to be. The genius of this book is in the simple beauty of its premise: What would life be like for a square living in a two-dimensional world?

 Abbott wrings a remarkable amount out of this simple question. First, he gives us a satire of Victorian culture—perhaps the less enduring part of this work, though certainly keen and ruthless in its modest way. To me, the most interesting point Abbott makes in his satire has to do with education. The residents of Flatland spend all their time learning various methods to identify the shapes of others. For if you are living on a two-dimensional plane, telling a square from a circle is no easy matter, as they all appear to you as flat lines. And this question of shapes is important in Flatland, as one’s status depends on one’s shape, with irregulars being the lowest and circles the highest. So was Abbott implying that, when we educate our own youngsters, most of this “education” consists in merely teaching them to navigate our own social hierarchy?

 But of course, the more fascinating part of the work has to do with dimensions. How would the possibility of two dimensions appear to a one-dimensional creature? Incomprehensible. And how would the prospect of three dimensions seem to a two-dimensional creature? Nonsense. To the residents of Flatland, tales of cubes and spheres appear like so much absurd metaphysics. Abbott uses this point to show how narrow is our mental framework, how completely blind we are to realities outside our everyday, commonsense world. Doing so, Abbott elevates this work from novelty to true art. For after satirizing the world we know, he gives us a glimpse of a world beyond.
 novels-novellas-short-stories
 25 likes
 9 comments
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 Alice
 229 reviews 43 followers
 January 16, 2018
 5*
 A world where every character is a shape, but only seen on a side view so everybody looks like a straight line. That's why the would is called flatland because everything is in 2 dimensions.

 THIS IS THE BEST BOOK I HAVE EVER READ! It's so trippy and it's really funny too. I can't just give funny quotes though because you need to know the context from the beginning of the chapter and then the context of the chapter before that to get the humor.

 Some quotes to give an idea of what the book is like:
 "Place a penny on the middle of one of your tables in Space, and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander), the penny will then have ceased to appear oval at all and will have become, so far as you can see, a Straight Line."

 "Our Women are Straight Lines. Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed, when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight Lines or Women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles, and by this name I shall refer to them in the following pages. Our Middle Class consists of Equilateral or Equal-Sided Triangles."

 "The thought flashed across me that I might have before me a burglar or cutthroat, some monstrous Irregular Isosceles, who, by feigning the voice of a Circle, had obtained admission somehow into the house and was now preparing to stab me with his acute angle."

 HERE'S A FREE LEGAL LINK FOR THIS BOOK SO YOU DON'T GET A VIRUS: (The author has been dead for 100 years of course it's legal.)
 https://www.gutenberg.org/ebooks/97
 4-star-5-star 5-star
 25 likes
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 Daria
 30 reviews 41 followers
 August 20, 2016
 Unico, inclassificabile, geniale. Come dice Giorgio Manganelli nella postfazione "un capolavoro di illusionismo prospettico". Questa lettura è stata uno stimolante esercizio mentale e di immaginazione, un invito al ragionamento come non ne apprezzavo da tanto, tanto tempo. Si sente che Abbott era un insegnante, perchè il linguaggio è didattico e la struttura metodica. Tuttavia, per le sue implicazioni profonde, mi ha commossa e fatto venire la pelle d'oca. Consigliato a chiunque. Leggetelo, assaporatelo, regalatelo ai ragazzi. Questi sono libri speciali.
 preferiti racconti-e-storie-brevi
 25 likes
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 JennyCash
 590 reviews 8 followers
 March 21, 2022
 Published in 1884, this is meant to be a satire on Victorian culture but it's also just a math nerd's dream. Very cleverly done. The first half is the history and explanation of Flatland. The second half is the opening of the mind of A Square to understand a third or even fourth dimension.
 mustich novella read-in-2022
 24 likes
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 Jan-Maat
 1,525 reviews 1,772 followers
 Read
 April 2, 2017
 The narrator, a shape living in a two-dimensional universe, has his thought-world turned upside down went he meets a mysterious being from a three-dimensional world. 3D creature proceeds to blow 2D creature's mind by exposing him indeed gender apparently is trans-dimensional to 1 dimensional world, who however in turn refuses to accept the possibility of 4, or more D , world (s). This notion of perspective and liberation from one's own perspective gives the work a transcendent slyness and power as it offers a freedom beyond whatever the limited conceptions of the author were.

 Comes with illustrations showing the exciting worlds of triangles and such.
 19th-century british-isles humour
 ...more
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Author  5 books101 followers     March 2, 2009   When you read this book, keep two things in mind. First, it was written back in 1880, when relativity had not yet been invented, when quantum theory was not yet discovered, when only a handful of mathematicians had the courage (yet) to challenge Euclid and imagine curved space geometries and geometries with infinite dimensionality. As such, it is an absolutely brilliant work of speculative mathematics deftly hidden in a peculiar but strangely amusing social satire.Second, its point, even about itself, is still as apropos today as it was then. We still do not really know what the true dimensionality of the Universe is. It seems somehow unlikely that it is just "four", even in terms of spacetime dimensions. String theory talks seriously about thousands of dimensions. Quantum theory implements very seriously infinite numbers of dimensions. And yet we are still stuck in our 3 space dimensions mentally, hardly able to visualize the 4 in which we live "properly" unless we study theoretical physics for a decade or three, and utterly unable to mentally imagine those four embedded in a veritable Hilbert's Grand Hotel of dimensions. Ultimately, this is a book about keeping an open mind. A really open mind -- avoiding the trap of scientific materialism and the trap of theistic idealism and the trap of any other favorite -ism you might come up with. Our entire visible space-time continuum could be nothing more than a single thin page in an infinitely thick book of similar pages, that book one of an infinite number of similar books on an infinite shelf, that shelf but one such shelf in an infinite bookcase of shelves, that bookcase but one in an infinite library of bookcases, that library but one... but by now you get the idea. We have a hard time opening our minds up to the enormous range of possibilities, preferring to live our lives mentally trapped in a single tiny period on just one of those pages, in pointland. We may be quite unable to actually perceive the space in which our tiny point is embedded, but our minds are capable of conceiving it, and Abbot's lovely parable is a mind-expanding work to those who choose to read it that way. rgb                   1,517 reviews10.8k followers     April 27, 2012   Take a classically styled, 19th century satire about Victorian social mores…dress it up in dimensional geometry involving anthropomorphized shapes (e.g., lines, squares, cubes, etc.)…bathe it in the sweet, scented waters of social commentary…and wrap it all around humble, open-minded Square as protagonist. The result is Flatland, a unique “classic” parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Since I’m recommending the book, I’m really hoping for the former, as I do not want to incur a cyber-flogging (or worse) from my fellow “goodreaders.”  So...um...math.  Let’s get this out of the way right now. As I alluded to in my intro, this book contains MATH. Now I hesitate to even mention that, because of the potential angst that subject causes many of my friends. I certainly don’t want people going all  
 
  
 
  
 
 …and dashing away in a panic.  Rest easy and increase your calm, the math is very minor. It’s really limited to discussions of geometric figures in the context of how many spatial dimensions they inhabit. Damn, that didn’t sound good either….just trust me, you won’t need a slide rule, an abacus or a lifeline to Stephen Hawking to read the book.   However, with that said, while the math is not tricky, some of the concepts can be a little brain twisty to try and visualize. Thus, I want to caution that when you get to the section where a three dimensional “Sphere” is explaining a universe containing only one dimension to our two-dimensional protagonist, you should….IMMEDIATELY…DISCONTINUE…READING…until you have:  1. burned some incense,  2. poured a big tumbler of whiskey, and  3. eaten a few “peyote” brownies,  because the SHIT is about to get… 
 
    PLOT SUMMARY:  Written in 1884, the story is told by “A. Square,” who lives in Flatland, a world of two-dimensions, which means length and width, but no depth (just like the Kardashians). The men of Flatland are multi-sided polygons, and the more sides an individual has, the greater their social standing. On the other hand, women are all simple lines and have no voice in the governing of the society.  Yep...the Flatlanders are chauvinists.  The book begins with “A Square” describing his life as part of the “professional class” and providing details on daily life in Flatland. This section serves as a In reality, this is a pretty good satire on Victorian London society, the social caste system and gender inequality.  Later, “A Square” dreams of a one-dimensional world called Lineland, where the inhabitants exist as simple points along a straight line, as there is no other width or depth. I seriously hope you have that tumbler of whiskey and some brownies close by because you are going to need them. What follows is a fun, but somewhat confusing discussions during which “A Square” tries to explain the two-dimensional world to the king of Lineland.  Eventually, our protagonist wakes up back in Flatland, only to find that he is now being visited by a Sphere from a three-dimensional universe…whiskey…peyote…now. Sphere takes our flatlander on a mind-expanding, eye opening journey to witness the wonders and mysteries of the higher and higher dimensions (3rd, 4th, 5th, etc.). Afterwards, “A Square” returns to Flatland to teach the wonders of such “enlightened” dimensions to his fellow flatlanders, the result of which is… …nope…no spoilers here!    THOUGHTS:  As I sit here, sober and “mostly” peyote free, I think I enjoyed the “ideas and concepts” of the story more than the actual plot. The writing was fine, but nothing that struck me as particularly eloquent. However, I’ve the concepts of the story have stayed with me and I have actually become more appreciative of the material as time has gone by.  Overall, I liked the book. I think it’s worth reading, but more for the interesting ideas and mental gymnastics that the narrative puts you through than for the simply enjoyment of the plot. Still, a worthwhile read, and since it’s actually a novella, you can get through it quickly without a large time commitment.  3.0 stars. Recommended!     1800s classics classics-european               1,032 reviews1,677 followers     June 18, 2018    حجمستان یادداشتی بر داستان «پختستان» نوشتۀ ادوین ابوت  معرفی ادوین ابوت رمان پختستان را در سال ۱۸۸۴ در انگلستان دوران ویکتوریا منتشر کرد: دوران نظام اجتماعی و اخلاقی خشک، و ازلی‌ابدی.رمان از دو فصل تشکیل شده: در فصل اول راوی که مربعی از اهالی پختستان است سرزمین دو بعدی خود را توصیف می‌کند، شکل و شمایل هندسی و فیزیکی پختستان، این چگونه همدیگر را می‌بینند، همدیگر را می‌شناسند. همچنین از ساختار اجتماعی و سیاسی پختستان می‌گوید، اختلاف طبقاتی و تنش‌های بین اشکال مختلف، انقلاب‌ها و سرکوب‌ها، تبعیض‌های جنسیتی، و... در فصل دوم، مربع برای نخستین بار با دنیاهای جدیدی رو به رو می‌شود، دنیاهایی که حتی تصورشان برای اهالی پختستان ناممکن است و صحبت کردن از آن، جرم. اگر فصل اول انتقاد از وضع کنونی است، فصل دوم را می‌توان نوید امکان تغییر به وضعی جدید دانست، وضعی جدیدی که همه ناممکنش می‌دانند، تنها از آن جهت که هنوز یاد نگرفته‌اند به جهت درست نگاه کنند، و به محض آن که یاد بگیرند، تعجب خواهند کرد که چطور در تمام این مدت از دیدن آن عاجز بودند.  شبی تابستانی ادوین ابوت در کتابخانه نشسته بود و به مسأله‌ی بغرنجی فکر می‌کرد. مسأله از این قرار بود که آیا می‌توان بعدی مکانی غیر از سه بعد تصور کرد که در جهتی غیر از جهاتی که می‌شناسیم امتداد داشته باشد؟ و اگر چنین جهان چهار بعدی ممکن باشد، در مقایسه با ما چه شکلی خواهد داشت؟ در همین فکرها بود، که ناگهان اتفاق شگفت‌انگیزی افتاد. در وسط اتاق مطالعه‌اش، نقطه‌ای پدید آمد، در مقابل چشمان حیرت‌زده‌اش به سرعت رشد کرد، به جنینی بدل شد، سپس کودکی شد و نوجوانی و جوانی، و در عرض چند ثانیه، پیرمردی در مقابل او ایستاده بود.  ادوین ابوت وحشت‌زده فریاد کشید و به قفسه‌ی کتاب‌ها چنگ زد تا خودش را از افتادن نگاه دارد و چند کتاب با سر و صدا زمین ریخت. زنش از این همه داد و فریاد هراسان به اتاق دوید و پرسید: «چه خبر شده؟»ابوت بی آن که بتواند حرف بزند پیرمرد را نشان داد و زن که تازه متوجه حضور پیرمرد محترم و موقری در کتابخانه‌ی شوهرش شده بود، با رعایت آداب چند کلمه‌ای با او خوش و بش کرد و رو به ابوت گفت: «ادوین، نمی‌فهمم سبب این رفتار بدون نزاکت چیست؟ از آقای محترم دعوت کن بنشیند. من هم‌اکنون چای می‌آورم.» و از اتاق خارج شد. پیرمرد رو کرد به ابوت، که هنوز به قفسه چنگ زده بود، و گفت: «معذرت می‌خواهم که این طور ظاهر شدم. همیشه وارد شدن به حجمستان دردسر ساز است.» ابوت با لکنت گفت: «شما که هستید؟» «ببخشید، فراموش کردم خودم را معرفی کنم. من متوازی الانسان هستم. در جهان چهار بعدی که از آن می‌آیم نام من این است.» «متوازی الانسان؟» «بله، خب این طور تصور کنید که تمام وجود شما در جهان سه بعدی، فقط یکی از اضلاع ما در جهان چهار بعدی است. همان طور که تمام وجود مربع در جهان دو بعدی، فقط یکی از پهلوهای مکعب در جهان سه بعدی است. من هم چون از انسان‌هایی دو به دو متوازی ساخته شده‌ام، متوازی الانسان نامیده می‌شوم.» ابوت دهانش را چنان باز کرده بود که انگار در نیمه‌راه یک ناسزا متوقف شده. پیرمرد گفت: «بیایید، بگذارید نشان‌تان دهم.» و قبل از آن که ابوت بتواند کاری بکند، دست او را گرفت و او را در جهتی، نه بالا و پایین، نه چپ و راست، نه درون و بیرون، بلکه در جهتی به کلی متفاوت بلند کرد، از جهان سه بعدی برداشت و بیرون برد. ابوت از وحشت جهان چهار بعدی یک بند فریاد می‌زد، مخصوصاً وقتی چشمش به میهمانش افتاد که به شکلی غیر قابل توصیف، از انسان‌هایی دو به دو متوازی ساخته شده بود و هر انسان با تمام سه بعدش تنها یکی از اضلاع او را تشکیل می‌داد. متوازی الانسان صبر کرد تا وحشت ابوت به انس بدل شود، و آن گاه برای او شرح داد که چطور در تمام این مدت جهانی چهار بعدی درست جلوی چشم تمام اهالی حجمستان بود، اما هیچ کس سر را به جهت درست نمی‌گرداند تا آن را ببیند، جهتی غیر از بالا و پایین و چپ و راست. و از ابوت خواست که دیگر اهالی حجمستان را از وجود این جهان عظیم مطلع کند، جهانی که حجمستان با تمام عظمتش در قیاس با آن، همچون نقش روی دیوار است. ابوت به جهان سه بعدی نگاه کرد که همچون نقش روی دیوار، بدون حجم به نظر می‌رسید. از آن جا می‌توانست داخل کتابخانه‌اش را ببیند، انگار که سقفی به کار نباشد، با آن که سقف بود، و همسرش که سینی چای به دست سرگردان در میان اتاق ایستاده بود و سر در نمی‌آورد که مردها کجا رفته‌اند. گفت: «اما هیچ کس حرف من را درک نخواهد کرد.» متوازی الانسان گفت: «خب چرا یک داستان نمی‌نویسی تا فهمش راحت‌تر شود؟» «چه داستانی؟» «نمی‌دانم. مثلاً داستان یک مربع ساکن جهان دو بعدی، که روزی کره‌ای از جهان سه بعدی در خانه‌اش ظاهر می‌شود و سعی می‌کند بعد سوم را برای او توضیح دهد.» ابوت به تمام چند صد چشم متوازی الانسان نگاه کرد، و به نشان پذیرش سر تکان داد. از همین حالا عنوان داستان را انتخاب کرده بود: «پختستان». این یادداشت برای سایت پلاتو نوشته شده، به این آدرس: لینک      داستان-خارجی طنز فانتزی               1,095 reviews3,838 followers     May 26, 2022    Imagine losing or gaining a spatial dimension Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute Action Lab video, explaining what a 4D ball would look like in 3D. I sent it to Apatt who likened it to  And He Built a Crooked House, which in turn, reminded me of a book I’d heard of, Flatland.  Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both.   And He Built a Crooked House, by Robert Heinlein This is an early short story (1941) by a big name in sci-fi. It's about a 4D construction. Quintus Teal is a young architect who thinks of a house as “a machine for living, a vital process, a live dynamic thing”. His big idea is to use the fourth spatial dimension to “put an eight-room house on the land now occupied by a one-room house. Like a tesseract”. He goes on to explain a lot of geometry, and I would have been bemused if I hadn’t already seen illustrations of what a tesseract, aka hypercube, would look like.  We’re all familiar with a cube and its net:  Then add a dimension for a hypercube and its net:  For more of an explanation, see video links at the end of this review.  Teal achieves his dream “by using strong girders and folding money” and takes his friends, Mr and Mrs Bailey to see it.“That's the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation.  But four dimensions don’t fit easily into a three dimensional world, and things become strange. Stranger than any staircases or buildings that Escher drew.  Flatland, by Edwin A Abbott About a 2D world and published in 1884.  This short book uses geometry as an analogy for a socio-political satire of Victorian attitudes to class and social mobility; gender (in)equality; biological determinism, evolution, and eugenics; religion and the supernatural. It probably works better for those with more knowledge of and interest in the period than I have. Fortunately, my edition had lots of notes, and Abbot included several illustrations.  The key concept is that in a two-dimensional world, a three-dimensional figure is observed as a cross-section. If it's moving, it is seen as a series of cross-sections, and can appear to appear and disappear out of nowhere. In the first half, the narrator, A Square, explains the very hierarchical social system of the two-dimensional Flatland. The more sides a shape has, and the more regular it is, the higher up the scale it is. “Delicate females” are are mere lines, “wholly devoid of brain-power, and have neither reflection, judgement, nor forethought, and hardly any memory”, but Abbot himself was a priest and headmaster who believed in women’s education, including at university.  The second half has more of a story: “my initiation into the mysteries of Space” and “the Gospel of Three Dimensions”. A Square develops a theoretical and then practical understanding of other spatial dimensions. The trouble is, that’s unimaginable and heretical in Flatland.  The progression of understanding of different spatial dimensions is well explained, with a few illustrations: A square is “a Line of Lines” and a sphere is “many Circles in one”. However, Abbott’s love of initial capital letters was a little distracting, and in part of the second section the language becomes overly Biblical and deferential (thee, thou, My Lord etc).   Image: “The Weeping Woman”, in which “Picasso used cubist forms of fragmentation to depict the face in a series of angular planes”. (Source)  Clearly explained information about 2D and 4D  To understand the fourth dimension, you need a firm grasp of the zeroth, first, second, and third dimensions. Unless you have a mathematical background, I strongly suggest you watch one or two of these videos before reading either story. I found it helpful to see the same ideas explained in slightly different ways. •	The fourth dimension explained, via second and third, in six minutes, HERE.  •	Hypercubes explained and illustrated, without sound, in five minutes, HERE.  •	Five-minute TED animation, summarising the story of Flatland and explaining 2D and 4D, HERE.  •	Animation of the story of Flatland, narrated by Carl Sagan, in four minutes, HERE.  •	Animation of the story of Flatland, made in 1965, eleven minutes, HERE.  •	Carl Sagan explains Flatland and goes on to the fourth dimension, in nine minutes, HERE.   The two stories  •	You can read Flatland, free, in a variety of digital formats, on Gutenberg, HERE.  •	You also can find the text of And He Built a Crooked House online.    Image: “Mr Osborne, may I be excused? My brain is full.” (The Far Side, by Gary Larson)  See also  •	If it’s all too much, there’s Norton Juster’s delightful picture book, The Dot and the Line, which I reviewed HERE. I included illustrations and a link to an Oscar-winning animation. •	Malcolm wrote two short stories about very high-tech homes in The Martian Chronicles, which I reviewed HERE. Usher II is a subversive dystopian comedy that's also a tribute to Poe's Fall of the House of Usher. There Will Come Soft Rains starts off almost slapstick, but takes a very tragic turn.      humour maths politics               Author  3 books5,415 followers     March 23, 2017   A curious little novella about a man a two-dimensional world thinking literally out of the box. First he explains his world in which the angles you have the higher social status you have in Flatland - Circles being the highest rank. He meets someone from Lineland (one-dimensional) who is incapable of understanding Flatland and he meets Sphere from Spaceland (three dimenions) and he is able himself to comprehend the difference between "up" and "North". However, Sphere cannot extrapolate to 4+ dimensions and when the protagonist returns to Flatland and tries to explain Spaceland, he is imprisoned as a heretic. The text is a social criticism on the rigid thinking of hierarchal social ranks, the dogmatism and often anti-scientific bent of religion, and also has a feminist bent to it as well. A fascinating and mind-bending little book that has not aged a day after almost a century and a half.     english-20th-c fiction geek-classics               934 reviews17.6k followers     January 19, 2023   I will start my own brief multi-dimensional romance on this book - but dangerously, perhaps, exploring elements of my own experiences out into Spaceland that led me back, like Abbott, to my home-sweet-home of Flatland - with a caveat that I am a rather odd duck.Being born with ASD didn't help at all.  We Aspies, like Supertramp, always Take the Long Way Home. The prolonged ingenuous Springtime of The Soul. And the soul rejoices in the bright laughter of - as Mallarme says - the Jeu Suprême - as all reality curls up comfortably at its Ironic Edges. But the simplicity of higher mathematics in high school soon became in my eyes an overgrown jungle. It was, to me, unworkable, because we Aspies come from a psychological Flatland: to the world, Dullsville. So my apologies at the outset to my GR friends who were math majors. No, I took this book at a personal EXISTENTIAL level! So please: take this review very much with a grain of salt!*** As you probably know, I like to often change the subject. My adventures in Spaceland taught me that when my interlocutors dug deep, their interjections were to me like speeding bullets. I dodged them: I knew they would spell my mediocre death-in-life: I didn't want to go there. Didn't even want to go to Spaceland - no - but the philosophical skills my teenaged reading skills gave me PUSHED me into a sophisticated outer spaceland.  That sophistication fed my nascent knowledge. So when I went to college, I explored Spaceland heuristically. And of course - that path leads us into the Den of the Minotaur.  Yikes. Anyway, after King Minos' foul beast had thoroughly chewed me up and expectorated me... alone, I found myself back home in Flatland! *** An awakening refused leads back to simplicity, as Abbott found - And it's where I am now writing this: In "a state of simplicity (which cost me) not less than EVERYTHING." And won me Flatland forever... Flatland - AKA God's Peace - a patient, silent witness to an Ugly World.                   9,568 reviews55.6k followers     August 18, 2020   Flatland: A Romance of Many Dimensions, Edwin A. AbbottFlatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley &amp; Co. of London.  Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.  The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides.  The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions.  The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium.  On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points".  These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so.  In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. ... عنوانها: «پـَختِستان»؛ «افسانه ی دو بعدی»؛ «سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه»؛ نویسنده: ادوین ابوت؛ تاریخ نخستین خوانش سال 1997میلادی عنوان: پـَختِستان؛ نویسنده: ادوین ابوت؛ بازنگری و مقدمه از: یانش هوفمان؛ مترجم منوچهر انور؛ تهران، روشنگران و مطالهات زنان، 1375؛ در 195ص؛ شابک 9645512433؛ چاپ دیگر تهران، کارنامه، 1388؛ در 172ص؛ شابک 9789644310799؛ چاپ دوم 1393؛ موضوع بعد چهارم - از نویسندگان بریتانیایی - سده 19م عنوان: افسانه ی دو بعدی؛ نویسنده: ادوین ابوت؛ مترجم: جلال جامعی؛ شیراز، لورا، 1387، در 192ص؛ شابک 9789648851366؛ عنوان: سرگذشت زمین مسطح: داستان دلدادگی ابعاد چندگانه؛ نویسنده: یک مربع (ادوین ابوت)؛ برگردان: آهنگ کوثر؛ شیراز، نوید شیراز، 1397؛ شابک 9786001927768؛  پَختستان: رمان بُعدهای بسیار، رمان کوتاهی از الهی‌دان و استاد دانشگاه انگلیسی، «ادوین ابوت» است، که نخستین‌بار آن‌را در سال 1884میلادی با نام مستعار نویسندگی «یک مربع» منتشر کردند؛ در این کتاب از دنیای خیالی «دوبُعدی پَختستان»، برای نشان دادن فرهنگ سلسله‌ مراتبی «انگلستان» دوره ی «ویکتوریا» استفاده شده‌ است.؛ این نگاره بیشتر یک تمثیل عبرت‌ آموز است، تا یک داستان؛ و نیز نقدی تند و گزنده، از ساختار اجتماعی و سیاسی جامعه ی روزگار خود، و ارزش‌ها، و روابط انسانی در آن است؛ «ابوت» برای اینکه نشان دهد، انسان‌ها در این دنیا از نظر افق دانش و بینش، در چه قفس تنگی گرفتار هستند، از جهانی خیالی با باشندگانی دو بُعدی سود برده است.؛ این باشندگان دارای شکل‌های هندسی «مثلث»، «مربع»، «پنج‌بر»، «شش‌بر» و «بالا و بالاتر» تا «دایره‌» هستند، که ناگزیر در سطح می‌زیند.؛ نویسنده و راوی داستان، یک مربع است، که این دنیا را شرح می‌دهد.؛ «پَختستان» در زمان انتشار خود، مورد توجه قرار نگرفت، پس از انتشار نظریه ی نسبیت عام انیشتین، این کتاب دوباره به یاد همگان افتاد، چرا که در آن به مفهوم «بُعد چهارم» نیز اشاره شده بود.؛ در مقاله‌ ای تحت عنوان «اقلیدس، نیوتن و انیشتین»، که در شمارهٔ دوازدهم ماه فوریه سال 1920میلادی مجله ی «نیچر» منتشر شد، از این کتاب نام برده شد، و «ابوت» را از یک نظر همچون پیامبری دانست، که در آن زمان به درک اهمیت زمان، در شرح یک پدیده، آگاه بوده‌ است.؛ انتشارات «هارپرکالینز» در سال 1983میلادی، نسخه‌ ای از این کتاب را با پیشگفتار «آیزاک آسیموف» منتشر کرد.؛ عنوان «پَختستان» را، مترجم نخست این کتاب، جناب «منوچهر انور»، برای آن برگزیدند، که از واژه ی فارسی «پَخت» به معنای «پهن» و بی‌برجستگی، و پسوند ستان تشکیل شده‌ است.؛ تاریخ بهنگام رسانی 27/05/1399هجری خورشیدی؛ ا. شربیانی     19th-century british classics               87 reviews     January 4, 2009   This book should not be read in hopes of finding an entertaining story. As a novel, it's terrible. It's plot (if you can call it that) is simple and contrived. But, it wasn't written as a novel.Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them. The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear. In the course of the explanation, the book also describes "Lineland," a one dimensional world where the inhabitants would also have trouble understanding dimensions above their own. This book's excellence lies in the way it takes a complex topic and breaks it down into a metaphor that can be more easily understood. It argues quite well that if there is a fourth dimension, it probably isn't "time." This book isn't one that will win wide-spread acclaim from the general reading community. For those of us who enjoy higher math, though, it's excellent.                   507 reviews752 followers     April 6, 2017    “I used to be a renegade, I used to fool around But I couldn't take the punishment and had to settle down Now I'm playing it real straight, and yes, I cut my hair You might think I'm crazy, but I don't even care Because I can tell what's going onIt's hip to be square”  Huey Lewis And The News - Hip To Be Square According to IMDB, several film adaptations have been made of Flatland, but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can’t imagine a more appropriate theme song than the above Huey Lewis And The News number.  Flatland is set in a two-dimensional world and narrated in the first person by a square (or “A Square” as appears on the original edition’s book cover). In the first half of the book Square gives us a tour of his world where women are straight lines and, if you are symmetrical, the more sides you have the better. This means that circles are the elite of this society because they are really polygons with zillions of super tiny sides. Irregular polygons are abominations and isosceles are plebeians.  Special laws are applied to women because they are capable of accidentally stabbing people to death due to their pointiness. Use of colours is banned because they can be used as disguises. How these geometric persons move around without legs is deliberately left unexplained (with a bit of "lampshading"). The second half of the book tells the remarkable story of Square’s adventures in lands of different dimensions, one, three and even zero (no trip to the fourth dimension, though; no time, probably). Guided by an enigmatic Sphere who seems to have popped up out of nowhere (and who Square initially mistook to be a circle), these trips to other planes of existence enables Square to not only think outside the box but to introduce him to the existence of boxes. This was a steep learning curve for him but he adapts like a champ and becomes a more rounded individual because of it.  Flatland is a very odd novella it is part allegory, part satire, part geometry lessons, part spec fic. I generally avoid reading geometry books because they are full of problems I don’t want to consider (screw the hypotenuse, man!). However, for Flatland I don’t mind making an exception, for once I find the flat characters entirely acceptable and even find the more apparently rounded character to be arrogant and clearly obtuse in their outlook, if not in appearance. The satirical look at the class system makes this all too real issue painfully acute. One thing that blows my mind a bit is that prior to reading the book I visualized it as a story of different geometric shapes moving around going about their business. However, the denizens of the Flatland cannot actually see these different shapes. As the Square (or Edwin Abbott Abbott) mentions early in the book you have to imagine looking at these shapes with your line of sight on the same level as their surface. Mr. Abbott explains it very clearly as follows:  “Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.”   So all they really ever see is straight lines of different lengths, however, they can distinguish the different geometrical shapes by hearing, by touch (done by the working class only), and by sight with the aid of fog for estimating depths (different angles appear to fade differently into fog). In the one-dimensional Lineland everybody looks like a point and sideways movement is impossible; as for the zero-dimensional Pointland, there is only one denizen and he is weird! I really enjoyed Flatland, it is bizarre and thought-provoking; it definitely gave me a new perspective on life. The treatment of women may seem a little sexist but E.A. Abbott is perhaps satirizing sexism rather than perpetuating it. I definitely recommend you read Flatland before you flatline.   Notes: • Audiobook credit: Wonderfully read for Librovox (i.e. free) by Ruth Golding. (link)  • There are quite a few diagrams scattered over the book, drawn by AbbottX2 himself, they illustrate the geometrical concepts nicely. These should be in all editions as they are intrinsic to the story. • There is one error in the book where Square mentions a cellar: “So I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned.”. You can't have a bloody cellar if you only have two dimensions and you can’t “fall through” anything. • Another error (I think) is the existence of cupboards in Flatland. If there is no depth or verticality you can't have cupboards! • The 3D world is called Spaceland, it is not our world. Their most popular singer is probably Britney Sphere. (͡° ͜ʖ ͡°) • I initially thought this book was a collaboration between two abbots.  Quotes: Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name. In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself. Such at least is the painful teaching of my experience. Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life? You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions—how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration? Hipster Square     classics               475 reviews2,123 followers     March 19, 2015   This was one crazy, opium fuelled, brilliant book about geometry and different dimensions and I am going to explain it the best way I can but Edwin A Abbott does it so much better.Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off are women who are not even figures; they are just straight lines. They have few rights and no one actually takes their intellect seriously. On the other hand they are dangerous because being straight lines they can easily pierce any figure. A woman from behind looks just like a dot, you might miss her until it’s to late and she has stabbed you. Different parts of Flatland developed different strategies for dealing with the danger, from not allowing women to leave their houses, to forcing them to constantly wiggle their bums, so they are visible from far. They should also sound a ‘peace-cry’ when out and about, in case anyone missed the wiggling bum. Seriously children, don’t do drugs. It makes you write things like that.  The second part of the book gets more interesting as it delves deeper into the concept of dimensions. As I said, our hero lives in a two-dimension reality. Try to imagine such a world. You probably see it as a piece of paper with various figures drawn on it. Of course, that’s how a creature from 3D world would see it. You’re looking at it from above, i.e from the third dimension. If a 2D world was your entire reality you would only be able to see lines and dots. Your eyes would be on the same level as the figures and you would see everything in one dimension and infer the second dimension because you can move in it and you have learnt it through experience. The same way we can’t actually see the third dimension but we can tell it’s there. We know we can move in three dimensions and we know about perspective, light, shadow, etc. It is easier for us to understand a two-dimension reality than it is to imagine a four-dimension one. We can see it perfectly when our Square visits a one dimensional land and he laughs at it and tries to explain to the King that there is more to life than just looking at a dot in front of you. There is another dimension where there are not only dots but lines as well. The King of course laughs him off. Yet, when Square is confronted by Sphere who tells him about the third dimension and shows him ‘tricks’ that the third dimension allows him to do, Square is just as incredulous. Even though the mathematics tells him there must be another dimension (and another, and another), he can’t quite believe it until Sphere shows him a little bit of a 3D world. Then he is a convert, and he quickly assumes there must be more dimensions. Fourth and fifth and ad infinitum. I think while reading this I got as close as I would ever get to understanding and imagining a 4D world. If in a 3D world we can see the insides of everything of a 2D world, then I suppose a in 4D world we would be able to actually SEE all three dimensions, all the insides of everything. My brains hurts. Am I making any sense? I thought I could see it but now it’s been a week after I finished reading the book and had those vivid dreams about the fourth dimension. The vision pales. I still believe in it but I can no longer grasp it. Just like the poor Square, back in his 2D-Land, thrown in prison for preaching revolution, still believes in the third dimension, but can no longer conjure the image of a Sphere in his head. Sometimes he feels he can almost see it again for half a second, and then it’s gone.     gutenberg-project-project pub-1880s               5 reviews4,020 followers     October 6, 2016   Un racconto fantastico a più dimensioni con una velata (neanche poi troppo) critica alla chiusura mentale. Geniale.                  1,238 reviews2,207 followers     January 3, 2016   At the outset... the 5 stars are entirely subjective. I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did.I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland by Edwin A. Abbot and An Episode of Flatland by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.)  We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm. Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic. There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits. Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious. In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension). Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story. Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life. Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it.  Since it is available online free from Gutenberg, I suggest everyone to give it a try.     general-fiction mathematics               4,753 reviews635 followers     December 18, 2021   I have to be honest...did not get as much from this book as I could have because of my decayed math skills (not that there was ever much there to decay). But it was a "bucket-list" book that I thought was quite inventive. Think this would be a really good STEM book for 8th graders; if they can understand the concepts here then I think they are ready for high school math.     classics math               49 reviews5 followers     November 8, 2018   3.5 stars.This is a very personal rating. I think I would’ve enjoyed this far more if I’d read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew.  This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry and higher dimensions. It simply came a little too late for me.                   773 reviews552 followers     February 19, 2021   For the most part I hate maths, other than stats &amp; arithmetic, but I loved this absolutely mad book!My copy didn't come with the line drawings, but they are available on http://www.geom.uiuc.edu/~banchoff/Fl... I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe! I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may have made me try harder with maths - although I don't think anything could have made me &amp; trig friends! Knocked off a star for an often patronising attitude to women. Abbott may have thought he was being funny. I didn't. 
 
 
 
 
 
     classics how-bizarre victoriana               2,306 reviews20 followers     August 16, 2017   What a fantastic little thought-experiment, only really half-disguised as a story. Through his witty little parable, Abbott manages to explore the physical, mathematical, societal, philosophical and theological without once spoon-feeding his readers (OK, maybe there's a little bit of spoon-feeding in the earlier chapters).It's only a shame, then, that this is without a doubt the most misogynist book I've ever read in my forty-odd years... Oh, well; I suppose nothing's perfect...     books-read-in-2017               1,674 reviews170 followers     September 17, 2019   Very strangeReview of free Kindle editionASIN: B0083ZRQR4124 pages I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage about FLATLAND from THE POT THIEF WHO STUDIED EDWARD ABBEY by J. Michael Orenduff. Orenduff, a former college professor with his PhD in Mathematical Logic, a former university president and chancellor is now a full-time author known mainly for writing the Pot Thief Mystery Series. He should understand FLATLAND as a mathematician and as an author. Here is what his characters say about FLATLAND: “All work is 3-D,” said Martin. We stared at him. He looked at me. “Remember that book Flatland you made me read?”“I didn’t make you read it.”“When a white college student visits a fourteen-year-old dropout on the rez and suggests a book, that’s the same as making me read it.”“But you liked it, right?”“Yeah, because it made me feel smarter than the guy who wrote it.”“How so?” asked Sharice. “He says the men who live in Flatland are polygons. The fewer sides a man has, the lower he is on the social scale. So triangles are the lowest level, squares are higher, pentagons higher and so on. But he also says they can see each other and interact, which is impossible. Because if they were truly two-dimensional, they would have no sides, so there would be nothing to see.”“You could see them from the top,” said Susannah, “and from that vantage point, you could also see how many sides they have.”“No. To see them from on top, you’d have to be above them. But there is no up in Flatland. And there is no down. There is only north, south, east and west. So they wouldn’t even know other men existed.”“They would when they bumped into them,” she said. He shook his head and placed two pennies on the table, sliding them until they touched. “These pennies can bump into each other because they have sides. But imagine them without sides. I don’t mean just really flat. I mean no side dimension at all. The men in Flatland can’t bump into each other because they have no sides.”“Why do you keep calling them men? Aren’t there women in Flatland?”“Sure. The author says they are straight lines.”She shook her head. “Sheesh. I might have guessed. The women are the lowest life-forms because they have only one dimension.”“Right. And he makes the same sort of mistake in describing them, saying that seen from straight-on they look like a point. But you can’t see the end of a line because that would require that it have some height. Lines have only length. You could see them from below or above but not in a world that has only two dimensions.”“He says something else about women,” I noted. “Because of their lack of intelligence, they accidentally pierce and kill people without even knowing it. But ten minutes later they can’t remember it happening.”Sharice stared at me. “And you made him read that?”“For the math part. I knew he was smart enough not to believe the stuff about women.”“He was also smart enough not to believe the stuff about math. A guy who thinks you can see something that doesn’t have sides …wait, they can’t see anything anyway. If they had eyes, they would have to be on their surface, because they have no sides. So the only direction their eyes could look would be up. But there is no up.”“See,”I said, trying to move beyond my having forced a misogynist book on Martin, “You’re also smarter than the author.” I agree with Mr. Orenduff and his fictional characters. That's my position and I'm sticking to it. No illustrations in the free Kindle edition. However, Amazon offers the Distinguished Chiron Edition with illustrations by the author. This is supposed to be some kind of improvement of the original 1884 edition. The illustrations which I examined seem to confirm Mr. Orenduff's opinions by depicting a very flat three dimensional world instead of a two dimensional one.                   96 reviews129 followers     August 19, 2018   Quite a charming allegory for the English society of the time, and boy does it show it's age. This is basically covered by everyone who reviewed this book, so I am not going to talk about that. What I noticed and I haven't seen anybody mention this yet, is the fact that at the time when this book was written Darwinian evolution has already grasped popular imagination. Just look how he talked about careful pairings between men and women to produce an equilateral triangle and then how each generation after that is achieved gets more sides until it reaches their version of perfection that is the circle. As I am aware people looked towards evolution with quite an optimism at the time and started envisioning utopias that will come to existence with careful work, selection and patience. Just look at the squares enlightenment at the prospect of 3 then 4 and as many dimensions it can possibly go. Now this book, by it's writing style would get 3 stars, but no one can write something that after reading it makes me spend a night thinking about tesseracts (4 dimensional cubes) and glomes (4 dimensional spheres) and not be rewarded. Both mindfuckery and awesomeness.     sci-fi               97 reviews50 followers     March 7, 2020   This is without a doubt, the weirdest book I've ever read. Took me a little while to get into but once I did, I couldn't put the thing down. I would heartely recomend this to anyone not put off by the idea of shapes being the main characters.                  99 reviews296 followers     November 16, 2011     Questo libricino è talmente matto e bello che dovete andare a comprarlo, e siccome so che le mie maniere dispotiche, e poco convincenti (purtroppo non ho le doti dei venditori di cose inutili che riescono a farti comprare di tutti convincendoti che siano utili)forse non vi indurranno all'acquisto, armatevi di convincitudine vostra, e andate a comprarvelo, o a rubarlo, o a prenderlo in prestito dalla biblioteca.Perché? Leggete quanto segue  Se come me siete sempre stati delle perfette   schiappe in matematica e geometria  questo è il libro che vi illuminerà di sapienza, una volta finito di leggerlo vorrete andare dai vostri vecchi professori/maestri, sbattere loro Flatlandia in testa e urlare  MA CHE ACCIDENTI TI COSTAVA SPIEGARMELO COSì SEMPLICE?? . Purtroppo però temo si tratti di un provvedimento anticostituzionale, dunque, anziché prendervela con vecchi pedagoghi incapaci, potrete gentilmente ringraziare Abbott che nel 1882 ha scritto questo libro non so con quali intenti (devo ancora leggere saggi/articoli/, ma era troppo forte la voglia di parlarvene), ma di sicuro aveva capito che nel 1991 sarebbe nata una asina matematica come me, quindi ha voluto far parlare figure geometriche.Se  al contrario  siete divini, comprendete la matematica e la geometria, avete l'occulto dono del far di conto e del comprendere combinazioni di lati, angoli, e quant'altro, tranquilli, a Flatlandia ce n'è anche per voi. Per quanto siate saccenti, dubito infatti che in uno dei vostri compiti perfetti delle superiori o esami da 30/30 con lode dell'Università, le figure geometriche abbiano mai preso a muoversi o a parlare. Ma non è tutto qui. Se pensavate che Geometria e Politica e Filosofia potessero difficilmente incastrarsi tra loro, vi sbagliavate. Perché nella Geometria di Flatlandia la Politica sessista e razzista discrimina le Donne, gli Isosceli, gli Irregolari e assurge a razza perfetta i Circoli. Quando poi qualcuno vede o sente, anche per sua non colpa, qualcosa che non andava visto o sentito, viene fatto sparire. Che cosa assurda, si potrebbe pensare. E invece no. Succede anche da noi. Quindi tranquilli, a Flatlandia ci ritroverete molto. Non incazzatevi troppo con Abbott se ce l'aveva con le donne.Insomma, Dante ha reagito bene. Ma a volte gli approcci sessuali non vanno a finire in Commedie, sopratutto non in Divine. La mia cartolina da Flatlandia smette qui di essere priva di raziocinio, scusate, ma sono ancora troppo esaltata.Se decidete di farci un salto, tuttavia, chiedetemi l'indirizzo, perché colleziono cartoline, e da Flatlandia le ricevo ben volentieri.                   468 reviews113 followers     June 1, 2021    My 4th best read of 2020. An incredible, timeless book. Flatland should be prescribed reading for mathematics in secondary school, because it teaches so much conceptually using basic mathematics that everyone can understand. My interpretation below might clarify what I mean. It demonstrates the utility of mathematics is abstraction, not measurement. It's what the units 'represent' that enables and motivates quantitative calculations. By counting something we bring a perception into existence, and we count when we care about and can demonstrate that it can be counted by more than one observer. Counting is also a subject decision insofar as we attribute a value to the variable counted, and a meaning to what its counting could mean. 'What counts has been counted'... in a nutshell? It also demonstrates that mathematical models can model social systems. The strength of mathematical models of social systems is that they avoid any obvious sociocultural bias and so enables things that would normally be socially censored to be claimed as theoretical propositions. In short, it enables discourse about stereotypes and demonstrates the possibility of universal social or moral values. I feel a lot of the social norms of Flatland still apply today, in a way. The importance of Spaceland I think is to demonstrate how it is nearly impossible to mathematically, or universally, demonstrate evidence of realities outside of measurable reality, because they begin and end in the subjective experience of the individual. Which is used as an argument both for and against religion. I think Flatland as a theological text favours spiritual belief in its lowly depiction of atheism or 'man as God' in Pointland as a less diverse system, geometrically speaking. I guess in a way it's calling existentialists navel-gazers insofar as they take their perception to solipsistic levels that is perhaps theologically speaking commits the blasphemy of 'self-as-a-God'. This shows why Flatland is so brilliant — it can simply, concisely and thoroughly show a complex understanding of human nature — such as how theists fail to explain their conviction, and atheists fail not to reject any conviction that conflicts with their original sense of perception. Most people don't get get that far in a debate in an hour let alone in less than 100 pages!  Ok... I think I've made my point. I think most people read this as some 'goofy maths' essay, but I see it as a social commentary that somehow covers the archetypes of society and the perception of reality in less than 100 pages and is somehow still ahead of its time a century later.     on-philosophy               Author  16 books247 followers     February 3, 2023   Trama originale. Un po' lenta la prima parte, sin troppo veloce quella finale, ma non importa. Esclusione, pregiudizio, chiusura mentale e conseguente condanna di tutte e tre la fanno da padrone in questa storia godibile. Non sono in sé nuove le tematiche (basti pensare a Swift), ma il modo in cui sono trattate e la profondità con la quale vengono sviscerate le ragioni che sostengono la necessità di un fecondo relativismo culturale in luogo di una sterile dittatura assolutistica. Consigliato.    narrativa               Author  1 book8,092 followers     June 15, 2016    
 For why should you praise, for example, the integrity of a Square who faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of his right angles? Or again, why blame a lying Isosceles, when you ought rather to deplore the incurable inequality of his sides?
	This is one of those delightful little books, so difficult to review because its charms require no toil to appreciate, and also because the book is so short you might as well read it and skip the reviews. So I’ll keep my remarks brief.	The charm of the book lies in its conceit, rather than its execution. Indeed, though certainly able, Abbott is not an expert writer; nor does he pretend to be. The genius of this book is in the simple beauty of its premise: What would life be like for a square living in a two-dimensional world?  	Abbott wrings a remarkable amount out of this simple question. First, he gives us a satire of Victorian culture—perhaps the less enduring part of this work, though certainly keen and ruthless in its modest way. To me, the most interesting point Abbott makes in his satire has to do with education. The residents of Flatland spend all their time learning various methods to identify the shapes of others. For if you are living on a two-dimensional plane, telling a square from a circle is no easy matter, as they all appear to you as flat lines. And this question of shapes is important in Flatland, as one’s status depends on one’s shape, with irregulars being the lowest and circles the highest. So was Abbott implying that, when we educate our own youngsters, most of this “education” consists in merely teaching them to navigate our own social hierarchy? But of course, the more fascinating part of the work has to do with dimensions. How would the possibility of two dimensions appear to a one-dimensional creature? Incomprehensible. And how would the prospect of three dimensions seem to a two-dimensional creature? Nonsense. To the residents of Flatland, tales of cubes and spheres appear like so much absurd metaphysics. Abbott uses this point to show how narrow is our mental framework, how completely blind we are to realities outside our everyday, commonsense world. Doing so, Abbott elevates this work from novelty to true art. For after satirizing the world we know, he gives us a glimpse of a world beyond.     novels-novellas-short-stories               229 reviews43 followers     January 16, 2018   5* A world where every character is a shape, but only seen on a side view so everybody looks like a straight line. That's why the would is called flatland because everything is in 2 dimensions.  THIS IS THE BEST BOOK I HAVE EVER READ! It's so trippy and it's really funny too. I can't just give funny quotes though because you need to know the context from the beginning of the chapter and then the context of the chapter before that to get the humor.  Some quotes to give an idea of what the book is like: "Place a penny on the middle of one of your tables in Space, and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander), the penny will then have ceased to appear oval at all and will have become, so far as you can see, a Straight Line." "Our Women are Straight Lines. Our Soldiers and Lowest Class of Workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed, when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight Lines or Women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called Isosceles, and by this name I shall refer to them in the following pages. Our Middle Class consists of Equilateral or Equal-Sided Triangles." "The thought flashed across me that I might have before me a burglar or cutthroat, some monstrous Irregular Isosceles, who, by feigning the voice of a Circle, had obtained admission somehow into the house and was now preparing to stab me with his acute angle." HERE'S A FREE LEGAL LINK FOR THIS BOOK SO YOU DON'T GET A VIRUS: (The author has been dead for 100 years of course it's legal.) https://www.gutenberg.org/ebooks/97      4-star-5-star 5-star               30 reviews41 followers     August 20, 2016   Unico, inclassificabile, geniale. Come dice Giorgio Manganelli nella postfazione "un capolavoro di illusionismo prospettico". Questa lettura è stata uno stimolante esercizio mentale e di immaginazione, un invito al ragionamento come non ne apprezzavo da tanto, tanto tempo. Si sente che Abbott era un insegnante, perchè il linguaggio è didattico e la struttura metodica. Tuttavia, per le sue implicazioni profonde, mi ha commossa e fatto venire la pelle d'oca. Consigliato a chiunque. Leggetelo, assaporatelo, regalatelo ai ragazzi. Questi sono libri speciali.    preferiti racconti-e-storie-brevi               590 reviews8 followers     March 21, 2022   Published in 1884, this is meant to be a satire on Victorian culture but it's also just a math nerd's dream. Very cleverly done. The first half is the history and explanation of Flatland. The second half is the opening of the mind of A Square to understand a third or even fourth dimension.    mustich novella read-in-2022               1,525 reviews1,772 followers      Read  April 2, 2017   The narrator, a shape living in a two-dimensional universe, has his thought-world turned upside down went he meets a mysterious being from a three-dimensional world. 3D creature proceeds to blow 2D creature's mind by exposing him to 1 dimensional world, who however in turn refuses to accept the possibility of 4, or more D , world (s). This notion of perspective and liberation from one's own perspective gives the work a transcendent slyness and power as it offers a freedom beyond whatever the limited conceptions of the author were.Comes with illustrations showing the exciting worlds of triangles and such.     19th-century british-isles humour
Flatland: A Romance of Many Dimensions
https://www.goodreads.com/book/show/433567.Flatland
https://www.goodreads.com/book/show/214441.Euclid_s_Elements
Euclid's Elements
2021-08-01
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 Euclid's Elements

 Euclid , Dana Densmore , Thomas Little Heath ( Translator)

 4.32
 3,236 ratings 108 reviews
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 Green Lion Press has prepared a new one-volume edition of T.L. Heath's translation of the thirteen books of Euclid's Elements . In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.

 Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature.

 We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.
 Genres Mathematics Science Classics Philosophy Nonfiction History Reference
 ...more

 529 pages, Paperback

 First published January 1, 291

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 Euclid

 828 books 188 followers
 Euclid (Ancient Greek: Εὐκλείδης Eukleidēs -- "Good Glory", ca. 365-275 BC) also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Stoicheia (Elements) is a 13-volume exploration all corners of mathematics, based on the works of, inter alia, Aristotle, Eudoxus of Cnidus, Plato, Pythagoras. It is one of the most influential works in the history of mathematics, presenting the mathematical theorems and problems with great clarity, and showing their solutions concisely and logically. Thus, it came to serve as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements , Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. He is sometimes credited with one original theory, a method of exhaustion through which the area of a circle and volume of a sphere can be calculated, but he left a much greater mark as a teacher.

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 4.32
 3,236 ratings 108 reviews
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 Displaying 1 - 30 of 108 reviews
 Greg
 70 reviews 74 followers
 July 31, 2007
 I am rating this primarily to boost its 4.64 average rating. I feel ridiculous reviewing it.
 This book is good, and people with cerebral cortexes know that.
 For reference, one person who gave it one star gave Allan Moore's " Watchmen " "graphic novel" (read: comic book) 4 stars.
 . . .
 If this book is not perfection, I am not sure what perfection entails.

 The Elements is one of the ten most important, if not best, books ever written. There is no better course in deductive logic, much less geometry.
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 Orhan Pelinkovic
 96 reviews 225 followers
 November 15, 2021
 "The laws of nature are but the mathematical thoughts of God.”

 Euclid of Alexandria was a Greek mathematician who lived somewhere between the mid-4th and mid-3rd century BCE. Barely anything is known about Euclid's life, but through his books and works, his name became a synonym for geometry. Euclid's 13 unabridged books on geometry comprise this textbook titled Euclid's Elements which was the second most printed book, following The Bible, after the invention of the printing press.

 Although Euclid is known as the founder of geometry, one could assume that he possibly learned much geometry from his predecessors, such as the Pythagoreans, and the Pythagoreans from Pythagoras, and Pythagoras from the ancient Egyptians, and the ancient Egyptians for the ancient Babylonians and so on. Perhaps even the origin and inheritance of this knowledge was not so linear as I just presented. Therefore, bestowing anyone the title of being the founder of a study that deals with the fundamental symmetrical properties of space and things and their proportions and ratios could be an overstep. Nevertheless, what Euclid achieved in this volume of books was unifying the existing knowledge of geometry, introducing his own propositions, and meticulously, with firm argumentation, and a well-grounded methodology, proved and disproved the mathematical propositions of plane and solid geometry. Even though numbers were discussed a great deal, but they were nowhere in sight, as they were all illustrated by varying lengths of lines and geometrical figures and angles that made the study of integers challenging to follow.

 This reading experience of Euclid had little entertainment value as I suppose it did throughout history, but entertainment does not have to be a priority in reading. I knowingly read a tedious old book once in a while to bring me to a state of relaxation.
 ancient-greek astronomy mathematics
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 Victoria
 23 reviews 12 followers
 May 4, 2012
 "Euclid alone has looked on beauty bare." --Edna St. Vincent Millay

 This is a statement I believe more strongly as I experience more of Euclid's propositions for myself. Before encountering Euclid, I had never considered mathematics to be something beautiful. Now, however, the sheer logical clarity with which Euclid attempts to grapple with the principles of the world around him actually brings tears to my eyes. From how he uses the idea of equality as a foundation for everything else to how he presents the circle as a perfect figure capable of encompassing all else, Euclid truly has captured something captivating and universal in his mathematics. He even overcomes what he is able to himself explain by using ratios to comprehend incommensurability and, in fact, to speak what is unspeakable.
 st-john-s-reads
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 Roy Lotz
 Author 1 book 8,540 followers
 May 1, 2016
 Euclid’s Elements is one of the oldest surviving works of mathematics, and the very oldest that uses an axiomatic framework. As such, it is a landmark in the history of Western thought, and has proven so enduring that the Elements has been used nearly continuously since being written, only recently falling out of favor.

 Not much is known about Euclid, other than that he must have been an unparalleled genius. Nothing about his personality can be gleaned from this book either, other than that he was very persistent.

 I must admit, the primary reason I endeavored to read this book were the glowing reviews on Amazon. The very first one proclaims it the ‘best book ever written by a human’. That’s a bold statement, and especially after hearing of its supreme importance in the history of Western thought, it seemed like a good idea to give it a whirl.

 I’m not sure what I was expecting when I opened the book. Math, to be sure, but 500 pages of geometric proofs? I couldn’t believe it. I will never forget the feeling of reading it for the first time. I wanted to get through 30 pages. It took me three hours. By the time I was done, I was completely exhausted and had a throbbing headache.

 From then on, it became gradually easier, but it was certainly not a walk in the park. I would like to think that I somehow built some ‘mental muscle’ by slogging my way through the book. It felt like it. No book has ever taken as much effort or as much time. War and Peace took three weeks. This took six. Admittedly, I read Tolstoy all of my waking hours, while for this I found it wise not to exceed three hours per day. Any further and I could almost feel my brain seeping out of my eyes and ears.

 So, is this the best way to teach geometry? Probably not. One can only spend so much time with mathematical proofs. At a certain point, you need to use some numbers and see the theorems in action. But this book should be required reading for math majors, if only to see how their discipline evolved. It also is an excellent way to practice logical arguments.

 Of course, I didn’t absorb much of the book, perhaps most of it. Maybe it’s because I didn’t spend enough time on it, or maybe it’s because, in the end, it just didn’t send me. But, on those rare occasioned when I glimpsed, however dimly, what Euclid was getting at, it was a thrill.

 Q.E.D.

 [Note: Looking back, I'm really glad I read this. References to Euclid show up everywhere in Western classics, particularly in philosophy (the format is even copied in Spinoza's Ethics !). It seems that reading the Elements has a profound effect on a small subset of people, most of whom are destined to become mathematicians. For example, in his History of Western Philosophy , Bertrand Russell declares that this book is the perfect summation of the Grecian intellect, unequivocally better than their philosophy or literature. In G.H. Hardy's A Mathematician's Apology , he uses Euclid's proof of the infinite number of primes as an example of a beautiful piece of math. A reference to Euclid showed up in the Steven Spielberg's Lincoln , and Euclid is invoked in our Declaration of Independence ("We hold these truths to be self-evident..."). In short, the references alone make the book worth reading. And, who knows? Maybe you're destined to become a great mathematician yourself.]
 math oldie-but-goodie over-my-head
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 Huda Aweys
 Author 5 books 1,402 followers
 Currently reading
 March 4, 2015
 مبدئيا الرياضيات علم ممتع جدا .. و الهندسة بالذات بيني و بينها حكاية عشق قديم :) و حقيقي مستمتعة جدا و انا باقرأ الكتاب دا
 *****
 بسم الله :)... (عناصر إقليدس) أو (أصول إقليدس) أو (الأصول الهندسية) أو (اصول الهندسة) :) ! .. لـ إقليدس اللي كان معلم العلوم التعليمية في مدرسة الإسكندرية ، ترجمة كرنيليوس فان ديك المستشرق الأمريكي
 .....
 بيقولك :)
 الهندسة علم موضوعه قياس المقادير ، و المقدار هو كل ما له واحد من ثلاثة أشياء وهي ... طول و عرض و عمق
 رابط التحميل و القراءة المباشرة :
 http://download-engineering-pdf-ebook...
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 Adam Braus
 14 reviews 3 followers
 November 19, 2009
 Geometry is not a given, it is a mystery.

 Euclid invites the modern reader to rethink what a book is, and how we might have related to math differently as a child in school if The Elements had been our textbooks. What are the elements that the title refers to? What are the complexes that the elements make up?

 You cannot just read this book, I would suggest demonstrating the proofs one by one on a board in front of peers, then discussing each one.

 I have read a lot of books, this book is the most instructive one I have ever experienced.

 book ten is pretty boring. the fireworks are in books 1, 2, 5, 7 and 13

 11 likes
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 Diem
 475 reviews 163 followers
 February 25, 2014
 Update: Again, I find myself starting with the disclaimer that I did not actually read this in its entirety. And I never meant to. My goal was to work through the first four books and that I have done. Can I honestly say that I enjoyed it and am glad I did it. Yes, I really can. Not sure that it makes me a better or wiser person but it makes me SOUND like a better and wiser person when I get to say things like, "Oh, yes. It is like that time I worked through Book 3 of Euclid's 'Elements'..." That right there is so going to be worth the cost of admission.
 *************************

 Just finished Book I. I worked through the 48 proofs by taking about 4 - 7 per morning. Yesterday morning I worked through 5 proofs and had just about enough time for two more which would have allowed me to finish the book. But I was pretty fried already. But, I love a finish line so I dug deep. Then I looked at the figure for 47 and said, "Oh, hell no." Packed it in and headed to the gym.

 This morning I lit a candle, poured a coffee and sat down to look at 47 and laughed. The figure was a damn mess but even my tiny brain recognized the Pythagorean theorem in the enunciation. Okay, I could have done that yesterday. But, man, algebra certainly tidied that bit up didn't it?

 So, I'm not sure how much further I'm going to take this. Part of me wants to see it through the first 4 books. More of me wants to move on to Aristotle. Dunno what to do.

 Anyway, how the hell can a non-mathematician like me "rate" this book? What gives me any authority at all to have an opinion on it? Nothing. So, let's say the rating goes to the high quality of this particular edition. Also, the cover art is perfection.
 2014 shelved
 10 likes
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 Alexander
 7 reviews
 September 14, 2008
 I never really began to understand mathematics until I encountered Euclid. If I had had this book as a child, I feel like my eyes would have been opened to a lot more than they were.

 Euclid's Elements is the foundation of geometry and number theory. There is no long-winded explanation; instead, from a set of 23 definitions, 5 postulates, and 5 common notions, Euclid lays out 13 books of geometrical proofs. In each proof, he asserts a mathematical truth or asserts that a geometrical construction is possible, and then goes step by step through it.

 Most of the propositions require a bit of work to understand, but the moment of insight in which one goes from "What on Earth is this guy talking about?" to "Ohhhhhh...." is pure pleasure.
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 David Sarkies
 1,852 reviews 331 followers
 August 3, 2021
 The Original Maths Textbook
 1 Aug 2021

 So, I was sitting in a pub up in the Victorian town of Beechworth, reading this book when somebody leaned over to me to asked me what I was reading. When I told him, he laughed and made a comment that it seemed to be an appropriate book to read before going into lockdown – our fifth of the pandemic. Okay, I suspect that a lot of you out there will laugh at the fact that we are complaining about a lockdown considering that our case numbers, and our fatalities, are ridiculously low, but I guess we Australians really don’t know, or even appreciate, how good we have things.

 Mind you, it does raise the question as to why anybody would want to read Euclid considering it is basically no different to reading a mathematical textbook, and more so voluntarily as opposed to being instructed to by your school/university teacher. Mind you, I don’t particularly know all that many people who would read a textbook even if instructed to. Sure, I did, to an extent, but then again I’m something of an oddity, and I’m always looking for another book to add to my Goodreads list of books read, and to write a review on it.

 Anyway, if you can handle something like the following:


 Let ABCD be the given circle.
 It is required to inscribe a square in the circle ABCD.
 Draw two diameters AC and BD of the circle ABCD at right angles to one another, and join AB, BC, CD, and DA.
 Then, since BE equals ED, for E is the center, and EA is common and at right angles, therefore the base AB equals the base AD.
 For the same reason each of the straight lines BC and CD also equals each of the straight lines AB and AD. Therefore the quadrilateral ABCD is equilateral.
 I say next that it is also right-angled.
 For, since the straight line BD is a diameter of the circle ABCD, therefore BAD is a semicircle, therefore the angle BAD is right.
 For the same reason each of the angles ABC, BCD, and CDA is also right. Therefore the quadrilateral ABCD is right-angled.
 But it was also proved equilateral, therefore it is a square, and it has been inscribed in the circle ABCD.
 Therefore the square ABCD has been inscribed in the given circle.


 Then maybe Euclid’s Elements is a book for you, otherwise I suspect that your eyes will end up glazing over with boredom, as is prone to happen when you basically end up reading a mathematics textbook. However, there are quite a few interesting things relating to those works beyond it being little more than an ancient Mathematical textbook. For instance, apparently it was the second book to ever be printed by Gutenberg, with the Bible being the first. Also, it was the only maths textbook right up until the 19th Century, though I do sort of suspect that this might be an exaggeration considering that there was much more to maths than just Euclidean Geometry (and number theory – he goes into Number Theory in this book as well, and spends quite a lot of time exploring the concept of Prime Numbers).

 Mind you, it isn’t as if Euclid came up with all of this stuff. In fact, it is generally accepted that Pythagoras’ theorem was floating around for quite a bit of time before somebody decided to attribute it to Pythagoras (who apparently wasn’t a mathematician). Like, the Egyptians used it (how else do you think they were able to come up with Pyramids), and the Babylonian’s used it. There is also the Golden Ratio, which was used to build the Parthenon, which was constructed around 50 years prior to Euclid’s birth. As such, much of what is contained in this book was already known, it is just that Euclid did what pretty much many of the other writers of the period did, and that codifies all of the knowledge into one work. Also, considering that he was born in Alexandria, the place with the Library, it is probably not all that surprising that he ended up codifying mathematical knowledge of the time.

 The other interesting thing is that Euclid seems to use a primitive form of algebra, which is something like 1300 years before Mr Al Jebra (al-Khwarizmi) condified the concept in his book ‘The Science of Restoring and Balancing. However, Euclid’s version is basically discussing numbers based on lines, and how the lines happen to relate to each other. Even in the section on Number Theory, all of his concepts revolve around the use of lines, which shouldn’t be too much of a surprise considering most maths in those days generally involved building stuff (or lobbing rocks, but mostly building stuff), though I’m sure the merchants also used numbers to calculate their profit, and how much stock they happened to have on hand (yeah, we do have quite a lot of accounting work from the ancient time).

 Mind you, like a lot of textbooks, particularly one’s dedicated to maths, this is probably not the type of book that you would read cover to cover. Okay, I read it cover to cover, but that is probably because I wanted to read one of the classics, and one that has had a huge influence upon our society, and in fact the world. Sure, it certainly isn’t an easy read, but it is really rather interesting to see the source from which the mathematical foundations were developed.

 The other interesting thing that I picked up is that this book is probably the type of book that people in the medieval ages would have considered a ‘spell book’. The reason I suggest this is not that it is used to actually cast spells, but it is a book that gives us an insight into how the universe comes together, and it gives us insights into how we can build things that not only won’t fall down, but will actually stand the test of time. The fact that there are many buildings still standing that have stood for thousands of years goes to show how much the ancients knew, and how influential the contents of this book were.
 science
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 Clint
 7 reviews 4 followers
 April 8, 2011
 In order to fully enjoy Euclid, you must first completely rid yourself of preconceptions about the world of mathematics. Euclid sets up his postulates and from there he proves what he needs to prove. There is very much a sense of wonder and excitement in reading Euclid. He proves things that we would never think to prove and he does so in a completely logical and beautiful way. With a climactic end in which he proves that the five Platonic solids - the cube, octahedron, tetrahedron, icosahedron, and dodecahedron - can be constructed and then proves that these are the only five solids which are contained by equilateral and equiangular figures, Euclid is in a way very satisfying and at the same time he gives one a desire to delve further into the world of mathematics.
 great-books-program
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 Дарья
 72 reviews 34 followers
 August 23, 2016
 Most exquisite.
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 William Schram
 1,967 reviews 87 followers
 February 7, 2022
 "The Elements" is a series of books on mathematics written by Euclid. It is an ancient textbook, and for centuries it was the second most published work in the world behind the Bible.

 My copy takes the text from a 1908 translation. Each proposition and theorem gets an explanation. The book is lengthy and exhaustive; it makes the book dull. Finally, due to its size, it is hard to carry.

 On the other hand, "The Elements" is groundbreaking. As a textbook, it works to some extent. It wasn't questioned until the 19th century, giving it plenty of staying power. I suppose the main reason to read it now is for historical reasons. There has to be some reason for "The Elements" being so influential. My copy contains the original Greek text and a translation of what it says.

 We know little of Euclid, but he might have been a contemporary of Plato. We do know that Euclid did not originate these results. Instead, he is a great expositor. Euclid placed the results into a single framework, making it easy to reference. Furthermore, he builds on each axiom, logically leading from first principles to advanced ideas.

 Thanks for reading my review, and see you next time.
 classics history mathematics
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 Jackson Snyder
 33 reviews
 March 21, 2024
 This book genuinely changed the way I think about math and geometry. So amazing. I love shapes. Holy shit.
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 Roberto Rigolin F Lopes
 363 reviews 104 followers
 May 31, 2019
 We are in -290, Euclid is writing down some obvious stuff, also called axioms by educated fools. Here goes my favorite. "Let it be granted that things which are equal to the same thing are equal to one another". Also by transitivity, the author of this gem certainly was an interesting fool. A fool trying to be consistent. Nowadays, we call these peculiar animals mathematicians. From there he plays with his definitions… I am writing this blah in Greece and can tell how much of nature he had to ignore to be consistent around the birth of civilization. These days we can do much better because Descartes 1596-1650 connected algebra and geometry so Gauss 1777-1855 + Riemann 1826-1866 (*) finally build the tools to complement/challenge Euclid’s ideas. Hilbert 1862-1943 followed playing with the infinite geometries out there (or inside here, Plato). Then Einstein 1879-1955 showed that the universe is non-Euclidean. Then Gödel 1906-1978 showed that Euclid figured out the only way of constructing consistent arguments. They say this book has vast influences among our best thinkers and within civilization in a broad sense. But I didn't solve all the ancient problems within because it is okay to be incomplete. Quod Erat Faciendum (Q.E.F.). *Warning: in 2019 we are still missing the tools to do algebra with mathematicians.
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 Valentin Chirosca
 Author 7 books 10 followers
 December 9, 2012

 Often called the Father of Geometry, Euclid was a Greek mathematician living during the reign of Ptolemy I around 300 BC. Within his foundational textbook "Elements," Euclid presents the results of earlier mathematicians and includes many of his own theories in a systematic, concise book that utilized meticulous proofs and a brief set of axioms to solidify his deductions. In addition to its easily referenced geometry, "Elements" also includes number theory and other mathematical considerations. For 23 centuries, this work was the primary textbook of mathematics, containing the only possible geometry known by mathematicians until the late 19th century. Today, Euclid's "Elements" is acknowledged as one of the most influential mathematical texts in history.

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 Scott
 4 reviews
 June 28, 2012
 The original bible of geometry! Plato had an inscription above the entrance to his Academy: "Let no man enter here who is ignorant of geometry." From Plato's time to the 20th century, Euclid's "Elements" was the gold-standard for learning this most basic of the mathematical disciplines. When you read it, you will understand why. Every proof and every construction is worked out meticulously, step-by-step, such that there is zero doubt about the final result. Required reading for all truly educated people!
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 Francisco Tapiador
 Author 9 books 8 followers
 August 10, 2010
 There are three crucial science books in the history of mankind. This is one of them. I have no idea how this guy could devise these ideas so soon. Enormously influential. Forget sudokus, the problems here are more interesting.
 novel
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 Arnab Das
 8 reviews
 February 24, 2023
 Euclid's Elements is a timeless masterpiece of mathematical reasoning and logical deduction that has stood the test of time. Despite being written over two thousand years ago, its insights and methods still inspire and challenge contemporary mathematicians and scientists.

 Thomas Little Heath's translation is a remarkable rendition of the original text that maintains its elegance and precision. The clarity of the explanations and the inclusion of helpful diagrams make the book accessible to readers with varying levels of mathematical expertise. Additionally, the commentary and notes provide an informative and illuminating analysis of the historical and cultural context of Euclid's work, enriching the reader's understanding of the material.

 Euclid's Elements contains the principle that "the whole is greater than the part," which serves as the basis for many crucial theorems in geometry and arithmetic. Euclid rigorously proves this statement by assuming the opposite and deriving a contradiction, demonstrating the importance of axioms and the power of logical deduction in mathematics. Heath's translation fully captures the elegance and beauty of Euclid's reasoning, making it a valuable resource for anyone interested in mathematics. Students, teachers, and enthusiasts alike are highly recommended to explore this masterpiece of mathematical reasoning and logical deduction.
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 Dean
 65 reviews
 July 6, 2021
 Didn't read the entire thing (not insane enough to). 5 stars primarily for the historical significance and Euclid's overwhelming genius. Despite the anachronistic grammatical structure of the translation, it's actually quite an enjoyable read. The construction proofs are fun to figure out on your own and seeing the propositions of each book fit together is like watching a time-reversed video of a shattering cup. I recommend looking through at least the first few books just to get an idea for the rigor involved in laying the foundations of two millennia of math.
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 Valentin Chirosca
 Author 7 books 10 followers
 December 9, 2012

 This edition of Euclid’s Elements presents the definitive Greek text—i.e., that edited by J.L. Heiberg (1883–1885)—accompanied by a modern English translation, as well as a Greek-English lexicon. Neither the spurious books 14 and 15, nor the extensive scholia which have been added to the Elements...
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 Joshua Dew
 201 reviews
 August 1, 2021
 "Let no one ignorant of geometry enter here." It took me almost 2 years to trudge through this thing so I'm REALLY hoping Plato will let me into his Academy now. Glad to have Euclid knocked off my bucket list!
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 Peter
 24 reviews 19 followers
 Want to read
 December 31, 2008
 Wikipedia: "Euclid's Elements is the most successful and influential textbook ever written." Sounds promising :]
 mathematics
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 Jovany Agathe
 279 reviews
 December 4, 2021
 The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Love it.
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 Robin
 261 reviews 11 followers
 May 24, 2022
 Difficult, beautiful, worth working through. I needed help to understand it. But I am glad to have worked through it.
 classical-education for-teachers non-fiction
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 Marcos Augusto
 732 reviews 6 followers
 April 15, 2024
 Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (c. 440 bce). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle. The older elements were at once superseded by Euclid’s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids.

 A brief survey of the Elements belies a common belief that it concerns only geometry. This misconception may be caused by reading no further than Books I through IV, which cover elementary plane geometry. Euclid understood that building a logical and rigorous geometry (and mathematics) depends on the foundation—a foundation that Euclid began in Book I with 23 definitions, five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem.

 Book II has been called geometric algebra because it states algebraic identities as theorems about equivalent geometric figures. Book II contains a construction of “the section,” the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. (This division was renamed the golden section in the Renaissance after artists and architects rediscovered its pleasing proportions.) Book II also generalizes the Pythagorean theorem to arbitrary triangles, a result that is equivalent to the law of cosines. Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon.

 Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus to Eudoxus of Cnidus. While Book V can be read independently of the rest of the Elements, its solution to the problem of incommensurables (irrational numbers) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms, culminating in the “application of areas,” a procedure for solving quadratic problems by geometric means.

 Books VII–IX contain elements of number theory, where number (arithmos) means positive integers greater than 1. Beginning with 22 new definitions—such as unity, even, odd, and prime—these books develop various properties of the positive integers. For instance, Book VII describes a method, antanaresis (now known as the Euclidean algorithm), for finding the greatest common divisor of two or more numbers; Book VIII examines numbers in continued proportions, now known as geometric sequences; and Book IX proves that there are an infinite number of primes.

 According to Proclus, Books X and XIII incorporate the work of the Pythagorean Theaetetus (c. 417–369 bce). Book X, which comprises roughly one-fourth of the Elements, seems disproportionate to the importance of its classification of incommensurable lines and areas (although study of this book would inspire Johannes Kepler [1571–1630] in his search for a cosmological model).

 Books XI–XIII examine three-dimensional figures, in Greek stereometria. Book XI concerns the intersections of planes, lines, and parallelepipeds (solids with parallel parallelograms as opposite faces). Book XII applies Eudoxus’s method of exhaustion to prove that the areas of circles are to one another as the squares of their diameters and that the volumes of spheres are to one another as the cubes of their diameters. Book XIII culminates with the construction of the five regular Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) in a given sphere.

 Almost from the time of its writing, the Elements exerted a continuous and major influence on human affairs. Euclid set a standard for deductive reasoning and geometric instruction that persisted, practically unchanged, for more than 2,000 years.
 bce classical-antiquity greek-literature
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 JP
 1,163 reviews 40 followers
 May 18, 2013
 Quite a thorough work. From reading this masterpiece and cornerstone of geometry, one can understand how impressive the original development was as a human achievement. Euclid wrote his Elements around 300 BC. He was one of Plato's younger students, but older than Archimedes. The 13 books of his Elements cover angles, line segments, triangles, rectangles, squares, the irrational numbers, parallelagrams, parallelapipeds, spheres, cones, and polygons. He gives a full treatment of area and never quite defines it. Many of his proofs are much simpler with the tools of algebra and Cartesian space. It's impressive that Euclid reached the same conclusions without the benefit of either. The hundreds of propositions are completely proven, using a handful of definitions that begin each book and the previously proven propositions. Some of these propositions are interesting because there is no strong intuitive basis. Some are uninteresting and never again referenced. Some are fundamental building blocks. And many are "how to" type proofs, ensuring that a given figure can be created under certain circumstances, which again are used in other proofs when auxiliary figures are needed. Among his propositions are the Pythagorean theorem, a number of points regarding equal areas and relationships between areas and volumes, and examples of a variety of techniques. When he uses proof by contradiction, his "absurd" and "which is impossible" are so clear and final that one can understand how the early philosophers latched onto the new mathematics. His use of "absurd" is very reminiscent of a Hobbes' style of argument, as well as, I'm sure, so many others who applied the same approach to political and religious philosophy. Other areas he concentrates on include odd and even numbers, means, squares, ratios, and an assortment of types of "irrationals." The latter are much more detailed than anything I ever studied. Much of his middle chapters seem less applicable to anything other than number theory. Two anecdotes involve his early students. In response to a kingly student's wanting to know if there was an easier way, Euclid responded "There is no royal road to geometry." Another student asked what was the value of this study, to which Euclid replied: "Give him a coin since he must needs make gain by what he learns."
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 J
 730 reviews 502 followers
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 March 12, 2010
 Okay, so Euclid is hugely important because he more or less originated the idea of a closed, axiomatic system of thought, the sort of thing that would go on to influence people like Vico and Spinoza, not to mention pretty much every mathematician who ever lived. Reading the Elements is about as exciting as reading a cookbook. You start with these parts, mix them together in this way, and get this whole. This way of thinking is probably too heavily ingrained into our mindsets after all these millenia to seem like anything other than a rote, obvious exercise. If you really, REALLY love 2-D geometry, you'll dig it. If not, it will probably just feel like a textbook.
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 Luis Uribe
 19 reviews 1 follower
 January 25, 2011
 I tried to get through Elements in high school at the insistence of Fr. Rathmusen. Geometric construction was huge at Don Bosco Tech as were geometric proofs. I'm much more appreciative of the work today. It puts you in a very logical, regimented frame of mind; an essential for mathematics. This particular edition has notes, clear graphics comments that clarify the 19th century language nuances. This is a beautiful edition of a pillar of literature and science.
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 Johannes
 23 reviews 1 follower
 October 10, 2007
 Sometimes when I'm maximizing production functions I weep bitterly and think of my time with this book.
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 Andrew
 1 review
 January 2, 2010
 All great minds have found fascination in the books of Euclid.
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A History of π
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 A History of π

 Petr Beckmann

 3.94
 2,768 ratings 152 reviews
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 The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.
 Genres Mathematics History Science Nonfiction Popular Science History Of Science Education
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 208 pages, Paperback

 First published January 1, 1970

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 Petr Beckmann

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 3.94
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 Andrew Breslin
 Author 3 books 75 followers
 April 23, 2013
 I received this book on March 14, during my annual pi day celebration. We had finished the pizza, but hadn’t gotten to the apple pie yet. We were listening to a special music mix for the occasion, including “Circle Dream,” by 10,000 maniacs, “Wagon Wheel,” by Old Crow Medicine Show and of course, “American Pie,” by Don Mclean. And while the pie was delicious, this made for an even tastier dessert.

 What the world needs now are more opinionated and bellicose mathematicians, and I’m itching to pummel anyone who says otherwise. Everyone thinks mathematicians are a soporific lot who bring to their work all the passion and ardor of a three-toed sloth on barbiturates. But no! There are people out there who like math and haphazardly hurling invective at pretty much anyone who doesn’t have enough sense to duck out of the way.

 Beckmann is one such calculating curmudgeon, never for a moment dissuaded to let fly with a litany of political opinions even while right in the middle of an equation. (“Now before we go leaping to the other side of that equals sign, let me tell you what I really think of the Soviet Union.“) He’s got an axis to grind. A chi(p) on his shoulder. A bone to pick (specifically: a radius).

 You don’t have to love either math or getting into fur-flying cerebral brawls as much as Beckmann or myself in order to appreciate this book. But really: it doesn’t hurt. Don’t expect one of those popular math books that dumb it down and pretty it up to avoid offending or intimidating anyone. No punches are pulled here. Expect to be both offended and intimidated, and maybe a little confused. You might even be personally and directly insulted, and, what makes it worse: you won’t be sure.

 Some of the math went sailing right over my head. Fortunately I do have enough sense to duck or I would have been smacked in the face with a dangerously pointy arctangent function, and we all know how much that would have sucked. Or maybe we don’t. The point is that you are almost certainly not going to understand all the individual mathematical details, but this doesn’t matter much. You’ll pick up the gist of it, and what a fascinating gist it is. The unsolicited rants about the Romans, the Catholic Church, and assorted megalomaniacal mathematicasters are just a delightfully fractious bonus.

 I can hardly wait for March 14 to roll around again. I’m going to give this book to some worthy recipient, bringing its history with me, as well as this review, full circle.
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 Joe Hilley
 Author 17 books 377 followers
 March 1, 2020
 Great book. If you enjoy reading about the history of math, you'll enjoy this book. Even if you skip over the equations.
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 Chad
 254 reviews 49 followers
 October 12, 2008
 The fact that it was written in 1971 adds a little bit of out-of-date flavor that makes "A History of Pi" a lot more amusing than it otherwise might have been.

 As a history of pi, it kind of doesn't really work for a couple of reasons. First of all, its not really a history of pi. Its more like a history of mathematics in general. But even there, its far too anecdotal to serve as any real history lesson. Beckmann jumps and skips from one era to another giving you the lowdown on a random sampling of famous mathemeticians. The fact that he occasionally delves into the methods by which those mathemeticians were able to calculate pi with greater and greater accuracy over the years I guess justifies the book's title.

 Secondly, Beckmann does absolutely nothing to make pi seem like the awesomly inpenetratable number that it is. The main reason I picked this up to read in the first place was because I recently read the chapter from Richard Preston's most recent book about the Chudnovsky brothers and their strange obsession with calculating the digits of pi. In that single chapter, Preston did a fascinating job of pulling you into the bizarre world of pi, and made me understand why a mathemetician could get lost in all those infinite, endless numbers. Petr Beckmann never really attempts to get into the philosophical implications of pi, and that left me a little wanting.

 The third thing that bugged me was Beckmann's occasional lapses into opaque mathematical formulas. To his credit, he does include a helpful tip in his introduction:

 "The reader who find the mathematics too difficult in some places is urged to do what the mathemeticians will do when he finds it too trivial: Skip it."

 While I don't feel like I missed anything important in skipping over the many pages of equations, I am a little irked at being made to feel ignorant by the casual way in which Beckmann starts talking about things like the arcsin of the integrand.

 Among these little problems, however, arises the "1971 Factor". This Factor manifests itself in a few amusing ways, not the least notably in the book's final chapter (apparently added in its third edition) about "The Computer Age". You can't help but laugh as Beckmann describes the BASIC programming language as "simple, but powerful". Its like basking in the delight of a five year old's amazement when you pull a quarter out of their ear. It's just so adorable.

 The other amusing 1971 side effect is Beckmann's unmasked distate for those darned communists! Amid the sometimes dry historical accounts and the calculus equations and geometric theorems, the author just can't help himself and throws in several rather opinionated rants against those pesky Soviets. They made for some odd juxtapositions that brought a smile to my face every time they came up.

 [By the way, Beckmann is a native of Prague, Czechoslovakia, and was forced to flee his home at a young age to escape the Nazis, so his personal distate for any sort of totalitarianism is quite understandable. It's just a weird tangent to wander into in the middle of a text on the history of mathematics.]

 In the end, I didn't find "A History of Pi" to be a waste of my time. But it didn't quite live up to the mysterious awe inspired by the Preston artical that led me to pick it up in the first place.
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 Elentarri
 1,723 reviews 35 followers
 April 3, 2024
 I listened to the audiobook while doing chores. This was probably not the best way to "read" a book that ended up having a vast quantity of equations and geometrical diagrams etc. A fair amount of the maths/geometry went over my head, but no doubt it would have helped if I had had the text in front of me, rather than listening to the audiobook.

 Despite that, this book isn't so much a history of π, as an irreverent collection of historical factoids with some relevance to the advancement of mathematics (some of which are not accurate); mini-biographies of famous mathematicians; opinionated anecdotes; and the sometimes amusing rants in which the author attacks the Romans, the Church, institutionalized religion in general, imperialism in general, warmongers, communism and the Russians - woven throughout is the sequence of mathematical methods and proofs through time to determine the value of π with greater and greater accuracy. The original book and the next two editions were written in the 1970s during the cold war, providing a decidedly blunt and non-politically-correct vibe.

 While the bits of history were interesting and the rants fairly amusing (ok! I agreed with some of them), this book ended up being disappointed in terms of learning more about the subject matter in a coherent fashion. The book was "ok" but not something I would recommend.
 2024-read-books audiobook history-of-things
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 Satendra Deo
 11 reviews 3 followers
 February 2, 2018
 Easily readable for a mathematical book. Full of interesting anecdotes. A little light on Eastern mathematicians. Consider
 1. Chinese - Lui Hui’s (3rd century) Algorithm - With this method Zu Chongzhi obtained the eight-digit result: 3.1415926 < π < 3.1415927, which held the world record for the most accurate value of π for 1200 years, https://en.wikipedia.org/wiki/Liu_Hui...

 2. Japanese - Seki Takakazu (1642 – 1708 ) who knew Pi to 10 decimal places https://en.wikipedia.org/wiki/Seki_Ta...

 3. Arabic - Refer Moustafa Mawaldi articleon the Arabic influence here http://www.muslimheritage.com/article...

 4. Indians - have contributions from the greats Varahamihira, Brahmagupta, Sridhara , Aryabhatta and Madhava but one cannot go past Srinivasa Ramanujan whose fast (exponentially) converging infinite series of Pi opened the door for Digit Hunters to use computers to calculate Pi to trillions of decimal places. https://en.wikipedia.org/wiki/Sriniva...

 SDe0 02/02/2018
 history
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 Jimmy Ele
 236 reviews 92 followers
 July 13, 2017
 Brilliantly outlined history of pi, but just like Charles Seife's "Zero The Biography of a Dangerous Idea", I am left wanting more. I want the Chinese, Mayan, and Indian history of pi. The Mayan history of pi was most likely burned by that one bishop, but the Chinese and Indian history I believe to be still in existence. Other than that, it was a thoroughly engrossing read and definitely nice to have read for my continuing Mathematics education.
 definite-up-nexts
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 Jeff
 637 reviews 49 followers
 April 7, 2015
 Dear Goodreads Admins:

 Please rig your system so that the average star rating for this book is equal to the ratio of a circle's circumference to its diameter, rounded to three significant digits.

 Thanks,
 --jeff

 P.S. I am still almost as ignorant about π as i was before reading this book. Disappointing.
 non-fiction numbiz
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 Charles
 2,679 reviews 36 followers
 December 26, 2016
 This book earns five stars for the explanations of the history how the knowledge of the ratio of the circumference of a circle to the diameter (π) progressed. The rating was reduced due to the inclusion of several snarky and otherwise irrelevant comments regarding politics and the actions of governments.
 For reasons that have never been understood, π has received far more attention than all of the other constants. Even though other numbers, such as e, the base of the natural logarithms, are just as important in mathematics, they have not received the attention that π has. Beckmann does an excellent job of tracing the accuracy to which π is known as well as the many places where it has appeared as a component.
 There is also a section describing some of the people convinced that they have squared the circle, despite it having been proven that it cannot be done. Underwood Dudley did the mathematical world a favor when he coined the phrase “Mathematical Cranks” to describe such people. There is also a section on the attempt by the Indiana State Legislature in 1897 to decree the value of pi. The bill unanimously passed the Indiana House of Representatives before it was permanently tabled.
 The political viewpoint of the author is summarized well in the last paragraph of the content on the DJ describing the author.

 “He also publishes a monthly pro-science, pro-technology, pro-free enterprise newsletter ‘Access to Energy,’ in which he promotes the viewpoint that clean energy can be made plentiful, but that access to it is blocked by government interference and environmental paranoia.”

 Snippets of historical commentary similar to the tone of this passage are inserted throughout the book.
 Pi has received more than its deserved amount of attention down through history, making its history extensive and long. Beckmann has developed a readable account of how knowledge of the number and its value has been explored by the greats and some not so greats.
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 Jesse
 55 reviews 4 followers
 October 9, 2009
 The History of π is a fascinating work in the sense that it provides a narrative which frames for the reader, the development of this infamous mathematical constant’s calculation. The logical sequence of mathematical proofs as interwoven with the text is surely the strong point of the work. The weakness lies in the author’s multitude of obvious personal biases. Beckmann’s passionate political views quickly transform his attempt at a serious account in the history of science, to an ardent rant against all which he considers to be the root of societal evils. Consequently, his attack on Imperialism, the Church, and other institutions of power and orthodoxy should be expected, and they are not terribly callous. There are, however, some definite historical misrepresentations and oversights.
 The biggest error in Beckmann’s thesis is his attempt to draw a divisive line between those who were engaged in so called “true” science and those who flirted with the occult. Recent studies have clearly indicated that many of the greatest scientific minds in Western history –including Newton, whom the author holds in such high esteem- did in fact experiment with occult practices.
 Beside its flaws the book still stands as an interesting work of quasi-interdisciplinary scholarship.
 4 likes
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 Dustin
 92 reviews 16 followers
 August 21, 2008
 In the first few pages, the author describes this book as being 'light on the math.' Well, you could have fooled me! Clearly, it is a book about math, and more than that, it is a book about a transcendental number, a constant that can NOT be written. So, starting from that point, you know that any math this *is* included is likely to be bizarre. Fair enough.

 However, when the first few examples he gives of how the ancients found their values for pi are rendered into oh-so-simple differential calculus, it does not count as making the book math-lite to merely leave out the proof. Leave out the differential calculus, too! (Near as I can tell, the half-angle arctangent series are muy importanto to programming computers to figure out pi for us.)

 However, the upshot to this book is that the author barely escaped from Soviet Russia, and so has ZERO tolerance for oppression in any of its forms. Therefor, his tangents tend to turn into rants, including my favorite part of the book, where he (successfully, IMHO) compares that paragon of western civilization, the Holy Roman Empire, with a few other empires: Napoleon's ill-fated French empire, Russia's ill-fated Soviet empire, and Nazi Germany's ill-fated Third Reich. He also pulls no punches when dealing with forces that have stifled or otherwise countermanded the course of scientific and mathematical progress, saving special vitriol for those who burned libraries. And to be clear, that was EVERYONE, at some point or another.
 pop-science
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 Keith
 269 reviews 2 followers
 May 3, 2014
 When my oldest daughter was accepted to the North Carolina School of Science and Math (a college level high school for the smartest and nerdiest students in North Carolina), I went with her to orientation. At one of the sessions, the chairman of the math department came out and said, "This is what we teach in math here at NCSSM." Forty-five minutes later I leaned over to my daughter and said, "Have you understood anything in the last 45 minutes?" Saying that she had, I was baffled but reassured. My experience with that teacher is much the same as my experience with Petr Beckmann with this book. Beckmann relates some fascinating and rather opinionated stories about the history of mathematics and mathematicians while crossing my eyes with mind-numbing and incomprehensible (to me) formulae explaining how pi was calculated. Apparently one does not simply divide 22 by 7. Who knew? Beckmann comes down very hard on the Romans, who he equates with Nazi Germany (ouch) and relates some interesting stories about Archimedes, Newton, and other mathematicians whom I in my mathematical ignorance had never heard of. I skipped most of the real math (with the author's blessing, as he states in the preface), and stuck to the text which was satisfying for me in my own way. I'm sure someone well-versed in math would have gotten more out of it, but I can't say I was disappointed.
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 Roberto Rigolin F Lopes
 363 reviews 104 followers
 March 12, 2020
 We are in 1970, Petr assumes that history of pi matches well with history of human civilization. After all, we are tool-wielding animals (from a quote in the book). Given a century (say between - 2000 and < 1970), our sophistication computing pi is related to scientific developments in that time window. And Petr dares to go through the centuries sharing his sharp opinion on civilization (he is hilarious sometimes). For example, some religious texts (say > 1) were happy with pi = 3. But, many years before, Archimedes (-212) wanted to know a “bit” more but other ancient Greeks couldn't handle irrationals/transcendentals (-322). Archimedes was the first to come up with an algorithm to compute pi to any desired precision. I laughed-out-loud with Petr comparing “Archimedean science” with “Aristotelian mambo-jambo” (he makes a reference Aristotle's book on Physics; which I read but don't recommend). He also points out that the Roman empire halted mathematical developments and it took a great intellect like Galileo (1564) to challenge Aristotelian ideas to start doing experiments. Then, comes Kepler, Newton, ... Euler, Laplace and computers. Takeaway: the ratio wit/page is higher than pi.
 favorites
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 Diego
 15 reviews
 May 12, 2016
 Halfway through the book, the author writes that "the digits beyond the first few decimal places [of Pi] are of no practical scientific value. Four decimal places are sufficient for the design of the finest engines; ten decimal places would be sufficient to obtain the circumference of the earth within a fraction of an inch". And yet I find myself continuing reading through the rest of the book of how new methods to find more decimals places were discovered.
 Although a little outdated in the last chapters, the underlying narrative of the book is a brief history of man, beginning in the stone age all the way through the "computer age" at the end of the decade of 1960's, with Pi as protagonist.
 Curious is to grasp out how much progress we have done mathematically, but how much little progress we have done as human race. The author summarizes that throughout the history it has become fashionable to blame science and technology for the ills of society, and he writes in his last lines that perhaps the n-th generation of intelligent computers will make a better job of keeping peace among men and nations than men have ever been able to do.
 We have failed so far.
 3 likes
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 Donna Herrick
 570 reviews 7 followers
 February 10, 2022
 Why read a book about pi? Because pi is strange and interesting. Pi is the ratio of the circumference of a circle to it's diameter and area. So, if you want to figure out the number of servings in a family size pizza versus a medium or personal size pizza you need to understand and know the value of pi. For pizzas, the value of 3 is probably good enough. For sewing and planning building projects, an easy to remember and better approximation is 22/7.
 The book describes the history of how people have created methods of calculating increasingly precise values of pi, now using computers it is up to millions of digits. In fact, the speed and accuracy 0f the calculation of pi is now used as a measure of the quality of microprocessors. My method of calculating the value of pi is to use the method of Archimedes, interpolating between inscribed and circumscribed polygons. But far more precise and rapid methods are derived from trigonometric functions that are described in the book. Unfortunately, those discussions were beyond what I remember of high school trigonometry and the book does not go into depth about how those formula were derived. On the other hand, the book is filled with dozens of funny asides about modern "circle-squarers", politicians, theologians and other crackpots.
 history mathematics non-fiction
 2 likes
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 Davy Bennett
 636 reviews 14 followers
 December 31, 2023
 I liked the history portions of the book and tolerated the math parts.
 Some interesting stuff, dude doesnt pull punches.
 I like how he gives it to dictators like Frederic and Catherine the Great. I think he is a little hard on the Church.
 arts-art donated gone-went-away
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 Owen
 11 reviews 8 followers
 January 1, 2008
 This is the kind of book that Barnes & Noble publishes then practically gives away around Christmas as suggested stocking stuffers. I think that's how I ended up with it. Anyway, this book turned out to be much better than anticipated. It traces pi throughout history, going back to Babylonians and Egyptians and guessing how they might have arrived at their calculations. Practically every famous mathematician--Euclid, Descartes, Archimedes, Galileo Newton, Euler, etc--is discussed here, as pi has been a topic they've all either dabbled with or obsessed over.

 Not only does the author trace pi's progress, he discusses times when pi (and by extension, math, science, and knowledge) made scant progress. These were periods of religious intolerance towards science, which the author despises and makes no effort to eliminate anti-religion bias. Okay, so it was published in the 70s, but regardless, the book got too preachy for me; at one point I think he asks, "How many Newtons have died in Viet Nam?" Several other jabs at Soviet labor camps are thrown in, often with limited context.

 Pi in the computer age is a tacked-on last chapter in later editions. Even so, it's still two or three decades behind. Future editions should both expand on pi's use in modern math and update (or better, eliminate) the preachy Cold War side-notes.
 2008
 2 likes
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 Papias
 24 reviews 3 followers
 February 3, 2011
 I'm enjoying this book; even with Beckmann's rants. But my problem is with his willful ignoring of facts, especially when you consider how little tolerance Beckmann has for good research. For example take this passage from the chapter Night:
 In 1486, Torquemada sentenced the Spanish mathematician Valmes to be burned at the stake because Valmes had claimed to have found the solution of the quartic equation. It was the will of God, maintained the Grand Inquisitor of the Holy Office of the Inquisition Against Heretical Depravity, that such a solution was inaccessible to human understanding.
 But if you read the endnote for this passage you find:
 Depman. In fairness I must add that I have not found a reference to this event anywhere else, and Soviet books are unreliable where competitive religions are concerned.
 Beckmann rips the Roman Civilization and the Catholic Church for two full chapters for lesser scholastic violations than this.

 2 likes
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 Rod Innis
 752 reviews 9 followers
 August 9, 2018
 This book has a lot of the history of Pi - I can't type the symbol. It also has a lot of additional history of mathematics in general. I have read a number of such books. I just wish I could remember all that I have read!
 There are some parts of this book where the math becomes too complicated for my not so mathematical mind, but the author does a pretty good job of simplifying quite a bit of it for the non-mathematician.
 He does often show his bias against religion - particularly Christianity - particularly Catholicism especially in a time in history when they opposed good science for no good reason. Sometimes it is necessary to reject unbiblical scientific theories if they contradict biblical truth. He seems to reject Christianity as unscientific always. Science is right - religion is wrong! If you can get past his biases, you may enjoy this book. It is not a recent book. It was written in 1971. But since it deals with history, that only affects the most recent history.
 2 likes
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 Mikko Karvonen
 61 reviews 10 followers
 July 5, 2010
 Fascinating subject - awful book.

 While Beckman may know his mathematics and the story of pi, he lacks many other qualities necessary to write historical books. The writing is full of factual errors and problematic generalizations about non-mathematical things, as well as obnoxious and belittling attitude towards ancient cultures, their achivements and views of the world. A history books should not include off-hand remarks on how many historical mathematical documents arabs wiped their bottoms with or on priesthood of the time being more interested in religious non-sense than science.

 It's a shame as I would have loved to read a well-written story about the history of pi. Now I grew so disgusted with author's attitude that I quit after reading about one fifth.
 did-not-finish mathematics non-fiction
 2 likes
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 David
 103 reviews 5 followers
 June 22, 2018
 Overall a good book. It's a bit dated, especially when the author talks about "modern" attempts to calculate pi on computers and how the current record is 500,000 digits (as of 2018, 2.7 trillion digits are known). There is some heavy math in the book, but it's not important that you understand it in order to enjoy the book.

 My biggest complaint is how much of the book really isn't about pi. Entire chapters are about historical periods and other breakthroughs in mathematics with a spattering of "and during this time so-and-so calculated pi to 60 digits using Archimedes' method." I actually really enjoyed all of the other history in the book, it just didn't have anything to do with pi which is odd considering that the book is A History of Pi
 2018 tea-time-book-club-2018
 2 likes
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 Jack
 838 reviews 16 followers
 October 15, 2017
 An interesting history

 It’s hard to imagine that anyone could spend 220 pages talking about one number. It’s even harder to imagine how otherwise sane people would spend years trying to outdo each other in the number of decimal places they could achieve in calculating pi. That being said, the book turned out to be pretty entertaining. It has some interesting historical notes on great mathematicians and scholars as well as some righteous bashing of the church, the state, and the conquerors for suppression and destruction of scientific knowledge. Sadly, that still happens. Overall, I enjoyed the book.
 2 likes
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 melydia
 1,109 reviews 20 followers
 March 22, 2015
 I like books about the history of math and numbers, but this one was a bit of a slog at times. Lots of equations. It also was strangely dated, what with the author's frequent scathing commentary on the USSR. He also feels a strong hatred for the Romans. Putting all that aside, there are some really interesting nuggets here and there, but in general I imagine this book would only appeal to the truly diehard number nerds.
 2 likes
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 L. Scott
 72 reviews 3 followers
 January 27, 2019
 Entertaining, both for its handling of the topic, which is illuminating and entertaining in its own right when not jarringly interrupted by insufficiently introduced/notated mathematics, and for the bulk of the book, which vacillates between tangental to the topic and mere butterfly chasing and which contains much of the author's mockery of those who suffer from the Dunning-Kruger effect while often serving its own example of that. Some sort of Irony Tower (Dunning-Kruger-Turtle-Tower).
 2019
 2 likes
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 Mark
 18 reviews
 January 1, 2012
 I had no idea the history of a transcendental number could be so politicized! Wastes an entire chapter complaining about how the Romans were a bunch of pricks that he describes as a "thug state." Good for a giggle, and some good info about pi, but he holds nothing back when it comes to his Zionist agenda.
 2 likes
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 Ryan Muzzey
 12 reviews
 August 29, 2018
 Can’t give it a rating with six significant figures. Three is close enough, right? While I enjoyed reading the book, it veered away from the subject matter more than I would like. Some of the proofs were beyond me and might have been explained better. I still found it very interesting and learned quite a bit from it.
 2 likes
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 Jim Conant
 72 reviews 1 follower
 December 23, 2018
 I first read this book when I was in middle school, maybe 6th or 7th grade, and it really captured my imagination. I saw many of the formulae in there as an exciting promise of math to be learned in the future. Reading the book a second time now, I'm bemused by the author's many strong opinions. There are few places where you'll find Aristotle dismissed as a twit, but it's refreshing for sure.
 2 likes
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 Jim
 698 reviews 117 followers
 Want to read
 November 20, 2023
 unsure if this is the Pi book I read ten years ago?


 History records the names of royal bastards, but cannot tell us the origin of wheat. JEAN HENRI FABRE (1823-1915) is a great quote which starts the book.

 also in my book notes I am trying to save words that are new to me .
 aaaa-libby mathematics
 2 likes
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 Robert
 74 reviews 15 followers
 June 21, 2017
 Interesting presentation about PI, and a devastating critique of how first Rome then the Roman Catholic Church postponed progress for nearly two millennia.

 Just technical enough to tell the story, an enjoyable and fast read.
 2 likes
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 Uday Desai
 40 reviews 25 followers
 June 21, 2011
 Excellent book!! Petr Beckmann made this history so interesting, if you like mathematics or just curious, you will be able to enjoy it.

 2 likes
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 Junaid Selahadin
 1 review
 April 19, 2014
 I'm very interesting on pi and I'm very exiting now .i want read now .thank u
 2 likes
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A History of π
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 This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.

 From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"

 “… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”

 From the Reviews

 "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "

 Notices of the AMS, August 1999

 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."

 LMS Newsletter, January 1999

 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..."

 SIGACT News, December 2011


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 1. ISBN-10
 3662572648
 2. ISBN-13
 978-3662572641
 3. Edition
 6th ed. 2018
 4. Publisher
 Springer
 5. Publication date
 July 6, 2018
 6. Language
 English
 7. Dimensions
 7.8 x 0.8 x 9.7 inches
 8. Print length
 334 pages
 9. See all details
 Next page

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 1. Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
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 Editorial Reviews

 Review

 2018 Steele Prize for Mathematical Exposition

 From the Back Cover

 This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.

 From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"

 “… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”

 From the Reviews

 "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "

 Notices of the AMS, August 1999

 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."

 LMS Newsletter, January 1999

 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit fromreading this book. ... "

 SIGACT News, December 2011


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 Product details

 * Publisher ‏ : ‎ Springer; 6th ed. 2018 edition (July 6, 2018)
 * Language ‏ : ‎ English
 * Hardcover ‏ : ‎ 334 pages
 * ISBN-10 ‏ : ‎ 3662572648
 * ISBN-13 ‏ : ‎ 978-3662572641
 * Item Weight ‏ : ‎ 2.06 pounds
 * Dimensions ‏ : ‎ 7.8 x 0.8 x 9.7 inches
 * Best Sellers Rank: #206,786 in Books ( See Top 100 in Books )
 + #7 in Combinatorics (Books)
 + #26 in Number Theory (Books)
 + #49 in Mathematical Analysis (Books)
 * Customer Reviews:
 4.8 4.8 out of 5 stars 80 ratings
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  4.8 out of 5 stars
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  Archan
  5.0 out of 5 stars Must read I guess
  Reviewed in the United States on October 8, 2020
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  Must read got anyone starting on math or general anyone wanting to prove stuff.
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  2 people found this helpful
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  Nahatz
  5.0 out of 5 stars New and expanded.
  Reviewed in the United States on February 7, 2020
  Verified Purchase
  If you know the history of "the book" (first mentioned by Paul Erdos.) you know these had to be fantastitic.
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  6 people found this helpful
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  Plane Tree
  5.0 out of 5 stars as described
  Reviewed in the United States on August 17, 2019
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  new book as described
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  Ben Hsu
  5.0 out of 5 stars beautiful
  Reviewed in the United States on January 24, 2019
  I try to read a chapter a week -- the ideas leave me shaking my head at how beautiful math can be
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  7 people found this helpful
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  humberin
  5.0 out of 5 stars Bien
  Reviewed in the United States on October 23, 2020
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  Rafael W Lima
  5.0 out of 5 stars It is a beautiful master piece about math :) <3
  Reviewed in Brazil on March 9, 2022
  Verified Purchase
  It is a beautiful master piece about math :) <3
  Read more
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  Manuel Toribio Molinero
  5.0 out of 5 stars Sólo lo he encontrado en amazon
  Reviewed in Spain on September 4, 2023
  Verified Purchase
  Había buscado el libro por todas las librerías de Barcelona, y ni estaba ni se podía encargar. Lo cierto es que fue una entrega algo lenta, pero se puede comprender porque venía de fuera de España.
  El libro es una muy buena recopilación de demostraciones elegantes en los ámbitos de teoría de números, geometría, análisis, combinatoria y teoría de grafos. Para entenderlo completamente, la exposición supone una base de primero de carrera, aproximadamente.
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  Marko Razpet
  5.0 out of 5 stars Es ist eines der besten Bücher über Mathematik.
  Reviewed in Germany on July 16, 2021
  Verified Purchase
  Dieses Buch behandelt die elegantesten Beweise, die es in der Mathematik je gab. Ich benutze das Buch zur Ergänzung meiner mathematischen Kenntnisse und zur Unterhaltung.
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  Gregory Connor
  4.0 out of 5 stars Some memorable simple proofs
  Reviewed in the United Kingdom on July 7, 2020
  Verified Purchase
  The book has a number of simple, memorable and elegant proofs -- it is great fun to work through Erdos' clever proof that the infinite sum of the reciprocals of all prime numbers diverges, for example. It is a good book for dipping into and out of, but I did not read it thoroughly from cover to cover.
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  Peter Grogono
  5.0 out of 5 stars The "must have" book for everyone who loves mathematics
  Reviewed in Canada on November 25, 2018
  Verified Purchase
  "THE BOOK" is, of course, a creation by the late Hungarian mathematician Paul Erdős - a mythical "bible" containing the most elegant and insightful proofs of important theorems. You might think that only serious mathematicians would be able to understand these proofs, but it is not so. Many are quite elementary, and most are accessible to anyone with an undergraduate degree in mathematics or physics, or even people who just enjoy reading mathematics. There are many pleasant surprises: one of the first is a proof that there are an infinite number of primes - using topology! I won't give any more spoilers. The book is not cheap but it is good value: you will get many hours of delight and amazement from it.
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 Proofs from THE BOOK 6th ed. 2018 Edition
 by Martin Aigner (Author), Günter M. Ziegler (Author), Karl H. Hofmann (Illustrator)
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 Purchase options and add-ons
 This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.
 From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"
 “… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”
 From the Reviews
 "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "
 Notices of the AMS, August 1999
 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."
 LMS Newsletter, January 1999
 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..."
 SIGACT News, December 2011
 Read more
 Report an issue with this product or seller
 Previous page
 1. ISBN-10
 3662572648
 2. ISBN-13
 978-3662572641
 3. Edition
 6th ed. 2018
 4. Publisher
 Springer
 5. Publication date
 July 6, 2018
 6. Language
 English
 7. Dimensions
 7.8 x 0.8 x 9.7 inches
 8. Print length
 334 pages
 9. See all details
 Next page
 Frequently bought together
 This item: Proofs from THE BOOK
 $50.39 $ 50 . 39
 Only 1 left in stock - order soon.
 Ships from and sold by WhitePaper Books.
 +
 How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library, 34)
 $15.45 $ 15 . 45
 Get it as soon as Monday, May 6
 In Stock
 Ships from and sold by Amazon.com.
 +
 Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
 $17.07 $ 17 . 07
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 In Stock
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 1. Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
 Jay Cummings
 4.8 out of 5 stars 746
 Paperback
 #1 Best Seller
 in Discrete Mathematics
 $17.07 $ 17 . 07
 Get it as soon as Monday, May 6
 FREE Shipping on orders over $35 shipped by Amazon
 2. How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library, 34)
 G. Polya
 4.5 out of 5 stars 1,109
 Paperback
 $15.45 $ 15 . 45
 Get it as soon as Monday, May 6
 FREE Shipping on orders over $35 shipped by Amazon
 3. How to Prove It: A Structured Approach
 Daniel J. Velleman
 4.7 out of 5 stars 268
 Paperback
 $39.99 $ 39 . 99
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 Editorial Reviews
 Review
 2018 Steele Prize for Mathematical Exposition
 From the Back Cover
 This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.
 From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"
 “… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”
 From the Reviews
 "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "
 Notices of the AMS, August 1999
 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."
 LMS Newsletter, January 1999
 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit fromreading this book. ... "
 SIGACT News, December 2011
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 Product details
 * Publisher ‏ : ‎ Springer; 6th ed. 2018 edition (July 6, 2018)
 * Language ‏ : ‎ English
 * Hardcover ‏ : ‎ 334 pages
 * ISBN-10 ‏ : ‎ 3662572648
 * ISBN-13 ‏ : ‎ 978-3662572641
 * Item Weight ‏ : ‎ 2.06 pounds
 * Dimensions ‏ : ‎ 7.8 x 0.8 x 9.7 inches
 * Best Sellers Rank: #206,786 in Books ( See Top 100 in Books )
 + #7 in Combinatorics (Books)
 + #26 in Number Theory (Books)
 + #49 in Mathematical Analysis (Books)
 * Customer Reviews:
 4.8 4.8 out of 5 stars 80 ratings
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  Archan
  5.0 out of 5 stars Must read I guess
  Reviewed in the United States on October 8, 2020
  Verified Purchase
  Must read got anyone starting on math or general anyone wanting to prove stuff.
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  2 people found this helpful
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  Nahatz
  5.0 out of 5 stars New and expanded.
  Reviewed in the United States on February 7, 2020
  Verified Purchase
  If you know the history of "the book" (first mentioned by Paul Erdos.) you know these had to be fantastitic.
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  6 people found this helpful
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  Plane Tree
  5.0 out of 5 stars as described
  Reviewed in the United States on August 17, 2019
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  new book as described
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  Ben Hsu
  5.0 out of 5 stars beautiful
  Reviewed in the United States on January 24, 2019
  I try to read a chapter a week -- the ideas leave me shaking my head at how beautiful math can be
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  humberin
  5.0 out of 5 stars Bien
  Reviewed in the United States on October 23, 2020
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  Rafael W Lima
  5.0 out of 5 stars It is a beautiful master piece about math :)
Proofs from THE BOOK: Aigner, Martin, Ziegler, Günter M., Hofmann, Karl H.: 9783662572641: Amazon.com: Books
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https://www.amazon.com/Little-History-Science-William-Bynum/dp/0300197136/ref=msx_wsirn_v1_2/143-5462993-3297049?pd_rd_w=Etb6W&pf_rd_p=edd207be-8a1c-4e1d-9856-c764818e859d&pf_rd_r=QY2K9CHMWB5QYHSVNYJM&pd_rd_r=61c492c7-ba95-483c-a912-f63b696e85e0&pd_rd_wg=C0f1K&pd_rd_i=0300197136&psc=1
A Little History of Science (Little Histories): Bynum, William: 9780300197136: Amazon.com: Books
2013-09-10
William F Bynum
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 A Little History of Science (Little Histories) Paperback – Illustrated, September 10, 2013

 by William Bynum (Author)
 4.5 4.5 out of 5 stars 295 ratings
 Part of: Little Histories (13 books)
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 A spirited volume on the great adventures of science throughout history, for curious readers of all ages

 Science is fantastic. It tells us about the infinite reaches of space, the tiniest living organism, the human body, the history of Earth. People have always been doing science because they have always wanted to make sense of the world and harness its power. From ancient Greek philosophers through Einstein and Watson and Crick to the computer-assisted scientists of today, men and women have wondered, examined, experimented, calculated, and sometimes made discoveries so earthshaking that people understood the world—or themselves—in an entirely new way.

 This inviting book tells a great adventure story: the history of science. It takes readers to the stars through the telescope, as the sun replaces the earth at the center of our universe. It delves beneath the surface of the planet, charts the evolution of chemistry's periodic table, introduces the physics that explain electricity, gravity, and the structure of atoms. It recounts the scientific quest that revealed the DNA molecule and opened unimagined new vistas for exploration.

 Emphasizing surprising and personal stories of scientists both famous and unsung, A Little History of Science traces the march of science through the centuries. The book opens a window on the exciting and unpredictable nature of scientific activity and describes the uproar that may ensue when scientific findings challenge established ideas. With delightful illustrations and a warm, accessible style, this is a volume for young and old to treasure together.

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 Previous page
 1. Part of series
 Little Histories
 2. Print length
 272 pages
 3. Language
 English
 4. Publisher
 Yale University Press
 5. Publication date
 September 10, 2013
 6. Dimensions
 5.49 x 0.75 x 8.49 inches
 7. ISBN-10
 9780300197136
 8. ISBN-13
 978-0300197136
 9. See all details
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 Editorial Reviews

 Review

 "One advantage of a brief history is that this impressive roll of modern achievements unfolds while the leaps of prior centuries are still fresh in mind. That juxtaposition of what we know now verses what we knew then is breathtaking to contemplate. In Mr Bynum’s telling, a little history goes a long way."—Alan Hirshfeld, Wall Street Journal

 "This freshest entry in Yale’s youngster-friendly Little History series covers science from Babylonian astronomy to the Human Genome Project and the Higgs Boson, in a series of lucid short chapters on telescopes, gases, engines, planetary orbits, cells, magnetism, pneumatic chemistry, continental drift and so forth. The author is particularly interesting on the history of medicine (his own field) . . . and he shows a gentle tolerant humour throughout."—Steven Poole, The Guardian


 "Yale’s youngster-friendly Little History series continues with science from Babylonian astronomy to the Higgs boson particle in a series of lucid short chapters on telescopes, gases, engines, plantetary orbits, cells, magnetism, pneumatic chemistry, continental drift, and so forth . . . [Bynum] takes a sly pleasure in pointing out that famous scientists have been deeply religious, and shows a gentle, tolerant humour throughout."—Steven Poole, T he Guardian



 "[An] entertaining history . . . for curious teen and adult readers."— Publishers Weekly

 "A super-accessible introduction to science."—Booklist

 "Bynum’s lively narrative . . . certainly delivers on his opening line: 'Science is special.'"— Kirkus Reviews , starred review

 "A wonderful book to keep on the shelf and revisit over time."— PopMatters

 "The book is a noble enterprise, an attempt to pull it all together."—David H. Galaty, The Historian

 "I wish there had been such a book when I was a child. Bill Bynum's Little History of Science may be short but it tells a grand story: all of science lightly placed in ever-changing historical and philosophical contexts, but presented in a single arc from Empedocles to Tim Berners-Lee, Galen to Thomas Hunt Morgan, alchemy to insulin, the steam engine to the particle accelerator. It is a book I will be recommending for many years to come."—Christopher Potter, author of You Are Here: A Portable History of the Universe

 "Well done Bill Bynum, a master of the scientific ordinance from the Big Bang to the Digital Age."—David Bellamy

 "Science is not a dry recitation of data; it's thousands of years of questions that people have posed about the universe. In A Little History of Science , William Bynum ably distills this human saga into a delightfully clear tale. It may be little, but it manages to find room for galaxies, computers, chemistry, evolution and much more."—Carl Zimmer, author of A Planet of Viruses

 "Small, but perfectly formed. In this little history, Bill Bynum has done a splendid job of weaving all the material into a narrative that is easy to understand. You will not find a better summary of the history of science."—Bernard Wood, author of Human Evolution: A Very Short Introduction


 About the Author

 William Bynum is professor emeritus, history of medicine, University College London. He is author or editor of numerous publications, including most recently Great Discoveries in Medicine . He lives in Suffolk, UK.

 Product details

 * ASIN ‏ : ‎ 0300197136
 * Publisher ‏ : ‎ Yale University Press; Illustrated edition (September 10, 2013)
 * Language ‏ : ‎ English
 * Paperback ‏ : ‎ 272 pages
 * ISBN-10 ‏ : ‎ 9780300197136
 * ISBN-13 ‏ : ‎ 978-0300197136
 * Item Weight ‏ : ‎ 2.31 pounds
 * Dimensions ‏ : ‎ 5.49 x 0.75 x 8.49 inches
 * Best Sellers Rank: #151,005 in Books ( See Top 100 in Books )
 + #332 in History of Civilization & Culture
 + #459 in History & Philosophy of Science (Books)
 * Customer Reviews:
 4.5 4.5 out of 5 stars 295 ratings
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 a little history of...

 We are more resilient during challenging times if we keep learning and expanding our minds; not just through childhood, but in all stages of life. Following in the footsteps of E. H. Gombrich's worldwide bestseller A Little History of the World, the books in our Little Histories series explore the history of the world's most remarkable people, events and ideas. With engaging personal insights, our authors will take you on a whistle-stop journey from ancient times to the present exploring all of life's big subjects from archaeology to science.

 ‘Have you ever come across an old school exercise book or something else you once wrote and, on leafing through it, been amazed at how much you have changed in such a short time? Amazed by your mistakes, but also by the good things you had written? Yet at the time you hadn’t noticed that you were changing. Well, the history of the world is just the same.’ – E. H. Gombrich, A Little History of the World

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  Susan schroeder
  5.0 out of 5 stars Refresher from school days
  Reviewed in the United States on April 21, 2019
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  I recently retired. For the past 40 years I’ve been busy raising kids, working, etc. This book was a great refresher for things I learned or should have learned durning my school years, plus updates of more modern times. It was technical but easy enough to read and understand for the layman.

  Really enjoyed it. Thirsty for more learning now!
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  6 people found this helpful
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  The Bookworm Sailor
  5.0 out of 5 stars How did he do it?
  Reviewed in the United States on February 6, 2017
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  It is amazing how well this massive topic is covered on 40 chapters of 6 pages each. Very accessible language, presented in a way that I think the non-scientist will find comprehensible and interesting. Although this is presumably intended as bait to pique interest in a young non-specialist, I enjoyed every bit of it (I have tertiary arts and sciences background) and I'm sure an intelligent and inquisitive 12-year old would love it too.
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  9 people found this helpful
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  Paul J. McArdle
  4.0 out of 5 stars Valuable outline of the history of science.
  Reviewed in the United States on September 25, 2023
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  Of course this is just a brief summary of a very complex subject. That being so, I find it very helpful.
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  Alice Arnold
  5.0 out of 5 stars The book arrived
  Reviewed in the United States on August 12, 2023
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  The book arrived and everything went well with the order.
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  Dilettante
  5.0 out of 5 stars How the world works? Find out in this very easily readable book
  Reviewed in the United States on June 20, 2017
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  With a degree in physics many decades ago. This was a wonderful review – putting everything together. It is interesting that through the ages people tried to make sense of the world around us. From observing the stars with primitive instruments to discovering that there are different gases in the atmosphere etc.
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  6 people found this helpful
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  Núbia Vargas Marafiga
  5.0 out of 5 stars Excellent book of History Science!
  Reviewed in the United States on June 1, 2014
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  I looked inside the book in Amazon site and I enjoyed the way it is organized. I also checked the index and I liked the intersting topics about world science. That's why I ordered it.
  If you like to know how things are created and developed, you will profict the book a lot. I bought the CDs of the same book too, they are also pretty good.
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  Shagbark
  3.0 out of 5 stars Good for children, but fails to clearly distinguish science from magic
  Reviewed in the United States on November 17, 2023
  This is a very fast review of the history of science, in very simple language, aimed at children. The coverage is very good; I can't argue with what Bynum chose to include or exclude. It's fine for children, or adults who don't know much about the history of science. People with a good background in the subject don't need to read it. Children past 7th grade may be insulted by it, as it is aimed slightly below them.

  It doesn't do a careful job of explaining what science is, and how it differs from magic or religion. On the first page it says that technology is about doing, while science is about knowing. This would be a good distinction, if it weren't for the fact that Platonists have for thousands of years perpetuated the myth that science is rational using just that language. To a Platonist, "knowing" doesn't mean having a very good understanding or explanation, or being reliably able to predict how something will behave; it means having a formal specification and an infallible proof of that specification. Science is, and has been since at least the time of Epicurus and the skeptics, specifically the /renunciation of knowing/. That is what distinguishes it from religion. A scientist never claims to know anything in the absolute, Platonic sense of "knowing". This is the single most-important thing to understand about science, and this book perpetuates the Platonist myth instead. (To be fair, so do most histories of science, and most philosophers of science even today remain ignorant of this single most-important fact.)

  It is correct to say that, thousands of years ago, there was no distinction between science, magic, and religion. But we now see a clear distinction between them, and it is important for us to do so. Bynum allows the distinction to remain vague. He says that (Western) astrology is not science, but describes traditional Indian humour-based medicine without mentioning that it's just as false as Western humour-based medicine. Its attitude toward magic and religion is inconsistent, sometimes saying these things aren't science, but sometimes describing them from the point of view of a believer. There are hints throughout that the author sympathizes with religion; one bad one is when he says that atomism "is a pretty bleak view".

  It has some minor inaccuracies, which aren't harmful ones, but make me doubt that Bynum is deeply familiar with the history he covers. I noticed this on the second page, when, after saying that the Babylonians decided there would be sixty seconds in a minute, wrote, "It is funny to think that there is no real reason why sixty seconds make a minute... Other numbers would have worked just as well." No; the Babylonians picked 60 because it has the most divisors of any number under 100, so that you can divide the minute in half, thirds, quarters, fifths, sixths, and tenths. It makes no sense to say that Aristotle left Athens in 348 BCE because "as a foreigner, he felt unsafe"; Athens was a trading city. And it's odd to say that "the branch of philosophy that most excited [Aristotle] was logic", rather like saying "Shakespeare was especially interested in the history of the Henrys."
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  OreofeOluwakiitan
  4.0 out of 5 stars A Little History of Science, a big beautiful further education for me
  Reviewed in the United States on October 21, 2019
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  Ha! What a book, an eye opener. Lots of things I didn't know about numbers, medicine, astronomy, etc. This is a book I picked up in solidarity with our son to encourage him in a particular course and it turned out to be a very illuminating and educating material for me in particular. I find myself going back to this book again and again. I have even cited it in my new book released April 2019. Thank you.
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  RAFAEL
  5.0 out of 5 stars A book that is both entertaining as well as lucid for going quickly into a short history of science
  Reviewed in Mexico on September 20, 2020
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  This is a so well written book, both entertaining as well as lucid, for either a laymen or a scholar who wants to recap on how different subjects of science came to be. Easy to read and remarkable informative despite the very short chapters that cover different sciences. Not an easy balancing task that was well achieved by the author.
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  Shashi Shekar M
  5.0 out of 5 stars A must read tome
  Reviewed in India on September 8, 2020
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  Excellent book
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  Lynda Alexander
  5.0 out of 5 stars Five Stars
  Reviewed in Canada on May 25, 2018
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  great gift for son-in-law
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  Tobi-lea McGowan
  1.0 out of 5 stars Seems like it was written for 8 year olds
  Reviewed in Australia on January 4, 2022
  Verified Purchase
  This writer doesn't seem very travelled or mentally alert, he waffles alot, it seems to be written for very young primary school children and he doesn't even seem to grasp half of the concepts he talks about because his language is so overly simplistic. A real displeasure to read as every sentence just seems a waste of time.
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  ED Quinton
  5.0 out of 5 stars The perfect gift for young teenagers.
  Reviewed in the United Kingdom on October 2, 2015
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  Very easy to read and interesting for a non scientific layman but above all excellent and entertaining reading for young people. It's written as a parallel to Gombrich's 'A Little History of the World' which is also very well worth reading.
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 A Little History of Science (Little Histories) Paperback – Illustrated, September 10, 2013
 by William Bynum (Author)
 4.5 4.5 out of 5 stars 295 ratings
 Part of: Little Histories (13 books)
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 A spirited volume on the great adventures of science throughout history, for curious readers of all ages
 Science is fantastic. It tells us about the infinite reaches of space, the tiniest living organism, the human body, the history of Earth. People have always been doing science because they have always wanted to make sense of the world and harness its power. From ancient Greek philosophers through Einstein and Watson and Crick to the computer-assisted scientists of today, men and women have wondered, examined, experimented, calculated, and sometimes made discoveries so earthshaking that people understood the world—or themselves—in an entirely new way.
 This inviting book tells a great adventure story: the history of science. It takes readers to the stars through the telescope, as the sun replaces the earth at the center of our universe. It delves beneath the surface of the planet, charts the evolution of chemistry's periodic table, introduces the physics that explain electricity, gravity, and the structure of atoms. It recounts the scientific quest that revealed the DNA molecule and opened unimagined new vistas for exploration.
 Emphasizing surprising and personal stories of scientists both famous and unsung, A Little History of Science traces the march of science through the centuries. The book opens a window on the exciting and unpredictable nature of scientific activity and describes the uproar that may ensue when scientific findings challenge established ideas. With delightful illustrations and a warm, accessible style, this is a volume for young and old to treasure together.
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 1. Part of series
 Little Histories
 2. Print length
 272 pages
 3. Language
 English
 4. Publisher
 Yale University Press
 5. Publication date
 September 10, 2013
 6. Dimensions
 5.49 x 0.75 x 8.49 inches
 7. ISBN-10
 9780300197136
 8. ISBN-13
 978-0300197136
 9. See all details
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 1. A Little History of the World (Little Histories)
 E. H. Gombrich
 4.5 out of 5 stars 2,778
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 2. A Little History of Philosophy (Little Histories)
 Nigel Warburton
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 Niall Kishtainy
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 4. The Scientists: A History of Science Told Through the Lives of Its Greatest Inventors
 John Gribbin
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 5. Informal Logical Fallacies
 Jacob Van Vleet
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 6. A Little History of Religion (Little Histories)
 Richard Holloway
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 Editorial Reviews
 Review
 "One advantage of a brief history is that this impressive roll of modern achievements unfolds while the leaps of prior centuries are still fresh in mind. That juxtaposition of what we know now verses what we knew then is breathtaking to contemplate. In Mr Bynum’s telling, a little history goes a long way."—Alan Hirshfeld, Wall Street Journal
 "This freshest entry in Yale’s youngster-friendly Little History series covers science from Babylonian astronomy to the Human Genome Project and the Higgs Boson, in a series of lucid short chapters on telescopes, gases, engines, planetary orbits, cells, magnetism, pneumatic chemistry, continental drift and so forth. The author is particularly interesting on the history of medicine (his own field) . . . and he shows a gentle tolerant humour throughout."—Steven Poole, The Guardian
 "Yale’s youngster-friendly Little History series continues with science from Babylonian astronomy to the Higgs boson particle in a series of lucid short chapters on telescopes, gases, engines, plantetary orbits, cells, magnetism, pneumatic chemistry, continental drift, and so forth . . . [Bynum] takes a sly pleasure in pointing out that famous scientists have been deeply religious, and shows a gentle, tolerant humour throughout."—Steven Poole, T he Guardian
 "[An] entertaining history . . . for curious teen and adult readers."— Publishers Weekly
 "A super-accessible introduction to science."—Booklist
 "Bynum’s lively narrative . . . certainly delivers on his opening line: 'Science is special.'"— Kirkus Reviews , starred review
 "A wonderful book to keep on the shelf and revisit over time."— PopMatters
 "The book is a noble enterprise, an attempt to pull it all together."—David H. Galaty, The Historian
 "I wish there had been such a book when I was a child. Bill Bynum's Little History of Science may be short but it tells a grand story: all of science lightly placed in ever-changing historical and philosophical contexts, but presented in a single arc from Empedocles to Tim Berners-Lee, Galen to Thomas Hunt Morgan, alchemy to insulin, the steam engine to the particle accelerator. It is a book I will be recommending for many years to come."—Christopher Potter, author of You Are Here: A Portable History of the Universe
 "Well done Bill Bynum, a master of the scientific ordinance from the Big Bang to the Digital Age."—David Bellamy
 "Science is not a dry recitation of data; it's thousands of years of questions that people have posed about the universe. In A Little History of Science , William Bynum ably distills this human saga into a delightfully clear tale. It may be little, but it manages to find room for galaxies, computers, chemistry, evolution and much more."—Carl Zimmer, author of A Planet of Viruses
 "Small, but perfectly formed. In this little history, Bill Bynum has done a splendid job of weaving all the material into a narrative that is easy to understand. You will not find a better summary of the history of science."—Bernard Wood, author of Human Evolution: A Very Short Introduction
 About the Author
 William Bynum is professor emeritus, history of medicine, University College London. He is author or editor of numerous publications, including most recently Great Discoveries in Medicine . He lives in Suffolk, UK.
 Product details
 * ASIN ‏ : ‎ 0300197136
 * Publisher ‏ : ‎ Yale University Press; Illustrated edition (September 10, 2013)
 * Language ‏ : ‎ English
 * Paperback ‏ : ‎ 272 pages
 * ISBN-10 ‏ : ‎ 9780300197136
 * ISBN-13 ‏ : ‎ 978-0300197136
 * Item Weight ‏ : ‎ 2.31 pounds
 * Dimensions ‏ : ‎ 5.49 x 0.75 x 8.49 inches
 * Best Sellers Rank: #151,005 in Books ( See Top 100 in Books )
 + #332 in History of Civilization & Culture
 + #459 in History & Philosophy of Science (Books)
 * Customer Reviews:
 4.5 4.5 out of 5 stars 295 ratings
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 1. William F. Bynum
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 2. Little Histories
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 a little history of...
 We are more resilient during challenging times if we keep learning and expanding our minds; not just through childhood, but in all stages of life. Following in the footsteps of E. H. Gombrich's worldwide bestseller A Little History of the World, the books in our Little Histories series explore the history of the world's most remarkable people, events and ideas. With engaging personal insights, our authors will take you on a whistle-stop journey from ancient times to the present exploring all of life's big subjects from archaeology to science.
 ‘Have you ever come across an old school exercise book or something else you once wrote and, on leafing through it, been amazed at how much you have changed in such a short time? Amazed by your mistakes, but also by the good things you had written? Yet at the time you hadn’t noticed that you were changing. Well, the history of the world is just the same.’ – E. H. Gombrich, A Little History of the World
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  Susan schroeder
  5.0 out of 5 stars Refresher from school days
  Reviewed in the United States on April 21, 2019
  Verified Purchase
  I recently retired. For the past 40 years I’ve been busy raising kids, working, etc. This book was a great refresher for things I learned or should have learned durning my school years, plus updates of more modern times. It was technical but easy enough to read and understand for the layman.
  Really enjoyed it. Thirsty for more learning now!
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  6 people found this helpful
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  The Bookworm Sailor
  5.0 out of 5 stars How did he do it?
  Reviewed in the United States on February 6, 2017
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  It is amazing how well this massive topic is covered on 40 chapters of 6 pages each. Very accessible language, presented in a way that I think the non-scientist will find comprehensible and interesting. Although this is presumably intended as bait to pique interest in a young non-specialist, I enjoyed every bit of it (I have tertiary arts and sciences background) and I'm sure an intelligent and inquisitive 12-year old would love it too.
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  9 people found this helpful
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  Paul J. McArdle
  4.0 out of 5 stars Valuable outline of the history of science.
  Reviewed in the United States on September 25, 2023
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  Of course this is just a brief summary of a very complex subject. That being so, I find it very helpful.
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  Alice Arnold
  5.0 out of 5 stars The book arrived
  Reviewed in the United States on August 12, 2023
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  The book arrived and everything went well with the order.
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  Dilettante
  5.0 out of 5 stars How the world works? Find out in this very easily readable book
  Reviewed in the United States on June 20, 2017
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  With a degree in physics many decades ago. This was a wonderful review – putting everything together. It is interesting that through the ages people tried to make sense of the world around us. From observing the stars with primitive instruments to discovering that there are different gases in the atmosphere etc.
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  6 people found this helpful
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  Núbia Vargas Marafiga
  5.0 out of 5 stars Excellent book of History Science!
  Reviewed in the United States on June 1, 2014
  Verified Purchase
  I looked inside the book in Amazon site and I enjoyed the way it is organized. I also checked the index and I liked the intersting topics about world science. That's why I ordered it.
  If you like to know how things are created and developed, you will profict the book a lot. I bought the CDs of the same book too, they are also pretty good.
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  2 people found this helpful
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  Shagbark
  3.0 out of 5 stars Good for children, but fails to clearly distinguish science from magic
  Reviewed in the United States on November 17, 2023
  This is a very fast review of the history of science, in very simple language, aimed at children. The coverage is very good; I can't argue with what Bynum chose to include or exclude. It's fine for children, or adults who don't know much about the history of science. People with a good background in the subject don't need to read it. Children past 7th grade may be insulted by it, as it is aimed slightly below them.
  It doesn't do a careful job of explaining what science is, and how it differs from magic or religion. On the first page it says that technology is about doing, while science is about knowing. This would be a good distinction, if it weren't for the fact that Platonists have for thousands of years perpetuated the myth that science is rational using just that language. To a Platonist, "knowing" doesn't mean having a very good understanding or explanation, or being reliably able to predict how something will behave; it means having a formal specification and an infallible proof of that specification. Science is, and has been since at least the time of Epicurus and the skeptics, specifically the /renunciation of knowing/. That is what distinguishes it from religion. A scientist never claims to know anything in the absolute, Platonic sense of "knowing". This is the single most-important thing to understand about science, and this book perpetuates the Platonist myth instead. (To be fair, so do most histories of science, and most philosophers of science even today remain ignorant of this single most-important fact.)
  It is correct to say that, thousands of years ago, there was no distinction between science, magic, and religion. But we now see a clear distinction between them, and it is important for us to do so. Bynum allows the distinction to remain vague. He says that (Western) astrology is not science, but describes traditional Indian humour-based medicine without mentioning that it's just as false as Western humour-based medicine. Its attitude toward magic and religion is inconsistent, sometimes saying these things aren't science, but sometimes describing them from the point of view of a believer. There are hints throughout that the author sympathizes with religion; one bad one is when he says that atomism "is a pretty bleak view".
  It has some minor inaccuracies, which aren't harmful ones, but make me doubt that Bynum is deeply familiar with the history he covers. I noticed this on the second page, when, after saying that the Babylonians decided there would be sixty seconds in a minute, wrote, "It is funny to think that there is no real reason why sixty seconds make a minute... Other numbers would have worked just as well." No; the Babylonians picked 60 because it has the most divisors of any number under 100, so that you can divide the minute in half, thirds, quarters, fifths, sixths, and tenths. It makes no sense to say that Aristotle left Athens in 348 BCE because "as a foreigner, he felt unsafe"; Athens was a trading city. And it's odd to say that "the branch of philosophy that most excited [Aristotle] was logic", rather like saying "Shakespeare was especially interested in the history of the Henrys."
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  OreofeOluwakiitan
  4.0 out of 5 stars A Little History of Science, a big beautiful further education for me
  Reviewed in the United States on October 21, 2019
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  Ha! What a book, an eye opener. Lots of things I didn't know about numbers, medicine, astronomy, etc. This is a book I picked up in solidarity with our son to encourage him in a particular course and it turned out to be a very illuminating and educating material for me in particular. I find myself going back to this book again and again. I have even cited it in my new book released April 2019. Thank you.
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  RAFAEL
  5.0 out of 5 stars A book that is both entertaining as well as lucid for going quickly into a short history of science
  Reviewed in Mexico on September 20, 2020
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  This is a so well written book, both entertaining as well as lucid, for either a laymen or a scholar who wants to recap on how different subjects of science came to be. Easy to read and remarkable informative despite the very short chapters that cover different sciences. Not an easy balancing task that was well achieved by the author.
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  Shashi Shekar M
  5.0 out of 5 stars A must read tome
  Reviewed in India on September 8, 2020
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  Excellent book
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  Lynda Alexander
  5.0 out of 5 stars Five Stars
  Reviewed in Canada on May 25, 2018
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  great gift for son-in-law
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  Tobi-lea McGowan
  1.0 out of 5 stars Seems like it was written for 8 year olds
  Reviewed in Australia on January 4, 2022
  Verified Purchase
  This writer doesn't seem very travelled or mentally alert, he waffles alot, it seems to be written for very young primary school children and he doesn't even seem to grasp half of the concepts he talks about because his language is so overly simplistic. A real displeasure to read as every sentence just seems a waste of time.
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  ED Quinton
  5.0 out of 5 stars The perfect gift for young teenagers.
  Reviewed in the United Kingdom on October 2, 2015
  Verified Purchase
  Very easy to read and interesting for a non scientific layman but above all excellent and entertaining reading for young people. It's written as a parallel to Gombrich's 'A Little History of the World' which is also very well worth reading.
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A Little History of Science (Little Histories): Bynum, William: 9780300197136: Amazon.com: Books
https://www.amazon.com/Little-History-Science-William-Bynum/dp/0300197136/ref=msx_wsirn_v1_2/143-5462993-3297049?pd_rd_w=Etb6W&pf_rd_p=edd207be-8a1c-4e1d-9856-c764818e859d&pf_rd_r=QY2K9CHMWB5QYHSVNYJM&pd_rd_r=61c492c7-ba95-483c-a912-f63b696e85e0&pd_rd_wg=C0f1K&pd_rd_i=0300197136&psc=1
https://www.goodreads.com/book/show/3869.A_Brief_History_of_Time
A Brief History of Time
2014-10-11
Author
<div><div><p></p><h3>Friends &amp; Following </h3><p></p></div><div><p>Displaying 1 - 30 of 11,529 reviews</p><div><div><article><div><section><a href="https://www.goodreads.com/user/show/1478106-bill"></a></section><section><p>Author <i></i>6 books133 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/32454332">August 30, 2022</a></section><div><p>This book puts me in mind of the story about how a Harvard number theorist, through some malfunction of the scheduling computer, got assigned to teach an introductory course in pre-calculus. Being one of those individuals to whom math came so easily that they couldn't grasp how difficult others found it, the professor had no idea what to cover in such a course. <p>So, he went to the chair of the department, who told him: "You'll want to start with the real number-line and then progress to inequalities; from there, move on to quadratic equations, then trigonometry and the wrapping function, Cartesian and polar coordinate systems, and, if time permits, conic sections."</p><p>The professor thanked the chairperson and went off to meet with his first class. Next week, he was back.</p><p>"What should I teach them now?" he said.</p><p><i>A Brief History of Time</i> is like that -- Professor Hawking doesn't seem to notice when his treatment progresses from the obvious to the arcane, ending with his concept of "imaginary time" (very nearly incomprehensible in this overly brief presentation).</p><p>Fun nonetheless.</p><p>* * *<br />August 30, 2022 addendum --</p><p>Time to jump in here, I fear:</p><p>Having garnered over 650 "Likes," this far-from-serious scribble is by far my most popular review ever — and, truth be told, undeservedly so.</p><p>For a more thoughtful consideration of a somewhat related book, try my take on Jim Holt's <i>Why Does the World Exist?</i> here: <a href="https://www.goodreads.com/book/show/8854815-why-does-the-world-exist?ac=1&amp;from_search=true&amp;qid=xFU3lri3rw&amp;rank=1">https://www.goodreads.com/book/show/8...</a></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1478106?shelf=cosmology">cosmology</a> <a href="https://www.goodreads.com/review/list/1478106?shelf=physics">physics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/272430-daniel"></a></section><section><p>149 reviews8 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/6618727">September 25, 2007</a></section><div><p>It is not clear to me who is in the target audience for this book. At times it tries to explain basic concepts of modern physics in simple language, and at other times it assumes a familiarity with the same subject. For the first time I think I "understand" why absolute time is not consistent with relativity theory or that space-time curvature supplants the notion of gravity, and for that I thank the author. There are a few other things I believe I have a glimpse of having (finally) slogged through the book.<br />On the other hand, there are many places where he writes as if it were clear what he is talking about even though it would require a good deal of background knowledge. To give but one example, he starts talking about summing up over possible world histories (I cannot locate the quotation) without explaining what that would mean. Trained in statistics, I have some idea that he is talking about mathematical expectation in the context of quantum mechanics, but I don't know how another reader might make any sense of it (and I certainly don't have more than a vague notion). <br />There are irritating writing practices that could have used some editing, e.g., the use of the naked pronominal adjective "this" when in the middle of a dense explanation of an abstruse concept(e.g., "This had serious implications for the ultimate fate of massive stars."). <br />My biggest complaints, however, are about his philosophical opinions. Obviously he is entitled to think as he wishes about the ultimate questions, but his assertion that his hypothesis of a finite world without beginning or end would leave no place for God seems beside the point. The classic divide has not changed: some folks look around and say stuff just is, and other folks say there's a power behind the stuff that has at least as much going for it as we do. That argument hasn't changed with his theories. At one point in the book he claims that the late John Paul II told gathered scientists that they mustn't inquire into the Big Bang because that was God's territory. I would wager with anyone reading this comment that such an assertion is just plain false. JPII was a flawed mortal, to be sure, but he was no dope; it certainly sounds to me like someone hearing what he thinks the pope would say. (And the Galileo jokes are pretty dumb -- does anyone think that JPII, who apologized for the embarrassing Galileo fiasco, would go after this guy? It must be all that influence the Vatican has had in Britain over the last 400 years that has him scared.) <br />Other philosophical complaints involve his use of entropy (he defines it first within closed systems and then uses it to explain why the "thermodynamic arrow of time" and the "personal arrow of time" must run in the same direction -- leaping from a box of molecules to the entire universe!), his droning on about what black holes are like when he doesn't know for sure they exist, his statements about "random" and being 95% certain a theory is true (does that mean about 95 out of 100 theories like that are true??). His opinions may be very rich, deep, though-provoking, but how would I (or most general readers) know? You can't really evaluate a judgment unless you know something in the field. <br />And so that is why I ultimately cannot recommend this book: if you know physics inside and out, you might find his opinions interesting. If you don't, you can only walk around parroting what he says about black holes as if you had a clue what you were talking about. What we all really need is a remedial course in physics!</p></div><section><ul><a href="https://www.goodreads.com/review/list/272430?shelf=general-nonfiction">general-nonfiction</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/7878381"></a></section><section><p>Author <i></i>8 books15.9k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/563282205">April 18, 2019</a></section><div><p><br />‎‏‏<b><br />=وداعا هوكنج=<br />صرت حرا الآن<br />---------<br />هناك لذّةٌ ما ،، في أن تفتحَ كتاباً تشعُّ من سطوره ألوان الفضاء <br />شيءٌ ما في فعلِ المعرفةِ ،، والتأمل فيها <br />شيءٌ يأخذ عقلك إلى أمكنةٍ أخرى <br />...<br />لا بين المجرات<br />ولا في خضّم الكونِ الواسع<br />بل هنا بداخلك<br />عند هذا النبض الأخّاذ في قلبك<br />حيث تبدأ المتعة في التحرر <br />لتغمر مسامّك برائحة الدهشة<br />فالكون في داخلك أنت يا صاحبي<p>تاريخٌ موجز للزمن ،، يُعتبر من أهم الكتب العلمية الحديثة<br />يأخذك ستيفن هوكنج في رحلةٍ عبر تاريخ العلم <br />ويشرح لك كيف تغيّرت نظرتنا للكون ،، ولمجرتنا ،، ‏ولكرتنا الأرضية ،، ولأنفسنا كذلك عبر العصور</p><p>هذه هي قراءتي الثانية لستيفن هوكنج ،وقد أعجبتُ أيّما إعجاب بقراءتي الأولي "التصميم العظيم" ‏،وإن قارنت هذا بذاك ،فأرجّحُ كفّة الأخير</p><p>لا أعلم إن كانت للترجمة دورٌ في ذلك ،فلقد قرأت التصميم العظيم بلغته الأصلية</p><p>لقد توقّعت أكثر مما وجدتُّ في هذا الكتاب ،فقد حسبته أكثر متعة وجمالاً في سرده أو في ترابط فصوله<br />ولكن لن تجد هُنا سوى متعةَ المادة العلمية ذاتها ، فـ اسلوب هوكنج جافٌ قليلاً‏</p><p>كما وضع كارل ساجان مقدمة جميلة للكتاب <br />ليثير شهيتي أكثر </p><p>============================================<br />فلنتعرف على مؤلف سطور المعرفة الشهية إذا<br />============================================<br /></p><p>يقول ستيفن <br />_______________________________________________<br />‏لقد كنتُ مصدر يأس لوالدي في صباي، إذ كنتُ ‏دائماً أقوم بفك الأجهزة لأرى ما الذي ‏يجعلها ‏تصدر أصواتاً، وبالطّبع لم يكن بإمكاني - عادة - ‏جمع أجزائها مرة أخرى، إلاّ أنّني ‏شعرت بإمكان السيطرة على أيّ شيء - بطريقة أو بأخرى - إذا ‏فهمت كيفيّة عمله، وأنا موقن ‏من وجود الشعور ‏نفسه لدى الآخرين<br /> فنحن نجد أنفسنا في عالم لا ‏يلحظ وجودنا في الغالب ولا ‏يهتم به، بل - أحياناً - ‏يعادي هذا الوجود صراحةً</p><p>لذا، لو أمكننا فك ‏‏"اللوحة الأماميّة" للكون والنّظر خلفها فربّما نصبح ‏قادرين على فهم كيف تعمل ‏تلك العجلات ‏الصغيرة، أعني المجرات، ولشعرنا ببعض التحكّم ‏فيما يجري من أحداث، ولحسن ‏الحظ فنحن غير ‏مدعوين لإعادة تجميع الكون مرة أخرى بعد فك ‏لوحته الأماميّة‎ <br />_______________________________________________</p><p>هل تعلم أن هذا العالم العبقري قدأُصيب بمرض التصلب الجانبي الضموري؟<br />هذا المرض يصيب الجهاز العصبي الحركي ،ويُفقد المصاب به قدرته على التحكم في عضلاته<br />وهل تعلم أن الأطباء قد أخبروه بأنه لن يعيش لأكثر من عامين؟<br />ولكن يبدو أن إصرار الرجل وعزيمته جعلتاه يعيش كل هذا العمر<br />لبملأ الأرض بإبداعاته</p><p>كان ستيفن وقتها يحضّر رسالته في الفيزياء النظرية بجامعة كامبريدج <br />ولم يمنعه مرضه من إكمالها ليشغل منصب أستاذ الرياضيات الذي كان يشغله نيوتن في نفس الجامعة<br /><br />حتى عام1974 كان هوكنج يستطيع العناية بنفسه بعض الشيء<br />إلا أن تفاقم المرض جعله حبيساً لكرسي متحرك ،بالإضافة إلى ذلك فقد عانى من عملية استئصال للحنجرة ليفقد صوته تماما</p><p>ولحسن حظه ،فقد أهداه والت وولتوز ،خبير الكمبيوتر، برنامجا عبقريا يتيح له أن يختار كلمات من سلسلة قوائم على الحاسوب، بمجرد كبسة على مفتاح في يده، بل ويستطيع أن يتحكّم به بعينيه، وحركة رأسه كذلك وعندما ينتهي من بناء جملته يرسلها إلى ناطق الكلمات <br />وقد ثبتّ الجهاز على كرسيه المتحرك ليستطيع ستيفن التحدث مع الحركة بحرية أكبر<br />[image error]</p><p>احتل هوكنج كرسي الرياضيات في كامبريدج ،وهو أعلى منصب يحتله أستاذ في اختصاصه<br />حيث شغله علماء أمثال نيوتن وتشارلز بابيج	وبول ديراك	</p><p>لهوكنج أبحاث نظرية في علم الكون وفي العلاقة بين الثقوب السوداء والديناميكا الحرارية<br />ودراسات في التسلسل الزمني</p><p>كما وضع نظريات عديدة عن ‏بداية الكون منذ الانفجار الكبير<br />وأيضاً عن الثقوب السوداء <br />والتي أطلق على إشعاعها إشعاع هوكنج</p><p><a href="http://www.youtube.com/watch?v=4OmSoZzvXcM">http://www.youtube.com/watch?v=4OmSoZ...</a></p><u>جزء من مقابلة له مع لاري كينج</u><br />============================================================<br />عن الكتاب<br />=======================<br />هذا الكتاب وبصورة مبسّطة نوعاً ، يعرض بعض نظريات العلماءالتي تحدثت عن الكون والزمن كنظريات ‏أرسطو وآينشتين وجاليليو ونيوتن أيضاً‏<p>يدور الكتاب في أساسه حول الكون<br />عن تمدده ،وإنكماشه وحدوده ،وعن أبعاد ‏الزمان</p><p>هذا الرجل جعل عقلي يروح يميناً ويساراً<br />دوخني معه بكمِّ معلوماته الهائل ،، وأفكاره المستنيرة</p><p>في البداية يحدثك ستيفن عن التصور ‏القديم للكون بإختصار ويمثل لك بتصور ‏أرسطو الأشهر مروراً ببطليموس وغيرهم</p><p>تصور أرسطو كان كالتالي<br />‏============================‏‏===========‏<br />المادة تتكون من 4 عناصر أولية‏<br />الماء،النار،الهواء،الأرض<br />تؤثر في هذه العناصر قوتان<br />الجاذبية ،،أي نزعة الأرض والماء إلى الهبوط<br />والخفّة ،،أي نزعة الهواء والنار إلى الصعود<br />‏============================‏‏===========‏<br /></p><p>وإكتشاف أن الكون يتمدد كما يرى ‏هوكنج ،هو ‏إحدى الثورات الثقافية ‏العظيمة في القرن العشرين</p><u>فيقول</u><br />_______________________________________________<br />‎وبالتأمل وراء، فإن من السهل التعجب لآن ‏أحدا لم يفكر في ذلك من قبل ، فقد كان ينبغي على ‏‏نيوتن وغيره أن يتبينوا أن كونا ستاتيكيا لن يلبث أن ‏يبدأ سريعا في الانكماش بتأثير الجاذبية<br />‏ولكن ‏لنفرض بدلا من ذلك أن الكون يتمدد . فلو كان يتمدد ‏بسرعة بطيئة إلى حد ما ، فإن قوة ‏الجاذبية ستجعله ‏في النهاية يتوقف عن التمدد ليبدأ بعدها في ‏الانكماش . أما إذا كان يتمدد بسرعة ‏أكبر من معدل ‏حرج عين ، فإن الجاذبية لن تكون قط قوية بما يكفي ‏لوقف تمدده ، وسوف يستمر ‏الكون في التمدد للأبد <p> ‏وهذا يشبه ، نوعا ، ما يحدث عندما يطلق أحدهم من ‏فوق سطح الأرض ‏صاروخا لأعلى . فإذا كانت ‏سرعته بطيئة إلى حد ما ، فإن الجاذبية ستوقف ‏الصاروخ في النهاية ���وسيبدأ في السقوط عائدا <br />ومن ‏الجهة الأخرى ، إذا كانت سرعة الصاروخ أكبر من ‏سرعة ‏حرجة معينة ( حوالي سبعة أميال في الثانية ‏‏) فإن الجاذبية لا تكون قوية بما يكفي لشدة إلى ‏‏الوراء ، وهكذا فإنه سيستمر في الانطلاق بعيدا عن ‏الأرض إلى الأبد . وسلوك الكون هكذا كان ‏يمكن ‏التنبؤ به من نظرية نيوتن عن الجاذبية في أي وقت ‏من القرن التاسع عشر ، أو الثامن ‏عشر أو حتى ‏أواخر القرن السابع عشر‎‏ ‏<br />‎‏ ‏<br />إلا أن الإيمان بثبات الكون كان من القوة بحيث ظل ‏باقيا لأوائل القرن العشرين<br />_______________________________________________</p><p>وعن الإرتباط بين المكان والزمان، يحدثك ‏ستيفن ‏عن أهمية نظريات نيوتن والتي ‏توجها بوضعه ‏لقانون الجاذبية الكونية <br />‏ووقتها بدأ التعارض بين الفكر القديم الذي يرجح ‏‏ثبات النجوم وبين ما جاء به نيوتن ومن خلال ‏تفكيره ‏للخروج من هذا التساؤل أوضح إن تجاذب ‏النجوم ‏يحدث إذا كان عددها صغير ‏<br />أما إن كانت عددها غير محدود ومتناسقة التوزيع ‏‏بطريقة أو بأخرى في الفضاء الشاسع ، فلن تكون ‏‏هناك نقطة مركزية لتتجمع عليها ‏</p><p>وبالمناسبة فقد اعتبر أينشتين الكون ثابتاًً حين ‏وضع ‏النظرية النسبية العامة<br />وقد اعتبرها أكبر غلطة قام بها في حياته، عدّل ‏فيها ‏فيما بعد</p><u>فيقول</u><p>_______________________________________________<br />‎‏ ‏<br />نظرية أينشتاين عن النسبية العامة ، هي في ‏ذاتها تتنبأ بأن الزمكان يبدأ عند مفردة الانفجار ‏‏الكبير وسوف يصل إلى نهايته عند مفردة الانسحاق ‏الكبير ( إذا تقلص الكون كله ثانية ) أو عند ‏مفردة ‏من داخل ثقب أسود ( لو تقلصت منطقة محددة ، ‏مثل أحد النجوم ) <br />وأي مادة ستهوي إلى ‏داخل ‏الثقب ستتدمر عند المفردة ، ولن يظل محسوسا في ‏الخارج إلا تأثير جاذبية كتلتها <br />ومن ‏الناحية ‏الأخرى ، عندما يؤخذ في الحسبان تأثيرات الكم ، ‏فإنه يبدو أن كتلة أو طاقة المادة ستُعاد ‏في النهاية ‏إلى باقي الكون ، وأن الثقب الأسود هو وأي مفردة ‏من داخله ، سوف يتبخر بعيدا ‏ليختفي في النهاية<br />هل يكون لميكانيك الكم تأثير درامي مساوٍ لذلك ‏على مفردتي الانفجار الكبير ‏والانسحاق الكبير ؟ ما ‏الذي يحدث حقاً أثناء الأطوال المبكرة جداً أو ‏المتأخرة جداً من الكون ‏عندما تكون مجالات ‏الجاذبية من القوة بحيث لا يمكن تجاهل تأثيرات ‏الكم ؟ هل للكون حقيقة ‏بداية أو نهاية ؟ وإذا كان ‏الأمر كذلك ، فكيف تبدوان ؟‎ <br />_______________________________________________</p><p>و يقوم ستيفن بعدها بتوسيع مداركك عن ‏الكون ،، ‏كيف نشأ ،، ما معنى التمدد و ‏كيف بدأ الإنسان ‏يستكشف مجموعته ‏الشمسية وأرضه والكون من ‏حوله<br />ليذهب بنا إلى نظرية الإنفجار الكبير</p><p>لقد استمر الجدال حول نشأة الكون وتاريخه في ‏‏الزمان ‏<br />هل له بداية في الزمان؟ أو كان محدودا في الفضاء ‏؟</p><p>في عام 1929 ،قام هابل بإثبات أن المجرات ‏والنجوم ‏تتباعد بسرعة كبيرة وان الكون ككل آخذ ‏في التمدد ‏والإتساع ‏</p><p>وقد أدّى ذلك إلى ظهور منابت نظرية الانفجار ‏الكبير ،وبدأت فكرة تتخيل كيف كان الكون متناهياً ‏في الصغر ‏وكثافته لا متناهية‏<br />وترجّح أن الزمن بدأ مع الانفجار الكبير</p><p>يعتقد أصحاب النظرية أن الكون كان عبارة عن كتلة صغيرة ذات كثافة وحرارة لا يمكن تصورها<br />ثم انفجرت هذه الكتلة انفجاراً هائلاً منذ قرابة 13 مليار سنة لينتج عن انفجارها سحابة هائلة من الغاز والغبار الكوني</p><p>ويؤكد لك الكاتب أن الزمان قبل الانفجار الكبير لا ‏‏يمكن تحديده<br />بمعنى آخر لم يكن هناك ما يسمى ‏بالزمان أصلاً</p><p> <br />a computer-generated explosion representing the Big Bang</p><u>فيقول</u><br />_______________________________________________<br />‏مع ذلك، كان الاكتشاف المتميّز، الذي تم في ‏نهاية ‏القرن العشرين، هو تيقننا بالفعل من وجود ‏حدث ‏أول: الانفجار العظيم، الذي قد يشبه البيضة ‏أكثر ‏ممّا يشبه الدجاجة، ومع ذلك ليس كأيٍ منهما<br />فقد ظهر كل من الكون والزمان للوجود أول مرة ‏‏عندم الانفجار العظيم، وذلك هو السبب الأول، فإذا ‏‏استطعنا فهم الانفجار العظيم فسنعرف سبب ظهور ‏‏الكون على صورته تلك<br />_______________________________________________<p>وينتقل بعدها إلى عناصر تكوين المادة<br />كيف توصلنا إلى إكتشاف الذرة ،، وكيف ‏كنا نتخيل ‏أجزاء المادة وقابليتها للإنشطار ‏من قبل ،، ويحيلك ‏إلى الجاذبية بصفتها ‏من القوى المؤثرة على عناصر ‏كوننا ‏الأساسية</p><p>حتى يومنا هذا ،يعتبر الكوارك هو أصغر ‏‏الجسيمات<br />والكوارك هو جسيم أولي مشحون يحس بالقوى الكبرى <br />البروتونات والنيترونات يتكون كل منهما من 3 كواركات<br />================================<br />يصل بك الكاتب أخيراً إلى الثقوب السوداء ‏‏_أمتع ‏فصول الكتاب<br />ليحدثك عن مفهومها</p><p> والثقب الأسود هو منطقة في المكان -الزمان <br />لا يستطيع أي شيء الهروب منها ولا حتى الضوء<br />لقوة جاذبيتها الشديدة</p><p>ويذهب بك بعد ذلك إلى أن الثقوب ‏السوداء ليست ‏جد سوداء<br />كما أن الثقوب كلما كانت أصغر كلما كانت ‏أشد ‏توهجاً ،وبالتالي تكون قدرتنا على ‏رصدها أفضل</p><p>================================</p><p>من أمتع ما قرأت عنه هنا أيضاً هو الجسيم ومضاده<br />فكل نوع من جسيمات المادة له مضاد جسيم مناظر له<br />وعندما يصطدم الجسيم بمضاده فإنهما يفنيان<br />ولا يتخلف عن ذلك إلا الطاقة<br />ويدلل بأمثلة ممتعة كذلك<br />^_^</p><p>الفكرة التي وجدتها مثيرة هي عدم تساوي عدد الكاوركات مع مضاداتها و هذا من حسن حظنا فلو كانت متماثلة لكان أفنى أحدهما الآخر في الكون المبكر لتترك كوناً مليئاً بالإشعاع لا يكاد يحتوي أي مادة</p><u>تخيّل معي <br />لا مجرات ولا نجوم ولا كواكب<br />ولا نحن ‎</u><p>عندما تشرد قليلاً في ذلك<br />احم<br />:P<br />================================</p><u>الكون بلا بداية وبلا نهاية‎</u><br />‏ ‏<br />‎يرى هوكنج أن<br />‎‏ معظم الناس وصلوا إلى ‏الإيمان بأن الكون جُعل ‏ليتطور حسب مجموعة من القوانين التي لا تُكسر ‏،ولكن هذه القوانين ‏تخبرنا بما ينبغي أن يكون الكون ‏عليه عند بدايته وعلى أنه لو كان الكون بلا بداية ‏وبلا حرف ، ‏فإنه لا تكون له بداية ولا نهاية فهو ‏ببساطة موجود‎<br />‏ ‏<p>وفي فصل سهم الزمان ،، يحدثك هوكنج ‏عن مفهوم ‏الزمن ،، وارتباطه بنظرية ‏النسبية</p><p>يرى ستيفن أن هناك فارقاًً كبيراً بين ‏إتجاهي الأمام ‏والوراء للزمان الحقيقي ‏في الحياة العادية<br />‏<br />ويدلل لك بمثالأً طريفاً</p><u>فيقول</u><p>‏_______________________________________________</p><p>‏تصوّر قدح ماء يقع من على مائدة وينكسر ‏‏على الأرض إلى قطع<br />لو أخذت لذلك فيلماً سينمائياً ، فإنه ‏سيمكنك بسهولة ‏أن تعرف إذا كان الفيلم ‏يسير أماماً أو وراء ‏<br />ولو سيرته وراء فسوف ترى القطع تجمع ‏نفسها معاً ‏فجاة من على الأرضية وتقفز ‏عائدةً لتكون قدحاً ‏كاملاً على المائدة</p><p>‎…‎<br />ماذا سيحدث إن توقف الكون عن التمدد ‏وبدأ في ‏الإنكماش<br />سيؤدي هذا إلى صنوف الإحتمالات التي ‏من نوع ‏يشبه الروايات العلمية بالنسبة ‏للناس الذين سيبقون ‏أحياء من طور ‏التمدد حتى طور الإنكماش<br />هل سيرون الأقداح المكسورة تجمع ‏نفسها معاً من ‏على الأرضية وتب عائدة ‏فوق المائدة؟<br />‎…‎<br />على أن ثمة طريقة أسرع لمعرفة ما ‏سيحدث:هي ‏القفز في ثقب أسود<br />إن كان الإضطراب سيقل في طور ‏الإنكماش للكون ‏، فإن المرء قد يتوقع له ‏أيضاً أن يقل في الثقب ‏الأسود<br />وهكذا لعل الفلكي الذي سيسقط في ‏الثقب الأسود ‏سيتمكن من كسب نقوده ‏في لعبة الروليت بأن يتذكر ‏أين ذهبت ‏الكرة قبل أن يضع رهانه</p><p>‏(على أنه لن يتاح له لسوء الحظ زمن ‏طويل للعب ‏قبل أن يتم تحويله إلى ‏إسباجيتي)‏<br />:D<br />_______________________________________________</p><p>‏================‏</p><u>هذا الفيديو يوضَح شيئاً من وجهة نظره عن ‏نشأة الكون</u><p><a href="http://www.youtube.com/watch?v=Sq-%E2%80%8EWFJGTJaI">http://www.youtube.com/watch?v=Sq-‎WF...</a></p><p>================================</p><p>‏</p></b><p>‏ إن لم تكن قد قرأت كتاباً علمياً من قبل ،أو على الأقل تابعت بعض الدوريات و المواقع العلمية ، ‏فلا أنصحك بهذاالكتاب كبداية<br />فسوف تجده مملاً قليلاً ،وستجد نفسك غارقاً في المصطلحات التي ستشتّت ‏انتباهك،وتعيقك عن الإستمتاع به <br />وهذا الكتاب يحتاج للقراءة لكثيرٍ من المرّات كي تتشبع بمعلوماته ،و يحتاج لكثير من القراءات الخارجية كذلك</p><p>الكتاب معلوماته قيمة وشيقة لواحدٍ من أهم العلماء ‏الذين أنجبتهم الأرض</p><p>ولا يزال علم الفلك متعة عظيمة ،، ‏<br />وتحليقنا بين المجرّات محفّز عظيم للخيال</p><p></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/7878381?shelf=history">history</a> <a href="https://www.goodreads.com/review/list/7878381?shelf=philosophy">philosophy</a> <a href="https://www.goodreads.com/review/list/7878381?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/614778-ahmad-sharabiani"></a></section><section><p>9,567 reviews55.6k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/170142932">September 3, 2021</a></section><div><p><b>A Brief History of Time: From the Big Bang to Black Holes, Stephen Hawking</b><p>What is it that our eyes do that could possibly affect things? </p><p>A Brief History of Time: From the Big Bang to Black Holes is a popular-science book on cosmology (the study of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for nonspecialist readers with no prior knowledge of scientific theories. </p><p>In A Brief History of Time, Stephen Hawking attempts to explain a range of subjects in cosmology, including the Big Bang, black holes and light cones, to the non-specialist reader. </p><p>His main goal is to give an overview of the subject, but he also attempts to explain some complex mathematics. </p><p>In the 1996 edition of the book and subsequent editions, Hawking discusses the possibility of time travel and wormholes and explores the possibility of having a Universe without a quantum singularity at the beginning of time.</p><p>تاریخ نخستین خوانش: روز چهارم ماه مارس سال 1996میلادی</p><p>عنوان: تاریخچه زمان: از انفجار بزرگ تا سیاهچالها؛ نوشته: استیون هاوکینگ؛ مترجم: محمدرضا محجوب؛ نشر: تهران، انتشار، چاپ نخست 1369، مشخصات ظاهری 231ص، مصور، نمودار، چاپ سوم: زمستان 1369؛ ‏چاپ پنجم: 1375؛ چاپ ششم: 1378؛ چاپ هفتم: 1380؛ ‌شابک ایکس-964573519؛ موضوع نوشتارهای نویسندگان بریتانیا - سده 20م</p><p>این کتاب به عنوان پرخوانشگرترین کتاب «کیهان‌ شناسی» شهرت یافته، و به بیش از سی و سه زبان دنیا تا سال1993 میلادی، ترجمه و چاپ شده‌ است «هاوکینگ» در این کتاب با زبانی ساده به بازگویی داستان جهان پرداخته است</p><p>در مورد مفاهیم اساسی مانند «فضا» و «زمان»، بلوک‌های اساسی ساختاری، که جهان را تشکیل می‌دهد (مانند کوارک‌ها)، و نیروهای اساسی حاکم بر آن (همانند گرانش) گفتگو می‌کند؛ ایشان در مورد پدیده‌ های کیهان‌شناختی مانند «بیگ بنگ» و «سیاه ‌چاله‌ها» نیز می‌نویسند؛ «هاوکینگ» این کتاب را برای خوانشگرانی که هیچ دانش پیشین درباره ی گیتی ندارند، برای آنهایی که تنها علاقمند به یادگیری چیزهای تازه در اینباره هستند، نوشتند؛</p><p>مینویسند: (روزی یک دانشمند مشهور -گویا برتراند راسل- درباره ی نجوم یک سخنرانی عمومی کرد، در آن سخنرانی او شرح داد که چگونه زمین به دور خورشید می‌چرخد، و خورشید نیز به نوبه خود به دور مرکز مجموعه عظیمی از ستاره‌ها به نام کهکشان ما می‌چرخد؛ در پایان سخنرانی، پیرزن نحیفی در انتهای سالن به پا خاست و گفت: «آنچه که به ما گفتی مزخرف است؛ جهان صفحه‌ای صاف است که بر پشت یک لاک‌پشت غول‌پیکر قرار دارد.»؛ دانشمند قبل از پاسخ دادن لبخند متکبرانه‌ای زد و سپس گفت: «خوب آن لاک‌پشت بر روی چه ایستاده است؟»؛ پیرزن گفت: «مرد جوان، تو خیلی زیرکی، ولی لاک‌پشت‌های بیشماری تا آن پایین روی هم قرار دارند!»؛ اکثر مردم تصویری از جهان را به عنوان برج بلندی که از تعداد نامحدودی لاک‌پشت روی هم قرار گرفته و تشکیل شده است مضحک و مسخره می‌پندارند، اما چرا ما فکر می‌کنیم چیز بهتری می‌دانیم؟ ما درباره جهان چه می‌دانیم و چگونه این دانش را کسب کرده‌ایم؟ جهان از کجا پدید آمده است و به کجا می‌رود؟ آیا جهان آغازی دارد و اگر چنین است، قبل از آن چه اتفاقی روی داده است؟ ماهیت زمان چیست؟ آیا روزی به پایان خواهد رسید؟ آیا ما می‌توانیم در زمان به عقب برگردیم؟ پیشرفت‌های اخیر در فیزیک، که تا حدودی فن‌آوریهای جدید شگفت‌انگیز هستند، به این پرسش‌های دیرینه پاسخ‌هایی ارائه می‌دهند؛ ممکن است روزی این پاسخ‌ها به اندازه گردش زمین به دور خورشید برای ما بدیهی به نظر برسند، یا شاید به اندازه برجی از لاک‌پشت‌ها مسخره جلوه کنند. فقط گذشت زمان -هر چه که باشد- می‌تواند حقیقت را روشن کند.)؛ </p><p>تاریخ بهنگام رسانی 18/07/1399هجری خورشیدی؛ 11/06/1400هجری خورشیدی؛ ا. شربیانی</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/614778?shelf=20th-century">20th-century</a> <a href="https://www.goodreads.com/review/list/614778?shelf=astronomy">astronomy</a> <a href="https://www.goodreads.com/review/list/614778?shelf=british">british</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1742824-jason-koivu"></a></section><section><p>Author <i></i>7 books1,202 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1902626044">March 14, 2018</a></section><div><p>Isn't it amazing that a person can read a book like <i>A Brief History of Time</i> by Stephen Hawking and come away feeling both smarter and dumber than before he started? What a universe we live in!<p>It's quite short and generally a quick read. Not every page is filled with mind-blowing/numbing theories and brain-busting equations. Some of it is just history, say on Newton and such. However, there were a few pages worth of passages where my wee brain felt like it was getting sucked into a black hole...mainly during the black hole segment.</p><p>I've forgotten so much since I left school, and since school was such a long time ago, some of what was taught back then is now outdated, it was nice to read this refresher/cleanser. </p><p>I came away with a better understanding of the Big Bang theory and why it's plausible (Not the tv show. Its existence is not plausible). I'm trying to sort out the time/space quantifiability thing. That's going to require a reread...and probably further study elsewhere.</p><p>Surprisingly, I also came away with the idea that God and science can coexist. I didn't expect that. I figured someone like Hawking would be like, "God? Pssh, whatever." But that's not his take at all, or at least that not the impression this book left me with.</p><p><i>A Brief History of Time</i> was written with accessibility in mind, knowing full well idiots like me wouldn't buy it, read it or recommend it if it were impossibly dense. Hawking's sense of humor even comes through on occasion, which is always appreciated in these sciencey texty thingies. So, I'll probably move on to his <i>Briefer History...</i> next and I'd be quite willing to read others as well!</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1742824?shelf=non-fiction">non-fiction</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/15385951-mohammed-makram"></a></section><section><p>1,389 reviews2,827 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1259114955">October 12, 2022</a></section><div><p><b><br />بمناسبة الثقب الأسود الذي توقعه آينشتين و تحدث عنه هاوكينج كثيرا في هذا الكتاب و وضع له النظريات و السيناريوهات و القفشات أيضا و بمناسبة الصورة التي نشرت في ابريل 2019 فهذه المراجعة ربما تذكركم بالكتاب الملهم المختصر الغني جدا بالمعلومات و الذي أعتبره بوابة أساسية لمن يهتم بما يحدث في الفضاء البعيد<p>مع انى دارس هندسه فراغية و هندسة وصفية و مساحة جيوديسيه و رياضه بحته و تطبيقية و فيزياء عامه و ثيرمو دايناميك لكن حسيت و انا بقرأ الكتاب ده انى كنت أدبى و انى خريج دبلوم زخرفه</p><p>ده مش عيب فى الكتاب لكن عيب فيا انا لأنى درست علشان أشتغل و اهتميت بس بالمحتوى العلمى اللى هستخدمه فى السوق و كمان ممكن يكون طريقة التدريس أيامنا كانت مشى حالك و كل عيش</p><p>المهم الكتاب مع ذلك شيق و ممتع و مفيد جدا وأسلوبه رشيق و ترجمته ممتازه و دمه خفيف و فيه كمية معلومات تنوء بها العصبه أولى القوه<br />بعد ما بنقرأ الحاجات دى أكيد بنتحسر على بلادنا و علمائنا و على نفسنا و بنأمل يجى يوم ينصلح فيه الحال</p></b></p></div><section><ul><a href="https://www.goodreads.com/review/list/15385951?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/27788046-sean-barrs"></a></section><section><p>1,105 reviews44.2k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2803415986">June 21, 2019</a></section><div><p>Stephen Hawking writes in a very simple and approachable way. On the surface the book has been written for the common man, for he who has little knowledge of theoretical physics. <p>Hawking uses basic terminology and he tries not to overload his writing with explanations and information dumps, but at times it is very clear that the reader needs a certain level of knowledge to understand what he's talking about. As such, Hawking makes certain assumptions as he shifts from concept to concept which left me a little confused. Things that don't appear related are related and it made me question who the intended readership <i>really</i> was. </p><p>I do believe this is a book every reader should try because it is an important one, full of discussions and ideas that could really open up your mind. But I would warn you to be prepared, although this seems like light reading, much of it may go over your head. </p><p><b>Approach with caution. </b></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/27788046?shelf=non-fiction">non-fiction</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/5856247-david-sarkies"></a></section><section><p>1,775 reviews298 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1071517814">April 2, 2015</a></section><div><p><b>Things I learnt from Stephen Hawking</b><br />11 October 2014<p>	Ever since I took up physics in year 11 I have had a love affair with the subject, which is odd since I went on to study an arts/law degree (but that probably had something to do with the fact that I would not have had the staying power to pour all of my energy into helping human knowledge advance towards establishing a unified theory). I still wonder where I ended up getting this book, and it had been sitting on my shelf for quite a while (probably because I was too busy listening to people tell me why I shouldn't read this book), but it wasn't until <a href="https://goodreads.com/author/show/1044434.John_C__Lennox">John Lennox</a> said that it was the most unfinished book (that is people start reading it but do not have the staying power to get to the end) ever written (I'm sure there are other books that beat this book though). There are quite a few things that I have discovered while reading this book, and it is these discoveries that I wish to share with you:</p><p><b>1) This is not an anti-God book</b><br />	One of the impressions that I got from certain people was that this was a book that an atheist wrote to try to argue that God does not exist, in much the same way that <a href="https://goodreads.com/author/show/1194.Richard_Dawkins">Richard Dawkins</a> does in his books. However, that statement could not be further from the truth. In fact, throughout the book the question of the existence of God perpetually hangs in the background. Granted, Hawkings does suggest that if the concept of a infinite bounded universe (don't ask) turns out to be true then it would undermine God's existence, however he does not actually say that this may be the case. In fact his final sentence in this book is that the reason we study physics and try to find a unified theory is because we, as a race, seek to understand the mind of God.</p><p><b>2) Stephen Hawkings is actually a really good writer</b><br />	This probably goes without saying, especially since the cover of my book says that it is a 'record breaking best seller'. While he is involved in some very serious and complicated research he is able to write in a way that many of us who have probably studied physics up to a year twelve level (that is the end of High school) can understand. Okay, I probably have an advantage over most other people since my Dad is a theoretical physicist that we have regular conversations about some of these high level concepts (such as by having any more than three dimensions would cause the orbits of the planets to collapse), but I still found that he was very easy to follow and he explained many of these high level concepts in a way that many of us could understand.</p><p><b>3) Scientists have a strange way of viewing the universe</b><br />	Many of us would be familiar with this guy:</p><p></p><p>but as it turns out, after reading this book, I have come to the conclusion that a lot of theoretical physicists seem to live in the same world that he does. Okay, they probably don't spend their time at the comic book store, or arguing whether Babylon Five is better than Star Trek (actually, one of my primary school friends is a theoretical physicist, and we did have such an argument), but they do seem to see the world in a way that we ordinary people would consider strange.</p><p>	For instance, we see space as flat, meaning that if we look at a star, as far as we are concerned the star is in that direction. However physicists see space as being curved and that a straight line is not necessarily straight. We would see a brick wall as being a solid object and that the idea of walking through one would result in a sore nose. However physicists see it as being made up of mostly space, and the only reason we can't walk through it is because the nuclear forces (forces that exist inside an atom, not the force that can level an entire city) prevent us for doing so. Then there is the concept of dimensions: to us there are only three dimensions, however some scientists (and Hawking is not one of them) see that there are in fact ten, or even more, dimensions.</p><p><b>4) Why are so many scientists atheists</b><br />	 While reading this book I could not get past about how complex this universe is and it made me wonder why it is, with the mathematical precision of the universe, and the complexity that lies therein, that so many scientists seem to argue that it all came about by chance. Even Hawking argues, using the second law of thermodynamics, that the universe cannot move from a state of disorder to a state of order – a broken plate simply cannot mend itself. However, the argument also goes that with the Big Bang Theory (not the television show) that the universe began in a state of disorder and moved to a state of order, however the laws of physics seem to suggest otherwise because what the big bang did was sent in motion a series of laws that caused the universe to come about to what we have at the moment. However, to go into details would require some intense theoretical physics, something which I have do desire to delve into at the moment.</p><p><b>5) Scientists assume the speed of light is a constant</b><br />	The truth is that it is not. Okay, if light were travelling through a vacuum where there are no external forces acting upon it, then it is a constant, but that is very rarely the case. Take for instance this phenomena:</p><p></p><p>	The reason light behaves thus is because when it hits the prism it SLOWS DOWN, and when it slows down it refracts. Thus my point is proven, the speed of light is only a constant when there are no external forces acting upon it.</p><p>	So, what external forces may act upon light in space. Well, first of all there are black holes. When light hits a black hole the force of gravity is so strong that it will actually prevent light from escaping. Thus, gravity is a force that effects light and slows it down. Then there is the concept of <a href="http://en.wikipedia.org/wiki/Dark_matter">dark matter</a>, which are clouds of matter that do not emit light and float between the star systems. Okay, we know very little about the stuff (and it is also a theory, so it has not been proven) but my hypothesis is that if this stuff exists then would it not have an effect upon light, namely by slowing it down, which means that there is a possibility that our calculations as to the distance of stars from our own Sun could actually be wrong?</p><p><b>6) Scientists do not know as much as we think they know</b><br />	One of the things that Hawking stresses in this book is that theories are not actually proven. A theory is an idea that has some foundation based on mathematical calculations and empirical evidence. Therein lies the problem. Much of our understanding of the universe is based upon mathematical calculations, and it appears that if an event comes about which causes this mathematical calculation to break down, they immediately set out to try to find another mathematical equation to plug the hole.</p><p>	Take light for instance. For years we believed that light acted as a wave and suddenly it was discovered that it also behaves like a particle (a particle of light is called a photon). The same goes with matter – for years we believed that they were particles when all of the sudden we discovered that they can also behave like waves. As such, our understanding of the universe suddenly breaks down (meaning that we are not necessarily made up of atoms, but have wavelike properties as well).</p><p>	Mathematical equations have been very destructive in out modern world. Take the Global Financial Crisis for instance. A bunch of apparently really smart people create complex mathematical equations to determine when to buy and sell shares and how to make billions of dollars. However what these equations did not take into account was the fact that people could not simply continue to accumulate debt without having to pay it back and when people began to default on their loans enmass, the whole concept broke down and we were taken to the brink of financial armageddon.</p><p>	Another point goes back to Ancient Greece. Here we have the theory of Democritus, namely that matter was not infinitely indivisible (the smallest piece of matter is an atom), and then the theory of Aristotle, that is that matter is infinitely divisible. Scientists preferred Democritus' theory, however they soon discovered that you could break down the atom into protons and neutrons, and you could even break them down to quarks. So, maybe Aristotle was right after all.</p><p><b>7) We accept their theories because our gadgets work</b><br />	It goes without saying that their research and discoveries have lead to the computer that I am writing this on, the energy that powers our devices, and the bombs that can level entire cities. We know how to make a nuclear bomb, as well as a smart phone, so we don't question what they say, because it obviously works. However, as a friend of mine once said, it is still all based on theory, and just because something works does not necessarily mean that the theory is correct. Remember that penicillin was discovered by blind chance.</p><p><b>8) Nobel Prizes are simply shiny baubles that have no merit</b><br />	Okay, maybe the people that win these prizes are actually really smart, but then again, the guys who set up <a href="http://en.wikipedia.org/wiki/Long-Term_Capital_Management">Long-Term Capital Management</a> also won a Nobel prize, which proves my point.</p><p><b>9) Nobody really knows how gravity works</b><br />	Gravity is one of those odd forces that doesn't seem to connect with any of the other forces in our universe. As Hawking points out, there are four forces that have been identified: electro-magnetic, strong nuclear, weak nuclear, and gravity. Out of those four forces (five if you divide electric and magnetic, but since electricity will create a magnetic force, they are effectively combined) only gravity stands out. This is probably why Hawking spends so much time talking about black holes because black holes are where the gravitational pull is so strong that not even light can escape from its grasp. The other thing is that gravity does not, at least in our knowledge, have an opposing force. Gravity basically sucks, and that is all it does – it doesn't repulse as the other forces can.</p><p>	It is interesting that in some texts that I have read (maybe it is speculative science-fiction but I simply cannot remember off the top of my head) some people have suggested that gravity is actually a force from another universe that affects our universe and what it is effectively doing is sucking our universe into their universe. However, as I have said, that is incredibly speculative, and since I am not a theoretical physicist I can't really say any more on the subject.</p><p><b>10) The God of the Gaps is a cop-out</b><br />	The idea of the God of the Gaps is that where there are gaps in our knowledge we simply say 'oh, God did that' and think nothing more of it. This goes back to the days of paganism (and Medieval Europe) where all of the unknown forces, such as the weather, was attributed God (or the gods) and we could not know anything beyond that fact. However I am arguing that it is a cop out. Creation scientists who resort to this argument are at best lazy and at worst dangerous. The reason I say that is that it discourages research into areas that we do not understand. Okay, we may never be able to control the weather, or predict earthquakes, but that does not mean that we should throw our hands up in the air and say 'this is too hard'.</p><p>	While I may be taking a swipe at creation scientists here, I would also take a swipe at the atheists who claim that there is no God. The reason I say that is because there seems to be a fear within the scientific community that suggests that we may not be able to know everything, or that our understanding of the universe may be wrong. The problem that arises is that if we throw the idea of God out of the window and claim that the universe came about by chance, then we deny the fact that we live in an incredibly ordered universe that we can learn and understand through the development of mathematical formulae. If a formulae turns out to be wrong, that does not mean that the universe will collapse in on itself – it won't – it just means that we have to go back to the drawing board and start over from scratch.</p><p><b>11) Why are Creation Scientists so dogmatic</b><br />	Why is it that some members of the scientific community insist that we must take the Bible literally? The Bible is not a scientific text, and it was never meant to be a scientific text. It is a theological text that tells us how we should live with one another and how we should view God. Science exists beyond the Bible, and neither contradicts the other. Okay, granted, God has intervened in this world and done things that break the laws of science, but doesn't he have a right to do that – he created the universe? However, what the Bible tells us is that God is a god of order, and if he is a god of order then does it not make sense that the universe that he created is an ordered universe?</p><p>	So, maybe you are looking for a whiz bang conclusion to my exposition on this book, but all I can say is that what I have written above pretty much sums up what I have learnt from this book. In a nutshell (hey, this is me in a nutshell), all I can say is that what I have learnt from this book is that the world is an amazingly ordered place in which we live, and having now completed this book I am just as committed to my Christian faith as I ever was. However, if theoretical physics fascinates you, then this is certainly a book that you should give a read (though you have probably done that already).</p><p>This review also appears on my <a href="http://www.sarkology.net/2014/11/11-things-that-i-have-learnt-from.html">blog</a>. I have also commented on this book in my review on <a href="http://www.sarkology.net/2014/12/christopher-nolan-has-outdone-himself.html">Interstellar</a>.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/5856247?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/16783645-ahmad-ebaid"></a></section><section><p>281 reviews1,979 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/894288655">February 18, 2018</a></section><div><p><b><blockquote>"والواقع أننا قد أعدنا تحديد مهمة العلم لتصبح اكتشاف القوانين التي تمكننا من التنبؤ بالأحداث في الحدود التي يفرضها مبدأ عدم اليقين"</blockquote>
<p>بدأ ستيفن هوكينج, وهو عالم في الفيزياء النظرية, في كتابة هذا الكتاب في الفترة التي كان مازال يستطيع فيها أن يستخدم صوته وهو شبه مشلول على كرسيه المتحرك, ثم وبعد فترة, وقبل أن يكمل الكتاب, خضع لجراحة شقت فيها حنجرته, ليذهب صوته وهو الشيء الوحيد الذي كان يتواصل به مع العالم آنذاك</p><p>ظن في البداية أنه لن يستطيع إكمال الكتاب, ولكن أحد طلبته "بريان هويت" قام بمساعدته, ليس فقط على مراجعة المسودة, وإنما جعله أيضاً يستخدم برنامج لتخليق الأصوات, وهو ما فتح نافذة جديدة له على العالم.</p><p>وها هو ذا الكتاب بين يداي, وبين يدي الملايين.</p><p></p><p>أول كتبه الموجه للعامة, يشرح لنا فيه حصيلة أوراقه البحثية,<br />كتاب صغير الحجم <br />الثلث الأول من الكتاب تقريباً هو مقدمة تمهيدية عن الفيزياء التي سيشرح لنا قصته معها تالياً في الكتاب, وعن المحاولات والنتائج التاريخية التي سبقت أبحاثه.</p><p>ثم الثلثين الآخرين عن أوراقه البحثية, التي ارتكزت على الثقوب السوداء, والتي تعتبر نقطة تفرد خاصة حيث تكون الكثافة وانحناء الزمكان عندها لانهائيين, وتنهار عندها قوانين النسبية العامة<br />وقد قام هوكنج بمحاولة تفسيرها باستخدام مبادئ الكم تحت اسم: "الجاذبية الكمية", وهي إحدى محاولاته لصنع حلقة وصل بين قوى ثقالة الجاذبية وبين القوى الثلاث الأخرى التي تم توحيدها معاً في نظرية واحدة سابقاً</p><p>ثم ينهي بالمحاولات التي تلته لتوحيد القوى الأربعة, في نظرية واحدة, نظرية لكل شيء, تحديدا نظرية الأوتار, والأوتار الفائقة</p><p></p><p>إذن أين هو التاريخ الموجز للزمان؟ لقد أنبأتنا نظرية النسبية العامة بأنه إذا تحرك أحدهم بسرعة فسوف يمر الزمن عنده أبطأ. كما أنبأتنا بأن الجاذبية, تسبب تشويهاً في نسيج المكان لتجذب إليها الأشياء, وأيضاً تسبب تشويه الزمان, وبقربنا من مصدر قوي للجاذبية كأحد أطوار النجم كبير الحجم "الثقب الأسود", يسير الزمن عندنا أبطء من الزمن عند المراقب البعيد عند مصدر الجاذبية, وقد رأى معظمكم تطبيق هذه الفكرة في فيلم انترستلر.</p><p>وهكذا فالكتاب يتعرض في بعض مواضعه للجاذبية, والجاذبية تؤثر على الزمن. الزمن الذي لن يتطرق إليه الكاتب كثيراً في كتابه إذا ما استثنيا المقدمة التي حشر فيها الحديث عن الزمن حشراً لتتوافق مع هذا العنوان التجاري, والذي وُفّق في اختياره كعنوان جذّاب.</p><p>في المقدمة يعلل المؤلف كتابة هذا الكتاب, بأنه ورغم وجود عدد من الكتب الجيدة </p><blockquote>"على أني شعرت بأن أي منها لم يكن يخاطب حقاً الأسئلة التي أدت إلى القيام بالبحث في علم الكونيات ونظرية الكم: من أين أتى الكون, كيف ولماذا بدأ؟ هل سيصل إلى نهاية ؟ وإذا كان الأمر كذلك, فكيف ستكون النهاية</blockquote>
<br />وهنا تلاعب بالكلام, ليحوّل كتابه من مجرد كتاب يسرد به مسيرته العلمية في سياق البحث عن النظرية النهائية, إلى كتاب يعالج الأسئلة التي تؤرق الكل. الأسئلة التي لم يعد الفلاسفة قادرين على التعامل معها.<br />وهذه العبارات التي تحتمل التأويل تدعم ما قلته في الفقرة السابقة عن أن العنوان مقصود به أن يكون تجاري بغض النظر عن محتوى الكتاب ومدى خداع القاري به.<p></p><p>ونأتي أخيراً للسؤال الأكثر إلحاحاً للمعظم, هل الكتاب للمبتدئين؟ والجواب هو لا, فالكتاب فقط لمتابعي العلوم الذين لديهم الحصيلة الأساسية عن الفيزياء, والكتاب لا يشرح تلك الأساسيات سوى بجمل عارضة, لن تمكنك من استيعاب أي شيء</p><p>ولذلك قام الكاتب بإعداد نسخة أخرى من الكتاب أكثر بساطة بعنوان, "تاريخ أكثر إيجازاً للزمان" تجدونها مترجمة أيضاً</p><p>أما إذا كان لديك الحصيلة الأساسية, فالكتاب ولا شك تجربة مميزة, فالكتاب مليء بالعلم في كل سطر منه, <br />والكتاب يعتبر نصف تاريخي فمعظم ما فيه من نظريات تخطوها الآن, أو أنها لم تكن مكتملة في ذلك الحين</p><p>كان الشرح سلسل, واستنباط المعلومات وترابطها يشي بمدى تمكن الكاتب وعبقريته في إعادة صياغتها بسلاسة, إلا أنه هنالك استثناء بسيط في بضع صفحات يصف فيها آخر جزء من أبحاثه, وربما يرجع ذلك إلى أن الموضوع نفسه غامض</p><p></p><p>** <br />الكتاب من ترجمة مصطفى إبراهيم فهمي, مترجم قدير للبيولوجي, ولكنه تجاهل قاموس المصطلحات إلى حد كبير, فقام بترجمة التعبيرات بما يراه مناسبا دون أن يرجع إلى المصطلح المتَفَق عليه بالعربية في هذا المجال الغريب عنه<br />فنجده ينوب عن مصطلح "الأوتار الفائقة" بألفاظ أخ��ى</p><p>ويظهر أيضا عدم إلمامه بالفلسفة, فقد ترجم اسم الفيلسوف <br />"wittgenstein"<br />إلى "ويتجنشتين", وهذا خطأ, فهذا الإسم ألماني, وفي الألمانية ينطق حرف "W" بنفس نطق حرف الـ"V" في الإنجليزية<br />وبهذا يصبح النطق الصحيح لاسم الفيلسوف: "فيتجنشتين", وهكذا يترجم في كتب الفلسفة العربية. </p><p></p><p>*****</p><blockquote>"سيقولون أن الله يستطيع بقدرته بدء الكون بأي طريقة يشاء. ومع هذا فإن الله أيضاً كان يستطيع أن يجعله ينشأ على منوال تعسفي تماماً. ولكنه كما يظهر قد اختار أن يجعله يتطور على نحو جد منتظم حسب قوانين معينة. وهكذا فإنه مما يساوي ذلك عقلاً افتراض أن هناك أيضاً قوانين تحكم الحال المبدئي."</blockquote>
<br />لقد تطور فهمنا للعالم كثيراً. كنا في البداية نعزو الأحداث الخارجية لقوة فوقية تعبر عنها الطبيعة, وبعدها بدأنا نلاحظ أن الأشياء تتكرر بنظام معين.<br />وقد كانت الثلاثة قرون الأخيرة هي سعي متواصل لاكتشاف المزيد من هذه القوانين, وقد وصلت للذروة بعد أن اكتشف لابلاس في أول القرن التاسع عشر "الحتمية العلمية", أي أن كل ما يحدث في العالم من حولنا إنما هو يسير وفق معادلات رياضية تنبئنا بما سيحدث تالياً إذا ما عرفنا ما يحدث الآن.<br />وقد أدت هذه الثقة المفرطة إلى وجود أكثر من فجر كاذب, نذكر منهم أن:<br /><blockquote>"الفيزيائي ماكس بورن الحائز على جائزة نوبل في الفيزياء, ذكر في عام 1928 لمجموعة من الزائرين لجامعة جوتنجن أن الفيزياء كما نعرفها, ستنتهي بعد ستة شهور, وكانت ثقته مؤسسة على اكتشاف ديراك الحديث للمعادلة التي تتحكم في الإلكترون, وكان من المعتقد أن ثمة معادلة مماثلة ستحكم البروتون, الذي كان الجسيم الآخر الوحيد المعروف وقتها, وأن هذا سيكون ختام الفيزيائيات النظرية"</blockquote>
<br />ولكن كان هنالك المزيد مما لا نعرفه, بل وهنالك أيضاً المزيد مما لن نعرفه أبداً وفقاً لمبدأ "عدم اليقين" الذي اكتشفه هاينزبرج<br /><blockquote>"والواقع أننا قد أعدنا تحديد مهمة العلم لتصبح اكتشاف القوانين التي تمكننا من التنبؤ بالأحداث في الحدود التي يفرضها مبدأ عدم اليقين"</blockquote></b></p></div><section><ul><a href="https://www.goodreads.com/review/list/16783645?shelf=%D8%B9%D9%84%D9%88%D9%85">علوم</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/53209373-simon-clark"></a></section><section><p>Author <i></i>1 book4,911 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2530184829">December 17, 2018</a></section><div><p>This is an absolutely magical book, both objectively and for me specifically. I first read it when I was about 9 or 10, and ever since I've assumed that I didn't understand a thing, and read it as a childish boast. Fast forward nearly twenty years, degree and PhD in physics in hand, and I decided to give it a proper read. Much to my surprise I found that the book had permeated my brain! I remembered a huge number of the explanations, and the book resonated with the way I've thought about physics my entire academic career - I think I took in a great deal more than I first thought!<p>As a primer to physics (I would say modern physics, but the book is a little out of date) you really couldn't ask for anything better than this. Especially when it comes to cosmology, this is possibly the best popular physics book that I've ever read. It really is a classic for a reason. It's such a concise, understandable introduction to the field that I'm determined to get my girlfriend (a linguist with no real interest in physics) to read it. Not just because I think she'll understand it, but because I think she will enjoy it!</p><p>One peculiarity of the text is Hawking returning to the concept of God (with a capital G) over and over again. In some ways this feels like a transitional text, marking the passing of the public generation for whom the church determined the order of all things, and the coming of the current, secular generation. Unlike other authors (looking at you, Dawkins) Hawking always does so in a way that feels respectful while also forcefully stating his scientific case. It's quite feat of writing, much like the rest of the work.</p><p>You really should read this, it's fantastic.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/53209373?shelf=favorites">favorites</a> <a href="https://www.goodreads.com/review/list/53209373?shelf=physics-books">physics-books</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/25683251"></a></section><section><p>1,040 reviews1,678 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1159467848">August 7, 2017</a></section><div><p>خیلی وقت بود دنبال یه کتاب بودم که نظریات فیزیک جدید رو توضیح بده. زیاد از اصل عدم قطعیت و کوانتوم و نسبیت و نظریه ی ریسمان ها و سیاهچاله و کرمچاله و انفجار بزرگ و غیره و غیره شنیدیم، ولی شاید از هیچ کدوم تصور درستی نداشته باشیم. این کتاب خیلی از این نظریات رو مفصل توضیح میده.<br />استيون هاوكينگ يك مستند سه قسمتى داره، به نام "به سوى كيهان، همراه با استيون هاوكينگ" با صداى بى نظير بنديكت كامبربچ، كه بيشتر مباحث اين كتاب رو، بسيار بسيار ساده تر توضيح ميده. توصيه مى كنم كسانى كه تازه مى خوان مطالعات كيهان شناسى رو شروع كنن، قبل از اين كتاب اون مستند رو ببينن.<br />Into the Universe With Stephen Hawking<p><b>نکات منفی</b><br />مشکل اصلی کتاب، اینه گاهی زبانش خیلی فیزیکی میشه. به نظر میرسه آدم باید اطلاعات زیادی از فیزیک داشته باشه تا حرف کتاب رو بفهمه. من دانش فیزیکم در حد سوم دبیرستان و چیزهایی که جسته گریخته از این ور و اون ور خونده بودم هستش، در نتیجه شاید نصف کتاب رو آن چنان که باید و شاید نفهمیدم. خود استیون هاوکینگ میگه که ناشر بهش گفته بود: "به ازای هر فرمولی که در کتاب به کار ببری، فروش کتاب نصف میشه" و درسته که تقریباً هیچ فرمولی در کتاب به کار نرفته، اما همچنان زبان کتاب سنگینه. در مؤخره ی کتاب، نوشته بود این کتاب یکی از "ناخوانده" ترین کتاب های تاریخ ادبیاته. یعنی ��ده ی زیادی خریدن کتاب رو و حتی ادعا میکنن خوندنش، ولی در حقیقت نخوندنش! میشه فهمید چرا.</p><p><b>نکات مثبت</b><br />اما جاهایی که دانش ناقص فیزیکم یاری میکرد یا خود کتاب ساده بود، خیلی خیلی عالی بود کتاب. قصد دارم یه بار دیگه بخونمش به همین زودی ها. تاریخ فیزیک از دوره ی ارسطو تا نیوتون تا آینشتاین و هایزنبرگ، مباحث کیهان شناسی، مثل گسترش جهان یا محاسبه ی فاصله ی کهکشان ها، برخی از مباحث فیزیک جدید، مثل اصل عدم قطعیت و نسبیت، جزء جاهایی بود که کمابیش فهمیدم و خیلی لذت بردم. <br />گاهی هم مطالب علمی رو کلاً رها میکرد و شروع میکرد به تعریف زندگی خودش. مثلاً میگفت این نظریه در فلان تاریخ مطرح شد، در اون زمان من با دختری آشنا شده بودم و میخواستم باهاش ازدواج کنم و شروع میکنه ماجرای خودش رو تعریف کردن.</p><p>کتاب بعدی از این نویسنده، "کیهان در پوست گردو" هستش که قصد دارم به زودی بخرم.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/25683251?shelf=%D8%B9%D9%84%D9%88%D9%85-%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C-%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C">علوم-طبیعی-ریاضی</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1713956-manny"></a></section><section><p>Author <i></i>28 books13.4k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/38374232">November 3, 2011</a></section><div><p>Apparently this book tops the world list of "bought but not read", which may explain why it's so universally acclaimed as a work of genius. If you know anything much about relativity or cosmology, it comes across as a potboiler, admittedly a well-written one with a great final sentence. I wasn't impressed.<p>But... without it, we would never have had MC Hawking. If you haven't come across him, start with <a href="http://www.lyrics007.com/Mc%20Hawking%20Lyrics/E%3Dmc%20Hawking%20Lyrics.html">the lyrics to "E = MC Hawking"</a>. Then buy <i>A Brief History of Rhyme</i>.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1713956?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/2294090-darwin8u"></a></section><section><p>1,559 reviews8,659 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/180764365">December 13, 2015</a></section><div><p><i>“The universe doesn't allow perfection.”</i> <br />― Stephen Hawking, A Brief History of Time<p></p><p>I know. I know. I both loved and hated this book. I definitely should never have read this book, cut the pages, opened the box, etc.. Somehow Stephen Hawking has written a book that gently fluffs the tail on Schrödinger's cat (or perhaps Schrödinger's cat is fluffing Dr. Hawking). </p><p>Look, no doubt the guy is a genius and has a fantastic story (ALS, computer voice, nurses, Black Holes, strippers, movies, etc). My problem is the wussification of a large scientific narrative by one of Big “P” Physics primary scientists. Let someone else write a pop-GUT/Blackhole/Big Bang story. Let another writer do the pop-up Children's book with the scratch-n-sniff singularity, the rotating black hole, the pull-out universe. </p><p></p><p>I want Dr. Hawking doing smart stuff. Let Bill Bryson write the summary science. But it is too late for me. I already crossed the damn event horizon. I've just become entangled with his book, so my "observer state" now corresponds to the damn book and the damn book review being both five stars and 1 stars is no longer a possibility; my reader state is entangled or linked now with my own review so that the "observation of the book review's state" and the "review's state" correspond with each other. I am finished.</p><p>Hey, now to go see some movies about blackholes and wormholes and assholes.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/2294090?shelf=2014">2014</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/102484307-muhammad-abdullah"></a></section><section><p>87 reviews49 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2970545363">April 26, 2021</a></section><div><p>This is the first book I have ever read about science.This is one of the best selling book of the century.I have found it really infomative and my interest in science seems to build. This book is free from mathematical equations (except E=mc2) which is the best thing about the book. This book is so simple that even a lay person with basic knowledge of science can understand it. <p><i>Stephen Hawking, the author of the book, is one of the well renowned scientists of the century after Einstein. Some people even called him the successor of Einstein due to his work in the field of science. In this book, Hawking talks about <u>black holes, worm holes, time travel, cosmic background radiation (CBM), uncertainty principle, expansion of universe, space and time (or simply space-time), origin and fate of the universe, forces of nature and the most important The Grand Unification Theory</u> (the theory of everything) which is the biggest unsolved mystery of the present time. </i></p><p><br /><i>A brief intro to author, Stephen Hawking</i></p><p>This book is really amazing and is popular in both science and non-science related people. I enjoy it a lot and I would like to recommend it to all the science and nature loving people. And I hope they will also enjoy it.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/102484307?shelf=2019-reads">2019-reads</a> <a href="https://www.goodreads.com/review/list/102484307?shelf=non-fiction">non-fiction</a> <a href="https://www.goodreads.com/review/list/102484307?shelf=personal-library-books">personal-library-books</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/117399210-lu-s"></a></section><section><p>1,804 reviews452 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3731394008">May 30, 2022</a></section><div><p>This popularization book provides us with a portrait of the latest discoveries that have shaken the scientific world over the past hundred years: General relativity, quantum mechanics, the Principle of uncertainty, black holes, quarks, string theory, etc., enough to answer many questions: what will become of the the our universe? How was it formed? Why is CERN so determined to accelerate particles in a tunnel several kilometres long in Switzerland?<br />I will not claim to have assimilated all the concepts in a single reading. Still, the book allows me to have a good idea of the stakes and the research. Therefore, I recommend it to any science lover, especially as some of the theories explained will soon celebrate their century of existence and have not yet reached ordinary people.</p></div><section><ul><a href="https://www.goodreads.com/review/list/117399210?shelf=2021-readings">2021-readings</a> <a href="https://www.goodreads.com/review/list/117399210?shelf=brit-and-related">brit-and-related</a> <a href="https://www.goodreads.com/review/list/117399210?shelf=e-4">e-4</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/29002534-valeriu-gherghel"></a></section><section><p>Author <i></i>6 books1,184 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4503897020">February 7, 2022</a></section><div><p>Cam tot ce știu din / despre cosmologie provine din scrierile lui Hawking. Îndeosebi din acest volum care a fost un bestseller absolut. O glumă afirmă că toată lumea bună l-a cumpărat, dar foarte puțini l-au citit. <i>Scurtă istorie a timpului</i> ar fi, așadar, cel mai puțin citit bestseller dintre toate. Nu cred că pe autor l-a afectat prea tare acest amănunt nesemnificativ.<p>Mă aflu în situația bizară că știu multe fără să înțeleg totul. Știu, de pildă, că fizicienii încearcă să ofere „o descriere completă a universului”. Mai știu că o astfel de descriere nu este, deocamdată, cu putință. Mai știu că Hawking a fost obsedat de realizarea unei teorii fizice unificate (mecanica cuantică + teoria relativității generalizate), fără de care sus-numita descriere nu este posibilă. Prima teorie (cea cuantică) susține că „universul e guvernat de întîmplare”, fapt pe care Einstein nu l-a acceptat niciodată. A doua oferă o viziune deterministă.</p><p>Deși ne-am obișnuit să gîndim în termeni finaliști (omul ar fi scopul creației), știu, de asemenea, că evoluția universului nu este finalistă. Evoluția nu are un scop, o „intenție finală”: apariția unei conștiințe care să constate frumusețea și armonia acestei lumi. Pentru Pico della Mirandola, în schimb, acest lucru era evident: „Te-am așezat, Adame, în mijlocul universului, ca să-mi poți contempla măreția” (<i>De dignitate hominis</i>).</p><p>Știu că fizicienii au propus, la sfîrșitul anilor 60, un așa-zis Principiu antropic (îl comentează într-un articol și I. P. Culianu), care li s-a părut unora argumentul suprem al unei evoluții „dirijate după un plan” (un argument creaționist), dar mai știu că acest Principiu (comentat cu entuziasm odinioară de Penrose și Hawking) nu dovedește nimic. Formularea lui pare o imensă tautologie: „Vedem universul aşa cum este fiindcă, dacă ar fi diferit, noi nu am exista să-l observăm”. Altfel spus: „Vedem universul aşa cum este întrucît existăm". Afirmația lui Hawking seamănă cu alta, la fel de misterioasă, tot a lui: „Dezordinea creşte cu timpul, întrucît noi măsurăm timpul în direcţia în care dezordinea creşte”. Nimic mai limpede...</p><p>În fine, mai știu ce a afirmat Roger Penrose despre singularități și găuri negre (universul nostru provine dintr-o singularitate): „O stea care suferă un colaps datorită propriei gravitaţii este prinsă într-o regiune a cărei suprafaţă se reduce la dimensiunea zero. Şi deoarece suprafaţa regiunii se reduce la zero, aşa trebuie să se întîmple şi cu volumul său. Toată materia din stea va fi comprimată într-o regiune cu volum zero, astfel că densitatea materiei şi curbura spaţiu-timpului devin infinite. Cu alte cuvinte, există o singularitate conţinută într-o regiune a spaţiu-timpului numită gaură neagră”.</p><p>Cam atît...</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6237864-nandakishore-mridula"></a></section><section><p>1,238 reviews2,223 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/235263359">February 6, 2018</a></section><div><p>Manny says this book is in the "bought but not read" category for most people. Well, I'm proud to say that I bought and read it, that too in nearly one sitting - back in my geeky days, when I used to get a sexual high just from solving a hard maths puzzle.<p>Unfortunately, I don't remember much of it (time for a re-read!) but I remember taking away the idea that time is a sphere. Being Indian, I loved this - because we are strong champions of cyclical time. Also, if time and space are both curved, it creates the possibility of jumping from one place and time to another; which is just delicious.</p><p>(I bought a pirated edition of this book for 25 rupees from the roadside at Connaught Place in New Delhi. The vendor asked for 50, I said 25, and the bargaining was just starting when he spied a policeman approaching - so he let me have it for whatever I was offering! "Time" was on my side.)</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/6237864?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><section><section><a href="https://www.goodreads.com/review/show/5363928">August 30, 2007</a></section><div><p>Hawking is a brilliant physicist and a true expert in explaining highly complex aspects of our physical universe in terms that can be understood by most lay people.<p>Where Hawking fails, in my opinion, is his hubris. He proceeds in to the realm of metaphysics and religion in several portions of this book. For instance, in his chapter on the "arrow of time", he states that, essentially, the universe can only move in one direction of time. It cannot go backwards. He also states that this limits the powers of God himself. Now, Hawking never qualifies those statements by defining "God". However, if he is talking about the Biblical God, how can you honestly think you're so intelligent as to place limits on a limitless being? If God is so powerful as to have created the universe and all the physical laws, why wouldn't he be powerful enough to change those laws any time he chooses? It is the same concept as a scientist creating a computer simulation of the universe. The scientist can, at any time during the simulation, alter the underlying framework of the simulation, effectively changing the physical laws that simulated universe operates under.</p><p>Now, whether you believe in God or not, the mere fact that Hawking has the audacity to think he can assign limits on a limitless being should cause you some concern. Hawking, because of his fame and brilliance, is a man that people listen to when he speaks. That gives him immense power over the minds of his readers. He should be more careful in choosing his words.</p><p>When Hawking sticks to his strengths, however, the book is second to none. Hawking truly has a gift of explaining the powerful forces that shape our lives in ways anyone can understand.</p><p>If this book had been edited better, it would have received a few more stars from me, but I can't reward stubborn scientific pride resulting in false assumptions.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/175635-trevor"></a></section><section><p>1,281 reviews21.4k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/10153472">December 9, 2007</a></section><div><p>The main idea to take away from this book is that time has a clear direction. Entropy is the idea that the universe moves from highly ordered states to less ordered states. If you take the lid off a bottle of perfume, and leave it off for a few days the perfume will go from being highly ordered (all in the bottle) to highly disordered (all over the room). <p>Hawking uses this idea to explain why travelling back in time is impossible. It requires very little energy to knock a glass over and smash it - but think of how much energy it would take to make the glass jump back into place - all of the bits perfectly back where they were prior to the glass breaking. It would be impossible - and that impossibility is what gives time its clear direction.</p><p>Philosophically, I tend to feel that the book makes far too much of the Uncertainty Principle. But that is another story.</p><p>This isn't the easiest book to read in the world and is probably the most bought science book of all time while also being the one most likely gave up on after a chapter or two - but it is a fascinating read all the same.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/175635?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/76507338-saadia-b"></a></section><section><p>179 reviews61 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2325240056">July 7, 2021</a></section><div><p>Only Hawking could write this book - simple, to the point and extremely resourceful. Cosmology is not an easy subject neither can everyone understand its deep connotations. Hawking made it understandable in the most layman terms possible.<p><a href="https://saadiabakhtawar.blogspot.com/">Blog</a> | <a href="https://www.youtube.com/channel/UCcg9HVwNUIJleHeP6v4oqqA">YouTube </a> | <a href="https://www.instagram.com/saadia_lashari/">Instagram</a> | <a href="https://www.facebook.com/CritiConscience">Facebook</a> | <a href="https://www.linkedin.com/in/saadiabakhtawar/">LinkedIn</a></p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/35008106-ahmed-ibrahim"></a></section><section><p>1,196 reviews1,568 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2140315712">November 25, 2017</a></section><div><p> <b>يسعى هوكينج في هذا الكتاب لوضع خريطة أو مسار كوني، بداية من الكيفية التي بدأ بها الكون، إلى وضع الاحتمالات التي سينتهي إليها، وتوضيح ما بينهما من أمور كونية فلكية. <p>بدأ الكتاب بالحديث عن الانفجار الكبير والمتفردة التي بدأ منها، وفيما بعد سيتناول احتمالات تنفي وجود متفردة أولية تقول بأزلية الكون، لكن المتفق عليه بشكل كبير في حالة وجود المتفردة أو لا أنه ثمة انفجار كبير بدأ منه الكون ثم تمدد، ومن الأشياء التي ستناقش بعد هذا هو الكيفية التي تمدد بها الكون. الانفجار الكبير كما قال هوكينج لا ينفي وجود خالق. <br /> ثم يتحدث عن المكان والزمان، ويتناول فيه نظرية أرسطو الأولية التي دحضها جاليليو ثم نيوتن بقوانينه عن الحركة، ومن ثمَّ تناول بالحديث نظرية النسبية لآينشتين، الخاصة بتعارضها من قانون الجاذبية، والعامة المتسقة مع ذاتها. <br />ويتناول بعدها اكتشاف هابل بأن الكون يتمدد، بل ربما يكون لها نهاية حسب نظرية فريدمان. <br />وكانت هذه البداية للنظر إلى أن كوكبنا قطرة ماء في محيط الكون الفسيح، وتمت البرهنة بشكل كامل من قِبل هوكينج وبنروز على أنه لابد من بداية في الزمان على أساس أن نسبية آينشتين العامة جزئية واحدة من النظرة الكونية. <br />وكان مبدأ الريبة الذي قال به هايزنبرج وكم بلانك يمهدان الطريق لميكانيكا الكم، وبالرغم من أن آينشتين مُنح نوبل لمساهمته في نظرية الكم، لكنه كان معارضًا بشدة لها لوقوعها في فخ العشوائية، فلم يتقبل أن يكون الكون محكومًا بالصدفة، ومقولته: "إن الله لا يلعب النرد" توضح أفكاره. <br />لكن هذا لا يمنع أن معظم العلماء تقبلوا ميكانيكا الكم، يقول هوكينج: <br />"ليس لدينا بعد نظرية متماسكة كاملة توحِّد النسبية العامة وميكانيكا الكم، ولكننا نعرف بالفعل عددًا من الملامح التي ينبغي أن تكون فيها"<br />ويفصِّل الكاتب الحديث عن ميكانيكا الكم، فيتناول الجسيمات الأولية وقوى الطبيعة الأربعة.<br />ثم ينتقل للحديث عن الثقوب السوداء وهي جد شيقة، وفي هذا الجزء يستفيض هوكينج في الشرح والتحليل في كل ما يختص بالثقوب السوداء، وربما هذا لأنه كان مهتمًا بشكل كبير بها واكتشف بعض الأشياء حولها.<br />في أحد الفصول بعنوان: أصل ومصير الكون، وهو فصل مميز للغاية، وإن رأيته منفصل عن الكتاب بإعادته جزء بسيط باختصار مما قاله قبل هذا مع توضيح وتناول بعض الأشياء الجانبية، وفي هذا الفصل مناقشة بشكل أكبر للخالق، وإن توصل في النهاية إلى عدم نفي أو إثبات أي شيء، فكما هو الأمر في الفلسفة الإمر قائم على احتمالات لا يمكننا معرفة أيهما أصح، وعلى هذا أيضًا سينتهي الكتاب. <br />ثم بعد هذا يتناول البعد الزماني والمسار الذي يسير فيه الزمان فيما سيسمى بسهم الزمان المطلق للأمام، ومع حديثه عن الثقوب الدودية يضع احتمالات للسفر عبر الزمن وإن لم يستطع أحد البرهنة على هذا لكنه احتمال كبير، لكن الإشكالية تقع في كيفية السفر، وهل يمكن السفر للماضي أم للمستقبل فقط؟ ويدور هذا الجزء حول هذه النقطة بتحليله الأبعاد المكانية الثلاثة والبعد الزماني الواحد وما يمكن أن يكون من أبعاد أخرى. <br />ويأتي الفصل الأخير من الكتاب عن توحيد الفزياء، وهل يمكن أن نكتشف ما يجعل العلم متمكن من معرفة الأشياء بدقة وثقة متناهية؟ وقال بأن الفلسفة لم تعد تثمر في هذا المجال، بل اضمحلت واضمحل دور العقل في التقدم وفي مجاراة تطور العلم.<br />يقول هوكينج في الختام: <br />"وعلى كلٍّ، لو اكتشفنا فعلًا نظرية كاملة، فإنه ينبغي بمرور الوقت أن تكون قابلة لأن يفهمها كل فرد بالمعنى الواسع، وليس فقط مجرد علماء معدودين. وعندها فإننا كلنا، فلاسفة وعلماء وأناسًا عاديين، سنتمكن من المساهمة في مناقشة السؤال عن السبب في وجودنا، نحن والكون. لو وجدنا الإجابة عن ذلك، فسيكون في ذلك الانتصار النهائي للعقل البشري، لأننا وقتها سنعرف فكر الخالق."</p><p>كتاب عظيم ومبسط بشكل جميل، رحلة ممتعة وشيقة في محاولة لمعرفة الكون وحجمنا فيه، ومحاولة للتوصل للخالق، وإن باءت الأخيرة بالفشل، فقد خرجت أشد حيرة وانقسامًا أكثر مما دخلت، ويظل العلم والفلسفة والدين غير قادرين على إثبات أو نفي شيء عقليًا، كل شيء يخضع للاحتمال في كل الأحوال. </p></b></p></div><section><ul><a href="https://www.goodreads.com/review/list/35008106?shelf=2017">2017</a> <a href="https://www.goodreads.com/review/list/35008106?shelf=%D8%B9%D9%84%D9%88%D9%85">علوم</a> <a href="https://www.goodreads.com/review/list/35008106?shelf=%D9%83%D8%AA%D8%A8-%D9%85%D8%AA%D9%86%D9%88%D8%B9%D8%A9">كتب-متنوعة</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/112699911-orhan-pelinkovic"></a></section><section><p>85 reviews149 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3265738995">June 26, 2020</a></section><div><p>Theoretical Physics from the master himself. It's a great summary, but you need a little background knowledge to understand all the chapters. It's a summary of astrophysics, theoretical physics, and cosmology, and it's hard grasping it all in 200 some pages. I wish it was a little longer.<p>The definitions at the end of the book are very useful. You will not regret reading the book, but you need some peace and quiet while reading it in order to hopefully understand it.</p><p>I've read the A Bantam Book Edition published April 1988 / A Brief History of Time by Stephan W. Hawking / 226 pages / 56,997 words.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/112699911?shelf=astronomy">astronomy</a> <a href="https://www.goodreads.com/review/list/112699911?shelf=cosmology">cosmology</a> <a href="https://www.goodreads.com/review/list/112699911?shelf=history">history</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/50678504-elena"></a></section><section><p>124 reviews986 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2359888979">June 1, 2018</a></section><div><p>A pesar de estar escrito para un público "no científico" no puedo decir que creo que sea un libro accesible al 100%. Es cierto que Hawking cumple su promesa de no incluir ni una fórmula matemática (excepto la conocida fórmula sobre la teoría de la relativdad E=MC²) pero los conceptos en sí pueden ser difíciles de imaginar y comprender. De toda la información que Hawking intenta explicar en este libro, ha habido cosas que notaba que se me escapaban. Quizá con algo más de material gráfico habría resultado más sencillo.<br />Aún así, el concepto general de los temas que trata es impresionante si te apasiona conocer la esencia del universo. Realmente había momentos en los que dejaba de leer para procesar algunos conceptos y no podía menos de maravillarme.</p></div><section><ul><a href="https://www.goodreads.com/review/list/50678504?shelf=2018">2018</a> <a href="https://www.goodreads.com/review/list/50678504?shelf=non-fiction">non-fiction</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6823144-mohammed"></a></section><section><p>420 reviews511 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2531002510">October 22, 2019</a></section><div><p>كتاب سلس ويطرح المادة العلمية بطريقة شيقة.<p>لحظة!</p><p></p><p>إذا كتبت مراجعة من هذا النوع سأبدو ذكيا ورائعا. لكنها ليست الحقيقة، فلست ذكيا ولا رائعا، وإنما قارئ متوسط الاستيعاب، أشعر بحكة في دماغي عندما تتعقد الأمور وتطقطق جمجمتي من الداخل إذ يحاول مخي الصغير أن يتمدد ليستوعب بعض المعلومات، ولكنه لا ينجح دائما.</p><p>ليس هذا دأبي مع كل الكتب التي تناقش موضوعات علمية، فقد مضيت في كتاب الكون لكارل ساجان من الغلاف إلى الغلاف دون أي عسر. أعرف أن ساجان طرح المواضيع ذاتها ولكن من زاوية فلكية، بعكس هوكينغ الذي لا يحيد عن الفيزياء قيد أُنملة. هناك حديث مطول عن الذرات والجزيئات والفوتونات ومواضيع أخرى لم أكن أبحث عنها بصراحة.</p><p>ماسبق لا يعني أن الكتاب لم يضف إلى معلوماتي بل على العكس إذن ناقش الكتاب أهم نظريتين لشرح كل ما يجري في الكون: النظرية النسبية وميكانيكا الكم. تحدث هوكينغ أيضا عن الثقوب السوداء والثقوب الدودية والانفجار العظيم (ليس انفجارا بالمعنى الحرفي على فكرة) والتأثير المعكروني الموضح بالصورة أعلاه. هناك أطروحات حول بداية الكون ونهايته وإيراد لأهم النظريات التي اُكتشفت في ذلك الميدان. هذا إلى جانب الجانب التأملي في تاريخ العلم وتطور الفكر لدى الإنسان والتحدي الكبير المتمثل في مواجهة التيار التقليدي الذي يتصدى لأغلب الأفكار الجديدة.</p><p>كتاب يستحق القراءة، مع الكثير من الصبر لأصحاب الميول الأدبية الذين اعتادوا على النوم أو العبث في آذانهم في حصص الفيزياء. الكتاب يستحق العناء لكنني توقعت شيئا أشد تبسيطا وأكثر إمتاعا.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/223837-nicky"></a></section><section><p>4,138 reviews1,004 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/675506938">July 24, 2013</a></section><div><p>Stephen Hawking's book is easy to read, but harder to comprehend. In every chapter came a point where my brain couldn't hold another permutation of a theory, and as the book progressed, I ended up taking the same approach as I do when reading a Norse saga for the first time. With sagas, I just read, even if my brain doesn't seem to retain all the information about who is related to who and what they named their horse. Inevitably, at the end, I have a reasonable basic grasp of the saga, and then I have to read it over again to fit more information into that basic understanding.<p>I don't know if the same will hold true here, but it's a nice hope.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/223837?shelf=non-fiction">non-fiction</a> <a href="https://www.goodreads.com/review/list/223837?shelf=science-fact">science-fact</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/48483884-michael-finocchiaro"></a></section><section><p>Author <i></i>3 books5,433 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1771811876">February 10, 2017</a></section><div><p>A classic text where the amazing Stephen Hawking explains string theory and quantum mechanics "for dummies." Highly readable and even comical, it is a superb read. I need to go back and read this one again myself!</p></div><section><ul><a href="https://www.goodreads.com/review/list/48483884?shelf=american-20th-c">american-20th-c</a> <a href="https://www.goodreads.com/review/list/48483884?shelf=geek-classics">geek-classics</a> <a href="https://www.goodreads.com/review/list/48483884?shelf=non-fiction">non-fiction</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/68429005-p-e"></a></section><section><p>718 reviews500 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3125343794">April 5, 2021</a></section><div><p><b>Space opera</b><p><br /><i>
 <b>The Milky Way arch emerging from the Cerro Paranal, Chile, 3 December 2009. Author: Bruno Gilli/ESO</b>
</i></p><p>A highly articulate summary of the history of astrophysics and its breakthroughs from its origins to 1996 (updated edition). I wish I had had such an introduction to physics and chemistry when I was in secondary school and high school! The layout of the book allows a layman to follow the development of the discipline and its fields over time, while Stephen Hawking never scorns an evocative image to give a better notion to the reader of what, say, the electromagnetic spectrum, thermodynamics or gravity are all about. I definitely recommand to all of you in awe before the universe and its strange marvels :)</p><p><br /><b>
 <i>Detail of Eagle Nebula</i>
</b></p><p><b>Summary:</b></p><p>Chapter 1: Our Picture of the Universe<br />Chapter 2: Space and Time<br />Chapter 3: The Expanding Universe<br />Chapter 4: The Uncertainty Principle<br />Chapter 5: Elementary Particles and Forces of Nature<br />Chapter 6: Black Holes<br />Chapter 7: Hawking Radiation<br />Chapter 8: The Origin and Fate of the Universe<br />Chapter 9: The Arrow of Time<br />Chapter 10: Wormholes and Time Travel<br />Chapter 11: The Unification of Physics<br />Chapter 12: Conclusion</p><p>-----</p><p><br /><b>
 <i>Black Hole elements</i>
</b></p><p><br /><b>
 <i>Image of the night sky above Paranal, Chile on 21 July 2007, taken by ESO astronomer Yuri Beletsky</i>
</b></p><p><br /><b>
 <i>Galaxies in the Hubble deep field (detail)</i>
</b></p><p>Soundtrack:<br /><a href="https://www.youtube.com/watch?v=-iVYu5lyX5M">Lux Aeterna - György Ligeti</a></p></p></div><section><ul><a href="https://www.goodreads.com/review/list/68429005?shelf=astrophysics">astrophysics</a> <a href="https://www.goodreads.com/review/list/68429005?shelf=audiobook">audiobook</a> <a href="https://www.goodreads.com/review/list/68429005?shelf=guidebook">guidebook</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/56189373-shine-sebastian"></a></section><section><p>112 reviews91 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1724115159">December 22, 2016</a></section><div><p>Without a doubt a masterpiece!<br />It's just incredible how Hawking explains to us the complex and mindboggling secrets and concepts of physics and our universe, with amazing wit , clarity, and simplicity.<br />The questions that we all used to ask to ourselves and to our parents, about god, about time, life and it's meaning, the sky, stars, about who created our universe and about it's beginning, about our fate......<br />we had that unique quality called curiosity when we were children, but then, as we grew up , we somehow lost that ability to ask and question, we no longer felt the same thirst for knowledge and a deeper understanding of things as we reached adulthood, those questions we abandoned as our busy lives got in our way..<br /> But there are quite a few people, whose curiosity and desire to find out more, to explore the truths of this vast universe, never dies. They are always always on the lookout for answers to questions deemed unanswerable , and then to ask new questions , that one by one, fills the gap between us and the truth and makes our understanding of this universe and it's secrets a bit more clearer and deeper, <br /> Stephen Hawking is one such blessed genius! <br />In this book, Hawking familiarise us with the possible beginning of the universe or space-time , which is called the Big Bang Singularity, the Black Holes with extremely strong gravitational force so that even light can't escape from it, the reasons why we are at this time and space of the universe [ this might be because that the present condition, universe ( if there are other universes), and dimensions are the only configuration which allows the existence of intelligent beings like us who can observe and ask these questions], the long quest for a Grand Unification Theory ( that will explain the whole universe completely ) which still continues, and so many more fascinating and incredible stuff.<br /> The writing style is highly enjoyable, Hawking is a great teacher and a wonderful writer, his wit and engaging writing makes me forget that I'm reading a scientific book!<br /> Highly recommended to everyone who wants to know a little more about this universe and it's secrets. <br />5 stars.</p></div><section><ul><a href="https://www.goodreads.com/review/list/56189373?shelf=2016">2016</a> <a href="https://www.goodreads.com/review/list/56189373?shelf=books-i-own">books-i-own</a> <a href="https://www.goodreads.com/review/list/56189373?shelf=science">science</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/11586431-nasia"></a></section><section><p>348 reviews79 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2551288201">November 16, 2018</a></section><div><p>Ένα πολύ ωραίο βιβλίο εκλαϊκευμένης επιστήμης που εξηγεί βασικές έννοιες της Φυσικής και πώς αυτές διαμορφώθηκαν ανα τους αιώνες - με κύρια κατεύθυνση στην μοντέρνα Φυσική που για πολλούς είναι ακατανόητη. Μου άρεσε πολύ ο τρόπος γραφής και το χιούμορ του Χώκινγκ αλλά θεωρώ πως κάποιος πρέπει να έχει κάποιες σχετικά γερές βάσεις Φυσικής για να το κατανοήσει. Θέλω πολύ να ξαναδιαβάσω τα κεφάλαια για την θεωρία των χορδών και τις μαύρες τρύπες γιατί νομίζω πως πολλά πράγματα τα έχασα. :( </p></div><section><ul><a href="https://www.goodreads.com/review/list/11586431?shelf=brace2018">brace2018</a> <a href="https://www.goodreads.com/review/list/11586431?shelf=readathon18">readathon18</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/43584061-alet"></a></section><section><p>275 reviews242 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3313424655">July 30, 2020</a></section><div><p>★★★ /5<p>This was an interesting and informative book, but sadly I just couldn‘t grasp everything that it tried to say.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/43584061?shelf=read-in-2020">read-in-2020</a></ul></section></section></article></div></div><p>Displaying 1 - 30 of 11,529 reviews</p></div>||||I|||| * Home
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 A Brief History of Time

 Stephen Hawking

 4.21
 399,244 ratings 11,524 reviews
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 A landmark volume in science writing by one of the great minds of our time, Stephen Hawking’s book explores such profound questions as: How did the universe begin—and what made its start possible? Does time always flow forward? Is the universe unending—or are there boundaries? Are there other dimensions in space? What will happen when it all ends?

 Told in language we all can understand, A Brief History of Time plunges into the exotic realms of black holes and quarks, of antimatter and “arrows of time,” of the big bang and a bigger God—where the possibilities are wondrous and unexpected. With exciting images and profound imagination, Stephen Hawking brings us closer to the ultimate secrets at the very heart of creation.
 Genres Science Nonfiction Physics History Classics Astronomy Philosophy
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 213 pages, Paperback

 First published September 1, 1988

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 Stephen Hawking

 130 books 11.6k followers
 Stephen William Hawking was born on 8 January 1942 in Oxford, England. His parents' house was in north London, but during the second world war Oxford was considered a safer place to have babies. When he was eight, his family moved to St Albans, a town about 20 miles north of London. At eleven Stephen went to St Albans School, and then on to University College, Oxford, his father's old college. Stephen wanted to do Mathematics, although his father would have preferred medicine. Mathematics was not available at University College, so he did Physics instead. After three years and not very much work he was awarded a first class honours degree in Natural Science.

 Stephen then went on to Cambridge to do research in Cosmology, there being no-one working in that area in Oxford at the time. His supervisor was Denis Sciama, although he had hoped to get Fred Hoyle who was working in Cambridge. After gaining his Ph.D. he became first a Research Fellow, and later on a Professorial Fellow at Gonville and Caius College. After leaving the Institute of Astronomy in 1973 Stephen came to the Department of Applied Mathematics and Theoretical Physics, and since 1979 has held the post of Lucasian Professor of Mathematics. The chair was founded in 1663 with money left in the will of the Reverend Henry Lucas, who had been the Member of Parliament for the University. It was first held by Isaac Barrow, and then in 1669 by Isaac Newton.

 Stephen Hawking worked on the basic laws which govern the universe. With Roger Penrose he showed that Einstein's General Theory of Relativity implied space and time would have a beginning in the Big Bang and an end in black holes. These results indicated it was necessary to unify General Relativity with Quantum Theory, the other great Scientific development of the first half of the 20th Century. One consequence of such a unification that he discovered was that black holes should not be completely black, but should emit radiation and eventually evaporate and disappear. Another conjecture is that the universe has no edge or boundary in imaginary time. This would imply that the way the universe began was completely determined by the laws of science.

 His many publications include The Large Scale Structure of Spacetime with G.F.R. Ellis, General Relativity: An Einstein Centenary Survey, with W. Israel, and 300 Years of Gravity, with W. Israel. Stephen Hawking has three popular books published; his best seller A Brief History of Time, Black Holes and Baby Universes and Other Essays and most recently in 2001, The Universe in a Nutshell.

 Professor Hawking received twelve honorary degrees, was awarded the CBE in 1982, and was made a Companion of Honour in 1989. He was the recipient of many awards, medals and prizes and is a Fellow of The Royal Society and a Member of the US National Academy of Sciences.

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 4.21
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 Bill
 Author 6 books 133 followers
 August 30, 2022
 This book puts me in mind of the story about how a Harvard number theorist, through some malfunction of the scheduling computer, got assigned to teach an introductory course in pre-calculus. Being one of those individuals to whom math came so easily that they couldn't grasp how difficult others found it, the professor had no idea what to cover in such a course.

 So, he went to the chair of the department, who told him: "You'll want to start with the real number-line and then progress to inequalities; from there, move on to quadratic equations, then trigonometry and the wrapping function, Cartesian and polar coordinate systems, and, if time permits, conic sections."

 The professor thanked the chairperson and went off to meet with his first class. Next week, he was back.

 "What should I teach them now?" he said.

 A Brief History of Time is like that -- Professor Hawking doesn't seem to notice when his treatment progresses from the obvious to the arcane, ending with his concept of "imaginary time" (very nearly incomprehensible in this overly brief presentation).

 Fun nonetheless.

 * * *
 August 30, 2022 addendum --

 Time to jump in here, I fear:

 Having garnered over 650 "Likes," this far-from-serious scribble is by far my most popular review ever — and, truth be told, undeservedly so.

 For a more thoughtful consideration of a somewhat related book, try my take on Jim Holt's Why Does the World Exist? here: https://www.goodreads.com/book/show/8...
 cosmology physics
 683 likes
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 Daniel
 149 reviews 8 followers
 September 25, 2007
 It is not clear to me who is in the target audience for this book. At times it tries to explain basic concepts of modern physics in simple language, and at other times it assumes a familiarity with the same subject. For the first time I think I "understand" why absolute time is not consistent with relativity theory or that space-time curvature supplants the notion of gravity, and for that I thank the author. There are a few other things I believe I have a glimpse of having (finally) slogged through the book.
 On the other hand, there are many places where he writes as if it were clear what he is talking about even though it would require a good deal of background knowledge. To give but one example, he starts talking about summing up over possible world histories (I cannot locate the quotation) without explaining what that would mean. Trained in statistics, I have some idea that he is talking about mathematical expectation in the context of quantum mechanics, but I don't know how another reader might make any sense of it (and I certainly don't have more than a vague notion).
 There are irritating writing practices that could have used some editing, e.g., the use of the naked pronominal adjective "this" when in the middle of a dense explanation of an abstruse concept(e.g., "This had serious implications for the ultimate fate of massive stars.").
 My biggest complaints, however, are about his philosophical opinions. Obviously he is entitled to think as he wishes about the ultimate questions, but his assertion that his hypothesis of a finite world without beginning or end would leave no place for God seems beside the point. The classic divide has not changed: some folks look around and say stuff just is, and other folks say there's a power behind the stuff that has at least as much going for it as we do. That argument hasn't changed with his theories. At one point in the book he claims that the late John Paul II told gathered scientists that they mustn't inquire into the Big Bang because that was God's territory. I would wager with anyone reading this comment that such an assertion is just plain false. JPII was a flawed mortal, to be sure, but he was no dope; it certainly sounds to me like someone hearing what he thinks the pope would say. (And the Galileo jokes are pretty dumb -- does anyone think that JPII, who apologized for the embarrassing Galileo fiasco, would go after this guy? It must be all that influence the Vatican has had in Britain over the last 400 years that has him scared.)
 Other philosophical complaints involve his use of entropy (he defines it first within closed systems and then uses it to explain why the "thermodynamic arrow of time" and the "personal arrow of time" must run in the same direction -- leaping from a box of molecules to the entire universe!), his droning on about what black holes are like when he doesn't know for sure they exist, his statements about "random" and being 95% certain a theory is true (does that mean about 95 out of 100 theories like that are true??). His opinions may be very rich, deep, though-provoking, but how would I (or most general readers) know? You can't really evaluate a judgment unless you know something in the field.
 And so that is why I ultimately cannot recommend this book: if you know physics inside and out, you might find his opinions interesting. If you don't, you can only walk around parroting what he says about black holes as if you had a clue what you were talking about. What we all really need is a remedial course in physics!
 general-nonfiction
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 هدى يحيى
 Author 8 books 15.9k followers
 April 18, 2019

 ‎‏‏
 =وداعا هوكنج=
 صرت حرا الآن
 ---------
 هناك لذّةٌ ما ،، في أن تفتحَ كتاباً تشعُّ من سطوره ألوان الفضاء
 شيءٌ ما في فعلِ المعرفةِ ،، والتأمل فيها
 شيءٌ يأخذ عقلك إلى أمكنةٍ أخرى
 ...
 لا بين المجرات
 ولا في خضّم الكونِ الواسع
 بل هنا بداخلك
 عند هذا النبض الأخّاذ في قلبك
 حيث تبدأ المتعة في التحرر
 لتغمر مسامّك برائحة الدهشة
 فالكون في داخلك أنت يا صاحبي


 تاريخٌ موجز للزمن ،، يُعتبر من أهم الكتب العلمية الحديثة
 يأخذك ستيفن هوكنج في رحلةٍ عبر تاريخ العلم
 ويشرح لك كيف تغيّرت نظرتنا للكون ،، ولمجرتنا ،، ‏ولكرتنا الأرضية ،، ولأنفسنا كذلك عبر العصور


 هذه هي قراءتي الثانية لستيفن هوكنج ،وقد أعجبتُ أيّما إعجاب بقراءتي الأولي "التصميم العظيم" ‏،وإن قارنت هذا بذاك ،فأرجّحُ كفّة الأخير

 لا أعلم إن كانت للترجمة دورٌ في ذلك ،فلقد قرأت التصميم العظيم بلغته الأصلية

 لقد توقّعت أكثر مما وجدتُّ في هذا الكتاب ،فقد حسبته أكثر متعة وجمالاً في سرده أو في ترابط فصوله
 ولكن لن تجد هُنا سوى متعةَ المادة العلمية ذاتها ، فـ اسلوب هوكنج جافٌ قليلاً‏

 كما وضع كارل ساجان مقدمة جميلة للكتاب
 ليثير شهيتي أكثر

 ============================================
 فلنتعرف على مؤلف سطور المعرفة الشهية إذا
 ============================================


 يقول ستيفن
 _______________________________________________
 ‏لقد كنتُ مصدر يأس لوالدي في صباي، إذ كنتُ ‏دائماً أقوم بفك الأجهزة لأرى ما الذي ‏يجعلها ‏تصدر أصواتاً، وبالطّبع لم يكن بإمكاني - عادة - ‏جمع أجزائها مرة أخرى، إلاّ أنّني ‏شعرت بإمكان السيطرة على أيّ شيء - بطريقة أو بأخرى - إذا ‏فهمت كيفيّة عمله، وأنا موقن ‏من وجود الشعور ‏نفسه لدى الآخرين
 فنحن نجد أنفسنا في عالم لا ‏يلحظ وجودنا في الغالب ولا ‏يهتم به، بل - أحياناً - ‏يعادي هذا الوجود صراحةً

 لذا، لو أمكننا فك ‏‏"اللوحة الأماميّة" للكون والنّظر خلفها فربّما نصبح ‏قادرين على فهم كيف تعمل ‏تلك العجلات ‏الصغيرة، أعني المجرات، ولشعرنا ببعض التحكّم ‏فيما يجري من أحداث، ولحسن ‏الحظ فنحن غير ‏مدعوين لإعادة تجميع الكون مرة أخرى بعد فك ‏لوحته الأماميّة‎
 _______________________________________________

 هل تعلم أن هذا العالم العبقري قدأُصيب بمرض التصلب الجانبي الضموري؟
 هذا المرض يصيب الجهاز العصبي الحركي ،ويُفقد المصاب به قدرته على التحكم في عضلاته
 وهل تعلم أن الأطباء قد أخبروه بأنه لن يعيش لأكثر من عامين؟
 ولكن يبدو أن إصرار الرجل وعزيمته جعلتاه يعيش كل هذا العمر
 لبملأ الأرض بإبداعاته

 كان ستيفن وقتها يحضّر رسالته في الفيزياء النظرية بجامعة كامبريدج
 ولم يمنعه مرضه من إكمالها ليشغل منصب أستاذ الرياضيات الذي كان يشغله نيوتن في نفس الجامعة

 حتى عام1974 كان هوكنج يستطيع العناية بنفسه بعض الشيء
 إلا أن تفاقم المرض جعله حبيساً لكرسي متحرك ،بالإضافة إلى ذلك فقد عانى من عملية استئصال للحنجرة ليفقد صوته تماما

 ولحسن حظه ،فقد أهداه والت وولتوز ،خبير الكمبيوتر، برنامجا عبقريا يتيح له أن يختار كلمات من سلسلة قوائم على الحاسوب، بمجرد كبسة على مفتاح في يده، بل ويستطيع أن يتحكّم به بعينيه، وحركة رأسه كذلك وعندما ينتهي من بناء جملته يرسلها إلى ناطق الكلمات
 وقد ثبتّ الجهاز على كرسيه المتحرك ليستطيع ستيفن التحدث مع الحركة بحرية أكبر
 [image error]

 احتل هوكنج كرسي الرياضيات في كامبريدج ،وهو أعلى منصب يحتله أستاذ في اختصاصه
 حيث شغله علماء أمثال نيوتن وتشارلز بابيج وبول ديراك

 لهوكنج أبحاث نظرية في علم الكون وفي العلاقة بين الثقوب السوداء والديناميكا الحرارية
 ودراسات في التسلسل الزمني

 كما وضع نظريات عديدة عن ‏بداية الكون منذ الانفجار الكبير
 وأيضاً عن الثقوب السوداء
 والتي أطلق على إشعاعها إشعاع هوكنج

 http://www.youtube.com/watch?v=4OmSoZ...
 جزء من مقابلة له مع لاري كينج
 ============================================================
 عن الكتاب
 =======================
 هذا الكتاب وبصورة مبسّطة نوعاً ، يعرض بعض نظريات العلماءالتي تحدثت عن الكون والزمن كنظريات ‏أرسطو وآينشتين وجاليليو ونيوتن أيضاً‏

 يدور الكتاب في أساسه حول الكون
 عن تمدده ،وإنكماشه وحدوده ،وعن أبعاد ‏الزمان

 هذا الرجل جعل عقلي يروح يميناً ويساراً
 دوخني معه بكمِّ معلوماته الهائل ،، وأفكاره المستنيرة

 في البداية يحدثك ستيفن عن التصور ‏القديم للكون بإختصار ويمثل لك بتصور ‏أرسطو الأشهر مروراً ببطليموس وغيرهم

 تصور أرسطو كان كالتالي
 ‏============================‏‏===========‏
 المادة تتكون من 4 عناصر أولية‏
 الماء،النار،الهواء،الأرض
 تؤثر في هذه العناصر قوتان
 الجاذبية ،،أي نزعة الأرض والماء إلى الهبوط
 والخفّة ،،أي نزعة الهواء والنار إلى الصعود
 ‏============================‏‏===========‏



 وإكتشاف أن الكون يتمدد كما يرى ‏هوكنج ،هو ‏إحدى الثورات الثقافية ‏العظيمة في القرن العشرين

 فيقول
 _______________________________________________
 ‎وبالتأمل وراء، فإن من السهل التعجب لآن ‏أحدا لم يفكر في ذلك من قبل ، فقد كان ينبغي على ‏‏نيوتن وغيره أن يتبينوا أن كونا ستاتيكيا لن يلبث أن ‏يبدأ سريعا في الانكماش بتأثير الجاذبية
 ‏ولكن ‏لنفرض بدلا من ذلك أن الكون يتمدد . فلو كان يتمدد ‏بسرعة بطيئة إلى حد ما ، فإن قوة ‏الجاذبية ستجعله ‏في النهاية يتوقف عن التمدد ليبدأ بعدها في ‏الانكماش . أما إذا كان يتمدد بسرعة ‏أكبر من معدل ‏حرج عين ، فإن الجاذبية لن تكون قط قوية بما يكفي ‏لوقف تمدده ، وسوف يستمر ‏الكون في التمدد للأبد

 ‏وهذا يشبه ، نوعا ، ما يحدث عندما يطلق أحدهم من ‏فوق سطح الأرض ‏صاروخا لأعلى . فإذا كانت ‏سرعته بطيئة إلى حد ما ، فإن الجاذبية ستوقف ‏الصاروخ في النهاية ���وسيبدأ في السقوط عائدا
 ومن ‏الجهة الأخرى ، إذا كانت سرعة الصاروخ أكبر من ‏سرعة ‏حرجة معينة ( حوالي سبعة أميال في الثانية ‏‏) فإن الجاذبية لا تكون قوية بما يكفي لشدة إلى ‏‏الوراء ، وهكذا فإنه سيستمر في الانطلاق بعيدا عن ‏الأرض إلى الأبد . وسلوك الكون هكذا كان ‏يمكن ‏التنبؤ به من نظرية نيوتن عن الجاذبية في أي وقت ‏من القرن التاسع عشر ، أو الثامن ‏عشر أو حتى ‏أواخر القرن السابع عشر‎‏ ‏
 ‎‏ ‏
 إلا أن الإيمان بثبات الكون كان من القوة بحيث ظل ‏باقيا لأوائل القرن العشرين
 _______________________________________________

 وعن الإرتباط بين المكان والزمان، يحدثك ‏ستيفن ‏عن أهمية نظريات نيوتن والتي ‏توجها بوضعه ‏لقانون الجاذبية الكونية
 ‏ووقتها بدأ التعارض بين الفكر القديم الذي يرجح ‏‏ثبات النجوم وبين ما جاء به نيوتن ومن خلال ‏تفكيره ‏للخروج من هذا التساؤل أوضح إن تجاذب ‏النجوم ‏يحدث إذا كان عددها صغير ‏
 أما إن كانت عددها غير محدود ومتناسقة التوزيع ‏‏بطريقة أو بأخرى في الفضاء الشاسع ، فلن تكون ‏‏هناك نقطة مركزية لتتجمع عليها ‏

 وبالمناسبة فقد اعتبر أينشتين الكون ثابتاًً حين ‏وضع ‏النظرية النسبية العامة
 وقد اعتبرها أكبر غلطة قام بها في حياته، عدّل ‏فيها ‏فيما بعد

 فيقول

 _______________________________________________
 ‎‏ ‏
 نظرية أينشتاين عن النسبية العامة ، هي في ‏ذاتها تتنبأ بأن الزمكان يبدأ عند مفردة الانفجار ‏‏الكبير وسوف يصل إلى نهايته عند مفردة الانسحاق ‏الكبير ( إذا تقلص الكون كله ثانية ) أو عند ‏مفردة ‏من داخل ثقب أسود ( لو تقلصت منطقة محددة ، ‏مثل أحد النجوم )
 وأي مادة ستهوي إلى ‏داخل ‏الثقب ستتدمر عند المفردة ، ولن يظل محسوسا في ‏الخارج إلا تأثير جاذبية كتلتها
 ومن ‏الناحية ‏الأخرى ، عندما يؤخذ في الحسبان تأثيرات الكم ، ‏فإنه يبدو أن كتلة أو طاقة المادة ستُعاد ‏في النهاية ‏إلى باقي الكون ، وأن الثقب الأسود هو وأي مفردة ‏من داخله ، سوف يتبخر بعيدا ‏ليختفي في النهاية
 هل يكون لميكانيك الكم تأثير درامي مساوٍ لذلك ‏على مفردتي الانفجار الكبير ‏والانسحاق الكبير ؟ ما ‏الذي يحدث حقاً أثناء الأطوال المبكرة جداً أو ‏المتأخرة جداً من الكون ‏عندما تكون مجالات ‏الجاذبية من القوة بحيث لا يمكن تجاهل تأثيرات ‏الكم ؟ هل للكون حقيقة ‏بداية أو نهاية ؟ وإذا كان ‏الأمر كذلك ، فكيف تبدوان ؟‎
 _______________________________________________

 و يقوم ستيفن بعدها بتوسيع مداركك عن ‏الكون ،، ‏كيف نشأ ،، ما معنى التمدد و ‏كيف بدأ الإنسان ‏يستكشف مجموعته ‏الشمسية وأرضه والكون من ‏حوله
 ليذهب بنا إلى نظرية الإنفجار الكبير

 لقد استمر الجدال حول نشأة الكون وتاريخه في ‏‏الزمان ‏
 هل له بداية في الزمان؟ أو كان محدودا في الفضاء ‏؟

 في عام 1929 ،قام هابل بإثبات أن المجرات ‏والنجوم ‏تتباعد بسرعة كبيرة وان الكون ككل آخذ ‏في التمدد ‏والإتساع ‏

 وقد أدّى ذلك إلى ظهور منابت نظرية الانفجار ‏الكبير ،وبدأت فكرة تتخيل كيف كان الكون متناهياً ‏في الصغر ‏وكثافته لا متناهية‏
 وترجّح أن الزمن بدأ مع الانفجار الكبير

 يعتقد أصحاب النظرية أن الكون كان عبارة عن كتلة صغيرة ذات كثافة وحرارة لا يمكن تصورها
 ثم انفجرت هذه الكتلة انفجاراً هائلاً منذ قرابة 13 مليار سنة لينتج عن انفجارها سحابة هائلة من الغاز والغبار الكوني

 ويؤكد لك الكاتب أن الزمان قبل الانفجار الكبير لا ‏‏يمكن تحديده
 بمعنى آخر لم يكن هناك ما يسمى ‏بالزمان أصلاً


 a computer-generated explosion representing the Big Bang

 فيقول
 _______________________________________________
 ‏مع ذلك، كان الاكتشاف المتميّز، الذي تم في ‏نهاية ‏القرن العشرين، هو تيقننا بالفعل من وجود ‏حدث ‏أول: الانفجار العظيم، الذي قد يشبه البيضة ‏أكثر ‏ممّا يشبه الدجاجة، ومع ذلك ليس كأيٍ منهما
 فقد ظهر كل من الكون والزمان للوجود أول مرة ‏‏عندم الانفجار العظيم، وذلك هو السبب الأول، فإذا ‏‏استطعنا فهم الانفجار العظيم فسنعرف سبب ظهور ‏‏الكون على صورته تلك
 _______________________________________________

 وينتقل بعدها إلى عناصر تكوين المادة
 كيف توصلنا إلى إكتشاف الذرة ،، وكيف ‏كنا نتخيل ‏أجزاء المادة وقابليتها للإنشطار ‏من قبل ،، ويحيلك ‏إلى الجاذبية بصفتها ‏من القوى المؤثرة على عناصر ‏كوننا ‏الأساسية

 حتى يومنا هذا ،يعتبر الكوارك هو أصغر ‏‏الجسيمات
 والكوارك هو جسيم أولي مشحون يحس بالقوى الكبرى
 البروتونات والنيترونات يتكون كل منهما من 3 كواركات
 ================================
 يصل بك الكاتب أخيراً إلى الثقوب السوداء ‏‏_أمتع ‏فصول الكتاب
 ليحدثك عن مفهومها

 والثقب الأسود هو منطقة في المكان -الزمان
 لا يستطيع أي شيء الهروب منها ولا حتى الضوء
 لقوة جاذبيتها الشديدة

 ويذهب بك بعد ذلك إلى أن الثقوب ‏السوداء ليست ‏جد سوداء
 كما أن الثقوب كلما كانت أصغر كلما كانت ‏أشد ‏توهجاً ،وبالتالي تكون قدرتنا على ‏رصدها أفضل

 ================================

 من أمتع ما قرأت عنه هنا أيضاً هو الجسيم ومضاده
 فكل نوع من جسيمات المادة له مضاد جسيم مناظر له
 وعندما يصطدم الجسيم بمضاده فإنهما يفنيان
 ولا يتخلف عن ذلك إلا الطاقة
 ويدلل بأمثلة ممتعة كذلك
 ^_^

 الفكرة التي وجدتها مثيرة هي عدم تساوي عدد الكاوركات مع مضاداتها و هذا من حسن حظنا فلو كانت متماثلة لكان أفنى أحدهما الآخر في الكون المبكر لتترك كوناً مليئاً بالإشعاع لا يكاد يحتوي أي مادة

 تخيّل معي
 لا مجرات ولا نجوم ولا كواكب
 ولا نحن ‎

 عندما تشرد قليلاً في ذلك
 احم
 :P
 ================================

 الكون بلا بداية وبلا نهاية‎
 ‏ ‏
 ‎يرى هوكنج أن
 ‎‏ معظم الناس وصلوا إلى ‏الإيمان بأن الكون جُعل ‏ليتطور حسب مجموعة من القوانين التي لا تُكسر ‏،ولكن هذه القوانين ‏تخبرنا بما ينبغي أن يكون الكون ‏عليه عند بدايته وعلى أنه لو كان الكون بلا بداية ‏وبلا حرف ، ‏فإنه لا تكون له بداية ولا نهاية فهو ‏ببساطة موجود‎
 ‏ ‏

 وفي فصل سهم الزمان ،، يحدثك هوكنج ‏عن مفهوم ‏الزمن ،، وارتباطه بنظرية ‏النسبية

 يرى ستيفن أن هناك فارقاًً كبيراً بين ‏إتجاهي الأمام ‏والوراء للزمان الحقيقي ‏في الحياة العادية
 ‏
 ويدلل لك بمثالأً طريفاً

 فيقول

 ‏_______________________________________________

 ‏تصوّر قدح ماء يقع من على مائدة وينكسر ‏‏على الأرض إلى قطع
 لو أخذت لذلك فيلماً سينمائياً ، فإنه ‏سيمكنك بسهولة ‏أن تعرف إذا كان الفيلم ‏يسير أماماً أو وراء ‏
 ولو سيرته وراء فسوف ترى القطع تجمع ‏نفسها معاً ‏فجاة من على الأرضية وتقفز ‏عائدةً لتكون قدحاً ‏كاملاً على المائدة

 ‎…‎
 ماذا سيحدث إن توقف الكون عن التمدد ‏وبدأ في ‏الإنكماش
 سيؤدي هذا إلى صنوف الإحتمالات التي ‏من نوع ‏يشبه الروايات العلمية بالنسبة ‏للناس الذين سيبقون ‏أحياء من طور ‏التمدد حتى طور الإنكماش
 هل سيرون الأقداح المكسورة تجمع ‏نفسها معاً من ‏على الأرضية وتب عائدة ‏فوق المائدة؟
 ‎…‎
 على أن ثمة طريقة أسرع لمعرفة ما ‏سيحدث:هي ‏القفز في ثقب أسود
 إن كان الإضطراب سيقل في طور ‏الإنكماش للكون ‏، فإن المرء قد يتوقع له ‏أيضاً أن يقل في الثقب ‏الأسود
 وهكذا لعل الفلكي الذي سيسقط في ‏الثقب الأسود ‏سيتمكن من كسب نقوده ‏في لعبة الروليت بأن يتذكر ‏أين ذهبت ‏الكرة قبل أن يضع رهانه

 ‏(على أنه لن يتاح له لسوء الحظ زمن ‏طويل للعب ‏قبل أن يتم تحويله إلى ‏إسباجيتي)‏
 :D
 _______________________________________________

 ‏================‏
 هذا الفيديو يوضَح شيئاً من وجهة نظره عن ‏نشأة الكون

 http://www.youtube.com/watch?v=Sq-‎WF...

 ================================

 ‏


 ‏ إن لم تكن قد قرأت كتاباً علمياً من قبل ،أو على الأقل تابعت بعض الدوريات و المواقع العلمية ، ‏فلا أنصحك بهذاالكتاب كبداية
 فسوف تجده مملاً قليلاً ،وستجد نفسك غارقاً في المصطلحات التي ستشتّت ‏انتباهك،وتعيقك عن الإستمتاع به
 وهذا الكتاب يحتاج للقراءة لكثيرٍ من المرّات كي تتشبع بمعلوماته ،و يحتاج لكثير من القراءات الخارجية كذلك

 الكتاب معلوماته قيمة وشيقة لواحدٍ من أهم العلماء ‏الذين أنجبتهم الأرض

 ولا يزال علم الفلك متعة عظيمة ،، ‏
 وتحليقنا بين المجرّات محفّز عظيم للخيال


 history philosophy science
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 Ahmad Sharabiani
 9,567 reviews 55.6k followers
 September 3, 2021
 A Brief History of Time: From the Big Bang to Black Holes, Stephen Hawking

 What is it that our eyes do that could possibly affect things?

 A Brief History of Time: From the Big Bang to Black Holes is a popular-science book on cosmology (the study of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for nonspecialist readers with no prior knowledge of scientific theories.

 In A Brief History of Time, Stephen Hawking attempts to explain a range of subjects in cosmology, including the Big Bang, black holes and light cones, to the non-specialist reader.

 His main goal is to give an overview of the subject, but he also attempts to explain some complex mathematics.

 In the 1996 edition of the book and subsequent editions, Hawking discusses the possibility of time travel and wormholes and explores the possibility of having a Universe without a quantum singularity at the beginning of time.

 تاریخ نخستین خوانش: روز چهارم ماه مارس سال 1996میلادی

 عنوان: تاریخچه زمان: از انفجار بزرگ تا سیاهچالها؛ نوشته: استیون هاوکینگ؛ مترجم: محمدرضا محجوب؛ نشر: تهران، انتشار، چاپ نخست 1369، مشخصات ظاهری 231ص، مصور، نمودار، چاپ سوم: زمستان 1369؛ ‏چاپ پنجم: 1375؛ چاپ ششم: 1378؛ چاپ هفتم: 1380؛ ‌شابک ایکس-964573519؛ موضوع نوشتارهای نویسندگان بریتانیا - سده 20م

 این کتاب به عنوان پرخوانشگرترین کتاب «کیهان‌ شناسی» شهرت یافته، و به بیش از سی و سه زبان دنیا تا سال1993 میلادی، ترجمه و چاپ شده‌ است «هاوکینگ» در این کتاب با زبانی ساده به بازگویی داستان جهان پرداخته است

 در مورد مفاهیم اساسی مانند «فضا» و «زمان»، بلوک‌های اساسی ساختاری، که جهان را تشکیل می‌دهد (مانند کوارک‌ها)، و نیروهای اساسی حاکم بر آن (همانند گرانش) گفتگو می‌کند؛ ایشان در مورد پدیده‌ های کیهان‌شناختی مانند «بیگ بنگ» و «سیاه ‌چاله‌ها» نیز می‌نویسند؛ «هاوکینگ» این کتاب را برای خوانشگرانی که هیچ دانش پیشین درباره ی گیتی ندارند، برای آنهایی که تنها علاقمند به یادگیری چیزهای تازه در اینباره هستند، نوشتند؛

 مینویسند: (روزی یک دانشمند مشهور -گویا برتراند راسل- درباره ی نجوم یک سخنرانی عمومی کرد، در آن سخنرانی او شرح داد که چگونه زمین به دور خورشید می‌چرخد، و خورشید نیز به نوبه خود به دور مرکز مجموعه عظیمی از ستاره‌ها به نام کهکشان ما می‌چرخد؛ در پایان سخنرانی، پیرزن نحیفی در انتهای سالن به پا خاست و گفت: «آنچه که به ما گفتی مزخرف است؛ جهان صفحه‌ای صاف است که بر پشت یک لاک‌پشت غول‌پیکر قرار دارد.»؛ دانشمند قبل از پاسخ دادن لبخند متکبرانه‌ای زد و سپس گفت: «خوب آن لاک‌پشت بر روی چه ایستاده است؟»؛ پیرزن گفت: «مرد جوان، تو خیلی زیرکی، ولی لاک‌پشت‌های بیشماری تا آن پایین روی هم قرار دارند!»؛ اکثر مردم تصویری از جهان را به عنوان برج بلندی که از تعداد نامحدودی لاک‌پشت روی هم قرار گرفته و تشکیل شده است مضحک و مسخره می‌پندارند، اما چرا ما فکر می‌کنیم چیز بهتری می‌دانیم؟ ما درباره جهان چه می‌دانیم و چگونه این دانش را کسب کرده‌ایم؟ جهان از کجا پدید آمده است و به کجا می‌رود؟ آیا جهان آغازی دارد و اگر چنین است، قبل از آن چه اتفاقی روی داده است؟ ماهیت زمان چیست؟ آیا روزی به پایان خواهد رسید؟ آیا ما می‌توانیم در زمان به عقب برگردیم؟ پیشرفت‌های اخیر در فیزیک، که تا حدودی فن‌آوریهای جدید شگفت‌انگیز هستند، به این پرسش‌های دیرینه پاسخ‌هایی ارائه می‌دهند؛ ممکن است روزی این پاسخ‌ها به اندازه گردش زمین به دور خورشید برای ما بدیهی به نظر برسند، یا شاید به اندازه برجی از لاک‌پشت‌ها مسخره جلوه کنند. فقط گذشت زمان -هر چه که باشد- می‌تواند حقیقت را روشن کند.)؛

 تاریخ بهنگام رسانی 18/07/1399هجری خورشیدی؛ 11/06/1400هجری خورشیدی؛ ا. شربیانی
 20th-century astronomy british
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 Jason Koivu
 Author 7 books 1,202 followers
 March 14, 2018
 Isn't it amazing that a person can read a book like A Brief History of Time by Stephen Hawking and come away feeling both smarter and dumber than before he started? What a universe we live in!

 It's quite short and generally a quick read. Not every page is filled with mind-blowing/numbing theories and brain-busting equations. Some of it is just history, say on Newton and such. However, there were a few pages worth of passages where my wee brain felt like it was getting sucked into a black hole...mainly during the black hole segment.

 I've forgotten so much since I left school, and since school was such a long time ago, some of what was taught back then is now outdated, it was nice to read this refresher/cleanser.

 I came away with a better understanding of the Big Bang theory and why it's plausible (Not the tv show. Its existence is not plausible). I'm trying to sort out the time/space quantifiability thing. That's going to require a reread...and probably further study elsewhere.

 Surprisingly, I also came away with the idea that God and science can coexist. I didn't expect that. I figured someone like Hawking would be like, "God? Pssh, whatever." But that's not his take at all, or at least that not the impression this book left me with.

 A Brief History of Time was written with accessibility in mind, knowing full well idiots like me wouldn't buy it, read it or recommend it if it were impossibly dense. Hawking's sense of humor even comes through on occasion, which is always appreciated in these sciencey texty thingies. So, I'll probably move on to his Briefer History... next and I'd be quite willing to read others as well!
 non-fiction
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 Mohammed-Makram
 1,389 reviews 2,827 followers
 October 12, 2022

 بمناسبة الثقب الأسود الذي توقعه آينشتين و تحدث عنه هاوكينج كثيرا في هذا الكتاب و وضع له النظريات و السيناريوهات و القفشات أيضا و بمناسبة الصورة التي نشرت في ابريل 2019 فهذه المراجعة ربما تذكركم بالكتاب الملهم المختصر الغني جدا بالمعلومات و الذي أعتبره بوابة أساسية لمن يهتم بما يحدث في الفضاء البعيد

 مع انى دارس هندسه فراغية و هندسة وصفية و مساحة جيوديسيه و رياضه بحته و تطبيقية و فيزياء عامه و ثيرمو دايناميك لكن حسيت و انا بقرأ الكتاب ده انى كنت أدبى و انى خريج دبلوم زخرفه

 ده مش عيب فى الكتاب لكن عيب فيا انا لأنى درست علشان أشتغل و اهتميت بس بالمحتوى العلمى اللى هستخدمه فى السوق و كمان ممكن يكون طريقة التدريس أيامنا كانت مشى حالك و كل عيش

 المهم الكتاب مع ذلك شيق و ممتع و مفيد جدا وأسلوبه رشيق و ترجمته ممتازه و دمه خفيف و فيه كمية معلومات تنوء بها العصبه أولى القوه
 بعد ما بنقرأ الحاجات دى أكيد بنتحسر على بلادنا و علمائنا و على نفسنا و بنأمل يجى يوم ينصلح فيه الحال
 science
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 Sean Barrs
 1,105 reviews 44.2k followers
 June 21, 2019
 Stephen Hawking writes in a very simple and approachable way. On the surface the book has been written for the common man, for he who has little knowledge of theoretical physics.

 Hawking uses basic terminology and he tries not to overload his writing with explanations and information dumps, but at times it is very clear that the reader needs a certain level of knowledge to understand what he's talking about. As such, Hawking makes certain assumptions as he shifts from concept to concept which left me a little confused. Things that don't appear related are related and it made me question who the intended readership really was.

 I do believe this is a book every reader should try because it is an important one, full of discussions and ideas that could really open up your mind. But I would warn you to be prepared, although this seems like light reading, much of it may go over your head.

 Approach with caution.
 non-fiction
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 David Sarkies
 1,775 reviews 298 followers
 April 2, 2015
 Things I learnt from Stephen Hawking
 11 October 2014

 Ever since I took up physics in year 11 I have had a love affair with the subject, which is odd since I went on to study an arts/law degree (but that probably had something to do with the fact that I would not have had the staying power to pour all of my energy into helping human knowledge advance towards establishing a unified theory). I still wonder where I ended up getting this book, and it had been sitting on my shelf for quite a while (probably because I was too busy listening to people tell me why I shouldn't read this book), but it wasn't until John Lennox said that it was the most unfinished book (that is people start reading it but do not have the staying power to get to the end) ever written (I'm sure there are other books that beat this book though). There are quite a few things that I have discovered while reading this book, and it is these discoveries that I wish to share with you:

 1) This is not an anti-God book
 One of the impressions that I got from certain people was that this was a book that an atheist wrote to try to argue that God does not exist, in much the same way that Richard Dawkins does in his books. However, that statement could not be further from the truth. In fact, throughout the book the question of the existence of God perpetually hangs in the background. Granted, Hawkings does suggest that if the concept of a infinite bounded universe (don't ask) turns out to be true then it would undermine God's existence, however he does not actually say that this may be the case. In fact his final sentence in this book is that the reason we study physics and try to find a unified theory is because we, as a race, seek to understand the mind of God.

 2) Stephen Hawkings is actually a really good writer
 This probably goes without saying, especially since the cover of my book says that it is a 'record breaking best seller'. While he is involved in some very serious and complicated research he is able to write in a way that many of us who have probably studied physics up to a year twelve level (that is the end of High school) can understand. Okay, I probably have an advantage over most other people since my Dad is a theoretical physicist that we have regular conversations about some of these high level concepts (such as by having any more than three dimensions would cause the orbits of the planets to collapse), but I still found that he was very easy to follow and he explained many of these high level concepts in a way that many of us could understand.

 3) Scientists have a strange way of viewing the universe
 Many of us would be familiar with this guy:



 but as it turns out, after reading this book, I have come to the conclusion that a lot of theoretical physicists seem to live in the same world that he does. Okay, they probably don't spend their time at the comic book store, or arguing whether Babylon Five is better than Star Trek (actually, one of my primary school friends is a theoretical physicist, and we did have such an argument), but they do seem to see the world in a way that we ordinary people would consider strange.

 For instance, we see space as flat, meaning that if we look at a star, as far as we are concerned the star is in that direction. However physicists see space as being curved and that a straight line is not necessarily straight. We would see a brick wall as being a solid object and that the idea of walking through one would result in a sore nose. However physicists see it as being made up of mostly space, and the only reason we can't walk through it is because the nuclear forces (forces that exist inside an atom, not the force that can level an entire city) prevent us for doing so. Then there is the concept of dimensions: to us there are only three dimensions, however some scientists (and Hawking is not one of them) see that there are in fact ten, or even more, dimensions.

 4) Why are so many scientists atheists
 While reading this book I could not get past about how complex this universe is and it made me wonder why it is, with the mathematical precision of the universe, and the complexity that lies therein, that so many scientists seem to argue that it all came about by chance. Even Hawking argues, using the second law of thermodynamics, that the universe cannot move from a state of disorder to a state of order – a broken plate simply cannot mend itself. However, the argument also goes that with the Big Bang Theory (not the television show) that the universe began in a state of disorder and moved to a state of order, however the laws of physics seem to suggest otherwise because what the big bang did was sent in motion a series of laws that caused the universe to come about to what we have at the moment. However, to go into details would require some intense theoretical physics, something which I have do desire to delve into at the moment.

 5) Scientists assume the speed of light is a constant
 The truth is that it is not. Okay, if light were travelling through a vacuum where there are no external forces acting upon it, then it is a constant, but that is very rarely the case. Take for instance this phenomena:



 The reason light behaves thus is because when it hits the prism it SLOWS DOWN, and when it slows down it refracts. Thus my point is proven, the speed of light is only a constant when there are no external forces acting upon it.

 So, what external forces may act upon light in space. Well, first of all there are black holes. When light hits a black hole the force of gravity is so strong that it will actually prevent light from escaping. Thus, gravity is a force that effects light and slows it down. Then there is the concept of dark matter , which are clouds of matter that do not emit light and float between the star systems. Okay, we know very little about the stuff (and it is also a theory, so it has not been proven) but my hypothesis is that if this stuff exists then would it not have an effect upon light, namely by slowing it down, which means that there is a possibility that our calculations as to the distance of stars from our own Sun could actually be wrong?

 6) Scientists do not know as much as we think they know
 One of the things that Hawking stresses in this book is that theories are not actually proven. A theory is an idea that has some foundation based on mathematical calculations and empirical evidence. Therein lies the problem. Much of our understanding of the universe is based upon mathematical calculations, and it appears that if an event comes about which causes this mathematical calculation to break down, they immediately set out to try to find another mathematical equation to plug the hole.

 Take light for instance. For years we believed that light acted as a wave and suddenly it was discovered that it also behaves like a particle (a particle of light is called a photon). The same goes with matter – for years we believed that they were particles when all of the sudden we discovered that they can also behave like waves. As such, our understanding of the universe suddenly breaks down (meaning that we are not necessarily made up of atoms, but have wavelike properties as well).

 Mathematical equations have been very destructive in out modern world. Take the Global Financial Crisis for instance. A bunch of apparently really smart people create complex mathematical equations to determine when to buy and sell shares and how to make billions of dollars. However what these equations did not take into account was the fact that people could not simply continue to accumulate debt without having to pay it back and when people began to default on their loans enmass, the whole concept broke down and we were taken to the brink of financial armageddon.

 Another point goes back to Ancient Greece. Here we have the theory of Democritus, namely that matter was not infinitely indivisible (the smallest piece of matter is an atom), and then the theory of Aristotle, that is that matter is infinitely divisible. Scientists preferred Democritus' theory, however they soon discovered that you could break down the atom into protons and neutrons, and you could even break them down to quarks. So, maybe Aristotle was right after all.

 7) We accept their theories because our gadgets work
 It goes without saying that their research and discoveries have lead to the computer that I am writing this on, the energy that powers our devices, and the bombs that can level entire cities. We know how to make a nuclear bomb, as well as a smart phone, so we don't question what they say, because it obviously works. However, as a friend of mine once said, it is still all based on theory, and just because something works does not necessarily mean that the theory is correct. Remember that penicillin was discovered by blind chance.

 8) Nobel Prizes are simply shiny baubles that have no merit
 Okay, maybe the people that win these prizes are actually really smart, but then again, the guys who set up Long-Term Capital Management also won a Nobel prize, which proves my point.

 9) Nobody really knows how gravity works
 Gravity is one of those odd forces that doesn't seem to connect with any of the other forces in our universe. As Hawking points out, there are four forces that have been identified: electro-magnetic, strong nuclear, weak nuclear, and gravity. Out of those four forces (five if you divide electric and magnetic, but since electricity will create a magnetic force, they are effectively combined) only gravity stands out. This is probably why Hawking spends so much time talking about black holes because black holes are where the gravitational pull is so strong that not even light can escape from its grasp. The other thing is that gravity does not, at least in our knowledge, have an opposing force. Gravity basically sucks, and that is all it does – it doesn't repulse as the other forces can.

 It is interesting that in some texts that I have read (maybe it is speculative science-fiction but I simply cannot remember off the top of my head) some people have suggested that gravity is actually a force from another universe that affects our universe and what it is effectively doing is sucking our universe into their universe. However, as I have said, that is incredibly speculative, and since I am not a theoretical physicist I can't really say any more on the subject.

 10) The God of the Gaps is a cop-out
 The idea of the God of the Gaps is that where there are gaps in our knowledge we simply say 'oh, God did that' and think nothing more of it. This goes back to the days of paganism (and Medieval Europe) where all of the unknown forces, such as the weather, was attributed God (or the gods) and we could not know anything beyond that fact. However I am arguing that it is a cop out. Creation scientists who resort to this argument are at best lazy and at worst dangerous. The reason I say that is that it discourages research into areas that we do not understand. Okay, we may never be able to control the weather, or predict earthquakes, but that does not mean that we should throw our hands up in the air and say 'this is too hard'.

 While I may be taking a swipe at creation scientists here, I would also take a swipe at the atheists who claim that there is no God. The reason I say that is because there seems to be a fear within the scientific community that suggests that we may not be able to know everything, or that our understanding of the universe may be wrong. The problem that arises is that if we throw the idea of God out of the window and claim that the universe came about by chance, then we deny the fact that we live in an incredibly ordered universe that we can learn and understand through the development of mathematical formulae. If a formulae turns out to be wrong, that does not mean that the universe will collapse in on itself – it won't – it just means that we have to go back to the drawing board and start over from scratch.

 11) Why are Creation Scientists so dogmatic
 Why is it that some members of the scientific community insist that we must take the Bible literally? The Bible is not a scientific text, and it was never meant to be a scientific text. It is a theological text that tells us how we should live with one another and how we should view God. Science exists beyond the Bible, and neither contradicts the other. Okay, granted, God has intervened in this world and done things that break the laws of science, but doesn't he have a right to do that – he created the universe? However, what the Bible tells us is that God is a god of order, and if he is a god of order then does it not make sense that the universe that he created is an ordered universe?

 So, maybe you are looking for a whiz bang conclusion to my exposition on this book, but all I can say is that what I have written above pretty much sums up what I have learnt from this book. In a nutshell (hey, this is me in a nutshell), all I can say is that what I have learnt from this book is that the world is an amazingly ordered place in which we live, and having now completed this book I am just as committed to my Christian faith as I ever was. However, if theoretical physics fascinates you, then this is certainly a book that you should give a read (though you have probably done that already).

 This review also appears on my blog . I have also commented on this book in my review on Interstellar .
 science
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 Ahmad Ebaid
 281 reviews 1,979 followers
 February 18, 2018
 "والواقع أننا قد أعدنا تحديد مهمة العلم لتصبح اكتشاف القوانين التي تمكننا من التنبؤ بالأحداث في الحدود التي يفرضها مبدأ عدم اليقين"


 بدأ ستيفن هوكينج, وهو عالم في الفيزياء النظرية, في كتابة هذا الكتاب في الفترة التي كان مازال يستطيع فيها أن يستخدم صوته وهو شبه مشلول على كرسيه المتحرك, ثم وبعد فترة, وقبل أن يكمل الكتاب, خضع لجراحة شقت فيها حنجرته, ليذهب صوته وهو الشيء الوحيد الذي كان يتواصل به مع العالم آنذاك

 ظن في البداية أنه لن يستطيع إكمال الكتاب, ولكن أحد طلبته "بريان هويت" قام بمساعدته, ليس فقط على مراجعة المسودة, وإنما جعله أيضاً يستخدم برنامج لتخليق الأصوات, وهو ما فتح نافذة جديدة له على العالم.

 وها هو ذا الكتاب بين يداي, وبين يدي الملايين.



 أول كتبه الموجه للعامة, يشرح لنا فيه حصيلة أوراقه البحثية,
 كتاب صغير الحجم
 الثلث الأول من الكتاب تقريباً هو مقدمة تمهيدية عن الفيزياء التي سيشرح لنا قصته معها تالياً في الكتاب, وعن المحاولات والنتائج التاريخية التي سبقت أبحاثه.

 ثم الثلثين الآخرين عن أوراقه البحثية, التي ارتكزت على الثقوب السوداء, والتي تعتبر نقطة تفرد خاصة حيث تكون الكثافة وانحناء الزمكان عندها لانهائيين, وتنهار عندها قوانين النسبية العامة
 وقد قام هوكنج بمحاولة تفسيرها باستخدام مبادئ الكم تحت اسم: "الجاذبية الكمية", وهي إحدى محاولاته لصنع حلقة وصل بين قوى ثقالة الجاذبية وبين القوى الثلاث الأخرى التي تم توحيدها معاً في نظرية واحدة سابقاً

 ثم ينهي بالمحاولات التي تلته لتوحيد القوى الأربعة, في نظرية واحدة, نظرية لكل شيء, تحديدا نظرية الأوتار, والأوتار الفائقة



 إذن أين هو التاريخ الموجز للزمان؟ لقد أنبأتنا نظرية النسبية العامة بأنه إذا تحرك أحدهم بسرعة فسوف يمر الزمن عنده أبطأ. كما أنبأتنا بأن الجاذبية, تسبب تشويهاً في نسيج المكان لتجذب إليها الأشياء, وأيضاً تسبب تشويه الزمان, وبقربنا من مصدر قوي للجاذبية كأحد أطوار النجم كبير الحجم "الثقب الأسود", يسير الزمن عندنا أبطء من الزمن عند المراقب البعيد عند مصدر الجاذبية, وقد رأى معظمكم تطبيق هذه الفكرة في فيلم انترستلر.

 وهكذا فالكتاب يتعرض في بعض مواضعه للجاذبية, والجاذبية تؤثر على الزمن. الزمن الذي لن يتطرق إليه الكاتب كثيراً في كتابه إذا ما استثنيا المقدمة التي حشر فيها الحديث عن الزمن حشراً لتتوافق مع هذا العنوان التجاري, والذي وُفّق في اختياره كعنوان جذّاب.


 في المقدمة يعلل المؤلف كتابة هذا الكتاب, بأنه ورغم وجود عدد من الكتب الجيدة
 "على أني شعرت بأن أي منها لم يكن يخاطب حقاً الأسئلة التي أدت إلى القيام بالبحث في علم الكونيات ونظرية الكم: من أين أتى الكون, كيف ولماذا بدأ؟ هل سيصل إلى نهاية ؟ وإذا كان الأمر كذلك, فكيف ستكون النهاية

 وهنا تلاعب بالكلام, ليحوّل كتابه من مجرد كتاب يسرد به مسيرته العلمية في سياق البحث عن النظرية النهائية, إلى كتاب يعالج الأسئلة التي تؤرق الكل. الأسئلة التي لم يعد الفلاسفة قادرين على التعامل معها.
 وهذه العبارات التي تحتمل التأويل تدعم ما قلته في الفقرة السابقة عن أن العنوان مقصود به أن يكون تجاري بغض النظر عن محتوى الكتاب ومدى خداع القاري به.



 ونأتي أخيراً للسؤال الأكثر إلحاحاً للمعظم, هل الكتاب للمبتدئين؟ والجواب هو لا, فالكتاب فقط لمتابعي العلوم الذين لديهم الحصيلة الأساسية عن الفيزياء, والكتاب لا يشرح تلك الأساسيات سوى بجمل عارضة, لن تمكنك من استيعاب أي شيء

 ولذلك قام الكاتب بإعداد نسخة أخرى من الكتاب أكثر بساطة بعنوان, "تاريخ أكثر إيجازاً للزمان" تجدونها مترجمة أيضاً

 أما إذا كان لديك الحصيلة الأساسية, فالكتاب ولا شك تجربة مميزة, فالكتاب مليء بالعلم في كل سطر منه,
 والكتاب يعتبر نصف تاريخي فمعظم ما فيه من نظريات تخطوها الآن, أو أنها لم تكن مكتملة في ذلك الحين


 كان الشرح سلسل, واستنباط المعلومات وترابطها يشي بمدى تمكن الكاتب وعبقريته في إعادة صياغتها بسلاسة, إلا أنه هنالك استثناء بسيط في بضع صفحات يصف فيها آخر جزء من أبحاثه, وربما يرجع ذلك إلى أن الموضوع نفسه غامض



 **
 الكتاب من ترجمة مصطفى إبراهيم فهمي, مترجم قدير للبيولوجي, ولكنه تجاهل قاموس المصطلحات إلى حد كبير, فقام بترجمة التعبيرات بما يراه مناسبا دون أن يرجع إلى المصطلح المتَفَق عليه بالعربية في هذا المجال الغريب عنه
 فنجده ينوب عن مصطلح "الأوتار الفائقة" بألفاظ أخ��ى

 ويظهر أيضا عدم إلمامه بالفلسفة, فقد ترجم اسم الفيلسوف
 "wittgenstein"
 إلى "ويتجنشتين", وهذا خطأ, فهذا الإسم ألماني, وفي الألمانية ينطق حرف "W" بنفس نطق حرف الـ"V" في الإنجليزية
 وبهذا يصبح النطق الصحيح لاسم الفيلسوف: "فيتجنشتين", وهكذا يترجم في كتب الفلسفة العربية.



 *****
 "سيقولون أن الله يستطيع بقدرته بدء الكون بأي طريقة يشاء. ومع هذا فإن الله أيضاً كان يستطيع أن يجعله ينشأ على منوال تعسفي تماماً. ولكنه كما يظهر قد اختار أن يجعله يتطور على نحو جد منتظم حسب قوانين معينة. وهكذا فإنه مما يساوي ذلك عقلاً افتراض أن هناك أيضاً قوانين تحكم الحال المبدئي."

 لقد تطور فهمنا للعالم كثيراً. كنا في البداية نعزو الأحداث الخارجية لقوة فوقية تعبر عنها الطبيعة, وبعدها بدأنا نلاحظ أن الأشياء تتكرر بنظام معين.
 وقد كانت الثلاثة قرون الأخيرة هي سعي متواصل لاكتشاف المزيد من هذه القوانين, وقد وصلت للذروة بعد أن اكتشف لابلاس في أول القرن التاسع عشر "الحتمية العلمية", أي أن كل ما يحدث في العالم من حولنا إنما هو يسير وفق معادلات رياضية تنبئنا بما سيحدث تالياً إذا ما عرفنا ما يحدث الآن.
 وقد أدت هذه الثقة المفرطة إلى وجود أكثر من فجر كاذب, نذكر منهم أن:
 "الفيزيائي ماكس بورن الحائز على جائزة نوبل في الفيزياء, ذكر في عام 1928 لمجموعة من الزائرين لجامعة جوتنجن أن الفيزياء كما نعرفها, ستنتهي بعد ستة شهور, وكانت ثقته مؤسسة على اكتشاف ديراك الحديث للمعادلة التي تتحكم في الإلكترون, وكان من المعتقد أن ثمة معادلة مماثلة ستحكم البروتون, الذي كان الجسيم الآخر الوحيد المعروف وقتها, وأن هذا سيكون ختام الفيزيائيات النظرية"

 ولكن كان هنالك المزيد مما لا نعرفه, بل وهنالك أيضاً المزيد مما لن نعرفه أبداً وفقاً لمبدأ "عدم اليقين" الذي اكتشفه هاينزبرج
 "والواقع أننا قد أعدنا تحديد مهمة العلم لتصبح اكتشاف القوانين التي تمكننا من التنبؤ بالأحداث في الحدود التي يفرضها مبدأ عدم اليقين"
 علوم
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 Simon Clark
 Author 1 book 4,911 followers
 December 17, 2018
 This is an absolutely magical book, both objectively and for me specifically. I first read it when I was about 9 or 10, and ever since I've assumed that I didn't understand a thing, and read it as a childish boast. Fast forward nearly twenty years, degree and PhD in physics in hand, and I decided to give it a proper read. Much to my surprise I found that the book had permeated my brain! I remembered a huge number of the explanations, and the book resonated with the way I've thought about physics my entire academic career - I think I took in a great deal more than I first thought!

 As a primer to physics (I would say modern physics, but the book is a little out of date) you really couldn't ask for anything better than this. Especially when it comes to cosmology, this is possibly the best popular physics book that I've ever read. It really is a classic for a reason. It's such a concise, understandable introduction to the field that I'm determined to get my girlfriend (a linguist with no real interest in physics) to read it. Not just because I think she'll understand it, but because I think she will enjoy it!

 One peculiarity of the text is Hawking returning to the concept of God (with a capital G) over and over again. In some ways this feels like a transitional text, marking the passing of the public generation for whom the church determined the order of all things, and the coming of the current, secular generation. Unlike other authors (looking at you, Dawkins) Hawking always does so in a way that feels respectful while also forcefully stating his scientific case. It's quite feat of writing, much like the rest of the work.

 You really should read this, it's fantastic.
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 فؤاد
 1,040 reviews 1,678 followers
 August 7, 2017
 خیلی وقت بود دنبال یه کتاب بودم که نظریات فیزیک جدید رو توضیح بده. زیاد از اصل عدم قطعیت و کوانتوم و نسبیت و نظریه ی ریسمان ها و سیاهچاله و کرمچاله و انفجار بزرگ و غیره و غیره شنیدیم، ولی شاید از هیچ کدوم تصور درستی نداشته باشیم. این کتاب خیلی از این نظریات رو مفصل توضیح میده.
 استيون هاوكينگ يك مستند سه قسمتى داره، به نام "به سوى كيهان، همراه با استيون هاوكينگ" با صداى بى نظير بنديكت كامبربچ، كه بيشتر مباحث اين كتاب رو، بسيار بسيار ساده تر توضيح ميده. توصيه مى كنم كسانى كه تازه مى خوان مطالعات كيهان شناسى رو شروع كنن، قبل از اين كتاب اون مستند رو ببينن.
 Into the Universe With Stephen Hawking

 نکات منفی
 مشکل اصلی کتاب، اینه گاهی زبانش خیلی فیزیکی میشه. به نظر میرسه آدم باید اطلاعات زیادی از فیزیک داشته باشه تا حرف کتاب رو بفهمه. من دانش فیزیکم در حد سوم دبیرستان و چیزهایی که جسته گریخته از این ور و اون ور خونده بودم هستش، در نتیجه شاید نصف کتاب رو آن چنان که باید و شاید نفهمیدم. خود استیون هاوکینگ میگه که ناشر بهش گفته بود: "به ازای هر فرمولی که در کتاب به کار ببری، فروش کتاب نصف میشه" و درسته که تقریباً هیچ فرمولی در کتاب به کار نرفته، اما همچنان زبان کتاب سنگینه. در مؤخره ی کتاب، نوشته بود این کتاب یکی از "ناخوانده" ترین کتاب های تاریخ ادبیاته. یعنی ��ده ی زیادی خریدن کتاب رو و حتی ادعا میکنن خوندنش، ولی در حقیقت نخوندنش! میشه فهمید چرا.

 نکات مثبت
 اما جاهایی که دانش ناقص فیزیکم یاری میکرد یا خود کتاب ساده بود، خیلی خیلی عالی بود کتاب. قصد دارم یه بار دیگه بخونمش به همین زودی ها. تاریخ فیزیک از دوره ی ارسطو تا نیوتون تا آینشتاین و هایزنبرگ، مباحث کیهان شناسی، مثل گسترش جهان یا محاسبه ی فاصله ی کهکشان ها، برخی از مباحث فیزیک جدید، مثل اصل عدم قطعیت و نسبیت، جزء جاهایی بود که کمابیش فهمیدم و خیلی لذت بردم.
 گاهی هم مطالب علمی رو کلاً رها میکرد و شروع میکرد به تعریف زندگی خودش. مثلاً میگفت این نظریه در فلان تاریخ مطرح شد، در اون زمان من با دختری آشنا شده بودم و میخواستم باهاش ازدواج کنم و شروع میکنه ماجرای خودش رو تعریف کردن.

 کتاب بعدی از این نویسنده، "کیهان در پوست گردو" هستش که قصد دارم به زودی بخرم.
 علوم-طبیعی-ریاضی
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 Manny
 Author 28 books 13.4k followers
 November 3, 2011
 Apparently this book tops the world list of "bought but not read", which may explain why it's so universally acclaimed as a work of genius. If you know anything much about relativity or cosmology, it comes across as a potboiler, admittedly a well-written one with a great final sentence. I wasn't impressed.

 But... without it, we would never have had MC Hawking. If you haven't come across him, start with the lyrics to "E = MC Hawking" . Then buy A Brief History of Rhyme .
 science
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 Darwin8u
 1,559 reviews 8,659 followers
 December 13, 2015
 “The universe doesn't allow perfection.”
 ― Stephen Hawking, A Brief History of Time



 I know. I know. I both loved and hated this book. I definitely should never have read this book, cut the pages, opened the box, etc.. Somehow Stephen Hawking has written a book that gently fluffs the tail on Schrödinger's cat (or perhaps Schrödinger's cat is fluffing Dr. Hawking).

 Look, no doubt the guy is a genius and has a fantastic story (ALS, computer voice, nurses, Black Holes, strippers, movies, etc). My problem is the wussification of a large scientific narrative by one of Big “P” Physics primary scientists. Let someone else write a pop-GUT/Blackhole/Big Bang story. Let another writer do the pop-up Children's book with the scratch-n-sniff singularity, the rotating black hole, the pull-out universe.



 I want Dr. Hawking doing smart stuff. Let Bill Bryson write the summary science. But it is too late for me. I already crossed the damn event horizon. I've just become entangled with his book, so my "observer state" now corresponds to the damn book and the damn book review being both five stars and 1 stars is no longer a possibility; my reader state is entangled or linked now with my own review so that the "observation of the book review's state" and the "review's state" correspond with each other. I am finished.

 Hey, now to go see some movies about blackholes and wormholes and assholes.
 2014
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 Muhammad Abdullah
 87 reviews 49 followers
 April 26, 2021
 This is the first book I have ever read about science.This is one of the best selling book of the century.I have found it really infomative and my interest in science seems to build. This book is free from mathematical equations (except E=mc2) which is the best thing about the book. This book is so simple that even a lay person with basic knowledge of science can understand it.

 Stephen Hawking, the author of the book, is one of the well renowned scientists of the century after Einstein. Some people even called him the successor of Einstein due to his work in the field of science. In this book, Hawking talks about black holes, worm holes, time travel, cosmic background radiation (CBM), uncertainty principle, expansion of universe, space and time (or simply space-time), origin and fate of the universe, forces of nature and the most important The Grand Unification Theory (the theory of everything) which is the biggest unsolved mystery of the present time.


 A brief intro to author, Stephen Hawking

 This book is really amazing and is popular in both science and non-science related people. I enjoy it a lot and I would like to recommend it to all the science and nature loving people. And I hope they will also enjoy it.
 2019-reads non-fiction personal-library-books
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 Luís
 1,804 reviews 452 followers
 May 30, 2022
 This popularization book provides us with a portrait of the latest discoveries that have shaken the scientific world over the past hundred years: General relativity, quantum mechanics, the Principle of uncertainty, black holes, quarks, string theory, etc., enough to answer many questions: what will become of the the our universe? How was it formed? Why is CERN so determined to accelerate particles in a tunnel several kilometres long in Switzerland?
 I will not claim to have assimilated all the concepts in a single reading. Still, the book allows me to have a good idea of the stakes and the research. Therefore, I recommend it to any science lover, especially as some of the theories explained will soon celebrate their century of existence and have not yet reached ordinary people.
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 Valeriu Gherghel
 Author 6 books 1,184 followers
 February 7, 2022
 Cam tot ce știu din / despre cosmologie provine din scrierile lui Hawking. Îndeosebi din acest volum care a fost un bestseller absolut. O glumă afirmă că toată lumea bună l-a cumpărat, dar foarte puțini l-au citit. Scurtă istorie a timpului ar fi, așadar, cel mai puțin citit bestseller dintre toate. Nu cred că pe autor l-a afectat prea tare acest amănunt nesemnificativ.

 Mă aflu în situația bizară că știu multe fără să înțeleg totul. Știu, de pildă, că fizicienii încearcă să ofere „o descriere completă a universului”. Mai știu că o astfel de descriere nu este, deocamdată, cu putință. Mai știu că Hawking a fost obsedat de realizarea unei teorii fizice unificate (mecanica cuantică + teoria relativității generalizate), fără de care sus-numita descriere nu este posibilă. Prima teorie (cea cuantică) susține că „universul e guvernat de întîmplare”, fapt pe care Einstein nu l-a acceptat niciodată. A doua oferă o viziune deterministă.

 Deși ne-am obișnuit să gîndim în termeni finaliști (omul ar fi scopul creației), știu, de asemenea, că evoluția universului nu este finalistă. Evoluția nu are un scop, o „intenție finală”: apariția unei conștiințe care să constate frumusețea și armonia acestei lumi. Pentru Pico della Mirandola, în schimb, acest lucru era evident: „Te-am așezat, Adame, în mijlocul universului, ca să-mi poți contempla măreția” ( De dignitate hominis ).

 Știu că fizicienii au propus, la sfîrșitul anilor 60, un așa-zis Principiu antropic (îl comentează într-un articol și I. P. Culianu), care li s-a părut unora argumentul suprem al unei evoluții „dirijate după un plan” (un argument creaționist), dar mai știu că acest Principiu (comentat cu entuziasm odinioară de Penrose și Hawking) nu dovedește nimic. Formularea lui pare o imensă tautologie: „Vedem universul aşa cum este fiindcă, dacă ar fi diferit, noi nu am exista să-l observăm”. Altfel spus: „Vedem universul aşa cum este întrucît existăm". Afirmația lui Hawking seamănă cu alta, la fel de misterioasă, tot a lui: „Dezordinea creşte cu timpul, întrucît noi măsurăm timpul în direcţia în care dezordinea creşte”. Nimic mai limpede...

 În fine, mai știu ce a afirmat Roger Penrose despre singularități și găuri negre (universul nostru provine dintr-o singularitate): „O stea care suferă un colaps datorită propriei gravitaţii este prinsă într-o regiune a cărei suprafaţă se reduce la dimensiunea zero. Şi deoarece suprafaţa regiunii se reduce la zero, aşa trebuie să se întîmple şi cu volumul său. Toată materia din stea va fi comprimată într-o regiune cu volum zero, astfel că densitatea materiei şi curbura spaţiu-timpului devin infinite. Cu alte cuvinte, există o singularitate conţinută într-o regiune a spaţiu-timpului numită gaură neagră”.

 Cam atît...
 65 likes
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 Nandakishore Mridula
 1,238 reviews 2,223 followers
 February 6, 2018
 Manny says this book is in the "bought but not read" category for most people. Well, I'm proud to say that I bought and read it, that too in nearly one sitting - back in my geeky days, when I used to get a sexual high just from solving a hard maths puzzle.

 Unfortunately, I don't remember much of it (time for a re-read!) but I remember taking away the idea that time is a sphere. Being Indian, I loved this - because we are strong champions of cyclical time. Also, if time and space are both curved, it creates the possibility of jumping from one place and time to another; which is just delicious.

 (I bought a pirated edition of this book for 25 rupees from the roadside at Connaught Place in New Delhi. The vendor asked for 50, I said 25, and the bargaining was just starting when he spied a policeman approaching - so he let me have it for whatever I was offering! "Time" was on my side.)
 science
 64 likes
 2 comments
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 Matthew
 20 reviews 2 followers
 August 30, 2007
 Hawking is a brilliant physicist and a true expert in explaining highly complex aspects of our physical universe in terms that can be understood by most lay people.

 Where Hawking fails, in my opinion, is his hubris. He proceeds in to the realm of metaphysics and religion in several portions of this book. For instance, in his chapter on the "arrow of time", he states that, essentially, the universe can only move in one direction of time. It cannot go backwards. He also states that this limits the powers of God himself. Now, Hawking never qualifies those statements by defining "God". However, if he is talking about the Biblical God, how can you honestly think you're so intelligent as to place limits on a limitless being? If God is so powerful as to have created the universe and all the physical laws, why wouldn't he be powerful enough to change those laws any time he chooses? It is the same concept as a scientist creating a computer simulation of the universe. The scientist can, at any time during the simulation, alter the underlying framework of the simulation, effectively changing the physical laws that simulated universe operates under.

 Now, whether you believe in God or not, the mere fact that Hawking has the audacity to think he can assign limits on a limitless being should cause you some concern. Hawking, because of his fame and brilliance, is a man that people listen to when he speaks. That gives him immense power over the minds of his readers. He should be more careful in choosing his words.

 When Hawking sticks to his strengths, however, the book is second to none. Hawking truly has a gift of explaining the powerful forces that shape our lives in ways anyone can understand.

 If this book had been edited better, it would have received a few more stars from me, but I can't reward stubborn scientific pride resulting in false assumptions.
 63 likes
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 Trevor
 1,281 reviews 21.4k followers
 December 9, 2007
 The main idea to take away from this book is that time has a clear direction. Entropy is the idea that the universe moves from highly ordered states to less ordered states. If you take the lid off a bottle of perfume, and leave it off for a few days the perfume will go from being highly ordered (all in the bottle) to highly disordered (all over the room).

 Hawking uses this idea to explain why travelling back in time is impossible. It requires very little energy to knock a glass over and smash it - but think of how much energy it would take to make the glass jump back into place - all of the bits perfectly back where they were prior to the glass breaking. It would be impossible - and that impossibility is what gives time its clear direction.

 Philosophically, I tend to feel that the book makes far too much of the Uncertainty Principle. But that is another story.

 This isn't the easiest book to read in the world and is probably the most bought science book of all time while also being the one most likely gave up on after a chapter or two - but it is a fascinating read all the same.
 science
 62 likes
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 Saadia B.
 179 reviews 61 followers
 July 7, 2021
 Only Hawking could write this book - simple, to the point and extremely resourceful. Cosmology is not an easy subject neither can everyone understand its deep connotations. Hawking made it understandable in the most layman terms possible.

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 Ahmed Ibrahim
 1,196 reviews 1,568 followers
 November 25, 2017
 يسعى هوكينج في هذا الكتاب لوضع خريطة أو مسار كوني، بداية من الكيفية التي بدأ بها الكون، إلى وضع الاحتمالات التي سينتهي إليها، وتوضيح ما بينهما من أمور كونية فلكية.

 بدأ الكتاب بالحديث عن الانفجار الكبير والمتفردة التي بدأ منها، وفيما بعد سيتناول احتمالات تنفي وجود متفردة أولية تقول بأزلية الكون، لكن المتفق عليه بشكل كبير في حالة وجود المتفردة أو لا أنه ثمة انفجار كبير بدأ منه الكون ثم تمدد، ومن الأشياء التي ستناقش بعد هذا هو الكيفية التي تمدد بها الكون. الانفجار الكبير كما قال هوكينج لا ينفي وجود خالق.
 ثم يتحدث عن المكان والزمان، ويتناول فيه نظرية أرسطو الأولية التي دحضها جاليليو ثم نيوتن بقوانينه عن الحركة، ومن ثمَّ تناول بالحديث نظرية النسبية لآينشتين، الخاصة بتعارضها من قانون الجاذبية، والعامة المتسقة مع ذاتها.
 ويتناول بعدها اكتشاف هابل بأن الكون يتمدد، بل ربما يكون لها نهاية حسب نظرية فريدمان.
 وكانت هذه البداية للنظر إلى أن كوكبنا قطرة ماء في محيط الكون الفسيح، وتمت البرهنة بشكل كامل من قِبل هوكينج وبنروز على أنه لابد من بداية في الزمان على أساس أن نسبية آينشتين العامة جزئية واحدة من النظرة الكونية.
 وكان مبدأ الريبة الذي قال به هايزنبرج وكم بلانك يمهدان الطريق لميكانيكا الكم، وبالرغم من أن آينشتين مُنح نوبل لمساهمته في نظرية الكم، لكنه كان معارضًا بشدة لها لوقوعها في فخ العشوائية، فلم يتقبل أن يكون الكون محكومًا بالصدفة، ومقولته: "إن الله لا يلعب النرد" توضح أفكاره.
 لكن هذا لا يمنع أن معظم العلماء تقبلوا ميكانيكا الكم، يقول هوكينج:
 "ليس لدينا بعد نظرية متماسكة كاملة توحِّد النسبية العامة وميكانيكا الكم، ولكننا نعرف بالفعل عددًا من الملامح التي ينبغي أن تكون فيها"
 ويفصِّل الكاتب الحديث عن ميكانيكا الكم، فيتناول الجسيمات الأولية وقوى الطبيعة الأربعة.
 ثم ينتقل للحديث عن الثقوب السوداء وهي جد شيقة، وفي هذا الجزء يستفيض هوكينج في الشرح والتحليل في كل ما يختص بالثقوب السوداء، وربما هذا لأنه كان مهتمًا بشكل كبير بها واكتشف بعض الأشياء حولها.
 في أحد الفصول بعنوان: أصل ومصير الكون، وهو فصل مميز للغاية، وإن رأيته منفصل عن الكتاب بإعادته جزء بسيط باختصار مما قاله قبل هذا مع توضيح وتناول بعض الأشياء الجانبية، وفي هذا الفصل مناقشة بشكل أكبر للخالق، وإن توصل في النهاية إلى عدم نفي أو إثبات أي شيء، فكما هو الأمر في الفلسفة الإمر قائم على احتمالات لا يمكننا معرفة أيهما أصح، وعلى هذا أيضًا سينتهي الكتاب.
 ثم بعد هذا يتناول البعد الزماني والمسار الذي يسير فيه الزمان فيما سيسمى بسهم الزمان المطلق للأمام، ومع حديثه عن الثقوب الدودية يضع احتمالات للسفر عبر الزمن وإن لم يستطع أحد البرهنة على هذا لكنه احتمال كبير، لكن الإشكالية تقع في كيفية السفر، وهل يمكن السفر للماضي أم للمستقبل فقط؟ ويدور هذا الجزء حول هذه النقطة بتحليله الأبعاد المكانية الثلاثة والبعد الزماني الواحد وما يمكن أن يكون من أبعاد أخرى.
 ويأتي الفصل الأخير من الكتاب عن توحيد الفزياء، وهل يمكن أن نكتشف ما يجعل العلم متمكن من معرفة الأشياء بدقة وثقة متناهية؟ وقال بأن الفلسفة لم تعد تثمر في هذا المجال، بل اضمحلت واضمحل دور العقل في التقدم وفي مجاراة تطور العلم.
 يقول هوكينج في الختام:
 "وعلى كلٍّ، لو اكتشفنا فعلًا نظرية كاملة، فإنه ينبغي بمرور الوقت أن تكون قابلة لأن يفهمها كل فرد بالمعنى الواسع، وليس فقط مجرد علماء معدودين. وعندها فإننا كلنا، فلاسفة وعلماء وأناسًا عاديين، سنتمكن من المساهمة في مناقشة السؤال عن السبب في وجودنا، نحن والكون. لو وجدنا الإجابة عن ذلك، فسيكون في ذلك الانتصار النهائي للعقل البشري، لأننا وقتها سنعرف فكر الخالق."

 كتاب عظيم ومبسط بشكل جميل، رحلة ممتعة وشيقة في محاولة لمعرفة الكون وحجمنا فيه، ومحاولة للتوصل للخالق، وإن باءت الأخيرة بالفشل، فقد خرجت أشد حيرة وانقسامًا أكثر مما دخلت، ويظل العلم والفلسفة والدين غير قادرين على إثبات أو نفي شيء عقليًا، كل شيء يخضع للاحتمال في كل الأحوال.
 2017 علوم كتب-متنوعة
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 Orhan Pelinkovic
 85 reviews 149 followers
 June 26, 2020
 Theoretical Physics from the master himself. It's a great summary, but you need a little background knowledge to understand all the chapters. It's a summary of astrophysics, theoretical physics, and cosmology, and it's hard grasping it all in 200 some pages. I wish it was a little longer.

 The definitions at the end of the book are very useful. You will not regret reading the book, but you need some peace and quiet while reading it in order to hopefully understand it.

 I've read the A Bantam Book Edition published April 1988 / A Brief History of Time by Stephan W. Hawking / 226 pages / 56,997 words.
 astronomy cosmology history
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 Elena
 124 reviews 986 followers
 June 1, 2018
 A pesar de estar escrito para un público "no científico" no puedo decir que creo que sea un libro accesible al 100%. Es cierto que Hawking cumple su promesa de no incluir ni una fórmula matemática (excepto la conocida fórmula sobre la teoría de la relativdad E=MC²) pero los conceptos en sí pueden ser difíciles de imaginar y comprender. De toda la información que Hawking intenta explicar en este libro, ha habido cosas que notaba que se me escapaban. Quizá con algo más de material gráfico habría resultado más sencillo.
 Aún así, el concepto general de los temas que trata es impresionante si te apasiona conocer la esencia del universo. Realmente había momentos en los que dejaba de leer para procesar algunos conceptos y no podía menos de maravillarme.
 2018 non-fiction
 51 likes
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 Mohammed
 420 reviews 511 followers
 October 22, 2019
 كتاب سلس ويطرح المادة العلمية بطريقة شيقة.

 لحظة!



 إذا كتبت مراجعة من هذا النوع سأبدو ذكيا ورائعا. لكنها ليست الحقيقة، فلست ذكيا ولا رائعا، وإنما قارئ متوسط الاستيعاب، أشعر بحكة في دماغي عندما تتعقد الأمور وتطقطق جمجمتي من الداخل إذ يحاول مخي الصغير أن يتمدد ليستوعب بعض المعلومات، ولكنه لا ينجح دائما.

 ليس هذا دأبي مع كل الكتب التي تناقش موضوعات علمية، فقد مضيت في كتاب الكون لكارل ساجان من الغلاف إلى الغلاف دون أي عسر. أعرف أن ساجان طرح المواضيع ذاتها ولكن من زاوية فلكية، بعكس هوكينغ الذي لا يحيد عن الفيزياء قيد أُنملة. هناك حديث مطول عن الذرات والجزيئات والفوتونات ومواضيع أخرى لم أكن أبحث عنها بصراحة.

 ماسبق لا يعني أن الكتاب لم يضف إلى معلوماتي بل على العكس إذن ناقش الكتاب أهم نظريتين لشرح كل ما يجري في الكون: النظرية النسبية وميكانيكا الكم. تحدث هوكينغ أيضا عن الثقوب السوداء والثقوب الدودية والانفجار العظيم (ليس انفجارا بالمعنى الحرفي على فكرة) والتأثير المعكروني الموضح بالصورة أعلاه. هناك أطروحات حول بداية الكون ونهايته وإيراد لأهم النظريات التي اُكتشفت في ذلك الميدان. هذا إلى جانب الجانب التأملي في تاريخ العلم وتطور الفكر لدى الإنسان والتحدي الكبير المتمثل في مواجهة التيار التقليدي الذي يتصدى لأغلب الأفكار الجديدة.

 كتاب يستحق القراءة، مع الكثير من الصبر لأصحاب الميول الأدبية الذين اعتادوا على النوم أو العبث في آذانهم في حصص الفيزياء. الكتاب يستحق العناء لكنني توقعت شيئا أشد تبسيطا وأكثر إمتاعا.
 49 likes
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 Nicky
 4,138 reviews 1,004 followers
 July 24, 2013
 Stephen Hawking's book is easy to read, but harder to comprehend. In every chapter came a point where my brain couldn't hold another permutation of a theory, and as the book progressed, I ended up taking the same approach as I do when reading a Norse saga for the first time. With sagas, I just read, even if my brain doesn't seem to retain all the information about who is related to who and what they named their horse. Inevitably, at the end, I have a reasonable basic grasp of the saga, and then I have to read it over again to fit more information into that basic understanding.

 I don't know if the same will hold true here, but it's a nice hope.
 non-fiction science-fact
 49 likes
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 Michael Finocchiaro
 Author 3 books 5,433 followers
 February 10, 2017
 A classic text where the amazing Stephen Hawking explains string theory and quantum mechanics "for dummies." Highly readable and even comical, it is a superb read. I need to go back and read this one again myself!
 american-20th-c geek-classics non-fiction
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 P.E.
 718 reviews 500 followers
 April 5, 2021
 Space opera


 The Milky Way arch emerging from the Cerro Paranal, Chile, 3 December 2009. Author: Bruno Gilli/ESO

 A highly articulate summary of the history of astrophysics and its breakthroughs from its origins to 1996 (updated edition). I wish I had had such an introduction to physics and chemistry when I was in secondary school and high school! The layout of the book allows a layman to follow the development of the discipline and its fields over time, while Stephen Hawking never scorns an evocative image to give a better notion to the reader of what, say, the electromagnetic spectrum, thermodynamics or gravity are all about. I definitely recommand to all of you in awe before the universe and its strange marvels :)


 Detail of Eagle Nebula


 Summary:

 Chapter 1: Our Picture of the Universe
 Chapter 2: Space and Time
 Chapter 3: The Expanding Universe
 Chapter 4: The Uncertainty Principle
 Chapter 5: Elementary Particles and Forces of Nature
 Chapter 6: Black Holes
 Chapter 7: Hawking Radiation
 Chapter 8: The Origin and Fate of the Universe
 Chapter 9: The Arrow of Time
 Chapter 10: Wormholes and Time Travel
 Chapter 11: The Unification of Physics
 Chapter 12: Conclusion


 -----


 Black Hole elements


 Image of the night sky above Paranal, Chile on 21 July 2007, taken by ESO astronomer Yuri Beletsky


 Galaxies in the Hubble deep field (detail)


 Soundtrack:
 Lux Aeterna - György Ligeti
 astrophysics audiobook guidebook
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 Shine Sebastian
 112 reviews 91 followers
 December 22, 2016
 Without a doubt a masterpiece!
 It's just incredible how Hawking explains to us the complex and mindboggling secrets and concepts of physics and our universe, with amazing wit , clarity, and simplicity.
 The questions that we all used to ask to ourselves and to our parents, about god, about time, life and it's meaning, the sky, stars, about who created our universe and about it's beginning, about our fate......
 we had that unique quality called curiosity when we were children, but then, as we grew up , we somehow lost that ability to ask and question, we no longer felt the same thirst for knowledge and a deeper understanding of things as we reached adulthood, those questions we abandoned as our busy lives got in our way..
 But there are quite a few people, whose curiosity and desire to find out more, to explore the truths of this vast universe, never dies. They are always always on the lookout for answers to questions deemed unanswerable , and then to ask new questions , that one by one, fills the gap between us and the truth and makes our understanding of this universe and it's secrets a bit more clearer and deeper,
 Stephen Hawking is one such blessed genius!
 In this book, Hawking familiarise us with the possible beginning of the universe or space-time , which is called the Big Bang Singularity, the Black Holes with extremely strong gravitational force so that even light can't escape from it, the reasons why we are at this time and space of the universe [ this might be because that the present condition, universe ( if there are other universes), and dimensions are the only configuration which allows the existence of intelligent beings like us who can observe and ask these questions], the long quest for a Grand Unification Theory ( that will explain the whole universe completely ) which still continues, and so many more fascinating and incredible stuff.
 The writing style is highly enjoyable, Hawking is a great teacher and a wonderful writer, his wit and engaging writing makes me forget that I'm reading a scientific book!
 Highly recommended to everyone who wants to know a little more about this universe and it's secrets.
 5 stars.
 2016 books-i-own science
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 Nasia
 348 reviews 79 followers
 November 16, 2018
 Ένα πολύ ωραίο βιβλίο εκλαϊκευμένης επιστήμης που εξηγεί βασικές έννοιες της Φυσικής και πώς αυτές διαμορφώθηκαν ανα τους αιώνες - με κύρια κατεύθυνση στην μοντέρνα Φυσική που για πολλούς είναι ακατανόητη. Μου άρεσε πολύ ο τρόπος γραφής και το χιούμορ του Χώκινγκ αλλά θεωρώ πως κάποιος πρέπει να έχει κάποιες σχετικά γερές βάσεις Φυσικής για να το κατανοήσει. Θέλω πολύ να ξαναδιαβάσω τα κεφάλαια για την θεωρία των χορδών και τις μαύρες τρύπες γιατί νομίζω πως πολλά πράγματα τα έχασα. :(
 brace2018 readathon18
 45 likes
 2 comments
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 ALet
 275 reviews 242 followers
 July 30, 2020
 ★★★ /5

 This was an interesting and informative book, but sadly I just couldn‘t grasp everything that it tried to say.
 read-in-2020
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Friends &amp; Following      Displaying 1 - 30 of 11,529 reviews          Author  6 books133 followers     August 30, 2022   This book puts me in mind of the story about how a Harvard number theorist, through some malfunction of the scheduling computer, got assigned to teach an introductory course in pre-calculus. Being one of those individuals to whom math came so easily that they couldn't grasp how difficult others found it, the professor had no idea what to cover in such a course. So, he went to the chair of the department, who told him: "You'll want to start with the real number-line and then progress to inequalities; from there, move on to quadratic equations, then trigonometry and the wrapping function, Cartesian and polar coordinate systems, and, if time permits, conic sections." The professor thanked the chairperson and went off to meet with his first class. Next week, he was back. "What should I teach them now?" he said.  A Brief History of Time is like that -- Professor Hawking doesn't seem to notice when his treatment progresses from the obvious to the arcane, ending with his concept of "imaginary time" (very nearly incomprehensible in this overly brief presentation). Fun nonetheless. * * *August 30, 2022 addendum -- Time to jump in here, I fear: Having garnered over 650 "Likes," this far-from-serious scribble is by far my most popular review ever — and, truth be told, undeservedly so. For a more thoughtful consideration of a somewhat related book, try my take on Jim Holt's Why Does the World Exist? here: https://www.goodreads.com/book/show/8...      cosmology physics               149 reviews8 followers     September 25, 2007   It is not clear to me who is in the target audience for this book. At times it tries to explain basic concepts of modern physics in simple language, and at other times it assumes a familiarity with the same subject. For the first time I think I "understand" why absolute time is not consistent with relativity theory or that space-time curvature supplants the notion of gravity, and for that I thank the author. There are a few other things I believe I have a glimpse of having (finally) slogged through the book.On the other hand, there are many places where he writes as if it were clear what he is talking about even though it would require a good deal of background knowledge. To give but one example, he starts talking about summing up over possible world histories (I cannot locate the quotation) without explaining what that would mean. Trained in statistics, I have some idea that he is talking about mathematical expectation in the context of quantum mechanics, but I don't know how another reader might make any sense of it (and I certainly don't have more than a vague notion). There are irritating writing practices that could have used some editing, e.g., the use of the naked pronominal adjective "this" when in the middle of a dense explanation of an abstruse concept(e.g., "This had serious implications for the ultimate fate of massive stars."). My biggest complaints, however, are about his philosophical opinions. Obviously he is entitled to think as he wishes about the ultimate questions, but his assertion that his hypothesis of a finite world without beginning or end would leave no place for God seems beside the point. The classic divide has not changed: some folks look around and say stuff just is, and other folks say there's a power behind the stuff that has at least as much going for it as we do. That argument hasn't changed with his theories. At one point in the book he claims that the late John Paul II told gathered scientists that they mustn't inquire into the Big Bang because that was God's territory. I would wager with anyone reading this comment that such an assertion is just plain false. JPII was a flawed mortal, to be sure, but he was no dope; it certainly sounds to me like someone hearing what he thinks the pope would say. (And the Galileo jokes are pretty dumb -- does anyone think that JPII, who apologized for the embarrassing Galileo fiasco, would go after this guy? It must be all that influence the Vatican has had in Britain over the last 400 years that has him scared.) Other philosophical complaints involve his use of entropy (he defines it first within closed systems and then uses it to explain why the "thermodynamic arrow of time" and the "personal arrow of time" must run in the same direction -- leaping from a box of molecules to the entire universe!), his droning on about what black holes are like when he doesn't know for sure they exist, his statements about "random" and being 95% certain a theory is true (does that mean about 95 out of 100 theories like that are true??). His opinions may be very rich, deep, though-provoking, but how would I (or most general readers) know? You can't really evaluate a judgment unless you know something in the field. And so that is why I ultimately cannot recommend this book: if you know physics inside and out, you might find his opinions interesting. If you don't, you can only walk around parroting what he says about black holes as if you had a clue what you were talking about. What we all really need is a remedial course in physics!    general-nonfiction               Author  8 books15.9k followers     April 18, 2019    ‎‏‏ =وداعا هوكنج=صرت حرا الآن---------هناك لذّةٌ ما ،، في أن تفتحَ كتاباً تشعُّ من سطوره ألوان الفضاء شيءٌ ما في فعلِ المعرفةِ ،، والتأمل فيها شيءٌ يأخذ عقلك إلى أمكنةٍ أخرى ...لا بين المجراتولا في خضّم الكونِ الواسعبل هنا بداخلكعند هذا النبض الأخّاذ في قلبكحيث تبدأ المتعة في التحرر لتغمر مسامّك برائحة الدهشةفالكون في داخلك أنت يا صاحبيتاريخٌ موجز للزمن ،، يُعتبر من أهم الكتب العلمية الحديثةيأخذك ستيفن هوكنج في رحلةٍ عبر تاريخ العلم ويشرح لك كيف تغيّرت نظرتنا للكون ،، ولمجرتنا ،، ‏ولكرتنا الأرضية ،، ولأنفسنا كذلك عبر العصور هذه هي قراءتي الثانية لستيفن هوكنج ،وقد أعجبتُ أيّما إعجاب بقراءتي الأولي "التصميم العظيم" ‏،وإن قارنت هذا بذاك ،فأرجّحُ كفّة الأخير لا أعلم إن كانت للترجمة دورٌ في ذلك ،فلقد قرأت التصميم العظيم بلغته الأصلية لقد توقّعت أكثر مما وجدتُّ في هذا الكتاب ،فقد حسبته أكثر متعة وجمالاً في سرده أو في ترابط فصولهولكن لن تجد هُنا سوى متعةَ المادة العلمية ذاتها ، فـ اسلوب هوكنج جافٌ قليلاً‏ كما وضع كارل ساجان مقدمة جميلة للكتاب ليثير شهيتي أكثر  ============================================فلنتعرف على مؤلف سطور المعرفة الشهية إذا============================================  يقول ستيفن _______________________________________________‏لقد كنتُ مصدر يأس لوالدي في صباي، إذ كنتُ ‏دائماً أقوم بفك الأجهزة لأرى ما الذي ‏يجعلها ‏تصدر أصواتاً، وبالطّبع لم يكن بإمكاني - عادة - ‏جمع أجزائها مرة أخرى، إلاّ أنّني ‏شعرت بإمكان السيطرة على أيّ شيء - بطريقة أو بأخرى - إذا ‏فهمت كيفيّة عمله، وأنا موقن ‏من وجود الشعور ‏نفسه لدى الآخرين فنحن نجد أنفسنا في عالم لا ‏يلحظ وجودنا في الغالب ولا ‏يهتم به، بل - أحياناً - ‏يعادي هذا الوجود صراحةً لذا، لو أمكننا فك ‏‏"اللوحة الأماميّة" للكون والنّظر خلفها فربّما نصبح ‏قادرين على فهم كيف تعمل ‏تلك العجلات ‏الصغيرة، أعني المجرات، ولشعرنا ببعض التحكّم ‏فيما يجري من أحداث، ولحسن ‏الحظ فنحن غير ‏مدعوين لإعادة تجميع الكون مرة أخرى بعد فك ‏لوحته الأماميّة‎ _______________________________________________ هل تعلم أن هذا العالم العبقري قدأُصيب بمرض التصلب الجانبي الضموري؟هذا المرض يصيب الجهاز العصبي الحركي ،ويُفقد المصاب به قدرته على التحكم في عضلاتهوهل تعلم أن الأطباء قد أخبروه بأنه لن يعيش لأكثر من عامين؟ولكن يبدو أن إصرار الرجل وعزيمته جعلتاه يعيش كل هذا العمرلبملأ الأرض بإبداعاته كان ستيفن وقتها يحضّر رسالته في الفيزياء النظرية بجامعة كامبريدج ولم يمنعه مرضه من إكمالها ليشغل منصب أستاذ الرياضيات الذي كان يشغله نيوتن في نفس الجامعة حتى عام1974 كان هوكنج يستطيع العناية بنفسه بعض الشيءإلا أن تفاقم المرض جعله حبيساً لكرسي متحرك ،بالإضافة إلى ذلك فقد عانى من عملية استئصال للحنجرة ليفقد صوته تماما ولحسن حظه ،فقد أهداه والت وولتوز ،خبير الكمبيوتر، برنامجا عبقريا يتيح له أن يختار كلمات من سلسلة قوائم على الحاسوب، بمجرد كبسة على مفتاح في يده، بل ويستطيع أن يتحكّم به بعينيه، وحركة رأسه كذلك وعندما ينتهي من بناء جملته يرسلها إلى ناطق الكلمات وقد ثبتّ الجهاز على كرسيه المتحرك ليستطيع ستيفن التحدث مع الحركة بحرية أكبر[image error] احتل هوكنج كرسي الرياضيات في كامبريدج ،وهو أعلى منصب يحتله أستاذ في اختصاصهحيث شغله علماء أمثال نيوتن وتشارلز بابيج	وبول ديراك	 لهوكنج أبحاث نظرية في علم الكون وفي العلاقة بين الثقوب السوداء والديناميكا الحراريةودراسات في التسلسل الزمني كما وضع نظريات عديدة عن ‏بداية الكون منذ الانفجار الكبيروأيضاً عن الثقوب السوداء والتي أطلق على إشعاعها إشعاع هوكنج  http://www.youtube.com/watch?v=4OmSoZ...  جزء من مقابلة له مع لاري كينج ============================================================عن الكتاب=======================هذا الكتاب وبصورة مبسّطة نوعاً ، يعرض بعض نظريات العلماءالتي تحدثت عن الكون والزمن كنظريات ‏أرسطو وآينشتين وجاليليو ونيوتن أيضاً‏يدور الكتاب في أساسه حول الكونعن تمدده ،وإنكماشه وحدوده ،وعن أبعاد ‏الزمان هذا الرجل جعل عقلي يروح يميناً ويساراًدوخني معه بكمِّ معلوماته الهائل ،، وأفكاره المستنيرة في البداية يحدثك ستيفن عن التصور ‏القديم للكون بإختصار ويمثل لك بتصور ‏أرسطو الأشهر مروراً ببطليموس وغيرهم تصور أرسطو كان كالتالي‏============================‏‏===========‏المادة تتكون من 4 عناصر أولية‏الماء،النار،الهواء،الأرضتؤثر في هذه العناصر قوتانالجاذبية ،،أي نزعة الأرض والماء إلى الهبوطوالخفّة ،،أي نزعة الهواء والنار إلى الصعود‏============================‏‏===========‏  وإكتشاف أن الكون يتمدد كما يرى ‏هوكنج ،هو ‏إحدى الثورات الثقافية ‏العظيمة في القرن العشرين فيقول _______________________________________________‎وبالتأمل وراء، فإن من السهل التعجب لآن ‏أحدا لم يفكر في ذلك من قبل ، فقد كان ينبغي على ‏‏نيوتن وغيره أن يتبينوا أن كونا ستاتيكيا لن يلبث أن ‏يبدأ سريعا في الانكماش بتأثير الجاذبية‏ولكن ‏لنفرض بدلا من ذلك أن الكون يتمدد . فلو كان يتمدد ‏بسرعة بطيئة إلى حد ما ، فإن قوة ‏الجاذبية ستجعله ‏في النهاية يتوقف عن التمدد ليبدأ بعدها في ‏الانكماش . أما إذا كان يتمدد بسرعة ‏أكبر من معدل ‏حرج عين ، فإن الجاذبية لن تكون قط قوية بما يكفي ‏لوقف تمدده ، وسوف يستمر ‏الكون في التمدد للأبد  ‏وهذا يشبه ، نوعا ، ما يحدث عندما يطلق أحدهم من ‏فوق سطح الأرض ‏صاروخا لأعلى . فإذا كانت ‏سرعته بطيئة إلى حد ما ، فإن الجاذبية ستوقف ‏الصاروخ في النهاية ���وسيبدأ في السقوط عائدا ومن ‏الجهة الأخرى ، إذا كانت سرعة الصاروخ أكبر من ‏سرعة ‏حرجة معينة ( حوالي سبعة أميال في الثانية ‏‏) فإن الجاذبية لا تكون قوية بما يكفي لشدة إلى ‏‏الوراء ، وهكذا فإنه سيستمر في الانطلاق بعيدا عن ‏الأرض إلى الأبد . وسلوك الكون هكذا كان ‏يمكن ‏التنبؤ به من نظرية نيوتن عن الجاذبية في أي وقت ‏من القرن التاسع عشر ، أو الثامن ‏عشر أو حتى ‏أواخر القرن السابع عشر‎‏ ‏‎‏ ‏إلا أن الإيمان بثبات الكون كان من القوة بحيث ظل ‏باقيا لأوائل القرن العشرين_______________________________________________ وعن الإرتباط بين المكان والزمان، يحدثك ‏ستيفن ‏عن أهمية نظريات نيوتن والتي ‏توجها بوضعه ‏لقانون الجاذبية الكونية ‏ووقتها بدأ التعارض بين الفكر القديم الذي يرجح ‏‏ثبات النجوم وبين ما جاء به نيوتن ومن خلال ‏تفكيره ‏للخروج من هذا التساؤل أوضح إن تجاذب ‏النجوم ‏يحدث إذا كان عددها صغير ‏أما إن كانت عددها غير محدود ومتناسقة التوزيع ‏‏بطريقة أو بأخرى في الفضاء الشاسع ، فلن تكون ‏‏هناك نقطة مركزية لتتجمع عليها ‏ وبالمناسبة فقد اعتبر أينشتين الكون ثابتاًً حين ‏وضع ‏النظرية النسبية العامةوقد اعتبرها أكبر غلطة قام بها في حياته، عدّل ‏فيها ‏فيما بعد فيقول _______________________________________________‎‏ ‏نظرية أينشتاين عن النسبية العامة ، هي في ‏ذاتها تتنبأ بأن الزمكان يبدأ عند مفردة الانفجار ‏‏الكبير وسوف يصل إلى نهايته عند مفردة الانسحاق ‏الكبير ( إذا تقلص الكون كله ثانية ) أو عند ‏مفردة ‏من داخل ثقب أسود ( لو تقلصت منطقة محددة ، ‏مثل أحد النجوم ) وأي مادة ستهوي إلى ‏داخل ‏الثقب ستتدمر عند المفردة ، ولن يظل محسوسا في ‏الخارج إلا تأثير جاذبية كتلتها ومن ‏الناحية ‏الأخرى ، عندما يؤخذ في الحسبان تأثيرات الكم ، ‏فإنه يبدو أن كتلة أو طاقة المادة ستُعاد ‏في النهاية ‏إلى باقي الكون ، وأن الثقب الأسود هو وأي مفردة ‏من داخله ، سوف يتبخر بعيدا ‏ليختفي في النهايةهل يكون لميكانيك الكم تأثير درامي مساوٍ لذلك ‏على مفردتي الانفجار الكبير ‏والانسحاق الكبير ؟ ما ‏الذي يحدث حقاً أثناء الأطوال المبكرة جداً أو ‏المتأخرة جداً من الكون ‏عندما تكون مجالات ‏الجاذبية من القوة بحيث لا يمكن تجاهل تأثيرات ‏الكم ؟ هل للكون حقيقة ‏بداية أو نهاية ؟ وإذا كان ‏الأمر كذلك ، فكيف تبدوان ؟‎ _______________________________________________ و يقوم ستيفن بعدها بتوسيع مداركك عن ‏الكون ،، ‏كيف نشأ ،، ما معنى التمدد و ‏كيف بدأ الإنسان ‏يستكشف مجموعته ‏الشمسية وأرضه والكون من ‏حولهليذهب بنا إلى نظرية الإنفجار الكبير لقد استمر الجدال حول نشأة الكون وتاريخه في ‏‏الزمان ‏هل له بداية في الزمان؟ أو كان محدودا في الفضاء ‏؟ في عام 1929 ،قام هابل بإثبات أن المجرات ‏والنجوم ‏تتباعد بسرعة كبيرة وان الكون ككل آخذ ‏في التمدد ‏والإتساع ‏ وقد أدّى ذلك إلى ظهور منابت نظرية الانفجار ‏الكبير ،وبدأت فكرة تتخيل كيف كان الكون متناهياً ‏في الصغر ‏وكثافته لا متناهية‏وترجّح أن الزمن بدأ مع الانفجار الكبير يعتقد أصحاب النظرية أن الكون كان عبارة عن كتلة صغيرة ذات كثافة وحرارة لا يمكن تصورهاثم انفجرت هذه الكتلة انفجاراً هائلاً منذ قرابة 13 مليار سنة لينتج عن انفجارها سحابة هائلة من الغاز والغبار الكوني ويؤكد لك الكاتب أن الزمان قبل الانفجار الكبير لا ‏‏يمكن تحديدهبمعنى آخر لم يكن هناك ما يسمى ‏بالزمان أصلاً  a computer-generated explosion representing the Big Bang فيقول _______________________________________________‏مع ذلك، كان الاكتشاف المتميّز، الذي تم في ‏نهاية ‏القرن العشرين، هو تيقننا بالفعل من وجود ‏حدث ‏أول: الانفجار العظيم، الذي قد يشبه البيضة ‏أكثر ‏ممّا يشبه الدجاجة، ومع ذلك ليس كأيٍ منهمافقد ظهر كل من الكون والزمان للوجود أول مرة ‏‏عندم الانفجار العظيم، وذلك هو السبب الأول، فإذا ‏‏استطعنا فهم الانفجار العظيم فسنعرف سبب ظهور ‏‏الكون على صورته تلك_______________________________________________وينتقل بعدها إلى عناصر تكوين المادةكيف توصلنا إلى إكتشاف الذرة ،، وكيف ‏كنا نتخيل ‏أجزاء المادة وقابليتها للإنشطار ‏من قبل ،، ويحيلك ‏إلى الجاذبية بصفتها ‏من القوى المؤثرة على عناصر ‏كوننا ‏الأساسية حتى يومنا هذا ،يعتبر الكوارك هو أصغر ‏‏الجسيماتوالكوارك هو جسيم أولي مشحون يحس بالقوى الكبرى البروتونات والنيترونات يتكون كل منهما من 3 كواركات================================يصل بك الكاتب أخيراً إلى الثقوب السوداء ‏‏_أمتع ‏فصول الكتابليحدثك عن مفهومها  والثقب الأسود هو منطقة في المكان -الزمان لا يستطيع أي شيء الهروب منها ولا حتى الضوءلقوة جاذبيتها الشديدة ويذهب بك بعد ذلك إلى أن الثقوب ‏السوداء ليست ‏جد سوداءكما أن الثقوب كلما كانت أصغر كلما كانت ‏أشد ‏توهجاً ،وبالتالي تكون قدرتنا على ‏رصدها أفضل ================================ من أمتع ما قرأت عنه هنا أيضاً هو الجسيم ومضادهفكل نوع من جسيمات المادة له مضاد جسيم مناظر لهوعندما يصطدم الجسيم بمضاده فإنهما يفنيانولا يتخلف عن ذلك إلا الطاقةويدلل بأمثلة ممتعة كذلك^_^ الفكرة التي وجدتها مثيرة هي عدم تساوي عدد الكاوركات مع مضاداتها و هذا من حسن حظنا فلو كانت متماثلة لكان أفنى أحدهما الآخر في الكون المبكر لتترك كوناً مليئاً بالإشعاع لا يكاد يحتوي أي مادة تخيّل معي لا مجرات ولا نجوم ولا كواكبولا نحن ‎ عندما تشرد قليلاً في ذلكاحم:P================================ الكون بلا بداية وبلا نهاية‎ ‏ ‏‎يرى هوكنج أن‎‏ معظم الناس وصلوا إلى ‏الإيمان بأن الكون جُعل ‏ليتطور حسب مجموعة من القوانين التي لا تُكسر ‏،ولكن هذه القوانين ‏تخبرنا بما ينبغي أن يكون الكون ‏عليه عند بدايته وعلى أنه لو كان الكون بلا بداية ‏وبلا حرف ، ‏فإنه لا تكون له بداية ولا نهاية فهو ‏ببساطة موجود‎‏ ‏وفي فصل سهم الزمان ،، يحدثك هوكنج ‏عن مفهوم ‏الزمن ،، وارتباطه بنظرية ‏النسبية يرى ستيفن أن هناك فارقاًً كبيراً بين ‏إتجاهي الأمام ‏والوراء للزمان الحقيقي ‏في الحياة العادية‏ويدلل لك بمثالأً طريفاً فيقول ‏_______________________________________________ ‏تصوّر قدح ماء يقع من على مائدة وينكسر ‏‏على الأرض إلى قطعلو أخذت لذلك فيلماً سينمائياً ، فإنه ‏سيمكنك بسهولة ‏أن تعرف إذا كان الفيلم ‏يسير أماماً أو وراء ‏ولو سيرته وراء فسوف ترى القطع تجمع ‏نفسها معاً ‏فجاة من على الأرضية وتقفز ‏عائدةً لتكون قدحاً ‏كاملاً على المائدة ‎…‎ماذا سيحدث إن توقف الكون عن التمدد ‏وبدأ في ‏الإنكماشسيؤدي هذا إلى صنوف الإحتمالات التي ‏من نوع ‏يشبه الروايات العلمية بالنسبة ‏للناس الذين سيبقون ‏أحياء من طور ‏التمدد حتى طور الإنكماشهل سيرون الأقداح المكسورة تجمع ‏نفسها معاً من ‏على الأرضية وتب عائدة ‏فوق المائدة؟‎…‎على أن ثمة طريقة أسرع لمعرفة ما ‏سيحدث:هي ‏القفز في ثقب أسودإن كان الإضطراب سيقل في طور ‏الإنكماش للكون ‏، فإن المرء قد يتوقع له ‏أيضاً أن يقل في الثقب ‏الأسودوهكذا لعل الفلكي الذي سيسقط في ‏الثقب الأسود ‏سيتمكن من كسب نقوده ‏في لعبة الروليت بأن يتذكر ‏أين ذهبت ‏الكرة قبل أن يضع رهانه ‏(على أنه لن يتاح له لسوء الحظ زمن ‏طويل للعب ‏قبل أن يتم تحويله إلى ‏إسباجيتي)‏:D_______________________________________________ ‏================‏ هذا الفيديو يوضَح شيئاً من وجهة نظره عن ‏نشأة الكون  http://www.youtube.com/watch?v=Sq-‎WF...  ================================ ‏  ‏ إن لم تكن قد قرأت كتاباً علمياً من قبل ،أو على الأقل تابعت بعض الدوريات و المواقع العلمية ، ‏فلا أنصحك بهذاالكتاب كبدايةفسوف تجده مملاً قليلاً ،وستجد نفسك غارقاً في المصطلحات التي ستشتّت ‏انتباهك،وتعيقك عن الإستمتاع به وهذا الكتاب يحتاج للقراءة لكثيرٍ من المرّات كي تتشبع بمعلوماته ،و يحتاج لكثير من القراءات الخارجية كذلك الكتاب معلوماته قيمة وشيقة لواحدٍ من أهم العلماء ‏الذين أنجبتهم الأرض ولا يزال علم الفلك متعة عظيمة ،، ‏وتحليقنا بين المجرّات محفّز عظيم للخيال       history philosophy science               9,567 reviews55.6k followers     September 3, 2021    A Brief History of Time: From the Big Bang to Black Holes, Stephen Hawking What is it that our eyes do that could possibly affect things?  A Brief History of Time: From the Big Bang to Black Holes is a popular-science book on cosmology (the study of the universe) by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for nonspecialist readers with no prior knowledge of scientific theories.  In A Brief History of Time, Stephen Hawking attempts to explain a range of subjects in cosmology, including the Big Bang, black holes and light cones, to the non-specialist reader.  His main goal is to give an overview of the subject, but he also attempts to explain some complex mathematics.  In the 1996 edition of the book and subsequent editions, Hawking discusses the possibility of time travel and wormholes and explores the possibility of having a Universe without a quantum singularity at the beginning of time. تاریخ نخستین خوانش: روز چهارم ماه مارس سال 1996میلادی عنوان: تاریخچه زمان: از انفجار بزرگ تا سیاهچالها؛ نوشته: استیون هاوکینگ؛ مترجم: محمدرضا محجوب؛ نشر: تهران، انتشار، چاپ نخست 1369، مشخصات ظاهری 231ص، مصور، نمودار، چاپ سوم: زمستان 1369؛ ‏چاپ پنجم: 1375؛ چاپ ششم: 1378؛ چاپ هفتم: 1380؛ ‌شابک ایکس-964573519؛ موضوع نوشتارهای نویسندگان بریتانیا - سده 20م این کتاب به عنوان پرخوانشگرترین کتاب «کیهان‌ شناسی» شهرت یافته، و به بیش از سی و سه زبان دنیا تا سال1993 میلادی، ترجمه و چاپ شده‌ است «هاوکینگ» در این کتاب با زبانی ساده به بازگویی داستان جهان پرداخته است در مورد مفاهیم اساسی مانند «فضا» و «زمان»، بلوک‌های اساسی ساختاری، که جهان را تشکیل می‌دهد (مانند کوارک‌ها)، و نیروهای اساسی حاکم بر آن (همانند گرانش) گفتگو می‌کند؛ ایشان در مورد پدیده‌ های کیهان‌شناختی مانند «بیگ بنگ» و «سیاه ‌چاله‌ها» نیز می‌نویسند؛ «هاوکینگ» این کتاب را برای خوانشگرانی که هیچ دانش پیشین درباره ی گیتی ندارند، برای آنهایی که تنها علاقمند به یادگیری چیزهای تازه در اینباره هستند، نوشتند؛ مینویسند: (روزی یک دانشمند مشهور -گویا برتراند راسل- درباره ی نجوم یک سخنرانی عمومی کرد، در آن سخنرانی او شرح داد که چگونه زمین به دور خورشید می‌چرخد، و خورشید نیز به نوبه خود به دور مرکز مجموعه عظیمی از ستاره‌ها به نام کهکشان ما می‌چرخد؛ در پایان سخنرانی، پیرزن نحیفی در انتهای سالن به پا خاست و گفت: «آنچه که به ما گفتی مزخرف است؛ جهان صفحه‌ای صاف است که بر پشت یک لاک‌پشت غول‌پیکر قرار دارد.»؛ دانشمند قبل از پاسخ دادن لبخند متکبرانه‌ای زد و سپس گفت: «خوب آن لاک‌پشت بر روی چه ایستاده است؟»؛ پیرزن گفت: «مرد جوان، تو خیلی زیرکی، ولی لاک‌پشت‌های بیشماری تا آن پایین روی هم قرار دارند!»؛ اکثر مردم تصویری از جهان را به عنوان برج بلندی که از تعداد نامحدودی لاک‌پشت روی هم قرار گرفته و تشکیل شده است مضحک و مسخره می‌پندارند، اما چرا ما فکر می‌کنیم چیز بهتری می‌دانیم؟ ما درباره جهان چه می‌دانیم و چگونه این دانش را کسب کرده‌ایم؟ جهان از کجا پدید آمده است و به کجا می‌رود؟ آیا جهان آغازی دارد و اگر چنین است، قبل از آن چه اتفاقی روی داده است؟ ماهیت زمان چیست؟ آیا روزی به پایان خواهد رسید؟ آیا ما می‌توانیم در زمان به عقب برگردیم؟ پیشرفت‌های اخیر در فیزیک، که تا حدودی فن‌آوریهای جدید شگفت‌انگیز هستند، به این پرسش‌های دیرینه پاسخ‌هایی ارائه می‌دهند؛ ممکن است روزی این پاسخ‌ها به اندازه گردش زمین به دور خورشید برای ما بدیهی به نظر برسند، یا شاید به اندازه برجی از لاک‌پشت‌ها مسخره جلوه کنند. فقط گذشت زمان -هر چه که باشد- می‌تواند حقیقت را روشن کند.)؛  تاریخ بهنگام رسانی 18/07/1399هجری خورشیدی؛ 11/06/1400هجری خورشیدی؛ ا. شربیانی     20th-century astronomy british               Author  7 books1,202 followers     March 14, 2018   Isn't it amazing that a person can read a book like A Brief History of Time by Stephen Hawking and come away feeling both smarter and dumber than before he started? What a universe we live in!It's quite short and generally a quick read. Not every page is filled with mind-blowing/numbing theories and brain-busting equations. Some of it is just history, say on Newton and such. However, there were a few pages worth of passages where my wee brain felt like it was getting sucked into a black hole...mainly during the black hole segment. I've forgotten so much since I left school, and since school was such a long time ago, some of what was taught back then is now outdated, it was nice to read this refresher/cleanser.  I came away with a better understanding of the Big Bang theory and why it's plausible (Not the tv show. Its existence is not plausible). I'm trying to sort out the time/space quantifiability thing. That's going to require a reread...and probably further study elsewhere. Surprisingly, I also came away with the idea that God and science can coexist. I didn't expect that. I figured someone like Hawking would be like, "God? Pssh, whatever." But that's not his take at all, or at least that not the impression this book left me with.  A Brief History of Time was written with accessibility in mind, knowing full well idiots like me wouldn't buy it, read it or recommend it if it were impossibly dense. Hawking's sense of humor even comes through on occasion, which is always appreciated in these sciencey texty thingies. So, I'll probably move on to his Briefer History... next and I'd be quite willing to read others as well!     non-fiction               1,389 reviews2,827 followers     October 12, 2022     بمناسبة الثقب الأسود الذي توقعه آينشتين و تحدث عنه هاوكينج كثيرا في هذا الكتاب و وضع له النظريات و السيناريوهات و القفشات أيضا و بمناسبة الصورة التي نشرت في ابريل 2019 فهذه المراجعة ربما تذكركم بالكتاب الملهم المختصر الغني جدا بالمعلومات و الذي أعتبره بوابة أساسية لمن يهتم بما يحدث في الفضاء البعيدمع انى دارس هندسه فراغية و هندسة وصفية و مساحة جيوديسيه و رياضه بحته و تطبيقية و فيزياء عامه و ثيرمو دايناميك لكن حسيت و انا بقرأ الكتاب ده انى كنت أدبى و انى خريج دبلوم زخرفه ده مش عيب فى الكتاب لكن عيب فيا انا لأنى درست علشان أشتغل و اهتميت بس بالمحتوى العلمى اللى هستخدمه فى السوق و كمان ممكن يكون طريقة التدريس أيامنا كانت مشى حالك و كل عيش المهم الكتاب مع ذلك شيق و ممتع و مفيد جدا وأسلوبه رشيق و ترجمته ممتازه و دمه خفيف و فيه كمية معلومات تنوء بها العصبه أولى القوهبعد ما بنقرأ الحاجات دى أكيد بنتحسر على بلادنا و علمائنا و على نفسنا و بنأمل يجى يوم ينصلح فيه الحال      science               1,105 reviews44.2k followers     June 21, 2019   Stephen Hawking writes in a very simple and approachable way. On the surface the book has been written for the common man, for he who has little knowledge of theoretical physics. Hawking uses basic terminology and he tries not to overload his writing with explanations and information dumps, but at times it is very clear that the reader needs a certain level of knowledge to understand what he's talking about. As such, Hawking makes certain assumptions as he shifts from concept to concept which left me a little confused. Things that don't appear related are related and it made me question who the intended readership really was.  I do believe this is a book every reader should try because it is an important one, full of discussions and ideas that could really open up your mind. But I would warn you to be prepared, although this seems like light reading, much of it may go over your head.   Approach with caution.       non-fiction               1,775 reviews298 followers     April 2, 2015    Things I learnt from Stephen Hawking 11 October 2014	Ever since I took up physics in year 11 I have had a love affair with the subject, which is odd since I went on to study an arts/law degree (but that probably had something to do with the fact that I would not have had the staying power to pour all of my energy into helping human knowledge advance towards establishing a unified theory). I still wonder where I ended up getting this book, and it had been sitting on my shelf for quite a while (probably because I was too busy listening to people tell me why I shouldn't read this book), but it wasn't until John Lennox said that it was the most unfinished book (that is people start reading it but do not have the staying power to get to the end) ever written (I'm sure there are other books that beat this book though). There are quite a few things that I have discovered while reading this book, and it is these discoveries that I wish to share with you:  1) This is not an anti-God book 	One of the impressions that I got from certain people was that this was a book that an atheist wrote to try to argue that God does not exist, in much the same way that Richard Dawkins does in his books. However, that statement could not be further from the truth. In fact, throughout the book the question of the existence of God perpetually hangs in the background. Granted, Hawkings does suggest that if the concept of a infinite bounded universe (don't ask) turns out to be true then it would undermine God's existence, however he does not actually say that this may be the case. In fact his final sentence in this book is that the reason we study physics and try to find a unified theory is because we, as a race, seek to understand the mind of God.  2) Stephen Hawkings is actually a really good writer 	This probably goes without saying, especially since the cover of my book says that it is a 'record breaking best seller'. While he is involved in some very serious and complicated research he is able to write in a way that many of us who have probably studied physics up to a year twelve level (that is the end of High school) can understand. Okay, I probably have an advantage over most other people since my Dad is a theoretical physicist that we have regular conversations about some of these high level concepts (such as by having any more than three dimensions would cause the orbits of the planets to collapse), but I still found that he was very easy to follow and he explained many of these high level concepts in a way that many of us could understand.  3) Scientists have a strange way of viewing the universe 	Many of us would be familiar with this guy:   but as it turns out, after reading this book, I have come to the conclusion that a lot of theoretical physicists seem to live in the same world that he does. Okay, they probably don't spend their time at the comic book store, or arguing whether Babylon Five is better than Star Trek (actually, one of my primary school friends is a theoretical physicist, and we did have such an argument), but they do seem to see the world in a way that we ordinary people would consider strange. 	For instance, we see space as flat, meaning that if we look at a star, as far as we are concerned the star is in that direction. However physicists see space as being curved and that a straight line is not necessarily straight. We would see a brick wall as being a solid object and that the idea of walking through one would result in a sore nose. However physicists see it as being made up of mostly space, and the only reason we can't walk through it is because the nuclear forces (forces that exist inside an atom, not the force that can level an entire city) prevent us for doing so. Then there is the concept of dimensions: to us there are only three dimensions, however some scientists (and Hawking is not one of them) see that there are in fact ten, or even more, dimensions.  4) Why are so many scientists atheists 	 While reading this book I could not get past about how complex this universe is and it made me wonder why it is, with the mathematical precision of the universe, and the complexity that lies therein, that so many scientists seem to argue that it all came about by chance. Even Hawking argues, using the second law of thermodynamics, that the universe cannot move from a state of disorder to a state of order – a broken plate simply cannot mend itself. However, the argument also goes that with the Big Bang Theory (not the television show) that the universe began in a state of disorder and moved to a state of order, however the laws of physics seem to suggest otherwise because what the big bang did was sent in motion a series of laws that caused the universe to come about to what we have at the moment. However, to go into details would require some intense theoretical physics, something which I have do desire to delve into at the moment.  5) Scientists assume the speed of light is a constant 	The truth is that it is not. Okay, if light were travelling through a vacuum where there are no external forces acting upon it, then it is a constant, but that is very rarely the case. Take for instance this phenomena:   	The reason light behaves thus is because when it hits the prism it SLOWS DOWN, and when it slows down it refracts. Thus my point is proven, the speed of light is only a constant when there are no external forces acting upon it. 	So, what external forces may act upon light in space. Well, first of all there are black holes. When light hits a black hole the force of gravity is so strong that it will actually prevent light from escaping. Thus, gravity is a force that effects light and slows it down. Then there is the concept of dark matter, which are clouds of matter that do not emit light and float between the star systems. Okay, we know very little about the stuff (and it is also a theory, so it has not been proven) but my hypothesis is that if this stuff exists then would it not have an effect upon light, namely by slowing it down, which means that there is a possibility that our calculations as to the distance of stars from our own Sun could actually be wrong?  6) Scientists do not know as much as we think they know 	One of the things that Hawking stresses in this book is that theories are not actually proven. A theory is an idea that has some foundation based on mathematical calculations and empirical evidence. Therein lies the problem. Much of our understanding of the universe is based upon mathematical calculations, and it appears that if an event comes about which causes this mathematical calculation to break down, they immediately set out to try to find another mathematical equation to plug the hole. 	Take light for instance. For years we believed that light acted as a wave and suddenly it was discovered that it also behaves like a particle (a particle of light is called a photon). The same goes with matter – for years we believed that they were particles when all of the sudden we discovered that they can also behave like waves. As such, our understanding of the universe suddenly breaks down (meaning that we are not necessarily made up of atoms, but have wavelike properties as well). 	Mathematical equations have been very destructive in out modern world. Take the Global Financial Crisis for instance. A bunch of apparently really smart people create complex mathematical equations to determine when to buy and sell shares and how to make billions of dollars. However what these equations did not take into account was the fact that people could not simply continue to accumulate debt without having to pay it back and when people began to default on their loans enmass, the whole concept broke down and we were taken to the brink of financial armageddon. 	Another point goes back to Ancient Greece. Here we have the theory of Democritus, namely that matter was not infinitely indivisible (the smallest piece of matter is an atom), and then the theory of Aristotle, that is that matter is infinitely divisible. Scientists preferred Democritus' theory, however they soon discovered that you could break down the atom into protons and neutrons, and you could even break them down to quarks. So, maybe Aristotle was right after all.  7) We accept their theories because our gadgets work 	It goes without saying that their research and discoveries have lead to the computer that I am writing this on, the energy that powers our devices, and the bombs that can level entire cities. We know how to make a nuclear bomb, as well as a smart phone, so we don't question what they say, because it obviously works. However, as a friend of mine once said, it is still all based on theory, and just because something works does not necessarily mean that the theory is correct. Remember that penicillin was discovered by blind chance.  8) Nobel Prizes are simply shiny baubles that have no merit 	Okay, maybe the people that win these prizes are actually really smart, but then again, the guys who set up Long-Term Capital Management also won a Nobel prize, which proves my point.  9) Nobody really knows how gravity works 	Gravity is one of those odd forces that doesn't seem to connect with any of the other forces in our universe. As Hawking points out, there are four forces that have been identified: electro-magnetic, strong nuclear, weak nuclear, and gravity. Out of those four forces (five if you divide electric and magnetic, but since electricity will create a magnetic force, they are effectively combined) only gravity stands out. This is probably why Hawking spends so much time talking about black holes because black holes are where the gravitational pull is so strong that not even light can escape from its grasp. The other thing is that gravity does not, at least in our knowledge, have an opposing force. Gravity basically sucks, and that is all it does – it doesn't repulse as the other forces can. 	It is interesting that in some texts that I have read (maybe it is speculative science-fiction but I simply cannot remember off the top of my head) some people have suggested that gravity is actually a force from another universe that affects our universe and what it is effectively doing is sucking our universe into their universe. However, as I have said, that is incredibly speculative, and since I am not a theoretical physicist I can't really say any more on the subject.  10) The God of the Gaps is a cop-out 	The idea of the God of the Gaps is that where there are gaps in our knowledge we simply say 'oh, God did that' and think nothing more of it. This goes back to the days of paganism (and Medieval Europe) where all of the unknown forces, such as the weather, was attributed God (or the gods) and we could not know anything beyond that fact. However I am arguing that it is a cop out. Creation scientists who resort to this argument are at best lazy and at worst dangerous. The reason I say that is that it discourages research into areas that we do not understand. Okay, we may never be able to control the weather, or predict earthquakes, but that does not mean that we should throw our hands up in the air and say 'this is too hard'. 	While I may be taking a swipe at creation scientists here, I would also take a swipe at the atheists who claim that there is no God. The reason I say that is because there seems to be a fear within the scientific community that suggests that we may not be able to know everything, or that our understanding of the universe may be wrong. The problem that arises is that if we throw the idea of God out of the window and claim that the universe came about by chance, then we deny the fact that we live in an incredibly ordered universe that we can learn and understand through the development of mathematical formulae. If a formulae turns out to be wrong, that does not mean that the universe will collapse in on itself – it won't – it just means that we have to go back to the drawing board and start over from scratch.  11) Why are Creation Scientists so dogmatic 	Why is it that some members of the scientific community insist that we must take the Bible literally? The Bible is not a scientific text, and it was never meant to be a scientific text. It is a theological text that tells us how we should live with one another and how we should view God. Science exists beyond the Bible, and neither contradicts the other. Okay, granted, God has intervened in this world and done things that break the laws of science, but doesn't he have a right to do that – he created the universe? However, what the Bible tells us is that God is a god of order, and if he is a god of order then does it not make sense that the universe that he created is an ordered universe? 	So, maybe you are looking for a whiz bang conclusion to my exposition on this book, but all I can say is that what I have written above pretty much sums up what I have learnt from this book. In a nutshell (hey, this is me in a nutshell), all I can say is that what I have learnt from this book is that the world is an amazingly ordered place in which we live, and having now completed this book I am just as committed to my Christian faith as I ever was. However, if theoretical physics fascinates you, then this is certainly a book that you should give a read (though you have probably done that already). This review also appears on my blog. I have also commented on this book in my review on Interstellar.     science               281 reviews1,979 followers     February 18, 2018     "والواقع أننا قد أعدنا تحديد مهمة العلم لتصبح اكتشاف القوانين التي تمكننا من التنبؤ بالأحداث في الحدود التي يفرضها مبدأ عدم اليقين"
بدأ ستيفن هوكينج, وهو عالم في الفيزياء النظرية, في كتابة هذا الكتاب في الفترة التي كان مازال يستطيع فيها أن يستخدم صوته وهو شبه مشلول على كرسيه المتحرك, ثم وبعد فترة, وقبل أن يكمل الكتاب, خضع لجراحة شقت فيها حنجرته, ليذهب صوته وهو الشيء الوحيد الذي كان يتواصل به مع العالم آنذاك ظن في البداية أنه لن يستطيع إكمال الكتاب, ولكن أحد طلبته "بريان هويت" قام بمساعدته, ليس فقط على مراجعة المسودة, وإنما جعله أيضاً يستخدم برنامج لتخليق الأصوات, وهو ما فتح نافذة جديدة له على العالم. وها هو ذا الكتاب بين يداي, وبين يدي الملايين.   أول كتبه الموجه للعامة, يشرح لنا فيه حصيلة أوراقه البحثية,كتاب صغير الحجم الثلث الأول من الكتاب تقريباً هو مقدمة تمهيدية عن الفيزياء التي سيشرح لنا قصته معها تالياً في الكتاب, وعن المحاولات والنتائج التاريخية التي سبقت أبحاثه. ثم الثلثين الآخرين عن أوراقه البحثية, التي ارتكزت على الثقوب السوداء, والتي تعتبر نقطة تفرد خاصة حيث تكون الكثافة وانحناء الزمكان عندها لانهائيين, وتنهار عندها قوانين النسبية العامةوقد قام هوكنج بمحاولة تفسيرها باستخدام مبادئ الكم تحت اسم: "الجاذبية الكمية", وهي إحدى محاولاته لصنع حلقة وصل بين قوى ثقالة الجاذبية وبين القوى الثلاث الأخرى التي تم توحيدها معاً في نظرية واحدة سابقاً ثم ينهي بالمحاولات التي تلته لتوحيد القوى الأربعة, في نظرية واحدة, نظرية لكل شيء, تحديدا نظرية الأوتار, والأوتار الفائقة   إذن أين هو التاريخ الموجز للزمان؟ لقد أنبأتنا نظرية النسبية العامة بأنه إذا تحرك أحدهم بسرعة فسوف يمر الزمن عنده أبطأ. كما أنبأتنا بأن الجاذبية, تسبب تشويهاً في نسيج المكان لتجذب إليها الأشياء, وأيضاً تسبب تشويه الزمان, وبقربنا من مصدر قوي للجاذبية كأحد أطوار النجم كبير الحجم "الثقب الأسود", يسير الزمن عندنا أبطء من الزمن عند المراقب البعيد عند مصدر الجاذبية, وقد رأى معظمكم تطبيق هذه الفكرة في فيلم انترستلر. وهكذا فالكتاب يتعرض في بعض مواضعه للجاذبية, والجاذبية تؤثر على الزمن. الزمن الذي لن يتطرق إليه الكاتب كثيراً في كتابه إذا ما استثنيا المقدمة التي حشر فيها الحديث عن الزمن حشراً لتتوافق مع هذا العنوان التجاري, والذي وُفّق في اختياره كعنوان جذّاب. في المقدمة يعلل المؤلف كتابة هذا الكتاب, بأنه ورغم وجود عدد من الكتب الجيدة  "على أني شعرت بأن أي منها لم يكن يخاطب حقاً الأسئلة التي أدت إلى القيام بالبحث في علم الكونيات ونظرية الكم: من أين أتى الكون, كيف ولماذا بدأ؟ هل سيصل إلى نهاية ؟ وإذا كان الأمر كذلك, فكيف ستكون النهاية
وهنا تلاعب بالكلام, ليحوّل كتابه من مجرد كتاب يسرد به مسيرته العلمية في سياق البحث عن النظرية النهائية, إلى كتاب يعالج الأسئلة التي تؤرق الكل. الأسئلة التي لم يعد الفلاسفة قادرين على التعامل معها.وهذه العبارات التي تحتمل التأويل تدعم ما قلته في الفقرة السابقة عن أن العنوان مقصود به أن يكون تجاري بغض النظر عن محتوى الكتاب ومدى خداع القاري به.  ونأتي أخيراً للسؤال الأكثر إلحاحاً للمعظم, هل الكتاب للمبتدئين؟ والجواب هو لا, فالكتاب فقط لمتابعي العلوم الذين لديهم الحصيلة الأساسية عن الفيزياء, والكتاب لا يشرح تلك الأساسيات سوى بجمل عارضة, لن تمكنك من استيعاب أي شيء ولذلك قام الكاتب بإعداد نسخة أخرى من الكتاب أكثر بساطة بعنوان, "تاريخ أكثر إيجازاً للزمان" تجدونها مترجمة أيضاً أما إذا كان لديك الحصيلة الأساسية, فالكتاب ولا شك تجربة مميزة, فالكتاب مليء بالعلم في كل سطر منه, والكتاب يعتبر نصف تاريخي فمعظم ما فيه من نظريات تخطوها الآن, أو أنها لم تكن مكتملة في ذلك الحين كان الشرح سلسل, واستنباط المعلومات وترابطها يشي بمدى تمكن الكاتب وعبقريته في إعادة صياغتها بسلاسة, إلا أنه هنالك استثناء بسيط في بضع صفحات يصف فيها آخر جزء من أبحاثه, وربما يرجع ذلك إلى أن الموضوع نفسه غامض   ** الكتاب من ترجمة مصطفى إبراهيم فهمي, مترجم قدير للبيولوجي, ولكنه تجاهل قاموس المصطلحات إلى حد كبير, فقام بترجمة التعبيرات بما يراه مناسبا دون أن يرجع إلى المصطلح المتَفَق عليه بالعربية في هذا المجال الغريب عنهفنجده ينوب عن مصطلح "الأوتار الفائقة" بألفاظ أخ��ى ويظهر أيضا عدم إلمامه بالفلسفة, فقد ترجم اسم الفيلسوف "wittgenstein"إلى "ويتجنشتين", وهذا خطأ, فهذا الإسم ألماني, وفي الألمانية ينطق حرف "W" بنفس نطق حرف الـ"V" في الإنجليزيةوبهذا يصبح النطق الصحيح لاسم الفيلسوف: "فيتجنشتين", وهكذا يترجم في كتب الفلسفة العربية.    ***** "سيقولون أن الله يستطيع بقدرته بدء الكون بأي طريقة يشاء. ومع هذا فإن الله أيضاً كان يستطيع أن يجعله ينشأ على منوال تعسفي تماماً. ولكنه كما يظهر قد اختار أن يجعله يتطور على نحو جد منتظم حسب قوانين معينة. وهكذا فإنه مما يساوي ذلك عقلاً افتراض أن هناك أيضاً قوانين تحكم الحال المبدئي."
لقد تطور فهمنا للعالم كثيراً. كنا في البداية نعزو الأحداث الخارجية لقوة فوقية تعبر عنها الطبيعة, وبعدها بدأنا نلاحظ أن الأشياء تتكرر بنظام معين.وقد كانت الثلاثة قرون الأخيرة هي سعي متواصل لاكتشاف المزيد من هذه القوانين, وقد وصلت للذروة بعد أن اكتشف لابلاس في أول القرن التاسع عشر "الحتمية العلمية", أي أن كل ما يحدث في العالم من حولنا إنما هو يسير وفق معادلات رياضية تنبئنا بما سيحدث تالياً إذا ما عرفنا ما يحدث الآن.وقد أدت هذه الثقة المفرطة إلى وجود أكثر من فجر كاذب, نذكر منهم أن: "الفيزيائي ماكس بورن الحائز على جائزة نوبل في الفيزياء, ذكر في عام 1928 لمجموعة من الزائرين لجامعة جوتنجن أن الفيزياء كما نعرفها, ستنتهي بعد ستة شهور, وكانت ثقته مؤسسة على اكتشاف ديراك الحديث للمعادلة التي تتحكم في الإلكترون, وكان من المعتقد أن ثمة معادلة مماثلة ستحكم البروتون, الذي كان الجسيم الآخر الوحيد المعروف وقتها, وأن هذا سيكون ختام الفيزيائيات النظرية"
ولكن كان هنالك المزيد مما لا نعرفه, بل وهنالك أيضاً المزيد مما لن نعرفه أبداً وفقاً لمبدأ "عدم اليقين" الذي اكتشفه هاينزبرج "والواقع أننا قد أعدنا تحديد مهمة العلم لتصبح اكتشاف القوانين التي تمكننا من التنبؤ بالأحداث في الحدود التي يفرضها مبدأ عدم اليقين"      علوم               Author  1 book4,911 followers     December 17, 2018   This is an absolutely magical book, both objectively and for me specifically. I first read it when I was about 9 or 10, and ever since I've assumed that I didn't understand a thing, and read it as a childish boast. Fast forward nearly twenty years, degree and PhD in physics in hand, and I decided to give it a proper read. Much to my surprise I found that the book had permeated my brain! I remembered a huge number of the explanations, and the book resonated with the way I've thought about physics my entire academic career - I think I took in a great deal more than I first thought!As a primer to physics (I would say modern physics, but the book is a little out of date) you really couldn't ask for anything better than this. Especially when it comes to cosmology, this is possibly the best popular physics book that I've ever read. It really is a classic for a reason. It's such a concise, understandable introduction to the field that I'm determined to get my girlfriend (a linguist with no real interest in physics) to read it. Not just because I think she'll understand it, but because I think she will enjoy it! One peculiarity of the text is Hawking returning to the concept of God (with a capital G) over and over again. In some ways this feels like a transitional text, marking the passing of the public generation for whom the church determined the order of all things, and the coming of the current, secular generation. Unlike other authors (looking at you, Dawkins) Hawking always does so in a way that feels respectful while also forcefully stating his scientific case. It's quite feat of writing, much like the rest of the work. You really should read this, it's fantastic.     favorites physics-books               1,040 reviews1,678 followers     August 7, 2017   خیلی وقت بود دنبال یه کتاب بودم که نظریات فیزیک جدید رو توضیح بده. زیاد از اصل عدم قطعیت و کوانتوم و نسبیت و نظریه ی ریسمان ها و سیاهچاله و کرمچاله و انفجار بزرگ و غیره و غیره شنیدیم، ولی شاید از هیچ کدوم تصور درستی نداشته باشیم. این کتاب خیلی از این نظریات رو مفصل توضیح میده.استيون هاوكينگ يك مستند سه قسمتى داره، به نام "به سوى كيهان، همراه با استيون هاوكينگ" با صداى بى نظير بنديكت كامبربچ، كه بيشتر مباحث اين كتاب رو، بسيار بسيار ساده تر توضيح ميده. توصيه مى كنم كسانى كه تازه مى خوان مطالعات كيهان شناسى رو شروع كنن، قبل از اين كتاب اون مستند رو ببينن.Into the Universe With Stephen Hawking نکات منفی مشکل اصلی کتاب، اینه گاهی زبانش خیلی فیزیکی میشه. به نظر میرسه آدم باید اطلاعات زیادی از فیزیک داشته باشه تا حرف کتاب رو بفهمه. من دانش فیزیکم در حد سوم دبیرستان و چیزهایی که جسته گریخته از این ور و اون ور خونده بودم هستش، در نتیجه شاید نصف کتاب رو آن چنان که باید و شاید نفهمیدم. خود استیون هاوکینگ میگه که ناشر بهش گفته بود: "به ازای هر فرمولی که در کتاب به کار ببری، فروش کتاب نصف میشه" و درسته که تقریباً هیچ فرمولی در کتاب به کار نرفته، اما همچنان زبان کتاب سنگینه. در مؤخره ی کتاب، نوشته بود این کتاب یکی از "ناخوانده" ترین کتاب های تاریخ ادبیاته. یعنی ��ده ی زیادی خریدن کتاب رو و حتی ادعا میکنن خوندنش، ولی در حقیقت نخوندنش! میشه فهمید چرا.  نکات مثبت اما جاهایی که دانش ناقص فیزیکم یاری میکرد یا خود کتاب ساده بود، خیلی خیلی عالی بود کتاب. قصد دارم یه بار دیگه بخونمش به همین زودی ها. تاریخ فیزیک از دوره ی ارسطو تا نیوتون تا آینشتاین و هایزنبرگ، مباحث کیهان شناسی، مثل گسترش جهان یا محاسبه ی فاصله ی کهکشان ها، برخی از مباحث فیزیک جدید، مثل اصل عدم قطعیت و نسبیت، جزء جاهایی بود که کمابیش فهمیدم و خیلی لذت بردم. گاهی هم مطالب علمی رو کلاً رها میکرد و شروع میکرد به تعریف زندگی خودش. مثلاً میگفت این نظریه در فلان تاریخ مطرح شد، در اون زمان من با دختری آشنا شده بودم و میخواستم باهاش ازدواج کنم و شروع میکنه ماجرای خودش رو تعریف کردن. کتاب بعدی از این نویسنده، "کیهان در پوست گردو" هستش که قصد دارم به زودی بخرم.     علوم-طبیعی-ریاضی               Author  28 books13.4k followers     November 3, 2011   Apparently this book tops the world list of "bought but not read", which may explain why it's so universally acclaimed as a work of genius. If you know anything much about relativity or cosmology, it comes across as a potboiler, admittedly a well-written one with a great final sentence. I wasn't impressed.But... without it, we would never have had MC Hawking. If you haven't come across him, start with the lyrics to "E = MC Hawking". Then buy A Brief History of Rhyme.     science               1,559 reviews8,659 followers     December 13, 2015    “The universe doesn't allow perfection.” ― Stephen Hawking, A Brief History of Time  I know. I know. I both loved and hated this book. I definitely should never have read this book, cut the pages, opened the box, etc.. Somehow Stephen Hawking has written a book that gently fluffs the tail on Schrödinger's cat (or perhaps Schrödinger's cat is fluffing Dr. Hawking).  Look, no doubt the guy is a genius and has a fantastic story (ALS, computer voice, nurses, Black Holes, strippers, movies, etc). My problem is the wussification of a large scientific narrative by one of Big “P” Physics primary scientists. Let someone else write a pop-GUT/Blackhole/Big Bang story. Let another writer do the pop-up Children's book with the scratch-n-sniff singularity, the rotating black hole, the pull-out universe.    I want Dr. Hawking doing smart stuff. Let Bill Bryson write the summary science. But it is too late for me. I already crossed the damn event horizon. I've just become entangled with his book, so my "observer state" now corresponds to the damn book and the damn book review being both five stars and 1 stars is no longer a possibility; my reader state is entangled or linked now with my own review so that the "observation of the book review's state" and the "review's state" correspond with each other. I am finished. Hey, now to go see some movies about blackholes and wormholes and assholes.     2014               87 reviews49 followers     April 26, 2021   This is the first book I have ever read about science.This is one of the best selling book of the century.I have found it really infomative and my interest in science seems to build. This book is free from mathematical equations (except E=mc2) which is the best thing about the book. This book is so simple that even a lay person with basic knowledge of science can understand it.  Stephen Hawking, the author of the book, is one of the well renowned scientists of the century after Einstein. Some people even called him the successor of Einstein due to his work in the field of science. In this book, Hawking talks about black holes, worm holes, time travel, cosmic background radiation (CBM), uncertainty principle, expansion of universe, space and time (or simply space-time), origin and fate of the universe, forces of nature and the most important The Grand Unification Theory (the theory of everything) which is the biggest unsolved mystery of the present time.     A brief intro to author, Stephen Hawking  This book is really amazing and is popular in both science and non-science related people. I enjoy it a lot and I would like to recommend it to all the science and nature loving people. And I hope they will also enjoy it.     2019-reads non-fiction personal-library-books               1,804 reviews452 followers     May 30, 2022   This popularization book provides us with a portrait of the latest discoveries that have shaken the scientific world over the past hundred years: General relativity, quantum mechanics, the Principle of uncertainty, black holes, quarks, string theory, etc., enough to answer many questions: what will become of the the our universe? How was it formed? Why is CERN so determined to accelerate particles in a tunnel several kilometres long in Switzerland?I will not claim to have assimilated all the concepts in a single reading. Still, the book allows me to have a good idea of the stakes and the research. Therefore, I recommend it to any science lover, especially as some of the theories explained will soon celebrate their century of existence and have not yet reached ordinary people.    2021-readings brit-and-related e-4               Author  6 books1,184 followers     February 7, 2022   Cam tot ce știu din / despre cosmologie provine din scrierile lui Hawking. Îndeosebi din acest volum care a fost un bestseller absolut. O glumă afirmă că toată lumea bună l-a cumpărat, dar foarte puțini l-au citit. Scurtă istorie a timpului ar fi, așadar, cel mai puțin citit bestseller dintre toate. Nu cred că pe autor l-a afectat prea tare acest amănunt nesemnificativ.Mă aflu în situația bizară că știu multe fără să înțeleg totul. Știu, de pildă, că fizicienii încearcă să ofere „o descriere completă a universului”. Mai știu că o astfel de descriere nu este, deocamdată, cu putință. Mai știu că Hawking a fost obsedat de realizarea unei teorii fizice unificate (mecanica cuantică + teoria relativității generalizate), fără de care sus-numita descriere nu este posibilă. Prima teorie (cea cuantică) susține că „universul e guvernat de întîmplare”, fapt pe care Einstein nu l-a acceptat niciodată. A doua oferă o viziune deterministă. Deși ne-am obișnuit să gîndim în termeni finaliști (omul ar fi scopul creației), știu, de asemenea, că evoluția universului nu este finalistă. Evoluția nu are un scop, o „intenție finală”: apariția unei conștiințe care să constate frumusețea și armonia acestei lumi. Pentru Pico della Mirandola, în schimb, acest lucru era evident: „Te-am așezat, Adame, în mijlocul universului, ca să-mi poți contempla măreția” (De dignitate hominis). Știu că fizicienii au propus, la sfîrșitul anilor 60, un așa-zis Principiu antropic (îl comentează într-un articol și I. P. Culianu), care li s-a părut unora argumentul suprem al unei evoluții „dirijate după un plan” (un argument creaționist), dar mai știu că acest Principiu (comentat cu entuziasm odinioară de Penrose și Hawking) nu dovedește nimic. Formularea lui pare o imensă tautologie: „Vedem universul aşa cum este fiindcă, dacă ar fi diferit, noi nu am exista să-l observăm”. Altfel spus: „Vedem universul aşa cum este întrucît existăm". Afirmația lui Hawking seamănă cu alta, la fel de misterioasă, tot a lui: „Dezordinea creşte cu timpul, întrucît noi măsurăm timpul în direcţia în care dezordinea creşte”. Nimic mai limpede... În fine, mai știu ce a afirmat Roger Penrose despre singularități și găuri negre (universul nostru provine dintr-o singularitate): „O stea care suferă un colaps datorită propriei gravitaţii este prinsă într-o regiune a cărei suprafaţă se reduce la dimensiunea zero. Şi deoarece suprafaţa regiunii se reduce la zero, aşa trebuie să se întîmple şi cu volumul său. Toată materia din stea va fi comprimată într-o regiune cu volum zero, astfel că densitatea materiei şi curbura spaţiu-timpului devin infinite. Cu alte cuvinte, există o singularitate conţinută într-o regiune a spaţiu-timpului numită gaură neagră”. Cam atît...                   1,238 reviews2,223 followers     February 6, 2018   Manny says this book is in the "bought but not read" category for most people. Well, I'm proud to say that I bought and read it, that too in nearly one sitting - back in my geeky days, when I used to get a sexual high just from solving a hard maths puzzle.Unfortunately, I don't remember much of it (time for a re-read!) but I remember taking away the idea that time is a sphere. Being Indian, I loved this - because we are strong champions of cyclical time. Also, if time and space are both curved, it creates the possibility of jumping from one place and time to another; which is just delicious. (I bought a pirated edition of this book for 25 rupees from the roadside at Connaught Place in New Delhi. The vendor asked for 50, I said 25, and the bargaining was just starting when he spied a policeman approaching - so he let me have it for whatever I was offering! "Time" was on my side.)     science           August 30, 2007   Hawking is a brilliant physicist and a true expert in explaining highly complex aspects of our physical universe in terms that can be understood by most lay people.Where Hawking fails, in my opinion, is his hubris. He proceeds in to the realm of metaphysics and religion in several portions of this book. For instance, in his chapter on the "arrow of time", he states that, essentially, the universe can only move in one direction of time. It cannot go backwards. He also states that this limits the powers of God himself. Now, Hawking never qualifies those statements by defining "God". However, if he is talking about the Biblical God, how can you honestly think you're so intelligent as to place limits on a limitless being? If God is so powerful as to have created the universe and all the physical laws, why wouldn't he be powerful enough to change those laws any time he chooses? It is the same concept as a scientist creating a computer simulation of the universe. The scientist can, at any time during the simulation, alter the underlying framework of the simulation, effectively changing the physical laws that simulated universe operates under. Now, whether you believe in God or not, the mere fact that Hawking has the audacity to think he can assign limits on a limitless being should cause you some concern. Hawking, because of his fame and brilliance, is a man that people listen to when he speaks. That gives him immense power over the minds of his readers. He should be more careful in choosing his words. When Hawking sticks to his strengths, however, the book is second to none. Hawking truly has a gift of explaining the powerful forces that shape our lives in ways anyone can understand. If this book had been edited better, it would have received a few more stars from me, but I can't reward stubborn scientific pride resulting in false assumptions.                   1,281 reviews21.4k followers     December 9, 2007   The main idea to take away from this book is that time has a clear direction. Entropy is the idea that the universe moves from highly ordered states to less ordered states. If you take the lid off a bottle of perfume, and leave it off for a few days the perfume will go from being highly ordered (all in the bottle) to highly disordered (all over the room). Hawking uses this idea to explain why travelling back in time is impossible. It requires very little energy to knock a glass over and smash it - but think of how much energy it would take to make the glass jump back into place - all of the bits perfectly back where they were prior to the glass breaking. It would be impossible - and that impossibility is what gives time its clear direction. Philosophically, I tend to feel that the book makes far too much of the Uncertainty Principle. But that is another story. This isn't the easiest book to read in the world and is probably the most bought science book of all time while also being the one most likely gave up on after a chapter or two - but it is a fascinating read all the same.     science               179 reviews61 followers     July 7, 2021   Only Hawking could write this book - simple, to the point and extremely resourceful. Cosmology is not an easy subject neither can everyone understand its deep connotations. Hawking made it understandable in the most layman terms possible. Blog | YouTube  | Instagram | Facebook | LinkedIn                    1,196 reviews1,568 followers     November 25, 2017    يسعى هوكينج في هذا الكتاب لوضع خريطة أو مسار كوني، بداية من الكيفية التي بدأ بها الكون، إلى وضع الاحتمالات التي سينتهي إليها، وتوضيح ما بينهما من أمور كونية فلكية. بدأ الكتاب بالحديث عن الانفجار الكبير والمتفردة التي بدأ منها، وفيما بعد سيتناول احتمالات تنفي وجود متفردة أولية تقول بأزلية الكون، لكن المتفق عليه بشكل كبير في حالة وجود المتفردة أو لا أنه ثمة انفجار كبير بدأ منه الكون ثم تمدد، ومن الأشياء التي ستناقش بعد هذا هو الكيفية التي تمدد بها الكون. الانفجار الكبير كما قال هوكينج لا ينفي وجود خالق.  ثم يتحدث عن المكان والزمان، ويتناول فيه نظرية أرسطو الأولية التي دحضها جاليليو ثم نيوتن بقوانينه عن الحركة، ومن ثمَّ تناول بالحديث نظرية النسبية لآينشتين، الخاصة بتعارضها من قانون الجاذبية، والعامة المتسقة مع ذاتها. ويتناول بعدها اكتشاف هابل بأن الكون يتمدد، بل ربما يكون لها نهاية حسب نظرية فريدمان. وكانت هذه البداية للنظر إلى أن كوكبنا قطرة ماء في محيط الكون الفسيح، وتمت البرهنة بشكل كامل من قِبل هوكينج وبنروز على أنه لابد من بداية في الزمان على أساس أن نسبية آينشتين العامة جزئية واحدة من النظرة الكونية. وكان مبدأ الريبة الذي قال به هايزنبرج وكم بلانك يمهدان الطريق لميكانيكا الكم، وبالرغم من أن آينشتين مُنح نوبل لمساهمته في نظرية الكم، لكنه كان معارضًا بشدة لها لوقوعها في فخ العشوائية، فلم يتقبل أن يكون الكون محكومًا بالصدفة، ومقولته: "إن الله لا يلعب النرد" توضح أفكاره. لكن هذا لا يمنع أن معظم العلماء تقبلوا ميكانيكا الكم، يقول هوكينج: "ليس لدينا بعد نظرية متماسكة كاملة توحِّد النسبية العامة وميكانيكا الكم، ولكننا نعرف بالفعل عددًا من الملامح التي ينبغي أن تكون فيها"ويفصِّل الكاتب الحديث عن ميكانيكا الكم، فيتناول الجسيمات الأولية وقوى الطبيعة الأربعة.ثم ينتقل للحديث عن الثقوب السوداء وهي جد شيقة، وفي هذا الجزء يستفيض هوكينج في الشرح والتحليل في كل ما يختص بالثقوب السوداء، وربما هذا لأنه كان مهتمًا بشكل كبير بها واكتشف بعض الأشياء حولها.في أحد الفصول بعنوان: أصل ومصير الكون، وهو فصل مميز للغاية، وإن رأيته منفصل عن الكتاب بإعادته جزء بسيط باختصار مما قاله قبل هذا مع توضيح وتناول بعض الأشياء الجانبية، وفي هذا الفصل مناقشة بشكل أكبر للخالق، وإن توصل في النهاية إلى عدم نفي أو إثبات أي شيء، فكما هو الأمر في الفلسفة الإمر قائم على احتمالات لا يمكننا معرفة أيهما أصح، وعلى هذا أيضًا سينتهي الكتاب. ثم بعد هذا يتناول البعد الزماني والمسار الذي يسير فيه الزمان فيما سيسمى بسهم الزمان المطلق للأمام، ومع حديثه عن الثقوب الدودية يضع احتمالات للسفر عبر الزمن وإن لم يستطع أحد البرهنة على هذا لكنه احتمال كبير، لكن الإشكالية تقع في كيفية السفر، وهل يمكن السفر للماضي أم للمستقبل فقط؟ ويدور هذا الجزء حول هذه النقطة بتحليله الأبعاد المكانية الثلاثة والبعد الزماني الواحد وما يمكن أن يكون من أبعاد أخرى. ويأتي الفصل الأخير من الكتاب عن توحيد الفزياء، وهل يمكن أن نكتشف ما يجعل العلم متمكن من معرفة الأشياء بدقة وثقة متناهية؟ وقال بأن الفلسفة لم تعد تثمر في هذا المجال، بل اضمحلت واضمحل دور العقل في التقدم وفي مجاراة تطور العلم.يقول هوكينج في الختام: "وعلى كلٍّ، لو اكتشفنا فعلًا نظرية كاملة، فإنه ينبغي بمرور الوقت أن تكون قابلة لأن يفهمها كل فرد بالمعنى الواسع، وليس فقط مجرد علماء معدودين. وعندها فإننا كلنا، فلاسفة وعلماء وأناسًا عاديين، سنتمكن من المساهمة في مناقشة السؤال عن السبب في وجودنا، نحن والكون. لو وجدنا الإجابة عن ذلك، فسيكون في ذلك الانتصار النهائي للعقل البشري، لأننا وقتها سنعرف فكر الخالق." كتاب عظيم ومبسط بشكل جميل، رحلة ممتعة وشيقة في محاولة لمعرفة الكون وحجمنا فيه، ومحاولة للتوصل للخالق، وإن باءت الأخيرة بالفشل، فقد خرجت أشد حيرة وانقسامًا أكثر مما دخلت، ويظل العلم والفلسفة والدين غير قادرين على إثبات أو نفي شيء عقليًا، كل شيء يخضع للاحتمال في كل الأحوال.       2017 علوم كتب-متنوعة               85 reviews149 followers     June 26, 2020   Theoretical Physics from the master himself. It's a great summary, but you need a little background knowledge to understand all the chapters. It's a summary of astrophysics, theoretical physics, and cosmology, and it's hard grasping it all in 200 some pages. I wish it was a little longer.The definitions at the end of the book are very useful. You will not regret reading the book, but you need some peace and quiet while reading it in order to hopefully understand it. I've read the A Bantam Book Edition published April 1988 / A Brief History of Time by Stephan W. Hawking / 226 pages / 56,997 words.     astronomy cosmology history               124 reviews986 followers     June 1, 2018   A pesar de estar escrito para un público "no científico" no puedo decir que creo que sea un libro accesible al 100%. Es cierto que Hawking cumple su promesa de no incluir ni una fórmula matemática (excepto la conocida fórmula sobre la teoría de la relativdad E=MC²) pero los conceptos en sí pueden ser difíciles de imaginar y comprender. De toda la información que Hawking intenta explicar en este libro, ha habido cosas que notaba que se me escapaban. Quizá con algo más de material gráfico habría resultado más sencillo.Aún así, el concepto general de los temas que trata es impresionante si te apasiona conocer la esencia del universo. Realmente había momentos en los que dejaba de leer para procesar algunos conceptos y no podía menos de maravillarme.    2018 non-fiction               420 reviews511 followers     October 22, 2019   كتاب سلس ويطرح المادة العلمية بطريقة شيقة.لحظة!   إذا كتبت مراجعة من هذا النوع سأبدو ذكيا ورائعا. لكنها ليست الحقيقة، فلست ذكيا ولا رائعا، وإنما قارئ متوسط الاستيعاب، أشعر بحكة في دماغي عندما تتعقد الأمور وتطقطق جمجمتي من الداخل إذ يحاول مخي الصغير أن يتمدد ليستوعب بعض المعلومات، ولكنه لا ينجح دائما. ليس هذا دأبي مع كل الكتب التي تناقش موضوعات علمية، فقد مضيت في كتاب الكون لكارل ساجان من الغلاف إلى الغلاف دون أي عسر. أعرف أن ساجان طرح المواضيع ذاتها ولكن من زاوية فلكية، بعكس هوكينغ الذي لا يحيد عن الفيزياء قيد أُنملة. هناك حديث مطول عن الذرات والجزيئات والفوتونات ومواضيع أخرى لم أكن أبحث عنها بصراحة. ماسبق لا يعني أن الكتاب لم يضف إلى معلوماتي بل على العكس إذن ناقش الكتاب أهم نظريتين لشرح كل ما يجري في الكون: النظرية النسبية وميكانيكا الكم. تحدث هوكينغ أيضا عن الثقوب السوداء والثقوب الدودية والانفجار العظيم (ليس انفجارا بالمعنى الحرفي على فكرة) والتأثير المعكروني الموضح بالصورة أعلاه. هناك أطروحات حول بداية الكون ونهايته وإيراد لأهم النظريات التي اُكتشفت في ذلك الميدان. هذا إلى جانب الجانب التأملي في تاريخ العلم وتطور الفكر لدى الإنسان والتحدي الكبير المتمثل في مواجهة التيار التقليدي الذي يتصدى لأغلب الأفكار الجديدة. كتاب يستحق القراءة، مع الكثير من الصبر لأصحاب الميول الأدبية الذين اعتادوا على النوم أو العبث في آذانهم في حصص الفيزياء. الكتاب يستحق العناء لكنني توقعت شيئا أشد تبسيطا وأكثر إمتاعا.                   4,138 reviews1,004 followers     July 24, 2013   Stephen Hawking's book is easy to read, but harder to comprehend. In every chapter came a point where my brain couldn't hold another permutation of a theory, and as the book progressed, I ended up taking the same approach as I do when reading a Norse saga for the first time. With sagas, I just read, even if my brain doesn't seem to retain all the information about who is related to who and what they named their horse. Inevitably, at the end, I have a reasonable basic grasp of the saga, and then I have to read it over again to fit more information into that basic understanding.I don't know if the same will hold true here, but it's a nice hope.     non-fiction science-fact               Author  3 books5,433 followers     February 10, 2017   A classic text where the amazing Stephen Hawking explains string theory and quantum mechanics "for dummies." Highly readable and even comical, it is a superb read. I need to go back and read this one again myself!    american-20th-c geek-classics non-fiction               718 reviews500 followers     April 5, 2021    Space opera   
 The Milky Way arch emerging from the Cerro Paranal, Chile, 3 December 2009. Author: Bruno Gilli/ESO
  A highly articulate summary of the history of astrophysics and its breakthroughs from its origins to 1996 (updated edition). I wish I had had such an introduction to physics and chemistry when I was in secondary school and high school! The layout of the book allows a layman to follow the development of the discipline and its fields over time, while Stephen Hawking never scorns an evocative image to give a better notion to the reader of what, say, the electromagnetic spectrum, thermodynamics or gravity are all about. I definitely recommand to all of you in awe before the universe and its strange marvels :)   
 Detail of Eagle Nebula
   Summary:  Chapter 1: Our Picture of the UniverseChapter 2: Space and TimeChapter 3: The Expanding UniverseChapter 4: The Uncertainty PrincipleChapter 5: Elementary Particles and Forces of NatureChapter 6: Black HolesChapter 7: Hawking RadiationChapter 8: The Origin and Fate of the UniverseChapter 9: The Arrow of TimeChapter 10: Wormholes and Time TravelChapter 11: The Unification of PhysicsChapter 12: Conclusion -----   
 Black Hole elements
    
 Image of the night sky above Paranal, Chile on 21 July 2007, taken by ESO astronomer Yuri Beletsky
    
 Galaxies in the Hubble deep field (detail)
  Soundtrack: Lux Aeterna - György Ligeti      astrophysics audiobook guidebook               112 reviews91 followers     December 22, 2016   Without a doubt a masterpiece!It's just incredible how Hawking explains to us the complex and mindboggling secrets and concepts of physics and our universe, with amazing wit , clarity, and simplicity.The questions that we all used to ask to ourselves and to our parents, about god, about time, life and it's meaning, the sky, stars, about who created our universe and about it's beginning, about our fate......we had that unique quality called curiosity when we were children, but then, as we grew up , we somehow lost that ability to ask and question, we no longer felt the same thirst for knowledge and a deeper understanding of things as we reached adulthood, those questions we abandoned as our busy lives got in our way.. But there are quite a few people, whose curiosity and desire to find out more, to explore the truths of this vast universe, never dies. They are always always on the lookout for answers to questions deemed unanswerable , and then to ask new questions , that one by one, fills the gap between us and the truth and makes our understanding of this universe and it's secrets a bit more clearer and deeper,  Stephen Hawking is one such blessed genius! In this book, Hawking familiarise us with the possible beginning of the universe or space-time , which is called the Big Bang Singularity, the Black Holes with extremely strong gravitational force so that even light can't escape from it, the reasons why we are at this time and space of the universe [ this might be because that the present condition, universe ( if there are other universes), and dimensions are the only configuration which allows the existence of intelligent beings like us who can observe and ask these questions], the long quest for a Grand Unification Theory ( that will explain the whole universe completely ) which still continues, and so many more fascinating and incredible stuff. The writing style is highly enjoyable, Hawking is a great teacher and a wonderful writer, his wit and engaging writing makes me forget that I'm reading a scientific book! Highly recommended to everyone who wants to know a little more about this universe and it's secrets. 5 stars.    2016 books-i-own science               348 reviews79 followers     November 16, 2018   Ένα πολύ ωραίο βιβλίο εκλαϊκευμένης επιστήμης που εξηγεί βασικές έννοιες της Φυσικής και πώς αυτές διαμορφώθηκαν ανα τους αιώνες - με κύρια κατεύθυνση στην μοντέρνα Φυσική που για πολλούς είναι ακατανόητη. Μου άρεσε πολύ ο τρόπος γραφής και το χιούμορ του Χώκινγκ αλλά θεωρώ πως κάποιος πρέπει να έχει κάποιες σχετικά γερές βάσεις Φυσικής για να το κατανοήσει. Θέλω πολύ να ξαναδιαβάσω τα κεφάλαια για την θεωρία των χορδών και τις μαύρες τρύπες γιατί νομίζω πως πολλά πράγματα τα έχασα. :(     brace2018 readathon18               275 reviews242 followers     July 30, 2020   ★★★ /5This was an interesting and informative book, but sadly I just couldn‘t grasp everything that it tried to say.     read-in-2020       Displaying 1 - 30 of 11,529 reviews
A Brief History of Time
https://www.goodreads.com/book/show/3869.A_Brief_History_of_Time
https://www.goodreads.com/book/show/10638.The_Road_to_Reality
The Road to Reality: A Complete Guide to the Laws of th…
2004-01-01
Author
<div><div><div><article><div><section><a href="https://www.goodreads.com/user/show/1713956-manny"></a></section><section><p>Author <i></i>28 books13.4k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/60011150">September 5, 2011</a></section><div><p>Many of my all-time favourite books make the list because they show you what it's like to be inside the mind of an extraordinary person. While you're reading them, Churchill's <i>History of the Second World War</i> and Yourcenar's <i>Mémoires d'Hadrien</i> let you be a great statesman at a pivotal moment in history. Simone de Beauvoir's autobiography, more than any other book I know, gives you the feeling of being a major literary figure. Polugayevsky's <i>Grandmaster Preparation</i>, which many chessplayers treat almost as a sacred text, is the only truly honest account I've seen of how a top Grandmaster thinks. <p>Penrose belongs in this select company: I finally believe I have some idea, no matter how faint, of how a great mathematical physicist sees the universe. Like the other books, it's not an easy read. You can't build up this kind of picture without including a huge number of details; if you took them away, the whole texture of the world would disappear with them. Churchill needs the maps, troop movements and political networking. De Beauvoir has to assume (in my case, alas, incorrectly), that you're conversant with most of French literature. And if you removed the chess from Polugayevsky, there wouldn't be any story.</p><p>In Penrose's case, it's mathematics and physics: he resolutely refuses to dumb it down, and includes a seriously frightening quantity of Greek letters. If it really were true that every equation halved your sales, he would not have sold a single copy. What saves him, and makes the book readable to non-experts like me who at least have some mathematical background, is his uniquely visual way of experiencing mathematics. Penrose can obviously hack the equations, but he also has to <i>see</i> them, and he is astonishingly resourceful at coming up with visualisations. The ones I liked most had to do with Special Relativity. You may recall this fairly well-known picture by Escher:</p><p></p><p>What I didn't know was that it illustrates the "hyperbolic geometry" which underlies Einstein's Special Theory. In Special Relativity, the speed of light is an absolute limit, so velocities can't simply be added: the correct formula for combining them is the one shown in the picture. You can add any number of fish together and never reach the edge; similarly, no matter how many time you add a velocity to itself, you never get to the speed of light. Believe it or not, the diagram exactly models the equation! And another geometrical argument he used here is nearly as beautiful. A great deal of nonsense has been written about the "Twins Paradox" <a href="http://www.goodreads.com/review/show/163521323">(for example, by Robert Heinlein)</a>. Penrose's explanation is wonderfully concise and elegant. In Minkowski-space, a straight line is counterintuitively the <i>longest</i> distance between two points. The twin who flies out into space has a less straight world-line than his twin who stays at home, so he ages less. Thanks to Penrose, I can now <i>see</i> it.</p><p>It turns out that theoretical physics is anything but a dry technical discipline: you come away feeling that these people are visionary poets who have chosen to write in mathematics rather than ordinary language. Blake is one comparison who came to mind, and I can't resist the temptation to juxtapose Blake's image of God:</p><p></p><p>with Penrose's:</p><p></p><p>If you're wondering what God is doing, it's actually pretty much the same as in Blake's version: the picture dramatizes the extremely low entropy of the Universe immediately after the Big Bang. I had not previously appreciated how remarkable this is, and the puzzle it represents is central to Penrose's exposition. Once again, the picture isn't gratuitous. He's illustrating, in a humorous way (the book is often funny), an extremely serious point.</p><p>As I've said, it's not an easy read. It demands a great deal of concentration, and I think I must have spent at least two or three hours a day over the last month ploughing my way through it. A lot of that time, I was supposed to be doing other things, but I'm glad I ignored them and read Penrose instead. He's changed my way of looking at the world as much as Dante did when I read <i>The Divine Comedy</i> in 1999.</p><p>Now, if only it were in <i>terza rima</i> with animated illustrations by Gustave Doré and Terry Gilliam. Then it would truly be perfect.<br />_____________________________________</p><p>We had another CERN physicist to dinner last night, an Australian post-doc who's working on validation of the Standard Model. I asked her if she'd read <i>Road to Reality</i>. </p><p>"I stopped reading popular science books when I was an undergraduate," she said apologetically. </p><p>I said it wasn't really a popular science book, and she opened it for a few seconds. "Hm, yes, it does seem to have quite a lot of equations," she muttered doubtfully, and then she put it down again. </p><p>Something seems to have gone slightly wrong with the marketing campaign for this book: laymen think it's a book for physicists, and physicists think it's a book for laymen. I'm reassured to see a fair sprinkling of reviews here from people who give every appearance of having read and enjoyed it.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1713956?shelf=life-is-dante">life-is-dante</a> <a href="https://www.goodreads.com/review/list/1713956?shelf=linguistics-and-philosophy">linguistics-and-philosophy</a> <a href="https://www.goodreads.com/review/list/1713956?shelf=science">science</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/16160897-warpdrive"></a></section><section><p>272 reviews380 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/868946760">August 4, 2016</a></section><div><p>I am finished, finally. All the 1050+ pages of this ambitious behemoth - including many exercises. What a ride!... <br />Finished? Well you are never finished with such a book, titled “The road to reality” but actually providing more than that: providing nothing less than a “road-map” to reality, and opening to the reader new beautiful vistas in modern mathematics and physics. I am sure that I will come back to this book in the future, as a source of inspiration and for future reference.<p>Before I start, I must confess that it feels slightly ridiculous for me to critique such a monumental work by a crazy genius like Penrose, who clearly lives in a higher realm of consciousness than the large majority of us common mortals. Never mind – the best I can do is to describe my personal, deeply humbling experience in reading this amazing piece of intellectual prowess. Penrose is clearly the Mozart of mathematical physics: genius, craziness, wild imagination and pure technical virtuosity all combined into a unique intellect. </p><p>Let me start by highlighting some of the peculiarities of this book (due, in my personal opinion, much to editorial/commercial choices/pressures, and only partially to personal choices by the author himself). This is also important to the proper positioning of this book within the overcrowded (and of hugely varying quality) world of popular science books: </p><p>A) this book is sold as a science “popularization” (probably with the objective to attract as wide an audience as possible): in reality this book requires a significant amount of background knowledge in mathematical physics; in fact there are some sections where the equivalent of a full maths/physics degree would be required to fully appreciate all the subtleties of some of the subjects being treated. I would personally recommend, as a prerequisite, the following minimum:<br />- calculus (including multivariate)<br />- ordinary and partial differential equations (at least at rudimentary level)<br />- complex analysis<br />- linear algebra<br />- basics of topology<br />- ideally, differential geometry at basic level<br />- in the physics area, some prior exposure to Maxwell's equations, the Lagrangian and Hamiltonian formalisms, the basics of quantum mechanics and relativity (at least special) would also be a great help. <br />If a reader tried this book with no prior exposure to any such topics, I am afraid that it all might prove a very steep learning curve indeed. I had all the above pre-reqs, and still it was, for me, an occasionally demanding if not challenging book in terms of required focus, time and intellectual stamina. But this is also a strength of this book - one of its greatly rewarding aspects is that the author does not refrain from exposing the reader to real maths (some of the exercises can be pretty hardcore), and to get into the heart of modern physical theories such as QFT and GR, if you want the real thing, you simply can't avoid getting into some real maths. </p><p>B) this book is not really a textbook, or at least not an ordinary textbook: it lacks the necessary structure and flow, and (too) many important derivations are left as exercises. The depth of mathematical analysis and rigour are uneven, and they seems also highly dependent on the occasionally whimsical personal level of the author's interest in the subject. Moreover, the formal treatment of many subjects is highly original and something that, unless you have had some previous exposure to them, might be confusing and certainly not easily reconcilable with what standard textbooks present. But this is part of the beauty of this masterpiece. </p><p>C) this book, contrarily to what stated in the title, is not a “complete” guide to the laws of the Universe. While managing to concentrate so many sophisticated and fascinating subjects into a single book, and at a serious level of detail (which is no mean feat, and something quite unique), I think that Penrose should have written two books (one on the mathematical underpinnings, and a separate one on the physical aspects) rather than trying to concentrate such a massive amount of information in one single big book. <br />This approach (admittedly less palatable from a commercial standpoint) would have allowed him to expand some important areas that he has unfortunately neglected in his otherwise magnificent book (such as finiteness and re-normalization issues in QFT) and which would have also allowed him to include other subject matters too – for example, the coverage of thermodynamics focuses mainly on the statistical view of the Second Law, neglecting all the other elements. <br />But make no mistake - this book feels like a "War and Peace" of mathematical physics – a colossal enterprise that just keeps giving and giving, a treasure trove of original insights, beautiful hidden connections, amazing stories and revelations. A fantastic and detailed exploration of quantum physics, relativity, of the current trends in the attempts to unify the two, and of cosmology. An exhilarating intellectual adventure in the company of a crazy genius.</p><p>Let me now make a few comments about the author's peculiar personal style and approach:<br />- Penrose's prose is beautiful, even if considered from a purely literary perspective; often very clear even if sometimes a bit too concise; it usually flows very smoothly, and it occasionally even acquires some poetical undertones in sections where aspects of philosophy of science and philosophy of mathematics are treated with insightful passion.<br />- Penrose relies heavily on a diagrammatical/pictorial/visual/topological representation of the concepts being treated. In doing so, many beautiful, eye-catching and highly informative hand-drawn diagrams/pictures are presented to the user. This approach generally works very well, but there are instances where (in my personal opinion) the most intuitive and simplest way to learn/teach a new concept is to present it analytically (in mathematical format), and where the purely visual approach might be quite limiting if not outright confusing. For example, the visual explanation of the concept of “covariant derivative”: while important and helpful, is in my opinion by itself not sufficient to get a real appreciation of the mathematical features of this entity: its analytical derivation, and its expression using the Christoffel symbols, would have actually better clarified its tensorial nature. <br />- In order to condense as many subjects as possible within the constraints of the space allowed by one single book (even one of 1050+ pages) Penrose has left the derivation of many important results as “exercises”. The exercises are therefore very important, they are a must in order to get a full appreciation of the underlying theory, and some of them are beautiful and rewarding (like exercise 22.32, which entails a beautifully elegant derivation of the Laplacian in spherical coordinates, using the curved metric and covariant derivatives). But some others should not have been left as exercises, and they seem no more than an editorial cop-out: there is one exercise that is even asking the reader to complete a significant derivation step of the GR field equations! (thankfully there is a website where many exercises have been solved by other readers (the majority of them clearly with a professional background in mathematical physics) – see <a href="https://sites.google.com/site/vascoprat/rtr-solutions">https://sites.google.com/site/vascopr...</a> ).<br />- I love Penrose's great intellectual honesty in not just debunking much of the hype behind String Theory and Multiverse Hypotheses in general, and in destroying the so-called “Strong Anthropic Principle”, but also in making very clear the speculative character of some of his own positions and theories. I also love his great originality and independence of mind, and his nuanced, multi-disciplinarian approach which includes aspects of philosophy of science and considerations of pure mathematical nature.<br />- Penrose has reached such a higher, rarefied level of proficiency in mathematical physics that he must have completely forgotten how common humans think in relation to mathematical formalism. Just as an example: after getting into pretty advanced stuff such as hyperfunctions, and treating it like if it is the simplest thing on Earth, the author then refuses to get into a detailed definition of differentiability of a many variable function (which is quite simple, really) because "it is too technical"!! So his ideas of what is complex can occasionally be significantly at variance with what the common mortal might think. </p><p>Finally, let me add here some miscellaneous notes about selected individual chapters of this majestic book (it is a very incomplete list, only a severely reduced sample, as there is simply too much stuff in this book for me to be able to analyse in just one review):<br />- In the first few chapters, after a fascinating introduction of overall philosophical character, Penrose briefly addresses some of the basic fundamentals of mathematics, including a short but intensely interesting discussion about the Axiom of Choice and its relationship to the Zermelo–Fraenkel set theory. A totally fascinating subject that unfortunately Penrose only touches, without developing into more detail. <br />There is also a fascinating treatment of hyperbolic geometry, and of the number system/s. However, when dealing with the relationship between real numbers and reality, the author does not make any reference to important aspects such as computability and irreducible complexity, as for example addressed by the excellent work done by G.Chaitin.<br />- The author then gets into one of the most beautiful and fascinating realms of mathematics - complex analysis. The treatment is concise but done well, and I completely share Penrose's enthusiasm and love for the aesthetically as well as functionally beautiful world of complex numbers, which he calls “magical” with good reason.<br />- Another subject of interest treated are the fascinating quaternions, which extend the complex numbers and provide the uncommon and interesting features of a non-commutative division algebra. There are in the book a couple of minor missing things in relation to the algebraic structure of quaternions: an algebra is a vector space that must also be equipped with a bilinear product, and a ring (being also an abelian group under addition) must be provided with an additive inverse. <br />Moreover, Penrose is dismissive of the utility of the quaternions in the development of physical theories – this is correct, but it must also be said that quaternions find important uses in Information technology applications, in particular for calculations involving three-dimensional rotations, computer graphics and computer vision.<br />- Penrose could not have forgotten the extremely important Clifford/Grassmann algebras, which are foundational to the entire architectural structure of mathematics, and he didn't; they are treated well, but a bit too succinctly in my opinion, considering their importance.<br />- Symmetry groups are treated really well, clearly and concisely. Very nice.<br />- Manifolds and calculus on manifolds: all is treated quite well, but I would have found quite helpful some more analytical detail rather than a focus almost exclusively on the visual/topological approach. I confess that here, in order to get a proper detailed handle of tensor calculus and exterior calculus, I had to consult other more traditional, “textbook-type” sources.<br />- Chapter 16 (Cantor's infinities, continuum hypothesis, Godel's incompleteness, Turing computability and similar) is OK and well written, and it would be utterly fascinating to a neophyte – but of course it could not have been detailed nor exhaustive, considering the complexity and width of such subjects. </p><p>- The “Physics” part proper starts with Chapter 17. Chapter 17 on spacetime, and chapter 18 on Minkowskian geometry (and special relativity of course) are succinct, but riveting and beautifully written. Just one small note: Penrose has a fetishism for non-standard, or uncommon, notational or representational choices, not always justified: for example, by using a non-standard metric tensor in page 434, Penrose gets himself into an error at the end of page 435 (c^4 should have been used rather than c^2) and I think that he would not have fallen into this typo, had he used the more standard and simple-to-use metric. <br />- Chapter 19 (Maxwell and Einstein) are beautiful; Maxwell equations and Einstein field equations in tensorial/differential form are mind-blowing for their mathematical conciseness and beauty, and this is where the reader can start to see the value of the mathematical apparatus described in the previous chapters: things such as manifolds, tensors, exterior derivatives and bundle connections. Einstein's fields equations of general relativity are beautiful. Very rewarding. It all seems so neat and perfect, but then, the bombshell (at least to me, who was never told of such a thing!): the energy/momentum stress tensor does not account for the energy density of the gravitational field itself, and it seems that conservation of energy/momentum is non-local !<br />- Chapter 20: Lagrangians and Hamiltonians: I must say that they are too hastily discussed - the derivation of the Euler–Lagrange equation (one of the most classic proofs in mathematics) is not treated, the Legrende transform to derive the Hamiltonian from the Lagrangian is not treated, the derivation of Hamilton's evolution equations is not treated either. Not very happy with this chapter.<br />- The subsequent chapters on quantum mechanics are beautiful, and the description of the EPR issue is really nice. The derivation of Dirac's equations is equally beautiful. I also love Penrose's discussion and perspectives about the measurement paradox. Beautiful stuff indeed. An exception to the overall masterful treatment of Quantum Physics is chapter 26 (Quantum Field Theory) which is is a bit too qualitative - more like a "popularization" rather than a treatment at the same good level as done in the other chapters of this book – and unfortunately the important subject of re-normalization is treated only briefly and qualitatively. <br />- The chapters on cosmology are very interesting and nicely written.<br />- Chapter 29 is essentially about the measurement paradox and the various interpretations of quantum mechanics – succinctly but beautifully written.<br />- The next chapters are essentially about the current unification attempts to reconcile QFT with GR. Penrose's FELIX experiment proposal (essentially testing the hypothesis of automatic quantum state-reduction as an objective gravitational effect) is utterly fascinating, but I feel that I should not bet any money on this daring hypothesis. <br />- I must say though that I was disappointed by the second part of chapter 33 (twistor theory): in section 33.8 Penrose uses several verbose sentences to express mathematical relationships, rather than writing down the actual underlying equations - result: something quite close to incomprehensible. I also fail to get the underlying physical intuition. Pity, as the other 33 chapters and a half are mostly beautifully written, and generally very rewarding.<br />- The last chapter (34) is beautifully written, and it deals primarily with aspects of philosophy of science and philosophy of mathematics. </p><p>To summarize: this is an immensely rewarding, even exhilarating book - a fantastic reading and learning experience. And it has opened my eyes on many aspects and connections that I was not aware of, and new beautiful vistas in modern mathematics (for example: tensor calculus, and exterior calculus in general) that I will now pursue in more depth. <br />After reading this great book, I can tell you that I now feel that the majority of popular science books I have read are dull and superficial by comparison.<br />It is not a perfect book by any means, but overall it is a great book, unique in its approach and contents. Not exhaustive, but with a huge and ambitious scope, virtually unrivaled in its category. It is much more than a “standard” popular science book. Very highly recommended, to be bought, studied, enjoyed and kept for future reference. <br />4.5 stars (rounded up to 5). </p><p>UPDATE: with link to a beautiful series of online lectures about Tensor Calculus and the Calculus of Moving Surfaces: <a href="https://www.youtube.com/playlist?list=PLlXfTHzgMRULkodlIEqfgTS-H1AY_bNtq">https://www.youtube.com/playlist?list...</a> (highly recommended to anybody interested in this subject).</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/16160897?shelf=owned">owned</a> <a href="https://www.goodreads.com/review/list/16160897?shelf=science-and-maths">science-and-maths</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/109780851-infinite-jen"></a></section><section><p>77 reviews180 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4663444383">January 21, 2023</a></section><div><p>The story begins with me in the garage with my high school sweet heart. The one who had made the playground swing problem seem rather trivial through a guileless intuition which cast my cynical calculations in a kind of hideous antimony. An actor whose relaxed demeanor and gentle earnestness, served to effortlessly unweave the kinks in those rusty chains, and in so doing, spun intractable knots in my own heart. It was a union of opposites, me with my chin in my hand, and he with a wrench in his. There were no problems we could not troubleshoot in tandem. Our separate talents had even began to cross pollinate, with me sometimes starring up at the undercarriage of a vehicle and asking for a socket while he perused whatever theoretical oddities I was currently obsessed with. I could, with some confidence, suggest to people that their alternator was having a giggle, their radiator was taking the piss, their starter motor was an asshole, or, my favorite, “Your fuel economy is gobshite, bruv.” And he could clearly identify the value of switching his choice in the Monty Hall Problem, understand that some infinities are bigger than others, and comprehend the threat that a quantum computer would present to our current encryption protocols. This reciprocal exchange of mental dexterity continued to unfold one rainy day, with me sliding under a car on a rickety creeper (which I had damaged by repeatedly using it to luge down steep driveways at high speeds, causing one wheel to catch and be ground into an irregular half moon.), and Nicolas Kim Coppola (known professionally as Nicolas Cage) (ie. Nic Cage) flipping through the book I had carried in. He asked me what The Road to Reality was about. Paraphrasing, I said the following:<p>Have you ever, while skidding down a vertiginous concrete pathway on a damaged creeper, felt the fixed vibrational frequency of healthy rotary friction give way to dissonant melodies which often presage the rapid, explosive disassembly of machinery under immense kinetic strain? Was all the blood in your superficial capillaries wrung out from clutching the sides of the sled in mortal terror, causing your knuckles to emerge from the dark like buds of white hibiscus and your pool-noodle arms to ripple like corded steel? Did your sweetheart, who you suspect must have reduced activity in his amygdala, (due to his performance in Ghost Rider: Spirit of Vengeance), leap from their stool and make to halt your (by now considerable) momentum using a bag of blood adumbrated by sticks of calcium (i.e. the vertebral column festooned in viscera and thinly veiled by contractile tissue that we call the human body)? During those tense moments you may have thought, in the heavily affected High English which is characteristic of all your poignant inner musings: Nicolas Cage, it is a pity that I can’t communicate with you more effectively. That our bandwidth is limited by verbal exchanges in which I must compress thoughts into packets of information and utter them as faithfully as I can in the hopes that you will receive and unpack them with minimal noise inserting itself during the transfer. Putting aside incidents in which my limbs have animated in the manner of an ecstatic Neil deGrasse Tyson, this is the extent of my ability to let you experience what it’s like to be me. I cannot understand your genius for seeing the good in every screenplay, and you cannot fathom the depths of my genius when it comes to nearly dying in bizarre ways. In those simple displays of affection where nothing is said, perhaps we say the most.</p><p>And what of inhabiting the mind of a true genius, and more difficult still; the mind of brilliant theoretical physicist and math prodigy? With art, something primal touches the soul, so that even if you don’t understand the creative flourishes of virtuosos, you are moved and made aware of their power. Who could read Nabokov and not be humbled by its beauty and precision? Who could hear Hangar 18 by Megadeth and not respect how a guitarist’s flanges dance across wires like the legs of camel spiders on a heroic doses of methamphetamines? Who could see the Venus of Urbino by Titian and not want to bury their face in her gorgeous tummy and blow a gentle raspberry? And finally, who could hear Anton Chigurh request a ‘screwgie’ in No Country for Old Men and not be gripped by a palpable dread? But here the scientific genius faces a problem, in elucidating the purely conceptual matters of their field to a general public, they must conceal much of their brilliance. If they were to riff like Dave Mustaine and fill pages with the lateral movements of their mutant intellects, the majority of us could but collectively shrug before these strange symbols. But imagine if there were a book that managed the impossible. One that was simultaneously accessible to the laymen audience, but omitted none of the technical jargon which made it possible to appreciate the operations of their brilliant minds? Perfectly comprehensible to curious high school freshmen. What you hold in your hands, Nicolas Cage...” Sliding out from under the car and standing next to him. “This..” I say, taking the book gently in my hands. “Is NOT that fucking book!” Throwing it viciously to the ground and jabbing my finger at it. “THIS is madness, Nicolas Cage! This is fucking popsci for math and physics PHDs! Calculus, Fourier series, hyper functions, Riemann surfaces, Riemann mapping theorem, quaternions, Clifford and Grassmann algebras, transformation groups, Lie algebras, parallel transport, geodesics, curvature, exterior derivatives, calculus of manifolds, connections, fibre bundles.. In the first third of a book which contains, in its preface, words that indicate he wrote it for his innumerate aunt. Show me the numerically deficient aunt that made it through this with even the foggiest notion of what the hell was going on and I will crawl inside myself and subsist on my own incredulity until the stars grow cold.”</p><p>Nicolas Cage, picking the book up and carefully inspecting it for damage, hands it back to me, saying, “It’s fine. You’ll understand it eventually. I know you will.”</p><p>Begrudgingly I put the book under my arm and nod. I feel an insurgent grin dismantle the severity of my countenance. I silently curse his ability to mollify my tantrums so easily. I seize this renewal of levity to suggest we take the creeper out for some limit testing.</p><p>“Wait!”</p><p>I can now appreciate a lot this book. If you’re someone with a strong background in math and physics and you’re interested, I can’t recommend it highly enough. It may be the most wide-ranging book on theoretical physics I’ve ever seen, not merely summarizing material, but offering an in-depth treatment of many of the more sophisticated ideas of the subject. The first half of the book takes you through most of the mathematical techniques that physicists use today, gradually moving through things like, Riemann surfaces and complex mapping, hypercomplex numbers, manifolds of n dimensions, symplectic groups and tensors. Equations are curated magnificently on the basis of explanatory power. And here I would add that Penrose, perhaps owing to his genius, has a level of idiosyncrasy in his presentation that I don’t think I’ve witnessed since Feynman. It is quite obvious that what goes on in his brain is an intensely visual phenomena. All of his diagrams and drawings are incredibly helpful, especially if you too think in this fashion. The second half of the book is devoted to physics and the ascent is quite dizzying as we approach the various hopeful theoretical bridges we’re constructing in order to reconcile the discontinuities between our two most successful theories (general relativity and quantum field theory) and so you have discussions (it may be more appropriate, considering the sheer rhetorical heft with which Roger slings these ideas against the wall like wet pieces of bologna, to call it evisceration.) String Theory, M Theory, Loop Quantum Gravity, and Penrose’s horse in this race: Twistor Theory. If you do not have a background in these things, and don’t pursue high level mathematics recreationally, I would not recommend it to you as a comprehensive place to start. If you just want to keep it around and flip through it to occasionally augment your understanding with some clever illustrations, or you simply wish to marvel at it as an enduring artifact of the human intellect, by all means. But if you’re planning to work through it from front to back, caveat emptor.</p><p>This is one of those rare gems that has brought me very close to experiencing the intuitive ease with which a mathematical genius operates. A beautiful work of staggering breadth and depth.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1433865-robert"></a></section><section><p>816 reviews44 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/68005248">February 12, 2016</a></section><div><p>Dave Langford, SF&amp;F critic and reviewer, in his long-since defunct column for White Dwarf magazine, once said that, "There is a tendency to over-praise big books simply because one has got through them." I agree that this tendency exists but note that Langford gave no reason for it. I think the reason is more or less macho intellectual pride; look at me! I read this honking great saga! It must be great or I'd have to admit wasting my time! And I need to show off my intellectual credentials! Now imagine that the book is not only huge, but really difficult because, say, it's dense with obscure references (e.g. Ulysses) or full of mathematics and not kiddie maths, either...the temptation must be even worse.<p>Hence I'm going to start my review with a couple of gripes: This book, which is full of maths, much of which would make your average undergrad scientist grunt with the strain at the very least, as well as physics to post-grad level in places, has <i>no glossary of technical terms</i>. There is ample cross-referencing and an index but these are no substitute. When you want to know, Clifford Algebra, which one was that again? (Because you've met ordinary algebra, complex algebra, Clifford Algebras, Lie Algebras and Grassman Algebras...), going back and reading through an entire section again to find out, is a bit annoying - a list of definitions at the back would have helped enormously. Admittedly this would have made a big book even bigger but it would have made it much more user-friendly.</p><p>Gripe number two is in a similar vein; Penrose fails to supply a list of the upper and lower case Greek alphabet symbols and their names or a similar list for obscure mathematical symbols, such as del and scri. Given that nobody without training in Greek or in science is going to know these and such a list would only take up one page, its omission is egregious.</p><p>This leads neatly into a topic that has been dicussed quite a bit here on Goodreads - namely, who is this book aimed at? What is it's purpose? Firstly I would point out that the subtitle "A Complete Guide to the Laws of the Universe" is not really true: Classical Thermodynamics is barely seen as we rush straight into the statistical view of the Second Law. Of the other three Laws of Thermodynamics, Zero is never mentioned and the others barely name-checked. I doubt many physicists would consider that all the basic theories have been covered in such a circumstance. But I think this is a marketing problem; I don't believe Penrose ever intended to write such a "Complete Guide." </p><p>In the preface Penrose talks about wanting, with this book, to make cutting edge physics available to people who struggle to understand fractions. Now, this can only be taken as a joke, considering what one is up against only in chapter 2, but I would guess that Penrose genuinely wants to have the widest possible audience for his book whilst not compromising his aims.</p><p>What are those aims? In my view he wants to give his personal views on the state of cosmology and fundamental physics but to be able to do it at an advanced technical and mathematical level and additionally to give his own philosophies regarding the nature of thought, science, maths and...Nature! This means that he wanted to deliver Chapters 27 - 33 on the physics/cosmology, bracketed by Chapters 1 and 34 of philosophising. The entirety of the rest of the book is simply there in order to equip readers to understand what he says in those six technical chapters! This requires 15 Chapters of maths and ten Chapters of physics/cosmology...</p><p>Looked at this way, the book begins to reflect the genius and madness of the author: Many of the explanations in earlier stages of the book left me thinking, why do it that way? That's <i>not</i> the easiest way to understand this if you've never come across it before! He also goes straight to very general mathematical principles, missing out intermediate levels of abstraction that might make what comes later easier. He chooses to emphasise the geometrical/topological view of everything, which, it might surprise one to know, is not always the easiest way to understand things. Many of the choices of what to emphasise and what to ignore seem odd...that is until one gets to the late stages of the book.</p><p>Upon arrival at Chapters 27 - 33 (i.e. what I think Penrose really wants to talk about) one can see that everything that has gone before has been put together in order to provide the most efficient route to understanding - hardly a page has been wasted. All those strange choices of what to emphasise, all the peculiar, non-standard explanations when easier explanations exist, all the leaping to the most general mathematical ideas, all the things missed out, all these things are done so that the points he wants to discuss can be followed without wasting time or space in what is a 1000+p book as it stands. The necessary skill, thought and effort required to do this impress me enormously.</p><p>Inevitably this means that most of what is covered in the book of "standard" physics has been explained better (by which I mean more readily comprehensibly), even at a mathematical level, elsewhere - but not in one volume! The consequence of this is that Penrose's widest possible audience may not be all that wide: although he suggests one could read the book and ignore every equation in it, (something I often do when reading technical literature!) I suspect one would rapidly become bored and disenchanted. The unavoidable fact is that the greater your mathematical capabilities, the more you will get from this book and additionally, the more maths and physics you know before starting, the more you will gain from this book. </p><p>Further, the more you are willing to <i>study</i> the book the more you will gain. Manny approached it by reading 3 hours per night until done. I would suggest that the nearer to that approach you can get the better off you will be, even though I failed miserably to do so. There are numerous excercises scattered through-out, which I did not attempt, but I would suggest that if you are determined to attempt them, you should read the remainder of each chapter as soon as you hit a hard problem, then go back and look at the problems again. (And note the solutions web address given in the preface!)</p><p>So what did <i>I</i> gain from the unavoidable slog of this book?</p><p>The general philosophising of Chapters 1 and 34 struck me as a waste of time; I either thought what was being espoused was obviously clap-trap or obviously true - and for me the questions he raises mostly aren't interesting to me anymore. (They were back when I hadn't reached my own conclusions yet.) Others, may feel very differently, however - and many would not agree about which parts are claptrap! The remainder offered me quite a bit, however.</p><p>For instance, a frankly embarressing mis-understanding of the EPR paradox I was labouring under was corrected! (Something of a body-blow to me as it is undergrad physics!) On the other hand, Penrose makes an astounding mistake at one point, where he gets himself horribly messed up with basic (high school) probability theory and time-reversal. (Pretty good combination to the head from me!) This is a good reminder that there is no argument from authority in science: just 'cos Penrose says it, doesn't make it right! This wrong argument is then used to go on to explain a completely freaky (and I suspect wrong) prediction about basic quantum theory. I am not clear that the <i>example</i>, which is definitely wrong, invalidates his whole line of reasoning, though; it may be that other examples show the general argument to be correct.</p><p>Then Penrose delivers the knock-out punch: <i>Conservation of energy/momentum/angular momentum in General Relativity is non-local! Not only that but it has only been proved to be true at all in a subset of cases!</i> Seriously, how could I have never known this before?! (Non-physicists may well have no clue why I am so thunder-struck by this revelation, but it is not far short of learning that there's a whole continent you'd never heard of before.) It's completely gob-smacking. And I can't see how I didn't get told as an undergrad.</p><p>Further, Penrose's main purpose was achieved; I have a much better understanding of the main approaches to tackling the outstanding problems in cosmology/fundamental physics than I did before and along the way I gained some insights I previously lacked. Two examples are the Higgs boson explanation of the origin of mass and spinors. The Higgs boson theory is barely touched upon and is one of the rare examples of something being included that is not strictly necessary later. I wish there had been more about it, whilst recognising precisely why there is not. What material there is made the theory seem much less arbitrary than it had previously.</p><p>Spinors are a mathematical concept that feature heavily in the book, mainly because they feature extremely strongly in Penrose's Twistor Theory of quantum gravitation. Penrose gives an assessment of his own theory that I respect enormously and cannot praise highly enough; he expresses clearly what it it can acheive and equally clearly and forthrightly what it cannot. Every weakness and limitation is mentioned and explained. The only time I have previously come across a scientist giving such an honest and complete assessment of the weaknesses of his own theories in a popular account is when I read Charles Darwin's Origin of Species. I cannot express how much respect Penrose earns from me by doing this. Suffice to say that most popular science books will make out that the author's ideas are obviously and unassailably correct. Further, many technical papers fail to match this level of dispassionate critical assessment.</p><p>But back to the spinors; they feature in the now well established Dirac Equation for a relativistic electron but the (non-standard) way Penrose shows this and explains their connection with the left-handedness of the Weak nuclear force and how they link to the Higgs boson ideas are fascinating. However I am not clear about them in one (crucial) regard: are they <i>real</i>? Penrose says they are. I am not sure (because my understanding is still muddy) and I find (somewhat to my horror!) that even though I've read all 1050p of the main text, all of Chapters 2-17 twice and many individual sections several more times, I am still not done with this book! I have to go back and see if I can make sense out of these spinors. Also, I owe Manny a discussion of Inflationary Cosmology: I'm going to have to read the relevant chapter again in order to provide it.</p><p>Wish me luck as I delve back into the very deep waters of this book!</p><p><b>Cosmology, Early Universe Symmetry Breaking and Inflation</b><br />So, Manny requested my views on the above topics: blame him!<br />I must say at the outset that I am no expert in this field and in fact Manny has read much more about modern cosmology than I have, so I’m not sure how much value should be placed on the following; it’s a pretty naïve collection of speculations and intuitions.</p><p><b>Early Universe Electro-weak Symmetry Breaking (EUSB) </b><br />The current theory of the weak nuclear force and the electromagnetic force relies on a “broken” symmetry. That is to say all the relevant particles and their interactions were more symmetrical when their temperature was higher; so high that one has to look back to shortly after the Big Bang to find anything with a high enough temperature. Penrose gives the (standard) analogy of a lump or iron cooling down; at some critical temperature, the atoms go through a phase change and instead of having randomly aligned magnetic fields, these fields all line up in one direction. This creates the macroscopic magnetic field but in the process reduces the symmetry of the iron. It used to look the same in every direction but now it has an obviously different look, depending on the direction the magnetic field is pointing. So the idea is something similar happened when the universe cooled down below a critical value and the weak nuclear force and the electromagnetic force now look different because of the reduction in symmetry. But the lump of iron in fact won’t spontaneously have <i>all</i> its atoms line up in exactly the same direction unless it is cooled very slowly. Instead, “domains” develop. Inside a domain all the atoms are lined up the same direction but each domain has its own direction, which is why any old lump of iron is in fact not a macroscopic magnet. All the fields from the microscopic domains, pointing in different directions tend to cancel each other out. Which leads to weirdness when talking about the particles and forces of the universe doing the same thing: there are equivalents of the directions of the magnetic domains that the cooling particles could drop into that are different from what we observe. So the fundamental interactions would look different in a different domain. And the universe did not cool slowly, so it is much more likely than not that such “domains” did form if the theory is true. Now the boundaries of these domains would look and behave very strangely. In fact one type of boundary predicted by the theory, Cosmic Strings, can lead to something really bizarre: time travel! That is, technically, space-like movement into the past.</p><p>Well, I just don’t believe time travel into the past is actually possible, which means I don’t believe cosmic strings exist which means I think there’s something wrong with current electro-weak theory. However all the “low” energy density tests done show electro-weak theory to do very well indeed, thanks! So I’m in a bind; the high-energy prediction of a low energy theory that works really well predicts something I don’t believe. What to do? Well, it is often possible to write a theory in more than one way, mathematically, so I would search for a different mathematical description of the low energy theory that did not rely on the EUSB idea, thus getting rid of the unwanted cosmic strings and parts of the universe that are radically different from ours altogether. I don’t know if this is possible. There has been one claim that a cosmic string has been observed but I don’t know if any corroboration of the claim exists. If they do, then electro-weak theory as it stands gets an extra-ordinary boost.</p><p><b>Inflation</b><br />Penrose states that the initial motivation for the idea of cosmological inflation was to “explain” why magnetic monopoles are not observed but exist anyway. Magnetic monopoles are neat as they would explain why electrical charge comes only as integer multiples of a fundamental value (though not what the value is). The trouble is, nobody has ever seen one and if they were formed at all it would have been with such concentration that they would have been easily spotted by now. Unless inflation had reduced their concentration radically by expanding the universe at a ridiculous rate…<br />Well, this seems to me to be only half the problem; the other half is demonstrating that monopoles <i>must</i> have formed and that they did so prior to inflation and not afterward. <br />Later, people suggested that inflation could explain homogeneity and flatness. Homogeneity is the fact that wherever we look the in the universe the matter seems to be distributed in a similar way (i.e. stars, galaxies, clusters, super-clusters…). Flatness is the idea that the universe is, over-all, expanding at a rate just high enough to prevent it collapsing again because of the gravity of all the stuff in it.</p><p>Penrose presents cogent arguments as to why inflation actually cannot explain homogeneity. They seem indisputable to me. That the universe started off in an extremely low entropy state seems an unavoidable fact. Why was it like that? I don’t know. It’s a big mystery.<br />Inflation cannot solve the problem of EUSB either, but hey! it’s a hypothesis and it can make predictions, so astronomers should try to see if they can prove it wrong or not. As far as I have gathered, the observational status of inflation is ambiguous. My feeling is that the whole idea is very arbitrary: a field occupying the whole universe must exist in order to provide the opportunity for inflation to occur. No hint of a carrier-boson for said field has ever been found. I don’t know if theory can predict anything at all about such a particle, apart from it must have integer spin. There is talk of a second inflation occurring because it seems that some astronomical objects are not only moving away from us but <i>accelerating</i> away from us. This suggests to me that whilst there may in fact have been inflation in the early universe, current theory is nowhere near adequate to explain it: why then? Why again now? What causes the transition? It could be a purely random event where the field transitions from one state to another quantum mechanically but to do so the new state must allow an immediate drop of energy in the field. How can one decide what the possible energy levels of the field are? Or if we are in the ground state now or not? The theory also has implications for the nature of the vacuum i.e. it is different before and after an inflation period starts. The vacuum in the quantum mechanical sense seems to me not to be understood at all well. I think that if inflation has ever happened it indicates that a deep theory explaining the nature of the vacuum is required.</p><p><b>The Anthropic Principle</b><br />This gets dragged up a lot in discussions of cosmology. It’s annoyingly persistent. It comes in a weak and a strong form. Starting with the weak form (WAP): Many adherents claim that the WAP has predictive power and is therefore in some sense “correct” i.e. some deep law of the universe. What it states is that there is sentient life therefore…X. X is a prediction of some phenomenon. The most famous example is a certain energy level of the Carbon nucleus. The argument went, we have life because we have heavy atoms so there must be a way of fusing lighter atoms to make heavier ones but to make any atom heavier than carbon, carbon itself must have this specific energy level…and it does! Triumph for the WAP! Except that is rubbish, because the argument doesn’t rely on the existence of life at all; it is easy to imaging a lot of heavy atoms floating about but no life. The <i>real</i> argument, stripped of inessential guff, is simply: there are atoms heavier than carbon – there must be this energy level of the carbon nucleus for that to happen. Life, let alone human sentience doesn’t feature at all. All WAP arguments fail in this manner: it turns out that life is inessential to the argument.<br />Then there is the strong anthropic principle (SAP): This states either the universe was fine-tuned for the existence of human sentience to be possible or there are in fact a huge number of universes that are somehow different from each other so ours is just a statistical freak. This assumes that the only possible way that sentience could occur is if physics follows the laws we see. I don’t buy this at all: are people seriously claiming that they know what all the possible emergent ramifications of some grand set of all possible sets of physical laws are and only a tiny fraction of them could sustain sentience? It seems to me we don’t even know all the ramifications of the laws of the observed universe yet, let alone any other one. But there is some sort of prediction here; there might be other universes. Maybe that is a testable proposition. I don’t know.</p><p><b>Spinors and Spin</b><br />I re-read the material on the Dirac Equation and spinors a while ago but I've only just got round to discussing it. The discussion is moved to the comments due to the character limit on reviews!</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1433865?shelf=non-fiction">non-fiction</a> <a href="https://www.goodreads.com/review/list/1433865?shelf=physics">physics</a> <a href="https://www.goodreads.com/review/list/1433865?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/10179929-sanjay-gautam"></a></section><section><p>222 reviews434 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1125177386">December 27, 2018</a></section><div><p>Its the greatest science book ever written in the whole world, since the beginning of the time. Its certainly not popular science, its hardcore science and maths, written for general audience.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/2309246-cassandra-kay-silva"></a></section><section><p>704 reviews277 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/181771323">August 19, 2011</a></section><div><p>Penrose, Penrose, Penrose. Oh how I LONG to know thee. I am becoming minorly obsessed with you and your work. I am pacing for crying out loud. I am running myself in circles. Opening, closing, referencing, coming back, straining my eyes as if that will make me see the world that you do. Why do you elude me so? Why does your tongue speak as if attached to the left temporal lobe itself? I catch glimpses of this reality you see. I feel myself drawn to it in longing for truth and understanding. For some reason I feel that to understand you, truly and completely I would find some kind of wholeness within myself. Oh someone save me I am in love. I am falling madly and passionately in love with physics. It has been coming on a long time, this slow fever. This lingering low hum, that is exploding in tiny bursts. As with lovers of old your elusive and coquettish nature has wooed my heart oh physics. I want so badly to truly understand, not some superficial knowledge, but some deep personal connective enlightenment. Cosmic if you will. <br />I pledge to re attend school. Career be damned I have to know you, and I can't know you without the mathematical background to do so. I can't truly understand you until I can follow this terse and sometimes insipid language of higher calculus. May the forces of this universe help me, I will not die until I know this form that physics takes. This is my pledge. </p></div><section><ul><a href="https://www.goodreads.com/review/list/2309246?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/655723-nick-black"></a></section><section><p>Author <i></i>1 book698 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/10181575">May 15, 2011</a></section><div><p>Penrose came to GT and gave an open lecture on cosmic parameters and cosmological arguments from the 2nd Law of Thermodynamics (chapter 27 in this book, one of the most ambitious and impressive -- if incomplete, a bit uneven, and just as taxing as you've heard -- catechisms I've ever read), and a closed lecture on <a href="http://en.wikipedia.org/wiki/Twistor_theory">twistor theory</a> (chapter 33), and signed my copy! w00t! I shook Sir Roger's hand as trillions of neutrinos passed through us both, completely undetected, our entangled <b>R-type</b> state evolution leaving an indelible imprint on all our lightcones forevermore at the cost of a little more entropy, order traded for disorder in the guise of order, orderly.<br /></p></div><section><ul><a href="https://www.goodreads.com/review/list/655723?shelf=autographed">autographed</a> <a href="https://www.goodreads.com/review/list/655723?shelf=important">important</a> <a href="https://www.goodreads.com/review/list/655723?shelf=incredibly-large">incredibly-large</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/206483-dj"></a></section><section><p>317 reviews227 followers</p></section></div><section><section><p><b>Want to read</b></p><a href="https://www.goodreads.com/review/show/20537409">November 15, 2009</a></section><div><p>I have a suspicion that Penrose hasn't spoken to a undergraduate in 30 years. His notion of "introductory material" is not just wrong, its downright strange.<p>The famed mathematician devotes several pages to discussing the addition of fractions then breezes through holomorphic functions and Reimann spheres.</p><p>I'll return to this book in a year or two when I have the mathematical background to qualify as a "non-mathematician."</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/206483?shelf=priority">priority</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/7531999-vagabond-of-letters-dlitt"></a></section><section><p>594 reviews252 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/2370943784">March 1, 2022</a></section><div><p>UPDATE 2022: <p>Several years later I found this work, including Feynman's lectures, to be a much better use of time, and thanks to it (and COVID) came to understand fundamental physics. These are the "years' worth of secondary sources" mentioned in the review: I could now comprehend the book. <a href="https://www.susanrigetti.com/physics">https://www.susanrigetti.com/physics</a></p><p>_______________³¹⁴⁸⁸⁵⁹_______________<br />t me start off by saying (its relevance will soon be revealed) I have a bachelor of science in applied mathematics and a PhD-ABD in another strongly quantitative discipline* (both are top-50 schools, and I wasn't in the bottom 50% of the class), and after the first 300 or so pages (out of 1200) the math in this book (and it's at least 40% or more straight math, not text, and often without text explaining the math) is way above my head and is left often undefined in the text. The author doesn't even do the courtesy of pointing the reader to textbooks where these concepts, such as pseudo-Riemannian geometry and anti-de Sitter spaces and Seiberg-Witten manifolds, are defined and can be learned.</p><p>The book fails in its promise and purpose to be a self-contained guide to the current mathematical- or theoretical-physical understanding of the universe. It is far from accessible to the layman (I have postgraduate training in math and I was a good student and its inaccessible to me), and to grasp the concepts in this book, I'd have to spend probably a year of free time and a thousand or more dollars in secondary sources (if I bought them used and cheap). I bought this book to get a $20 overview (like Collier's 'A Most Incomprehensible Thing' for the theories of relativity [I prefer the original 'invariance'], which was technical but self-contained and comprehensible; reading that is the only thing that gave me any knowledge at all of tensors, which this book is chock full of): what I got was in essence a 1200 page bibliography without the authors being noted and without the important works being starred.</p><p>This is a very ambitious book which fails utterly in execution.</p><p>The author goes from explaining what complex and irrational numbers are and why they are useful (this is freshman high school math) in the introduction, accompanied by an apology for the necessity of using as difficult a concept as logarithms, to pseudo-Riemannian geometry (this is postgraduate pure math) 200 pages later. No joke. Penrose spends about five pages defining all of classical statics and dynamics, and then assumes that you understand classical mechanics. This same breakneck pace is kept up throughout, which is how he manages to range from logarithms and complex numbers to doctoral-level mathematics in 500 or 600 pages. Once he goes out of the pure math and back to applied math (i.e., physics proper) it gets a little easier but I'd still not recommend trying to tackle this book unless you're a graduate in maths or a self-taught prodigy in pure maths.</p><p>The book promises to be a self-contained guide to the best mathematical understanding of the universe we have, but it ends up more like the author just stuck the important theorems in with a minimum of explanation (he does hit almost all of them: one thing that struck me as unnecessarily erudite - showing off - and odd was the statement of Maxwell's field equations, which is mathematically simple and elegant, in terms of tensors, which are very, very difficult), so it's a complete guide if you already know all of the math (in which case you don't need the book): it's much more of a refresher and quick reference for people who already are familiar with and understand (or at one time understood) the concepts the author represents.</p><p>Required prerequisites: understanding of linear algebra (Lie, Poisson, Frobenius), TENSORS (and more tensors), several varieties of noneuclidean geometry (Minkowski, de Sitter, Riemann), scalars, topology and n-manifolds, group theory (Lie groups), gauge theory, etc., or the willingness to learn these from expensive secondary sources, because Penrose will not teach you them here and the arguments of the book are incomprehensible without them. Without them, one would be reduced to skimming the 20% of the book that is text (especially the final chapter, which is comprehensible to any semieducated layman) and taking the author's word for the rest of it. Just about the only thing he explains in full is twistor theory (his own invention).</p><p>I still have to award two stars for the obvious intensity and depths of erudition which Penrose funneled in to this work, but only two because it doesn't even partially fulfill its stated purpose or self-description.</p><p>*Redacted to protect the privacy of a member of Vagabond of Letters.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/7531999?shelf=dont-own">dont-own</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6603759-misericordia"></a></section><section><p>2,377 reviews18.8k followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3906279352">April 6, 2021</a></section><div><p>What is reality? How come that mathematics is so handy describing it? And often more astutely that our eyes? What are the laws governing it all? Are we getting it all right? What if we are trying for the wrong questions and answers? These and many other questions are what the 2020 Nobel Prize winner Roger Penrose's giving the reader a taste of working on: string theory, physics, the mindboggling quantum effects... - all through the prizm of mathematical apparatus.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/2658311-notgettingenough"></a></section><section><p>1,015 reviews1,164 followers</p></section></div><section><section><p><b>Read</b></p><a href="https://www.goodreads.com/review/show/180781840">June 30, 2011</a></section><div><p>So we had a physicist around to dinner the other day and thrust this at him. I can't call T---- by his real name, let's just say he rhymes with a dip made with chickpeas and tahini. The reason I can't call him by his real name is that he works at a place that starts with C and rhymes with a complete lack of humour. He likes his job, I don't want to get him sacked for reading Penrose.<p>He flicks through it and the first thing I note is that physicists take about 5 nanoseconds to read what it takes ordinary mortals eons to get through. He starts with the cover, of course. 'Reviewed in the Financial Times?' A disparaging snort follows. 'Ah,' he says after the third nanosecond. 'He's written <i>this</i> type of science book.' I like that. I have no idea what it means, but I like it.</p><p>After four nanoseconds he is up to page 1050 or thereabouts. He reads out a question from it and says 'That is a good question. I don't know the answer.' Slaps book shut. Really, I mostly get the impression that real physicists like him just wish those other ones would just stop it. Stop with all the philosophical 'should we be worried about this?' stuff. Let's just get on with it p-lease.</p><p>And he says 'You didn't say the dinner invitation came with a catch.' I say 'But I didn't say it didn't, did I?'</p><p>I am seriously thinking of reading this while skipping every page that doesn't have only words on it. Seriously.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/2658311?shelf=haven-t-read-but">haven-t-read-but</a> <a href="https://www.goodreads.com/review/list/2658311?shelf=science-fiction">science-fiction</a> <a href="https://www.goodreads.com/review/list/2658311?shelf=science-sort-of">science-sort-of</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/1263487-ezra"></a></section><section><p>28 reviews25 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/25691066">June 27, 2008</a></section><div><p>this book RULES. it is a sort of primer on the mathematics required to really understand quantum physics. of course, that is a pretty huge pile of stuff, and this is a damn huge book. it moves faaast too: the entire theoretical foundations of single-variable calculus takes up one chapter. the reader is rapidly pulled through pretty heavy cram sessions in multivariable calculus, algebraic topology, real analysis... everything you need! and yet, it does not feel at all dense, because roger penrose is one of the great living stylists in mathematical writing: even a healthy dose of equations can't obstruct the fluidity of his prose, the lucidity of his explanations, or the enthusiasm of his presentation. i took classes in some of these topics and felt like penroses's single chapters did at least as much for me. other topics i was only cursorily familiar with, and this was felt like a rocket-fuel-grade introduction. there are even some really really nice excercises, mainly in the form of proofs (the fun kind of excercise). exhaustive theoretial math books are rare but they do exist; what makes this one actually work (in contrast to some dogmatic behemoth like the classic whitehead &amp; russell) is that penrose is actually directed towards a somewhat taangible goal: educating a casually geeky, intellectually curious layperson about quantum physics, and leaving nothing out. for whatever reason, it works.<p>i brought this thing along as my only book on an 8-week tour, and it was perfect: a quick dose of clearly, beautifully written, brain twisting math a couple times a day. YES!</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/5361322-ivan-vukovi"></a></section><section><p>89 reviews44 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/546715922">February 27, 2019</a></section><div><p>wow... I actually managed to read it, 1050 pages, every single one of them.<p>But can I really say that I'm done with this book? I don't think so... Although it took me a year and a half to read it, I didn't even understand a significant part of it. Since I'm a physics student I understood most of it on some very basic level, but I'm pretty sure I'll have to open this book again and again to take a peek at some of the awesome ideas put here by Penrose.</p><p>Did I say awesome? That's a huge understatement. I meant incredibly brilliant, original, profound and refreshingly sober!</p><p>Sir Roger Penrose is the reason why I came to love physics as much as I do and he's probably the main reason why I chose theoretical physics and why I'd like to be a mathematical physicist. </p><p>You, sir, are a huge inspiration... Thank you!</p><p>I don't want to write anything else because I don't think I could give this book a truly proper review, you should simply try to read it... and if you manage to do it, I hope you'll understand what I mean.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/5361322?shelf=informal-but-technical">informal-but-technical</a> <a href="https://www.goodreads.com/review/list/5361322?shelf=mathematics">mathematics</a> <a href="https://www.goodreads.com/review/list/5361322?shelf=philosophy">philosophy</a> </ul></section><hr /></section></article></div><div><article><section><section><a href="https://www.goodreads.com/review/show/138653993">January 5, 2011</a></section><div><p>Amazing. While I can not exactly call <b>Road to Reality</b> a <i>popularization</i> of general relativity and quantum theory, it is a peerless introduction to and review of those topics. I have a PhD in mathematics, and studied physics and math as an undergraduate, and there was plenty for me to learn from this book. There are very few people in the world who would not learn much from reading it.<p>Many years ago, I read Penrose's <b>Emporer's New Mind</b> which was good as far as it went, but earned my derision with doubtful, hand-waving arguments for quantum origins of consciousness. Knowing Penrose is no dummy, I permitted a friend to convince me his work deserved another chance.</p><p>I am very glad to have read <b>RtR</b>, even though the process took me most of 2010. I now have a far better understanding of mathematical physics than I could have achieved with any other reading list. I did not complete most of the exercises; I suspect that if I had, then (A) I would not have finished until 2012, and (B) the exercises would have been sufficient to bring me to a fairly professional level of competence. Kudos to Mr. Penrose for including them.</p><p>The book begins with quite a few chapters of mathematics, quickly progressing to advanced undergraduate topics such as calculus on manifolds. In some ways I liked Penrose's clear treatment and drawings better than, say, Michael Spivak's beautiful but sparse texts. In order to provide a foundation for his chapters on physics, more mathematics is interspersed where necessary.</p><p>Penrose introduces complex manifolds, continuous groups (Lie groups), and principal bundles. This machinery is all truly essential to the physics, and it was enlightening to see it collected in a single place, however briefly explained. It is especially useful because most graduate students in physics or math end up missing a formal introduction to one or more of these topics.</p><p>The grand themes in <b>RtR</b> are the two major 20th century discoveries of general relativity and quantum theory. Penrose is particularly interested in probing how the two may be made consistent. He covers some of the cosmological work that treats both (e.g. Hawking radiation from black holes), and then discusses theories that seem to join them, including various level of detail on spin foams, string theory and M-theory, loop quantum gravity and his own invention, twistors.</p><p>A great strength of this magnum opus is Penrose's ability and willingness to discuss philosophical and aesthetic issues of the physics. Four of these stand out. First, I quite like his perspective on the futility of obtaining unified theories by (more-or-less) trying to guess a tractable Lagrangian. Second, his detailed treatment of entropy, especially the universe's original low-entropy state with respect to gravity and the cosmological implications, was really fascinating.</p><p>Third, Penrose seriously considers the various interpretations available for (apparent) collapse of the quantum wavefunction. His bias is toward objective collapse (environmental collapse), rather than being spookily dependent on "observation" by a conscious observer, and I agree with him that far. He suggests that general relativity, being the only other physical theory we have of similar stature to quantum theory) may somehow provide the mechanism. This is not an assertion but merely a suspicion on his part, and personally I lend it little credence. I do agree with him that general relativity is likely to remain a permanent Newtonian-style large-scale limit of the physics, while quantum theory seems ripe for some kind of fundamental reinterpretation.</p><p>Finally, Penrose revels in the aesthetics of what he labels <i>complex number magic</i>. That is, he considers the interesting ways in which physical reality is so well described not just by mathematics but specifically by complex analytic structures, a simple example being the phases of quantum wavefunctions. His fascinating twistors are the coolest example of this, where he changes the physical perspective utterly. No longer are points in spacetime the essential quantities; rather the physics is on the manifold of (potential) light rays. A spacetime point is a confluence of rays, and the interesting part is how fundamentally a point can be represented by, and treated as, a Riemann sphere (a compactified 1-dimensional complex line). As an ex-complex-manifolds guy, this was wonderful stuff to me.</p><p>I will conclude by noting that Penrose even redeemed, somewhat, his handwaving arguments from <b>New Mind</b>. I now understand that he is essentially pointing out that our conscious observations of physical phenomena are (or appear to be) collapsing the wavefunction. Since there must be a mechanism for that collapse, Penrose is arguing that something fundamental about conscious minds (as opposed to highly sophisticated computers) is triggering it. I still don't agree, because I believe consciousness is computational and emergent from complex systems, but his point no longer seems so silly.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/1575227?shelf=favorites">favorites</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/180908-tatiana"></a></section><section><p>148 reviews112 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/182613946">July 8, 2011</a></section><div><p>This book is too sprawling to wait and review all at once at the end, so I've decided to do it little by little as I go along.<p>I thought the </p><u>prologue</u> sucked, but immediately after that it became deeply fascinating, so don't get discouraged. I guess I should say why I hated it, though. It seemed as though he was judging former times and societies through a "presentist" lens, as though all people have always and only been scientists since the start of time, only they were really bad at it back then. It's kind of a scientist's way of ignoring everything else about reality besides science, and made me a bit nauseated, thinking "oh no I hope he's not going to be this dumb all the way through." Luckily, he quickly transitioned to extreme brilliance, in which he's jaw-droppingly continued since then. Even though he's talking so far about seemingly simple stuff, he keeps knocking me for a loop with his deep insights which I've never considered before.<p>Only in </p><u>chapter 3</u> so far, and discussing integers, irrational numbers, and the real numbers. I keep having to stop and think hard about the things he's saying. He asks the question if we lived in a universe where things were an amorphous soup would the integers exist there. He also points out that calculus (and stuff like momentum, velocity, and many of our physical concepts depend on calculus) is defined on the real numbers. If it turns out that the universe is discrete at the tiniest level, this math won't apply anymore (except as an approximation). However, he also observes that the real numbers first invented in Euclid's day when we had physical evidence spanning only some 15 orders of magnitudes (the smallest to largest distances known) are still going strong now when our knowledge spans something like 150 orders of magnitude, so they aren't doing too badly! These are the notions of someone who has thought deeply about how math and physics are intertwined. I keep being dumbstruck with things he casually asks about things that are ostensibly simple which I've known forever but never thought to ask that. Really important stuff. He is breathtakingly brilliant! I'm so glad I'm reading this book!<p>Aside: The more I read the more sure I am that Platonic essences exist independent of the nature of physical reality, and independent of their instantiation in some physical reality.</p><p>Spent some time going over familiar ground in the complex plane. It's been long enough since I studied or used this stuff that it's quite enjoyable and satisfying to do that. I think I've settled on the slow savoring method of reading this book rather than the quick devour. This review's going to be very long, but I hope it'll admit of savoring a bit as well. =)</p><p>In </p><u>Chapter 5</u> now, and talking about e and logarithms, I wondered why it is again that e is a more natural base for logarithms than any other number. So I spent some time adding it up from the formula e = (1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)+(1/5!)+... and watched the digits slowly materializing 2.7182.... so I believe that much. =) Next I'm reading again how e originally came up in playing around with logs and powers. This book has that effect that it makes me think again about stuff that I haven't thought about since I was young. I would really like to feel I understood what we know of reality inside and out when I'm done. I want to see the whole chain starting from one cow, two cows on up to the standard model and beyond. It's always been an obsession of mine just to understand how things freaking work, what the universe is like, what nature is based on, and I have this feeling I could get much closer by going through this volume carefully. The title keeps reminding me of the Royal Road to Geometry, which Aristotle reportedly told Alexander the Great did not exist, so that's some kind of warning, hah! <p>So far I've resisted the urge to jump ahead, except for reading the section called "beauty and miracles" near the very end. You have to admit that's an attractive section name! Alas, I understood it only in the broadest way, that beauty (mathematical elegance) and miracles (seemingly crazy mathematical coincidences such as all the complicated terms happening to drop out or whatever) act as a powerful but not unfailing guide so far to finding theories that fit how nature behaves. At that moment, my dear kitten Alai jumped up and sat right on the book, as if to say, "you want beauty and miracles? Just look at me!" As I pet him, I kept saying "beauty and miracles" affectionately. </p></p></div><section><ul><a href="https://www.goodreads.com/review/list/180908?shelf=nonfiction">nonfiction</a> <a href="https://www.goodreads.com/review/list/180908?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/30982871-james-f"></a></section><section><p>1,379 reviews86 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1488963916">January 1, 2016</a></section><div><p>For the past year and a half I have been reading heavily in popular works on physics and astronomy, at various levels ranging from the superficial gosh-wow (Michel Kaku) through total beginner level to the somewhat more sophisticated (Brian Greene, Kip Thorne, Lee Smolin); but almost always I have been frustrated in my understanding by the lack of any mathematics to support the often metaphorical discussions. At the same time, I understood that the real mathematics of relativity, let alone quantum and string theory, would be way over my head (as when I borrowed, and immediately returned, one or two books by Penrose himself, as well as books by Wald, Susskind, etc.) So when I saw the description of this book, that Penrose intended to supply the necessary mathematics to understand the physics as he went along, I thought that it would be just what I wanted -- if it were possible. I was also rather skeptical, whether in fact it was possible, in something under 1100 pages; and as it proved, rightly so. Penrose does not succeed in making the math understandable; he explains something at a very simple level and then assumes that the reader understands far more than the author has actually explained, and when he gets to something especially difficult to comprehend, that's when he gives a footnote: show why this works. At the beginning, I read this pencil in hand, but it soon exceeded my abilities to work out the problems.<p>I am not totally unmathematical (I say this because it is relevant to understanding the level of this book): I minored in math in college, and beyond the usual background in high school algebra and geometry, and physics (before the dumbing down of high school math and science circa 1970), I have taken two years of college calculus, a semester of calculus-based probability and statistics, several "fundamentals" courses, and a calculus-based (but entirely "classical") first-year physics course. Not a lot, really, but probably more than most non-math/science majors. And I have tutored high school and college students in math through early calculus for over ten years. So what did I understand of this book, with that background? The first six and a half chapters. Chapter six explains calculus in nineteen pages, and I'm fairly sure most of what he talks about was never included in my two years of calculus (maybe in a real analysis course?) Chapter seven was on complex analysis, and I understood about the first half. This was the model for the rest of the book -- I understood about the first half of each chapter, where he explains the basic concepts, and got lost when he tried to "make it clearer" through "the magic of complex numbers" (his favorite expression.) The same was true when he passed over into the physics of relativity, quantum theory, and the modern speculations about strings, twistors, etc. -- I understood about half of each chapter. (Actually the chapters on loop quantum gravity and twistors were totally out of my range from the beginning.) I would say that the minimum for really following him would be to already have taken at least a complex analysis course.</p><p>Was the book a total loss, then? No. If I didn't learn the various fields of math he covers (vector and tensor calculus, some projective geometry and topology, etc.) I did learn what those fields deal with; if I didn't learn what I needed to understand the physics, I did learn what I would need to study to learn it, and perhaps most important to an autodidact who will never be able to afford any more formal education, what order I would need to study the various fields in. In short, for me (and probably for most readers who don't have a strong math/science background) this was not the "Road" but more of a roadmap; I didn't make the trip, but I got a feel for where the route passes through. At the least, I was inspired to review my high school and college math, and perhaps to try to go a little beyond where I stopped. At my age (nearing retirement) I will never get all the way to an understanding of the physics, but maybe I will keep my mind working a little longer for having read this.</p><p>I should give a brief summary of what he is saying about the questions I have been reading about in other books: he is very skeptical of string theory, because of the higher dimensions (the problem of degrees of freedom, especially); he is somewhat more friendly to quantum loops and other alternatives; he is naturally most interested in his own theory of twistors, but admits that at present it doesn't have the solution either. He argues that to be consistent with general relativity, there must be significant modifications to standard quantum theory. I'm obviously not sufficiently informed to evaluate any of this.</p><p>I would recommend the book for what it is, but not for what it claims to be, unless the reader has a real background in mathematics and physics.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/10770371-dan"></a></section><section><p>1,059 reviews52 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/4375349061">January 30, 2023</a></section><div><p>3.5 stars<p>This is a mathematical and physics tome of more than a thousand pages. It is essentially everything you should know about the universe by the Nobel Prize winner himself, Roger Penrose.</p><p>Heavily formula based. Many of the later chapters were beyond my depth, unfortunately. </p><p>Writing was okay. Would have liked to heard more narrative but I suspect Penrose's open mindedness kept him from deviating from established theory. </p><p>3.5 stars</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/6226405-yasiru"></a></section><section><p>197 reviews117 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/257457958">February 23, 2012</a></section><div><p>As accurate a title as can be for this tremendously ambitious behemoth. I very much enjoyed the masterful laying of a mathematical framework when first I came across it (the first dozen or so chapters if memory serves; hence the rating, as well as for the aforementioned ambition in the task- I think this is a right way to go, though popular expositors seldom venture down this route), as Penrose does it so efficiently (and naturally too, so that the layman wouldn't shove it aside in disgust after hardly a half dozen pages, and for the price even that handful of beginning chapters are worthwhile). Something of an idiosyncratic emphasis might be noted in these chapters, but it doesn't take away from the breadth of the account and can't really be faulted because it's setting things up for what follows. <p>I never actually got to much of the 'meat' of it- which is the physics (and so unfortunately can't remark on it). I'd hoped to, but then I realised I was just putting it off out of apprehension that I'd find myself feeling the lack of formal first year physics at university (something I gleefully escaped as early as I could in favour of my chosen field- pure mathematics). This is probably an unfounded concern, since skipping ahead to chapter 17 on spacetime, I was able to follow the account, but nonetheless I closed the book at this point.</p><p>Perhaps I'll revisit it sometime with a few other references handy should I need rescue. This would certainly be worthwhile if you can give this the time and energy required; you're sure to come out richer in knowledge, in a way almost no other popular account of science can impart.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/6226405?shelf=physics-and-other-science">physics-and-other-science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/11509598-alex-lee"></a></section><section><p>894 reviews104 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1338916871">September 17, 2015</a></section><div><p>In this amazing book, Roger Penrose looks for a very fundamental issue.<p>He is looking for a single metric to describe everything.</p><p>This is not a unit of reality, however, although this is how he poses the issue.</p><p>The problem with selecting a metric, as he shows us over and over, lies in how different metrics arise from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics will threaten to buckle. In many instances, the metrics (and their attendant relationships) will no longer be applicable. What this means, in the Kantian (and Badiouian sense) is that these relationships's applicability will become "undecidable". In some extreme cases, the relationships may even break down. For instance, black holes are a problem because the expressed relationships that emerge from physics experiments prove to be untenable in black holes (and the big bang) as these relationships decohere and infinities and zeros pop out everywhere.</p><p>This search for a metric leads Penrose to reject string theory as a viable relationship form. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, weak force is a dimension. Each dimension is an independent mathematical vector of a different "inertial" influence. Additionally, the mathematics of string theory, as well as other theories, proves to be too illusionary. As with post-structural critiques of modernism, Penrose points out that the consistency of string theory relies on theoretical supplements/signs that are attached onto the positions of various types in order to maintain coherency. For instance, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions as well as its immanent affects proves to be unweldly to Penrose because the coherence of the relationships are maintained by theoretical enforcement rather than any direct correlation of math and physical experimentation.</p><p>If Penrose was familiar with Badiou, Kant and Derrida, he would be able to recognize that the undecideability of supersymmetry and string theory result from these theoretical supplements. The supplements provide the missing pieces to cohere the theory, so physical experiments prove to be incomplete in their testing. As Penrose points out, string theorists in failing to find superpartners can always push the calibration of their theory to include these partners, just at higher energy levels, which can always lie beyond the ability of technology to generate.</p><p>In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose falls fault to this when he theorizes that Quantum Field Theory can be modified (rather than the Einstein's general relativity) by changing the cut off metric. This is in line with all his discussions to "renormalize" the math so as to remove the variance accumulated by extending localized relations from beyond the area of origin on the manifold. We can always enforce a consistency of a given domain in two ways.</p><p>1. To provide a "superpartner" to supplement the terms, to keep phenomenon visible to one another within the domain, as a motion of immanence, as Derrida suggests.</p><p>Or.</p><p>2. To encapsulate a domain by limiting its identity to its other. From there, we can radically reduce the other to zero, thereby hiding the limitations of a domain, as with Moffe &amp; Laulau with their Hegemony or as with Badiou with a basic atomic "cut" to center the domain as with <i>Being and Event II</i>.</p><p>Both of these strategies amount to the same kind of forced coherency by mapping a domain rigidly.</p><p>Penrose does offer his own favorite solution; his Twistor theory, which removes the need for extra dimensions beyond 3 + 1. Additionally, he considers this theory by collapsing all the different vector differences held cosmically in string theory into immanent relations that are founded on the very "knots" of space, so that the pre-space twistors contain the information that wider "vibrations" are meant to express. Both theories are incompatible in this regard because of their huge difference in scale.</p><p>And while Penrose admits that twistor theory adds nothing physically; that it's just another way of viewing a situation mathematically, he also realizes the need for us to see things differently than we have.</p><p>It is this adherence to a particular view that causes all the problems in the first place. If you look at how these different views are constructed, you'll see the mathematicians switch from one domain to another through various class equivalences whenever it suits them. When they need to express vectors they will jump to a manifold model, or a more generic (abstract) deformation of an algebra. In other words, we lack enough views. So we supplement the one we have in an attempt to normalize them.</p><p>Curiousier still is Penrose's tiny discussion of consciousness in which he attempts to "renormalize" consciousness in terms of objective reduction. He theorizes that the waveform reduction that collapses due to quantum gravity may be at the seat of consciousness's ability to complexly surject different sensory views into coherency. This suggestion is of the same kind as his forced synthesis of twistor theory. The satisfaction of trying to find a single metric, a single complex knot of relations that cannot be unraveled but contains all the "moves" is like a physicist trapped on a chess board recognizing the orthogonal formation of board, or as in <i>Futurama</i> the Professor discovering the smallest unit that constitutes the universe is the pixel.</p><p>In a real way, Penrose seeks to calibrate physics to the mathematical domain. He doesn't want beautiful math that doesn't apply, that is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth of which the entirety of the physical is mapped; although mentality is generated from the physical and mathematical/Truth is generated from that.</p><p>The Platonic ideologue he insists on lies on the equivalence of function, on the purity of the sameness of process from point to point of the same type. Never-mind that the subatomic particles we find today are largely generated from artificial means. Penrose would assume as sameness of process that forces a universalization, but that is the way metaphysics and science both work, to equate different phenomenon as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we see, all relations are born locally, within a limited scope. Their extension cosmically creates the basis for which we start to see a degradation of relation qua variance (pollution, or various forces of form-fitting). After all, we can have no irrationality without first being able to posit a rational sheet of complete consistency.</p><p>Nonetheless, although this is a lengthy book it is still beautifully written. I wonder who Penrose's audience is, for he approaches much mathematical complexity in such a short time, talking about basic principles like polynomials and trigonometry before jumping into Lagrangian manifolds and so on. Still, if you hunger for complexity and abstraction, here it is. Much of his explanations of very complex concepts are very clear, although at times we could use more handholding. His pictures are also very interesting and complement his point nicely.</p><p>Well worth the effort to read.</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/11509598?shelf=2015">2015</a> <a href="https://www.goodreads.com/review/list/11509598?shelf=impressive">impressive</a> <a href="https://www.goodreads.com/review/list/11509598?shelf=mathematics">mathematics</a> </ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/37427599-enrique-oviedo"></a></section><section><p>232 reviews12 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/3553486082">December 5, 2020</a></section><div><p>Un libro con un objetivo tan ambicioso como describir el estado del conocimiento científico que poseemos sobre la realidad profunda de la naturaleza y los caminos para avanzar en lo que nos falta por descubrir es realmente difícil de valorar.<br />Este es el único libro científico que aparece entre los 100 primeros libros de la lista de Goodreads "Libros que te llevarías a una isla desierta". Creo que está ahí con todo merecimiento. Es un libro que admite muchas relecturas- Durante los casi dos meses que me ha llevado su lectura las cosas que leía me venían a la mente continuamente. Todo lo que plantea es interesante, estimulante y te expande la mente.<br />El único problema con este libro es que en una isla desierta no hay Internet. Me explico: a pesar de sus más de 1.400 páginas, el libro es casi imposible de seguir solo con la información que en él aparece. He tenido que recurrir en muchísimas ocasiones a la web a buscar la información necesaria para "rellenar los huecos" de lo que estaba leyendo. El autor te lleva de la mano durante la exposición pero frecuentemente te suelta y te obliga a hacer un acto de fe en la argumentación o da por sentada la evidencia de un razonamiento matemático. He echado de menos enormemente enlaces a recursos en Internet donde se explique el detalle de las ideas expuestas o aparezcan resueltos los ejercicios que propone. En mi caso, solo cuando he podido seguir la línea argumental en detalle he tenido una imagen clara de lo que está leyendo.<br />En cualquier caso, el esfuerzo de enfrentarse a la lectura de este libro es ampliamente recompensado por la ampliación de tus horizontes mentales.<br />Resulta también fascinante el vislumbrar cómo funciona la mente de un científico como Roger Penrose, para mí, uno de los más grandes pensadores vivos.</p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/20245481-mohamed-al-jamri"></a></section><section><p>174 reviews110 followers</p></section></div><section><section><p><b>Shelved as 'half-read'</b></p><a href="https://www.goodreads.com/review/show/1601269160">April 14, 2016</a></section><div><p>This book is not for those with no strong background in mathematics and physics and it is definitely not for lay readers.<p>Except for the first 40 pages or so the book material was very sophisticated and hard to understand for me. Today I decided to stop as for the past 30 or so oages I could only understand little of what I was reading.</p><p>I'm putting it on hold now and I may return to it later after establishing a strong base in mathematics and physics.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/8683240-f-avery"></a></section><section><p>30 reviews</p></section></div><section><section><a href="https://www.goodreads.com/review/show/341500332">January 19, 2013</a></section><div><p>By his own admission in the preface, this is Penrose' attempt to popularize the current thinking in theoretical physics, including quantum mechanics, relativity, and unification theories such as string theories and quantum gravity. In the introduction he says (paraphrased) that he has intentionally gone for the more mathematical route, in spite of advice to the contrary, but he hopes that those without a mathematical bent can just skip the equations and get the gist of the concepts anyway.<br />With due respect to the author, his attempt at “popularization” is a failure. I wonder who he thinks his target audience is when he goes to great pains to explain basic concepts such as imaginary numbers and why they aren't so mysterious and yet throws out higher level abstractions that take time even for a college graduate to feel comfortable with. His target audience seems to drift from the lay person on the street up to professional mathematicians and physicists. <br />In my opinion this book of over 1000 pages replete with equations and complex diagrams would be good fodder for several graduate courses in mathematical physics. He introduces such abstractions as complex analysis, abstract algebra, manifolds, bundles on manifolds, tensor fields, Lie groups, Hilbert spaces, etc with just a few words of explanation and a lot of hairy equations, after which he marches on with advanced theoretical concepts and applications to physics. I studied most of those topics in graduate school to some degree, but I was especially comfortable with Hilbert spaces and complex analysis. And yet, it was all I could do to keep up with him. Perhaps it's the fact that I was in my early thirties then and had more functioning neurons, but this 63 year old brain found it hard to track his descriptions, let alone the equations. I confess that (in spite of considering myself an erstwhile mathematician) I often attempted to take the route he had advised for the non-mathematically inclined: just gloss over the equations and get the general concept. But his descriptions are mostly so down in the details that I found it difficult to get to the general concepts from the text alone. <br />I also decided that I don't like his writing style much. It varies from overly verbose and redundant to cryptic and abstract in the extreme. And the edition I have was poorly edited: there were many mistakes such as unclosed parentheses, repeated words, missing words, and grammar mistakes. Given how turgid his prose is I don't envy the job of the editors, but it's still their job to find those kinds of obvious errors.<br />The one good thing from all this is that I think I finally (kind of) understand tensors and tensor fields. For whatever reason I didn’t get into tensors when I studied differential geometry in the early 80's and I’ve found this to be a deficiency in my education over the years (e.g. understanding the field equations of general relativity). His description prompted me to study up on tensors and I found a couple of good websites with detailed descriptions and examples. <br />In any case, I DO recommend the book if you have a knack for or interest in advance mathematics and theoretical physics. I DON’T recommend it if you want an easy read in popular science to make you feel smart :-).</p></div><section><ul><a href="https://www.goodreads.com/review/list/8683240?shelf=owned">owned</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/9914220-david"></a></section><section><p>384 reviews11 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/420638683">September 23, 2012</a></section><div><p>Penrose examines the turn modern theoretical physics has taken in pursuit of multi-dimensional mathematical models to develop a unified model of the sub-atomic realm. His argument is not entirely mathematical, though he does have good arguments against unnecessary complexity from the point of view of the straightforward progress made by theoretical physics in discovering the mathematical elegance of relationships among various observed constants. His most profound argument against String Theory is a failure to make any predictions which could be tested by observation. He makes an eloquent argument for pursuing alternate models instead of mathematical physics being caught in what may ultimately prove to be a dead end. He proposes several ways forward, including his own twistor theory. <p>Penrose reminds me of Feynman in his fresh thinking. Feynman's development of quantum-electrodynamics required thinking of observed phenomena in a new way. For those willing to scratch the surface of modern physics, Penrose provides a lucid primer. He even devotes nearly a third of the book to laying out the math so the reader can begin to understand what follows. At more than a thousand pages, this is a serious primer.</p><p>I thank the friend who loaned me this book a few years ago and allowed me ample time to digest what I could. Yes, I did return it, but I may need to acquire my own copy.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/3357765-jimmy"></a></section><section><p>Author <i></i>5 books199 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/112508830">July 20, 2010</a></section><div><p>Not an easy read because of all of the math, but well worth the effort for those who can make it. </p></div><section><ul><a href="https://www.goodreads.com/review/list/3357765?shelf=science">science</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/4885706"></a></section><section><p>Author <i></i>2 books95 followers</p></section></div><section><section><p><b>Read</b></p><a href="https://www.goodreads.com/review/show/2022807271">June 7, 2017</a></section><div><p>Най-накрая приключи.<br />И само това да бях коригирала, щях да се гордея със себе си.</p></div><section><ul><a href="https://www.goodreads.com/review/list/4885706?shelf=%D0%B8-%D0%B7">и-з</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/11862588-maarten"></a></section><section><p>18 reviews4 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/649625097">September 6, 2019</a></section><div><p>The story goes that Stephen Hawking was once told by a book publisher that every formula in his book would halve the amount of readers (or sales, almost the same thing, but not to a publisher). He was , of course, totally and utterly wrong. The Road to Reality contains about 1100 pages and, on average, there's about 9 formulas per page. That makes roughly 10,000 formulas. According to this publisher's law, that would halve the sales ten thousand times (2^(-10000)), so a rough estimate of the amount of readers left is around 5x10^(-3001), which is a number so absurdly and unimaginably small, you have to be a Belgian surrealist painter to be able to imagine it. Roger Penrose would be left with much, much less than a single quark of a reader. Judging by the amount of readers here, this is obviously not the case.<p>What this publisher was pointing out, however, was that, in order to attract a lay public, you have to shun formulas, because they might chase them away and you wouldn't be able to teach anybody anything because there wouldn't be anyone left. Hawking followed the advice, wrote a book for the layman and, in my humble opinion, failed miserably. The layman didn't understand anything from his cryptic text, because they were missing several dozens of books of background information needed to understand most of the concepts. The more informed readers were chased away because of the lack of depth, the haphazard and disconnected way the concepts were presented and the absence of the mathematical beauty. It did sell well, so from this perspective, the publisher was undoubtedly right (and this was probably the only perspective he was interested in).</p><p>This fiasco teaches us something very important: writing and reading about present-day physics is no small feat. Lots of background is needed (yes, mathematical as well). However, unfortunately, most writers listen to publishers and omit the formulas and lots of the difficult bits as well, so the task for the physics reader is greatly hindered.</p><p>Luckily, Penrose is a kind old British gentleman, not afraid to take up the glove and rise to the challenge. The Road to Reality is his magnum opus, introducing the reader to modern physics (mostly cosmology and to a lesser degree quantum mechanics) , without oversimplification or the omission of essential formulas. He doesn't muck about either. If mathematics is what you need to understand it, mathematics is what you'll get. No less than 16 of the 33 chapters are devoted solely to mathematical foundations. After that, Penrose gives an overview of the established physics (mostly special and general relativity, quantum mechanics and some thermodynamics. The last few chapters are concerned with the more controversial topics, like string theory.</p><p>The mathematical part is, to the best of my knowledge, quite complete. The established physics is concise and omits most things that aren't related to the aim of the book: present-day speculative cosmology. For the last part, Penrose focuses on string theory (currently still the most popular group of theories), loop quantum gravity (the most interesting contender) and twistor theory (Penrose's own field of research). His account of these theories is very honest, making no secret of his critiques on certain fields of research and warning the reader to take his interpretations with a pinch of salt and often pointing the reader towards books containing views conflicting with his own.</p><p>Does this make The Road to Reality the ultimate physics book for the dauntless layman? Of course not. The task Penrose set himself is neigh impossible. One cannot replace several dozen textbooks by one, albeit bulky, volume, even if it is written by someone as erudite as him. A lot of his explanations are just too brief. He would need another two to three thousand pages to be able to explain everything thoroughly. Furthermore, the splitting of the maths and physics is different chapters is probably necessary, but it means Penrose refers a lot to previous chapters. Since I have a hard time exactly remembering some subtle mathematical notion from 400 pages ago, I needed to skip backwards and forwards a lot, making for quite a laborious read (not something to do while commuting by bus, for example). The subject itself is very slippery too. Current theories cannot be verified (yet) by experiments, so theoreticians are only guided by very abstract notions, such as mathematical beauty, or instincts honed by years of hard work. Such things are often very hard to convey to anyone not a specialist in that particular field, although Penrose does a good job, nonetheless.</p><p>It is probably the closest you'll get to a textbook without actually reading a textbook. The Road to Reality trumps A Brief History of Time in many ways, but ultimately it cannot be avoided that one needs to read a lot more to truly understand physics, but that's not necessarily a bad thing (publishers will agree).</p></p></div><section><ul><a href="https://www.goodreads.com/review/list/11862588?shelf=natuurkunde">natuurkunde</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/23888196-rama-rao"></a></section><section><p>713 reviews100 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/860619752">February 20, 2014</a></section><div><p>Deciphering the laws of physics to create universal reality<p>This is an exhaustive review of the laws of physics as related to physical reality with significant emphasis on the mathematical component. The author is an outstanding mathematical physicist of our times, and in this book of 1100 pages, he describes the concept of space, time, and matter (energy) in terms of classical physics, quantum physics, string theory and its derivatives. </p><p>In physics, the behavior of objects is understood in terms of the action of a force; a vector quantity, which has both magnitude and direction. The force acts on a matter and produces a causative action that results in an effect. The cause - effect is one of the fundamental aspects of classical reality, but it gets fuzzy and uncertain at submicroscopic levels (quantum physical reality.) The main object of physical law is to describe the reality we observe. Our observation includes this universe that is made of space, time, matter, and energy. All objects are made of matter, which exists as complex structures composed of molecules, atoms and fundamental particles. Matter is also a form of energy and the two forms can interconvert as described by the Einstein's famous equation. The fundamental particles has certain physical properties and the manner in which energy (and force) is expressed is though their association with the so called force particles that are responsible for four fundamental forces that operate in nature, they are; electromagnetism, gravity, strong and weak nuclear forces. The four forces mediate matter-matter interaction and facilitate matter-energy conversions in spacetime and thus explain physical reality. The key to the understanding of nature and physical reality is to discover a theory that satisfactorily explains all the four forces and this theory must be experimentally verifiable. Unfortunately, this has not been achieved so far, but we have theories that can be verified but explains only three forces. One single physical theory that explains both quantum and classical realities have not been successful mainly because the nature of gravitational force (curved spacetime) is difficult to describe in a unified situation, since space and time at the most fundamental level are also quantized (exist in discrete quanta) and are they dynamic (not static background). </p><p>To understand this book the reader is required to have undergraduate level physics and mathematics; the author explains in the introductory part of the book why he chose to include mathematics despite its negative impact on the book's marketing potential. It would suffice to say that the interplay between mathematical ideas and physical behavior played an important aesthetic role in the minds of great physicists, and Albert Einstein is one of the most important figures in being attracted aesthetically to a particular idea. You can skip chapters 1-16, and from chapters 17-30, general discussion about geometry of spacetime, quantum physics, quantum field theory, quantum cosmology and the standard model of particle physics is presented. I found the last four chapters to be most interesting. </p><p>A brief summary is as follows: The unification of special relativity and quantum theory led to quantum field theory (QFT) which produced a minefield of infinities, but with some ingenuity, the infinity problem was circumvented leading to standard model of particle physics which is in good agreement with nature. The controversy between the quantum relativity group and the QFT side is that the latter group tries renormalizability or finiteness as the primary goal, but the former group likes to solve the conceptual difficulties between the two theories. The combination of two theories of particles physics into one framework to describe all interactions of subatomic particles, except due to gravity, is called standard model. These two theories are electroweak theory and quantum chromodynamics. They describe force interactions between particles in terms of exchange of intermediary particles. The author also engages the reader in an insightful discussion of many other theories. </p></p></div><section><ul><a href="https://www.goodreads.com/review/list/23888196?shelf=physics">physics</a></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/34560388-sa-rah-muhammad"></a></section><section><p>24 reviews264 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/1240519963">April 22, 2015</a></section><div><p>This is an extraordinary book and certainly there is nothing else available on the market that is quite like it.<p>Penrose is a pre-eminent mathematician whose work has affected my own thinking in deep ways. Often I've discovered, to my surprise, that some viewpoint which I learned from another source in fact derived ultimately from Penrose himself, the author of this other source having been, as it turns out, a student of Penrose. As an example I offer "Visual Complex Analysis" by Tristan Needham. I encountered this book in high school and so powerful was its exposition that it stuck with me all through college and beyond to the present day. I couldn't help but notice, while reading "The Road to Reality," that Penrose engaged in a similar revelry around complex numbers -- and so it was a pleasant surprise to see that Needham indeed had studied directly under Penrose! Despite having this book in my collection for a few years only recently did I discover the connection.</p><p>With this tangential introduction out of the way, let me say at the outset that I cannot recommend this book to just anyone. It requires a great deal of mathematical acumen -- or perhaps, more accurately, a great deal of explicitly mathematical *interest*. You needn't be a mathematician, but you positively must delight in the opportunity of learning the mathematics of the universe. Even if you have a degree in mathematics you're likely to find something here you haven't encountered before -- for instance, I had not previously seen the notion of a hyperfunction which Penrose enthusiastically presents in connection with the Fourier transform.</p><p>The book's mathematical explanations are quite idiosyncratic, and I think this reflects the depth of Penrose's intuition on the topics. It elevates this book from an encyclopedic reference to a personal outpouring of the author's vision of the world. Not only does the book feature unique topics that aren't commonly taught, the aforementioned hyperfunctions being an example, but even those which are commonly taught are explicated here in a unique manner. Penrose's style is unabashedly geometric, and so even partial differential operators on manifolds he almost always thinks of as vector fields. The book is filled with many beautiful hand-drawn diagrams showing everything from a fanciful vision of the creation of the cosmos to a field of one-forms on a surface to the conservation of electric charge in spacetime. And the book prominently features throughout his diagrammatic notation for tensor algebra, something again which I had never encountered elsewhere.</p><p>I should say that this book approaches its physical topics from an exceptionally high level. You will probably not be able to learn electrodynamics from Penrose, not here. I don't recall the common form of Maxwell's equations even occurring in this book. Rather, he simply writes them down in the simplest, most beautiful, and most abstract form, using differential forms and exterior calculus. To delve in deeper, rather than expanding out these equations, he instead focuses on how they can arise as the curvature of a bundle connection via gauge theory. This is both stunningly beautiful and horrendously detached from practice.</p><p>Despite the overwhelming emphasis on theory and mathematics, the book is quite adamant in insisting that physics still must be physics. Penrose is not optimistic about string theory, though he does give it some treatment towards the end for completeness. He's perhaps like Feynman in that regard -- he possess a deep appreciation for the mathematics and the theory, but at the same time is very uneasy with the lack of testability of much of modern theoretical physics. His own theory, twistor theory, is just as untestable, though he's honest about that.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/3346363-matt-heavner"></a></section><section><p>865 reviews10 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/224453891">June 29, 2013</a></section><div><p>This is quite a challenging read -- but definitely worth the effort! The first half is primarily "math" while the second half is "physics." Penrose did an amazing job of writing a guidebook to a great deal of the breadth of both of these fields. I felt there were some uneven sections -- I remember a great deal of discussion on Fourier transforms and thinking that if a whole section of discussion is needed there, how will the reader keep up through differential topology, twistor theory, diagrammatic and group theory notation, etc.. But overall, it was great. The writing was almost playful at times, especially as the book progressed. Penrose did a nice job of self-identifying his biases. I enjoyed the discussions of the relationship between math and reality (p 631 "What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description and then trying to regard that description as describing a 'reality'?"). The last two chapters of the book really explored this idea further.<p>The discussion of string theory was especially understandable (and self-admittedly biased).</p><p>It struck me as a bit funny that (especially later in the book) there was more and more reference to the "magic of complex numbers" and yet in one of the final sections there was an argument that there is nothing more or less confusing between real numbers and complex numbers).</p><p>This book was extremely "hyperlinked"/self referential. At first all the links were "forward links" (necessarily..) and mostly I ignored them. As I got further into the books, I started following the "links" (both forward and backward) much more. I found myself using the index and really engaging with the text. As I started the review -- it takes some work and is definitely worth it!</p><p>I plan to reread this book in a few years.</p></p></div><section><ul></ul></section><hr /></section></article></div><div><article><div><section><a href="https://www.goodreads.com/user/show/586851-michael"></a></section><section><p>12 reviews2 followers</p></section></div><section><section><a href="https://www.goodreads.com/review/show/45442747">February 9, 2009</a></section><div><p>I desperately want to make it through this book. I might be crazy. I think part of my fascination with finishing it is to compensate for not finishing engineering school. I can tell you this... It would be a lot easier to read if I had attained my degree (and actually learned the material along the way). Nonetheless, this book opens in the most interesting and captivating fashion, which says a lot about a book that works to explain the universe by walking through the history of mathematics. A couple of years ago I saw a man reading it while on the treadmill at the gym. The book is 1000 pages long and after seeing the title I asked him about it. I asked him if one had to have a firm grasp on upper level mathematics to read it (which, despite going through Calculus 1-4, I do NOT). He said: "Oh no, I don't know much math but I am enjoying it anyhow". Well, it became apparent early on in the book that the guy at the gym was off his rocker (er, off his treadmill). After the opening attention grabber, the author details the beginnings of mathematics, the definitions of "proof", "theorem", and "postulates", and aims to start from "point A" and go through to what ever lies beyond mathematical "point Z". So, with an initial giddiness I started through the book. Soon I had a scratch pad handy. Then I was reading and re-reading sections to try and get a grasp before moving on. It was reminiscent of my struggles during my calculus classes while at Michigan Tech. I have a strong interest in the material and a desire to learn it but it hurts my little brain. In summary, I am still grappling with the first 100 pages, but would still highly reccommend this book, especially to those with an interest and aptitude for math &amp; science. I'll keep at it.<br />~ Mike - February 2009</p></div><section><ul></ul></section></section></article></div></div>||||I|||| * Home
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 The Road to Reality: A Complete Guide to the Laws of the Universe

 Roger Penrose

 4.14
 7,559 ratings 219 reviews
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 Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.
 Genres Science Physics Nonfiction Mathematics Philosophy Reference Popular Science
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 1099 pages, Paperback

 First published January 1, 2004

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 Roger Penrose

 84 books 1,001 followers
 Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. He has received a number of prizes and awards, including the 2020 Nobel prize in physics, shared with Reinhard Genzel and Andrea Ghez for the black hole discoveries, and the 1988 Wolf Prize for physics which he shared with Stephen Hawking for their contribution to our understanding of the universe. He is renowned for his work in mathematical physics, in particular his contributions to general relativity and cosmology. He is also a recreational mathematician and philosopher.

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 4.14
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 Manny
 Author 28 books 13.4k followers
 September 5, 2011
 Many of my all-time favourite books make the list because they show you what it's like to be inside the mind of an extraordinary person. While you're reading them, Churchill's History of the Second World War and Yourcenar's Mémoires d'Hadrien let you be a great statesman at a pivotal moment in history. Simone de Beauvoir's autobiography, more than any other book I know, gives you the feeling of being a major literary figure. Polugayevsky's Grandmaster Preparation , which many chessplayers treat almost as a sacred text, is the only truly honest account I've seen of how a top Grandmaster thinks.

 Penrose belongs in this select company: I finally believe I have some idea, no matter how faint, of how a great mathematical physicist sees the universe. Like the other books, it's not an easy read. You can't build up this kind of picture without including a huge number of details; if you took them away, the whole texture of the world would disappear with them. Churchill needs the maps, troop movements and political networking. De Beauvoir has to assume (in my case, alas, incorrectly), that you're conversant with most of French literature. And if you removed the chess from Polugayevsky, there wouldn't be any story.

 In Penrose's case, it's mathematics and physics: he resolutely refuses to dumb it down, and includes a seriously frightening quantity of Greek letters. If it really were true that every equation halved your sales, he would not have sold a single copy. What saves him, and makes the book readable to non-experts like me who at least have some mathematical background, is his uniquely visual way of experiencing mathematics. Penrose can obviously hack the equations, but he also has to see them, and he is astonishingly resourceful at coming up with visualisations. The ones I liked most had to do with Special Relativity. You may recall this fairly well-known picture by Escher:



 What I didn't know was that it illustrates the "hyperbolic geometry" which underlies Einstein's Special Theory. In Special Relativity, the speed of light is an absolute limit, so velocities can't simply be added: the correct formula for combining them is the one shown in the picture. You can add any number of fish together and never reach the edge; similarly, no matter how many time you add a velocity to itself, you never get to the speed of light. Believe it or not, the diagram exactly models the equation! And another geometrical argument he used here is nearly as beautiful. A great deal of nonsense has been written about the "Twins Paradox" (for example, by Robert Heinlein) . Penrose's explanation is wonderfully concise and elegant. In Minkowski-space, a straight line is counterintuitively the longest distance between two points. The twin who flies out into space has a less straight world-line than his twin who stays at home, so he ages less. Thanks to Penrose, I can now see it.

 It turns out that theoretical physics is anything but a dry technical discipline: you come away feeling that these people are visionary poets who have chosen to write in mathematics rather than ordinary language. Blake is one comparison who came to mind, and I can't resist the temptation to juxtapose Blake's image of God:



 with Penrose's:



 If you're wondering what God is doing, it's actually pretty much the same as in Blake's version: the picture dramatizes the extremely low entropy of the Universe immediately after the Big Bang. I had not previously appreciated how remarkable this is, and the puzzle it represents is central to Penrose's exposition. Once again, the picture isn't gratuitous. He's illustrating, in a humorous way (the book is often funny), an extremely serious point.

 As I've said, it's not an easy read. It demands a great deal of concentration, and I think I must have spent at least two or three hours a day over the last month ploughing my way through it. A lot of that time, I was supposed to be doing other things, but I'm glad I ignored them and read Penrose instead. He's changed my way of looking at the world as much as Dante did when I read The Divine Comedy in 1999.

 Now, if only it were in terza rima with animated illustrations by Gustave Doré and Terry Gilliam. Then it would truly be perfect.
 _____________________________________

 We had another CERN physicist to dinner last night, an Australian post-doc who's working on validation of the Standard Model. I asked her if she'd read Road to Reality .

 "I stopped reading popular science books when I was an undergraduate," she said apologetically.

 I said it wasn't really a popular science book, and she opened it for a few seconds. "Hm, yes, it does seem to have quite a lot of equations," she muttered doubtfully, and then she put it down again.

 Something seems to have gone slightly wrong with the marketing campaign for this book: laymen think it's a book for physicists, and physicists think it's a book for laymen. I'm reassured to see a fair sprinkling of reviews here from people who give every appearance of having read and enjoyed it.
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 WarpDrive
 272 reviews 380 followers
 August 4, 2016
 I am finished, finally. All the 1050+ pages of this ambitious behemoth - including many exercises. What a ride!...
 Finished? Well you are never finished with such a book, titled “The road to reality” but actually providing more than that: providing nothing less than a “road-map” to reality, and opening to the reader new beautiful vistas in modern mathematics and physics. I am sure that I will come back to this book in the future, as a source of inspiration and for future reference.

 Before I start, I must confess that it feels slightly ridiculous for me to critique such a monumental work by a crazy genius like Penrose, who clearly lives in a higher realm of consciousness than the large majority of us common mortals. Never mind – the best I can do is to describe my personal, deeply humbling experience in reading this amazing piece of intellectual prowess. Penrose is clearly the Mozart of mathematical physics: genius, craziness, wild imagination and pure technical virtuosity all combined into a unique intellect.

 Let me start by highlighting some of the peculiarities of this book (due, in my personal opinion, much to editorial/commercial choices/pressures, and only partially to personal choices by the author himself). This is also important to the proper positioning of this book within the overcrowded (and of hugely varying quality) world of popular science books:

 A) this book is sold as a science “popularization” (probably with the objective to attract as wide an audience as possible): in reality this book requires a significant amount of background knowledge in mathematical physics; in fact there are some sections where the equivalent of a full maths/physics degree would be required to fully appreciate all the subtleties of some of the subjects being treated. I would personally recommend, as a prerequisite, the following minimum:
 - calculus (including multivariate)
 - ordinary and partial differential equations (at least at rudimentary level)
 - complex analysis
 - linear algebra
 - basics of topology
 - ideally, differential geometry at basic level
 - in the physics area, some prior exposure to Maxwell's equations, the Lagrangian and Hamiltonian formalisms, the basics of quantum mechanics and relativity (at least special) would also be a great help.
 If a reader tried this book with no prior exposure to any such topics, I am afraid that it all might prove a very steep learning curve indeed. I had all the above pre-reqs, and still it was, for me, an occasionally demanding if not challenging book in terms of required focus, time and intellectual stamina. But this is also a strength of this book - one of its greatly rewarding aspects is that the author does not refrain from exposing the reader to real maths (some of the exercises can be pretty hardcore), and to get into the heart of modern physical theories such as QFT and GR, if you want the real thing, you simply can't avoid getting into some real maths.

 B) this book is not really a textbook, or at least not an ordinary textbook: it lacks the necessary structure and flow, and (too) many important derivations are left as exercises. The depth of mathematical analysis and rigour are uneven, and they seems also highly dependent on the occasionally whimsical personal level of the author's interest in the subject. Moreover, the formal treatment of many subjects is highly original and something that, unless you have had some previous exposure to them, might be confusing and certainly not easily reconcilable with what standard textbooks present. But this is part of the beauty of this masterpiece.

 C) this book, contrarily to what stated in the title, is not a “complete” guide to the laws of the Universe. While managing to concentrate so many sophisticated and fascinating subjects into a single book, and at a serious level of detail (which is no mean feat, and something quite unique), I think that Penrose should have written two books (one on the mathematical underpinnings, and a separate one on the physical aspects) rather than trying to concentrate such a massive amount of information in one single big book.
 This approach (admittedly less palatable from a commercial standpoint) would have allowed him to expand some important areas that he has unfortunately neglected in his otherwise magnificent book (such as finiteness and re-normalization issues in QFT) and which would have also allowed him to include other subject matters too – for example, the coverage of thermodynamics focuses mainly on the statistical view of the Second Law, neglecting all the other elements.
 But make no mistake - this book feels like a "War and Peace" of mathematical physics – a colossal enterprise that just keeps giving and giving, a treasure trove of original insights, beautiful hidden connections, amazing stories and revelations. A fantastic and detailed exploration of quantum physics, relativity, of the current trends in the attempts to unify the two, and of cosmology. An exhilarating intellectual adventure in the company of a crazy genius.


 Let me now make a few comments about the author's peculiar personal style and approach:
 - Penrose's prose is beautiful, even if considered from a purely literary perspective; often very clear even if sometimes a bit too concise; it usually flows very smoothly, and it occasionally even acquires some poetical undertones in sections where aspects of philosophy of science and philosophy of mathematics are treated with insightful passion.
 - Penrose relies heavily on a diagrammatical/pictorial/visual/topological representation of the concepts being treated. In doing so, many beautiful, eye-catching and highly informative hand-drawn diagrams/pictures are presented to the user. This approach generally works very well, but there are instances where (in my personal opinion) the most intuitive and simplest way to learn/teach a new concept is to present it analytically (in mathematical format), and where the purely visual approach might be quite limiting if not outright confusing. For example, the visual explanation of the concept of “covariant derivative”: while important and helpful, is in my opinion by itself not sufficient to get a real appreciation of the mathematical features of this entity: its analytical derivation, and its expression using the Christoffel symbols, would have actually better clarified its tensorial nature.
 - In order to condense as many subjects as possible within the constraints of the space allowed by one single book (even one of 1050+ pages) Penrose has left the derivation of many important results as “exercises”. The exercises are therefore very important, they are a must in order to get a full appreciation of the underlying theory, and some of them are beautiful and rewarding (like exercise 22.32, which entails a beautifully elegant derivation of the Laplacian in spherical coordinates, using the curved metric and covariant derivatives). But some others should not have been left as exercises, and they seem no more than an editorial cop-out: there is one exercise that is even asking the reader to complete a significant derivation step of the GR field equations! (thankfully there is a website where many exercises have been solved by other readers (the majority of them clearly with a professional background in mathematical physics) – see https://sites.google.com/site/vascopr... ).
 - I love Penrose's great intellectual honesty in not just debunking much of the hype behind String Theory and Multiverse Hypotheses in general, and in destroying the so-called “Strong Anthropic Principle”, but also in making very clear the speculative character of some of his own positions and theories. I also love his great originality and independence of mind, and his nuanced, multi-disciplinarian approach which includes aspects of philosophy of science and considerations of pure mathematical nature.
 - Penrose has reached such a higher, rarefied level of proficiency in mathematical physics that he must have completely forgotten how common humans think in relation to mathematical formalism. Just as an example: after getting into pretty advanced stuff such as hyperfunctions, and treating it like if it is the simplest thing on Earth, the author then refuses to get into a detailed definition of differentiability of a many variable function (which is quite simple, really) because "it is too technical"!! So his ideas of what is complex can occasionally be significantly at variance with what the common mortal might think.


 Finally, let me add here some miscellaneous notes about selected individual chapters of this majestic book (it is a very incomplete list, only a severely reduced sample, as there is simply too much stuff in this book for me to be able to analyse in just one review):
 - In the first few chapters, after a fascinating introduction of overall philosophical character, Penrose briefly addresses some of the basic fundamentals of mathematics, including a short but intensely interesting discussion about the Axiom of Choice and its relationship to the Zermelo–Fraenkel set theory. A totally fascinating subject that unfortunately Penrose only touches, without developing into more detail.
 There is also a fascinating treatment of hyperbolic geometry, and of the number system/s. However, when dealing with the relationship between real numbers and reality, the author does not make any reference to important aspects such as computability and irreducible complexity, as for example addressed by the excellent work done by G.Chaitin.
 - The author then gets into one of the most beautiful and fascinating realms of mathematics - complex analysis. The treatment is concise but done well, and I completely share Penrose's enthusiasm and love for the aesthetically as well as functionally beautiful world of complex numbers, which he calls “magical” with good reason.
 - Another subject of interest treated are the fascinating quaternions, which extend the complex numbers and provide the uncommon and interesting features of a non-commutative division algebra. There are in the book a couple of minor missing things in relation to the algebraic structure of quaternions: an algebra is a vector space that must also be equipped with a bilinear product, and a ring (being also an abelian group under addition) must be provided with an additive inverse.
 Moreover, Penrose is dismissive of the utility of the quaternions in the development of physical theories – this is correct, but it must also be said that quaternions find important uses in Information technology applications, in particular for calculations involving three-dimensional rotations, computer graphics and computer vision.
 - Penrose could not have forgotten the extremely important Clifford/Grassmann algebras, which are foundational to the entire architectural structure of mathematics, and he didn't; they are treated well, but a bit too succinctly in my opinion, considering their importance.
 - Symmetry groups are treated really well, clearly and concisely. Very nice.
 - Manifolds and calculus on manifolds: all is treated quite well, but I would have found quite helpful some more analytical detail rather than a focus almost exclusively on the visual/topological approach. I confess that here, in order to get a proper detailed handle of tensor calculus and exterior calculus, I had to consult other more traditional, “textbook-type” sources.
 - Chapter 16 (Cantor's infinities, continuum hypothesis, Godel's incompleteness, Turing computability and similar) is OK and well written, and it would be utterly fascinating to a neophyte – but of course it could not have been detailed nor exhaustive, considering the complexity and width of such subjects.

 - The “Physics” part proper starts with Chapter 17. Chapter 17 on spacetime, and chapter 18 on Minkowskian geometry (and special relativity of course) are succinct, but riveting and beautifully written. Just one small note: Penrose has a fetishism for non-standard, or uncommon, notational or representational choices, not always justified: for example, by using a non-standard metric tensor in page 434, Penrose gets himself into an error at the end of page 435 (c^4 should have been used rather than c^2) and I think that he would not have fallen into this typo, had he used the more standard and simple-to-use metric.
 - Chapter 19 (Maxwell and Einstein) are beautiful; Maxwell equations and Einstein field equations in tensorial/differential form are mind-blowing for their mathematical conciseness and beauty, and this is where the reader can start to see the value of the mathematical apparatus described in the previous chapters: things such as manifolds, tensors, exterior derivatives and bundle connections. Einstein's fields equations of general relativity are beautiful. Very rewarding. It all seems so neat and perfect, but then, the bombshell (at least to me, who was never told of such a thing!): the energy/momentum stress tensor does not account for the energy density of the gravitational field itself, and it seems that conservation of energy/momentum is non-local !
 - Chapter 20: Lagrangians and Hamiltonians: I must say that they are too hastily discussed - the derivation of the Euler–Lagrange equation (one of the most classic proofs in mathematics) is not treated, the Legrende transform to derive the Hamiltonian from the Lagrangian is not treated, the derivation of Hamilton's evolution equations is not treated either. Not very happy with this chapter.
 - The subsequent chapters on quantum mechanics are beautiful, and the description of the EPR issue is really nice. The derivation of Dirac's equations is equally beautiful. I also love Penrose's discussion and perspectives about the measurement paradox. Beautiful stuff indeed. An exception to the overall masterful treatment of Quantum Physics is chapter 26 (Quantum Field Theory) which is is a bit too qualitative - more like a "popularization" rather than a treatment at the same good level as done in the other chapters of this book – and unfortunately the important subject of re-normalization is treated only briefly and qualitatively.
 - The chapters on cosmology are very interesting and nicely written.
 - Chapter 29 is essentially about the measurement paradox and the various interpretations of quantum mechanics – succinctly but beautifully written.
 - The next chapters are essentially about the current unification attempts to reconcile QFT with GR. Penrose's FELIX experiment proposal (essentially testing the hypothesis of automatic quantum state-reduction as an objective gravitational effect) is utterly fascinating, but I feel that I should not bet any money on this daring hypothesis.
 - I must say though that I was disappointed by the second part of chapter 33 (twistor theory): in section 33.8 Penrose uses several verbose sentences to express mathematical relationships, rather than writing down the actual underlying equations - result: something quite close to incomprehensible. I also fail to get the underlying physical intuition. Pity, as the other 33 chapters and a half are mostly beautifully written, and generally very rewarding.
 - The last chapter (34) is beautifully written, and it deals primarily with aspects of philosophy of science and philosophy of mathematics.

 To summarize: this is an immensely rewarding, even exhilarating book - a fantastic reading and learning experience. And it has opened my eyes on many aspects and connections that I was not aware of, and new beautiful vistas in modern mathematics (for example: tensor calculus, and exterior calculus in general) that I will now pursue in more depth.
 After reading this great book, I can tell you that I now feel that the majority of popular science books I have read are dull and superficial by comparison.
 It is not a perfect book by any means, but overall it is a great book, unique in its approach and contents. Not exhaustive, but with a huge and ambitious scope, virtually unrivaled in its category. It is much more than a “standard” popular science book. Very highly recommended, to be bought, studied, enjoyed and kept for future reference.
 4.5 stars (rounded up to 5).

 UPDATE: with link to a beautiful series of online lectures about Tensor Calculus and the Calculus of Moving Surfaces: https://www.youtube.com/playlist?list... (highly recommended to anybody interested in this subject).


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 Infinite Jen
 77 reviews 180 followers
 January 21, 2023
 The story begins with me in the garage with my high school sweet heart. The one who had made the playground swing problem seem rather trivial through a guileless intuition which cast my cynical calculations in a kind of hideous antimony. An actor whose relaxed demeanor and gentle earnestness, served to effortlessly unweave the kinks in those rusty chains, and in so doing, spun intractable knots in my own heart. It was a union of opposites, me with my chin in my hand, and he with a wrench in his. There were no problems we could not troubleshoot in tandem. Our separate talents had even began to cross pollinate, with me sometimes starring up at the undercarriage of a vehicle and asking for a socket while he perused whatever theoretical oddities I was currently obsessed with. I could, with some confidence, suggest to people that their alternator was having a giggle, their radiator was taking the piss, their starter motor was an asshole, or, my favorite, “Your fuel economy is gobshite, bruv.” And he could clearly identify the value of switching his choice in the Monty Hall Problem, understand that some infinities are bigger than others, and comprehend the threat that a quantum computer would present to our current encryption protocols. This reciprocal exchange of mental dexterity continued to unfold one rainy day, with me sliding under a car on a rickety creeper (which I had damaged by repeatedly using it to luge down steep driveways at high speeds, causing one wheel to catch and be ground into an irregular half moon.), and Nicolas Kim Coppola (known professionally as Nicolas Cage) (ie. Nic Cage) flipping through the book I had carried in. He asked me what The Road to Reality was about. Paraphrasing, I said the following:

 Have you ever, while skidding down a vertiginous concrete pathway on a damaged creeper, felt the fixed vibrational frequency of healthy rotary friction give way to dissonant melodies which often presage the rapid, explosive disassembly of machinery under immense kinetic strain? Was all the blood in your superficial capillaries wrung out from clutching the sides of the sled in mortal terror, causing your knuckles to emerge from the dark like buds of white hibiscus and your pool-noodle arms to ripple like corded steel? Did your sweetheart, who you suspect must have reduced activity in his amygdala, (due to his performance in Ghost Rider: Spirit of Vengeance), leap from their stool and make to halt your (by now considerable) momentum using a bag of blood adumbrated by sticks of calcium (i.e. the vertebral column festooned in viscera and thinly veiled by contractile tissue that we call the human body)? During those tense moments you may have thought, in the heavily affected High English which is characteristic of all your poignant inner musings: Nicolas Cage, it is a pity that I can’t communicate with you more effectively. That our bandwidth is limited by verbal exchanges in which I must compress thoughts into packets of information and utter them as faithfully as I can in the hopes that you will receive and unpack them with minimal noise inserting itself during the transfer. Putting aside incidents in which my limbs have animated in the manner of an ecstatic Neil deGrasse Tyson, this is the extent of my ability to let you experience what it’s like to be me. I cannot understand your genius for seeing the good in every screenplay, and you cannot fathom the depths of my genius when it comes to nearly dying in bizarre ways. In those simple displays of affection where nothing is said, perhaps we say the most.

 And what of inhabiting the mind of a true genius, and more difficult still; the mind of brilliant theoretical physicist and math prodigy? With art, something primal touches the soul, so that even if you don’t understand the creative flourishes of virtuosos, you are moved and made aware of their power. Who could read Nabokov and not be humbled by its beauty and precision? Who could hear Hangar 18 by Megadeth and not respect how a guitarist’s flanges dance across wires like the legs of camel spiders on a heroic doses of methamphetamines? Who could see the Venus of Urbino by Titian and not want to bury their face in her gorgeous tummy and blow a gentle raspberry? And finally, who could hear Anton Chigurh request a ‘screwgie’ in No Country for Old Men and not be gripped by a palpable dread? But here the scientific genius faces a problem, in elucidating the purely conceptual matters of their field to a general public, they must conceal much of their brilliance. If they were to riff like Dave Mustaine and fill pages with the lateral movements of their mutant intellects, the majority of us could but collectively shrug before these strange symbols. But imagine if there were a book that managed the impossible. One that was simultaneously accessible to the laymen audience, but omitted none of the technical jargon which made it possible to appreciate the operations of their brilliant minds? Perfectly comprehensible to curious high school freshmen. What you hold in your hands, Nicolas Cage...” Sliding out from under the car and standing next to him. “This..” I say, taking the book gently in my hands. “Is NOT that fucking book!” Throwing it viciously to the ground and jabbing my finger at it. “THIS is madness, Nicolas Cage! This is fucking popsci for math and physics PHDs! Calculus, Fourier series, hyper functions, Riemann surfaces, Riemann mapping theorem, quaternions, Clifford and Grassmann algebras, transformation groups, Lie algebras, parallel transport, geodesics, curvature, exterior derivatives, calculus of manifolds, connections, fibre bundles.. In the first third of a book which contains, in its preface, words that indicate he wrote it for his innumerate aunt. Show me the numerically deficient aunt that made it through this with even the foggiest notion of what the hell was going on and I will crawl inside myself and subsist on my own incredulity until the stars grow cold.”

 Nicolas Cage, picking the book up and carefully inspecting it for damage, hands it back to me, saying, “It’s fine. You’ll understand it eventually. I know you will.”

 Begrudgingly I put the book under my arm and nod. I feel an insurgent grin dismantle the severity of my countenance. I silently curse his ability to mollify my tantrums so easily. I seize this renewal of levity to suggest we take the creeper out for some limit testing.

 “Wait!”

 I can now appreciate a lot this book. If you’re someone with a strong background in math and physics and you’re interested, I can’t recommend it highly enough. It may be the most wide-ranging book on theoretical physics I’ve ever seen, not merely summarizing material, but offering an in-depth treatment of many of the more sophisticated ideas of the subject. The first half of the book takes you through most of the mathematical techniques that physicists use today, gradually moving through things like, Riemann surfaces and complex mapping, hypercomplex numbers, manifolds of n dimensions, symplectic groups and tensors. Equations are curated magnificently on the basis of explanatory power. And here I would add that Penrose, perhaps owing to his genius, has a level of idiosyncrasy in his presentation that I don’t think I’ve witnessed since Feynman. It is quite obvious that what goes on in his brain is an intensely visual phenomena. All of his diagrams and drawings are incredibly helpful, especially if you too think in this fashion. The second half of the book is devoted to physics and the ascent is quite dizzying as we approach the various hopeful theoretical bridges we’re constructing in order to reconcile the discontinuities between our two most successful theories (general relativity and quantum field theory) and so you have discussions (it may be more appropriate, considering the sheer rhetorical heft with which Roger slings these ideas against the wall like wet pieces of bologna, to call it evisceration.) String Theory, M Theory, Loop Quantum Gravity, and Penrose’s horse in this race: Twistor Theory. If you do not have a background in these things, and don’t pursue high level mathematics recreationally, I would not recommend it to you as a comprehensive place to start. If you just want to keep it around and flip through it to occasionally augment your understanding with some clever illustrations, or you simply wish to marvel at it as an enduring artifact of the human intellect, by all means. But if you’re planning to work through it from front to back, caveat emptor.

 This is one of those rare gems that has brought me very close to experiencing the intuitive ease with which a mathematical genius operates. A beautiful work of staggering breadth and depth.
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 Robert
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 February 12, 2016
 Dave Langford, SF&F critic and reviewer, in his long-since defunct column for White Dwarf magazine, once said that, "There is a tendency to over-praise big books simply because one has got through them." I agree that this tendency exists but note that Langford gave no reason for it. I think the reason is more or less macho intellectual pride; look at me! I read this honking great saga! It must be great or I'd have to admit wasting my time! And I need to show off my intellectual credentials! Now imagine that the book is not only huge, but really difficult because, say, it's dense with obscure references (e.g. Ulysses) or full of mathematics and not kiddie maths, either...the temptation must be even worse.

 Hence I'm going to start my review with a couple of gripes: This book, which is full of maths, much of which would make your average undergrad scientist grunt with the strain at the very least, as well as physics to post-grad level in places, has no glossary of technical terms . There is ample cross-referencing and an index but these are no substitute. When you want to know, Clifford Algebra, which one was that again? (Because you've met ordinary algebra, complex algebra, Clifford Algebras, Lie Algebras and Grassman Algebras...), going back and reading through an entire section again to find out, is a bit annoying - a list of definitions at the back would have helped enormously. Admittedly this would have made a big book even bigger but it would have made it much more user-friendly.

 Gripe number two is in a similar vein; Penrose fails to supply a list of the upper and lower case Greek alphabet symbols and their names or a similar list for obscure mathematical symbols, such as del and scri. Given that nobody without training in Greek or in science is going to know these and such a list would only take up one page, its omission is egregious.

 This leads neatly into a topic that has been dicussed quite a bit here on Goodreads - namely, who is this book aimed at? What is it's purpose? Firstly I would point out that the subtitle "A Complete Guide to the Laws of the Universe" is not really true: Classical Thermodynamics is barely seen as we rush straight into the statistical view of the Second Law. Of the other three Laws of Thermodynamics, Zero is never mentioned and the others barely name-checked. I doubt many physicists would consider that all the basic theories have been covered in such a circumstance. But I think this is a marketing problem; I don't believe Penrose ever intended to write such a "Complete Guide."

 In the preface Penrose talks about wanting, with this book, to make cutting edge physics available to people who struggle to understand fractions. Now, this can only be taken as a joke, considering what one is up against only in chapter 2, but I would guess that Penrose genuinely wants to have the widest possible audience for his book whilst not compromising his aims.

 What are those aims? In my view he wants to give his personal views on the state of cosmology and fundamental physics but to be able to do it at an advanced technical and mathematical level and additionally to give his own philosophies regarding the nature of thought, science, maths and...Nature! This means that he wanted to deliver Chapters 27 - 33 on the physics/cosmology, bracketed by Chapters 1 and 34 of philosophising. The entirety of the rest of the book is simply there in order to equip readers to understand what he says in those six technical chapters! This requires 15 Chapters of maths and ten Chapters of physics/cosmology...

 Looked at this way, the book begins to reflect the genius and madness of the author: Many of the explanations in earlier stages of the book left me thinking, why do it that way? That's not the easiest way to understand this if you've never come across it before! He also goes straight to very general mathematical principles, missing out intermediate levels of abstraction that might make what comes later easier. He chooses to emphasise the geometrical/topological view of everything, which, it might surprise one to know, is not always the easiest way to understand things. Many of the choices of what to emphasise and what to ignore seem odd...that is until one gets to the late stages of the book.

 Upon arrival at Chapters 27 - 33 (i.e. what I think Penrose really wants to talk about) one can see that everything that has gone before has been put together in order to provide the most efficient route to understanding - hardly a page has been wasted. All those strange choices of what to emphasise, all the peculiar, non-standard explanations when easier explanations exist, all the leaping to the most general mathematical ideas, all the things missed out, all these things are done so that the points he wants to discuss can be followed without wasting time or space in what is a 1000+p book as it stands. The necessary skill, thought and effort required to do this impress me enormously.

 Inevitably this means that most of what is covered in the book of "standard" physics has been explained better (by which I mean more readily comprehensibly), even at a mathematical level, elsewhere - but not in one volume! The consequence of this is that Penrose's widest possible audience may not be all that wide: although he suggests one could read the book and ignore every equation in it, (something I often do when reading technical literature!) I suspect one would rapidly become bored and disenchanted. The unavoidable fact is that the greater your mathematical capabilities, the more you will get from this book and additionally, the more maths and physics you know before starting, the more you will gain from this book.

 Further, the more you are willing to study the book the more you will gain. Manny approached it by reading 3 hours per night until done. I would suggest that the nearer to that approach you can get the better off you will be, even though I failed miserably to do so. There are numerous excercises scattered through-out, which I did not attempt, but I would suggest that if you are determined to attempt them, you should read the remainder of each chapter as soon as you hit a hard problem, then go back and look at the problems again. (And note the solutions web address given in the preface!)

 So what did I gain from the unavoidable slog of this book?

 The general philosophising of Chapters 1 and 34 struck me as a waste of time; I either thought what was being espoused was obviously clap-trap or obviously true - and for me the questions he raises mostly aren't interesting to me anymore. (They were back when I hadn't reached my own conclusions yet.) Others, may feel very differently, however - and many would not agree about which parts are claptrap! The remainder offered me quite a bit, however.

 For instance, a frankly embarressing mis-understanding of the EPR paradox I was labouring under was corrected! (Something of a body-blow to me as it is undergrad physics!) On the other hand, Penrose makes an astounding mistake at one point, where he gets himself horribly messed up with basic (high school) probability theory and time-reversal. (Pretty good combination to the head from me!) This is a good reminder that there is no argument from authority in science: just 'cos Penrose says it, doesn't make it right! This wrong argument is then used to go on to explain a completely freaky (and I suspect wrong) prediction about basic quantum theory. I am not clear that the example , which is definitely wrong, invalidates his whole line of reasoning, though; it may be that other examples show the general argument to be correct.

 Then Penrose delivers the knock-out punch: Conservation of energy/momentum/angular momentum in General Relativity is non-local! Not only that but it has only been proved to be true at all in a subset of cases! Seriously, how could I have never known this before?! (Non-physicists may well have no clue why I am so thunder-struck by this revelation, but it is not far short of learning that there's a whole continent you'd never heard of before.) It's completely gob-smacking. And I can't see how I didn't get told as an undergrad.

 Further, Penrose's main purpose was achieved; I have a much better understanding of the main approaches to tackling the outstanding problems in cosmology/fundamental physics than I did before and along the way I gained some insights I previously lacked. Two examples are the Higgs boson explanation of the origin of mass and spinors. The Higgs boson theory is barely touched upon and is one of the rare examples of something being included that is not strictly necessary later. I wish there had been more about it, whilst recognising precisely why there is not. What material there is made the theory seem much less arbitrary than it had previously.

 Spinors are a mathematical concept that feature heavily in the book, mainly because they feature extremely strongly in Penrose's Twistor Theory of quantum gravitation. Penrose gives an assessment of his own theory that I respect enormously and cannot praise highly enough; he expresses clearly what it it can acheive and equally clearly and forthrightly what it cannot. Every weakness and limitation is mentioned and explained. The only time I have previously come across a scientist giving such an honest and complete assessment of the weaknesses of his own theories in a popular account is when I read Charles Darwin's Origin of Species. I cannot express how much respect Penrose earns from me by doing this. Suffice to say that most popular science books will make out that the author's ideas are obviously and unassailably correct. Further, many technical papers fail to match this level of dispassionate critical assessment.

 But back to the spinors; they feature in the now well established Dirac Equation for a relativistic electron but the (non-standard) way Penrose shows this and explains their connection with the left-handedness of the Weak nuclear force and how they link to the Higgs boson ideas are fascinating. However I am not clear about them in one (crucial) regard: are they real ? Penrose says they are. I am not sure (because my understanding is still muddy) and I find (somewhat to my horror!) that even though I've read all 1050p of the main text, all of Chapters 2-17 twice and many individual sections several more times, I am still not done with this book! I have to go back and see if I can make sense out of these spinors. Also, I owe Manny a discussion of Inflationary Cosmology: I'm going to have to read the relevant chapter again in order to provide it.

 Wish me luck as I delve back into the very deep waters of this book!

 Cosmology, Early Universe Symmetry Breaking and Inflation
 So, Manny requested my views on the above topics: blame him!
 I must say at the outset that I am no expert in this field and in fact Manny has read much more about modern cosmology than I have, so I’m not sure how much value should be placed on the following; it’s a pretty naïve collection of speculations and intuitions.

 Early Universe Electro-weak Symmetry Breaking (EUSB)
 The current theory of the weak nuclear force and the electromagnetic force relies on a “broken” symmetry. That is to say all the relevant particles and their interactions were more symmetrical when their temperature was higher; so high that one has to look back to shortly after the Big Bang to find anything with a high enough temperature. Penrose gives the (standard) analogy of a lump or iron cooling down; at some critical temperature, the atoms go through a phase change and instead of having randomly aligned magnetic fields, these fields all line up in one direction. This creates the macroscopic magnetic field but in the process reduces the symmetry of the iron. It used to look the same in every direction but now it has an obviously different look, depending on the direction the magnetic field is pointing. So the idea is something similar happened when the universe cooled down below a critical value and the weak nuclear force and the electromagnetic force now look different because of the reduction in symmetry. But the lump of iron in fact won’t spontaneously have all its atoms line up in exactly the same direction unless it is cooled very slowly. Instead, “domains” develop. Inside a domain all the atoms are lined up the same direction but each domain has its own direction, which is why any old lump of iron is in fact not a macroscopic magnet. All the fields from the microscopic domains, pointing in different directions tend to cancel each other out. Which leads to weirdness when talking about the particles and forces of the universe doing the same thing: there are equivalents of the directions of the magnetic domains that the cooling particles could drop into that are different from what we observe. So the fundamental interactions would look different in a different domain. And the universe did not cool slowly, so it is much more likely than not that such “domains” did form if the theory is true. Now the boundaries of these domains would look and behave very strangely. In fact one type of boundary predicted by the theory, Cosmic Strings, can lead to something really bizarre: time travel! That is, technically, space-like movement into the past.

 Well, I just don’t believe time travel into the past is actually possible, which means I don’t believe cosmic strings exist which means I think there’s something wrong with current electro-weak theory. However all the “low” energy density tests done show electro-weak theory to do very well indeed, thanks! So I’m in a bind; the high-energy prediction of a low energy theory that works really well predicts something I don’t believe. What to do? Well, it is often possible to write a theory in more than one way, mathematically, so I would search for a different mathematical description of the low energy theory that did not rely on the EUSB idea, thus getting rid of the unwanted cosmic strings and parts of the universe that are radically different from ours altogether. I don’t know if this is possible. There has been one claim that a cosmic string has been observed but I don’t know if any corroboration of the claim exists. If they do, then electro-weak theory as it stands gets an extra-ordinary boost.

 Inflation
 Penrose states that the initial motivation for the idea of cosmological inflation was to “explain” why magnetic monopoles are not observed but exist anyway. Magnetic monopoles are neat as they would explain why electrical charge comes only as integer multiples of a fundamental value (though not what the value is). The trouble is, nobody has ever seen one and if they were formed at all it would have been with such concentration that they would have been easily spotted by now. Unless inflation had reduced their concentration radically by expanding the universe at a ridiculous rate…
 Well, this seems to me to be only half the problem; the other half is demonstrating that monopoles must have formed and that they did so prior to inflation and not afterward.
 Later, people suggested that inflation could explain homogeneity and flatness. Homogeneity is the fact that wherever we look the in the universe the matter seems to be distributed in a similar way (i.e. stars, galaxies, clusters, super-clusters…). Flatness is the idea that the universe is, over-all, expanding at a rate just high enough to prevent it collapsing again because of the gravity of all the stuff in it.

 Penrose presents cogent arguments as to why inflation actually cannot explain homogeneity. They seem indisputable to me. That the universe started off in an extremely low entropy state seems an unavoidable fact. Why was it like that? I don’t know. It’s a big mystery.
 Inflation cannot solve the problem of EUSB either, but hey! it’s a hypothesis and it can make predictions, so astronomers should try to see if they can prove it wrong or not. As far as I have gathered, the observational status of inflation is ambiguous. My feeling is that the whole idea is very arbitrary: a field occupying the whole universe must exist in order to provide the opportunity for inflation to occur. No hint of a carrier-boson for said field has ever been found. I don’t know if theory can predict anything at all about such a particle, apart from it must have integer spin. There is talk of a second inflation occurring because it seems that some astronomical objects are not only moving away from us but accelerating away from us. This suggests to me that whilst there may in fact have been inflation in the early universe, current theory is nowhere near adequate to explain it: why then? Why again now? What causes the transition? It could be a purely random event where the field transitions from one state to another quantum mechanically but to do so the new state must allow an immediate drop of energy in the field. How can one decide what the possible energy levels of the field are? Or if we are in the ground state now or not? The theory also has implications for the nature of the vacuum i.e. it is different before and after an inflation period starts. The vacuum in the quantum mechanical sense seems to me not to be understood at all well. I think that if inflation has ever happened it indicates that a deep theory explaining the nature of the vacuum is required.

 The Anthropic Principle
 This gets dragged up a lot in discussions of cosmology. It’s annoyingly persistent. It comes in a weak and a strong form. Starting with the weak form (WAP): Many adherents claim that the WAP has predictive power and is therefore in some sense “correct” i.e. some deep law of the universe. What it states is that there is sentient life therefore…X. X is a prediction of some phenomenon. The most famous example is a certain energy level of the Carbon nucleus. The argument went, we have life because we have heavy atoms so there must be a way of fusing lighter atoms to make heavier ones but to make any atom heavier than carbon, carbon itself must have this specific energy level…and it does! Triumph for the WAP! Except that is rubbish, because the argument doesn’t rely on the existence of life at all; it is easy to imaging a lot of heavy atoms floating about but no life. The real argument, stripped of inessential guff, is simply: there are atoms heavier than carbon – there must be this energy level of the carbon nucleus for that to happen. Life, let alone human sentience doesn’t feature at all. All WAP arguments fail in this manner: it turns out that life is inessential to the argument.
 Then there is the strong anthropic principle (SAP): This states either the universe was fine-tuned for the existence of human sentience to be possible or there are in fact a huge number of universes that are somehow different from each other so ours is just a statistical freak. This assumes that the only possible way that sentience could occur is if physics follows the laws we see. I don’t buy this at all: are people seriously claiming that they know what all the possible emergent ramifications of some grand set of all possible sets of physical laws are and only a tiny fraction of them could sustain sentience? It seems to me we don’t even know all the ramifications of the laws of the observed universe yet, let alone any other one. But there is some sort of prediction here; there might be other universes. Maybe that is a testable proposition. I don’t know.

 Spinors and Spin
 I re-read the material on the Dirac Equation and spinors a while ago but I've only just got round to discussing it. The discussion is moved to the comments due to the character limit on reviews!
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 Sanjay Gautam
 222 reviews 434 followers
 December 27, 2018
 Its the greatest science book ever written in the whole world, since the beginning of the time. Its certainly not popular science, its hardcore science and maths, written for general audience.
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 Cassandra Kay Silva
 704 reviews 277 followers
 August 19, 2011
 Penrose, Penrose, Penrose. Oh how I LONG to know thee. I am becoming minorly obsessed with you and your work. I am pacing for crying out loud. I am running myself in circles. Opening, closing, referencing, coming back, straining my eyes as if that will make me see the world that you do. Why do you elude me so? Why does your tongue speak as if attached to the left temporal lobe itself? I catch glimpses of this reality you see. I feel myself drawn to it in longing for truth and understanding. For some reason I feel that to understand you, truly and completely I would find some kind of wholeness within myself. Oh someone save me I am in love. I am falling madly and passionately in love with physics. It has been coming on a long time, this slow fever. This lingering low hum, that is exploding in tiny bursts. As with lovers of old your elusive and coquettish nature has wooed my heart oh physics. I want so badly to truly understand, not some superficial knowledge, but some deep personal connective enlightenment. Cosmic if you will.
 I pledge to re attend school. Career be damned I have to know you, and I can't know you without the mathematical background to do so. I can't truly understand you until I can follow this terse and sometimes insipid language of higher calculus. May the forces of this universe help me, I will not die until I know this form that physics takes. This is my pledge.
 science
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 Nick Black
 Author 1 book 698 followers
 May 15, 2011
 Penrose came to GT and gave an open lecture on cosmic parameters and cosmological arguments from the 2nd Law of Thermodynamics (chapter 27 in this book, one of the most ambitious and impressive -- if incomplete, a bit uneven, and just as taxing as you've heard -- catechisms I've ever read), and a closed lecture on twistor theory (chapter 33), and signed my copy! w00t! I shook Sir Roger's hand as trillions of neutrinos passed through us both, completely undetected, our entangled R-type state evolution leaving an indelible imprint on all our lightcones forevermore at the cost of a little more entropy, order traded for disorder in the guise of order, orderly.
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 DJ
 317 reviews 227 followers
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 November 15, 2009
 I have a suspicion that Penrose hasn't spoken to a undergraduate in 30 years. His notion of "introductory material" is not just wrong, its downright strange.

 The famed mathematician devotes several pages to discussing the addition of fractions then breezes through holomorphic functions and Reimann spheres.

 I'll return to this book in a year or two when I have the mathematical background to qualify as a "non-mathematician."
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 Vagabond of Letters, DLitt
 594 reviews 252 followers
 March 1, 2022
 UPDATE 2022:


 Several years later I found this work, including Feynman's lectures, to be a much better use of time, and thanks to it (and COVID) came to understand fundamental physics. These are the "years' worth of secondary sources" mentioned in the review: I could now comprehend the book. https://www.susanrigetti.com/physics

 _______________³¹⁴⁸⁸⁵⁹_______________
 t me start off by saying (its relevance will soon be revealed) I have a bachelor of science in applied mathematics and a PhD-ABD in another strongly quantitative discipline* (both are top-50 schools, and I wasn't in the bottom 50% of the class), and after the first 300 or so pages (out of 1200) the math in this book (and it's at least 40% or more straight math, not text, and often without text explaining the math) is way above my head and is left often undefined in the text. The author doesn't even do the courtesy of pointing the reader to textbooks where these concepts, such as pseudo-Riemannian geometry and anti-de Sitter spaces and Seiberg-Witten manifolds, are defined and can be learned.

 The book fails in its promise and purpose to be a self-contained guide to the current mathematical- or theoretical-physical understanding of the universe. It is far from accessible to the layman (I have postgraduate training in math and I was a good student and its inaccessible to me), and to grasp the concepts in this book, I'd have to spend probably a year of free time and a thousand or more dollars in secondary sources (if I bought them used and cheap). I bought this book to get a $20 overview (like Collier's 'A Most Incomprehensible Thing' for the theories of relativity [I prefer the original 'invariance'], which was technical but self-contained and comprehensible; reading that is the only thing that gave me any knowledge at all of tensors, which this book is chock full of): what I got was in essence a 1200 page bibliography without the authors being noted and without the important works being starred.

 This is a very ambitious book which fails utterly in execution.

 The author goes from explaining what complex and irrational numbers are and why they are useful (this is freshman high school math) in the introduction, accompanied by an apology for the necessity of using as difficult a concept as logarithms, to pseudo-Riemannian geometry (this is postgraduate pure math) 200 pages later. No joke. Penrose spends about five pages defining all of classical statics and dynamics, and then assumes that you understand classical mechanics. This same breakneck pace is kept up throughout, which is how he manages to range from logarithms and complex numbers to doctoral-level mathematics in 500 or 600 pages. Once he goes out of the pure math and back to applied math (i.e., physics proper) it gets a little easier but I'd still not recommend trying to tackle this book unless you're a graduate in maths or a self-taught prodigy in pure maths.

 The book promises to be a self-contained guide to the best mathematical understanding of the universe we have, but it ends up more like the author just stuck the important theorems in with a minimum of explanation (he does hit almost all of them: one thing that struck me as unnecessarily erudite - showing off - and odd was the statement of Maxwell's field equations, which is mathematically simple and elegant, in terms of tensors, which are very, very difficult), so it's a complete guide if you already know all of the math (in which case you don't need the book): it's much more of a refresher and quick reference for people who already are familiar with and understand (or at one time understood) the concepts the author represents.

 Required prerequisites: understanding of linear algebra (Lie, Poisson, Frobenius), TENSORS (and more tensors), several varieties of noneuclidean geometry (Minkowski, de Sitter, Riemann), scalars, topology and n-manifolds, group theory (Lie groups), gauge theory, etc., or the willingness to learn these from expensive secondary sources, because Penrose will not teach you them here and the arguments of the book are incomprehensible without them. Without them, one would be reduced to skimming the 20% of the book that is text (especially the final chapter, which is comprehensible to any semieducated layman) and taking the author's word for the rest of it. Just about the only thing he explains in full is twistor theory (his own invention).

 I still have to award two stars for the obvious intensity and depths of erudition which Penrose funneled in to this work, but only two because it doesn't even partially fulfill its stated purpose or self-description.

 *Redacted to protect the privacy of a member of Vagabond of Letters.
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 ☘Misericordia☘ ⚡ϟ⚡⛈⚡☁ ❇️❤❣
 2,377 reviews 18.8k followers
 April 6, 2021
 What is reality? How come that mathematics is so handy describing it? And often more astutely that our eyes? What are the laws governing it all? Are we getting it all right? What if we are trying for the wrong questions and answers? These and many other questions are what the 2020 Nobel Prize winner Roger Penrose's giving the reader a taste of working on: string theory, physics, the mindboggling quantum effects... - all through the prizm of mathematical apparatus.
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 notgettingenough
 1,015 reviews 1,164 followers
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 June 30, 2011
 So we had a physicist around to dinner the other day and thrust this at him. I can't call T---- by his real name, let's just say he rhymes with a dip made with chickpeas and tahini. The reason I can't call him by his real name is that he works at a place that starts with C and rhymes with a complete lack of humour. He likes his job, I don't want to get him sacked for reading Penrose.

 He flicks through it and the first thing I note is that physicists take about 5 nanoseconds to read what it takes ordinary mortals eons to get through. He starts with the cover, of course. 'Reviewed in the Financial Times?' A disparaging snort follows. 'Ah,' he says after the third nanosecond. 'He's written this type of science book.' I like that. I have no idea what it means, but I like it.

 After four nanoseconds he is up to page 1050 or thereabouts. He reads out a question from it and says 'That is a good question. I don't know the answer.' Slaps book shut. Really, I mostly get the impression that real physicists like him just wish those other ones would just stop it. Stop with all the philosophical 'should we be worried about this?' stuff. Let's just get on with it p-lease.

 And he says 'You didn't say the dinner invitation came with a catch.' I say 'But I didn't say it didn't, did I?'

 I am seriously thinking of reading this while skipping every page that doesn't have only words on it. Seriously.

 haven-t-read-but science-fiction science-sort-of
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 Ezra
 28 reviews 25 followers
 June 27, 2008
 this book RULES. it is a sort of primer on the mathematics required to really understand quantum physics. of course, that is a pretty huge pile of stuff, and this is a damn huge book. it moves faaast too: the entire theoretical foundations of single-variable calculus takes up one chapter. the reader is rapidly pulled through pretty heavy cram sessions in multivariable calculus, algebraic topology, real analysis... everything you need! and yet, it does not feel at all dense, because roger penrose is one of the great living stylists in mathematical writing: even a healthy dose of equations can't obstruct the fluidity of his prose, the lucidity of his explanations, or the enthusiasm of his presentation. i took classes in some of these topics and felt like penroses's single chapters did at least as much for me. other topics i was only cursorily familiar with, and this was felt like a rocket-fuel-grade introduction. there are even some really really nice excercises, mainly in the form of proofs (the fun kind of excercise). exhaustive theoretial math books are rare but they do exist; what makes this one actually work (in contrast to some dogmatic behemoth like the classic whitehead & russell) is that penrose is actually directed towards a somewhat taangible goal: educating a casually geeky, intellectually curious layperson about quantum physics, and leaving nothing out. for whatever reason, it works.

 i brought this thing along as my only book on an 8-week tour, and it was perfect: a quick dose of clearly, beautifully written, brain twisting math a couple times a day. YES!
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 Ivan Vuković
 89 reviews 44 followers
 February 27, 2019
 wow... I actually managed to read it, 1050 pages, every single one of them.

 But can I really say that I'm done with this book? I don't think so... Although it took me a year and a half to read it, I didn't even understand a significant part of it. Since I'm a physics student I understood most of it on some very basic level, but I'm pretty sure I'll have to open this book again and again to take a peek at some of the awesome ideas put here by Penrose.

 Did I say awesome? That's a huge understatement. I meant incredibly brilliant, original, profound and refreshingly sober!

 Sir Roger Penrose is the reason why I came to love physics as much as I do and he's probably the main reason why I chose theoretical physics and why I'd like to be a mathematical physicist.

 You, sir, are a huge inspiration... Thank you!

 I don't want to write anything else because I don't think I could give this book a truly proper review, you should simply try to read it... and if you manage to do it, I hope you'll understand what I mean.
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 Brian
 131 reviews 8 followers
 January 5, 2011
 Amazing. While I can not exactly call Road to Reality a popularization of general relativity and quantum theory, it is a peerless introduction to and review of those topics. I have a PhD in mathematics, and studied physics and math as an undergraduate, and there was plenty for me to learn from this book. There are very few people in the world who would not learn much from reading it.

 Many years ago, I read Penrose's Emporer's New Mind which was good as far as it went, but earned my derision with doubtful, hand-waving arguments for quantum origins of consciousness. Knowing Penrose is no dummy, I permitted a friend to convince me his work deserved another chance.

 I am very glad to have read RtR , even though the process took me most of 2010. I now have a far better understanding of mathematical physics than I could have achieved with any other reading list. I did not complete most of the exercises; I suspect that if I had, then (A) I would not have finished until 2012, and (B) the exercises would have been sufficient to bring me to a fairly professional level of competence. Kudos to Mr. Penrose for including them.

 The book begins with quite a few chapters of mathematics, quickly progressing to advanced undergraduate topics such as calculus on manifolds. In some ways I liked Penrose's clear treatment and drawings better than, say, Michael Spivak's beautiful but sparse texts. In order to provide a foundation for his chapters on physics, more mathematics is interspersed where necessary.

 Penrose introduces complex manifolds, continuous groups (Lie groups), and principal bundles. This machinery is all truly essential to the physics, and it was enlightening to see it collected in a single place, however briefly explained. It is especially useful because most graduate students in physics or math end up missing a formal introduction to one or more of these topics.

 The grand themes in RtR are the two major 20th century discoveries of general relativity and quantum theory. Penrose is particularly interested in probing how the two may be made consistent. He covers some of the cosmological work that treats both (e.g. Hawking radiation from black holes), and then discusses theories that seem to join them, including various level of detail on spin foams, string theory and M-theory, loop quantum gravity and his own invention, twistors.

 A great strength of this magnum opus is Penrose's ability and willingness to discuss philosophical and aesthetic issues of the physics. Four of these stand out. First, I quite like his perspective on the futility of obtaining unified theories by (more-or-less) trying to guess a tractable Lagrangian. Second, his detailed treatment of entropy, especially the universe's original low-entropy state with respect to gravity and the cosmological implications, was really fascinating.

 Third, Penrose seriously considers the various interpretations available for (apparent) collapse of the quantum wavefunction. His bias is toward objective collapse (environmental collapse), rather than being spookily dependent on "observation" by a conscious observer, and I agree with him that far. He suggests that general relativity, being the only other physical theory we have of similar stature to quantum theory) may somehow provide the mechanism. This is not an assertion but merely a suspicion on his part, and personally I lend it little credence. I do agree with him that general relativity is likely to remain a permanent Newtonian-style large-scale limit of the physics, while quantum theory seems ripe for some kind of fundamental reinterpretation.

 Finally, Penrose revels in the aesthetics of what he labels complex number magic . That is, he considers the interesting ways in which physical reality is so well described not just by mathematics but specifically by complex analytic structures, a simple example being the phases of quantum wavefunctions. His fascinating twistors are the coolest example of this, where he changes the physical perspective utterly. No longer are points in spacetime the essential quantities; rather the physics is on the manifold of (potential) light rays. A spacetime point is a confluence of rays, and the interesting part is how fundamentally a point can be represented by, and treated as, a Riemann sphere (a compactified 1-dimensional complex line). As an ex-complex-manifolds guy, this was wonderful stuff to me.

 I will conclude by noting that Penrose even redeemed, somewhat, his handwaving arguments from New Mind . I now understand that he is essentially pointing out that our conscious observations of physical phenomena are (or appear to be) collapsing the wavefunction. Since there must be a mechanism for that collapse, Penrose is arguing that something fundamental about conscious minds (as opposed to highly sophisticated computers) is triggering it. I still don't agree, because I believe consciousness is computational and emergent from complex systems, but his point no longer seems so silly.
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 Tatiana
 148 reviews 112 followers
 July 8, 2011
 This book is too sprawling to wait and review all at once at the end, so I've decided to do it little by little as I go along.

 I thought the prologue sucked, but immediately after that it became deeply fascinating, so don't get discouraged. I guess I should say why I hated it, though. It seemed as though he was judging former times and societies through a "presentist" lens, as though all people have always and only been scientists since the start of time, only they were really bad at it back then. It's kind of a scientist's way of ignoring everything else about reality besides science, and made me a bit nauseated, thinking "oh no I hope he's not going to be this dumb all the way through." Luckily, he quickly transitioned to extreme brilliance, in which he's jaw-droppingly continued since then. Even though he's talking so far about seemingly simple stuff, he keeps knocking me for a loop with his deep insights which I've never considered before.

 Only in chapter 3 so far, and discussing integers, irrational numbers, and the real numbers. I keep having to stop and think hard about the things he's saying. He asks the question if we lived in a universe where things were an amorphous soup would the integers exist there. He also points out that calculus (and stuff like momentum, velocity, and many of our physical concepts depend on calculus) is defined on the real numbers. If it turns out that the universe is discrete at the tiniest level, this math won't apply anymore (except as an approximation). However, he also observes that the real numbers first invented in Euclid's day when we had physical evidence spanning only some 15 orders of magnitudes (the smallest to largest distances known) are still going strong now when our knowledge spans something like 150 orders of magnitude, so they aren't doing too badly! These are the notions of someone who has thought deeply about how math and physics are intertwined. I keep being dumbstruck with things he casually asks about things that are ostensibly simple which I've known forever but never thought to ask that. Really important stuff. He is breathtakingly brilliant! I'm so glad I'm reading this book!

 Aside: The more I read the more sure I am that Platonic essences exist independent of the nature of physical reality, and independent of their instantiation in some physical reality.

 Spent some time going over familiar ground in the complex plane. It's been long enough since I studied or used this stuff that it's quite enjoyable and satisfying to do that. I think I've settled on the slow savoring method of reading this book rather than the quick devour. This review's going to be very long, but I hope it'll admit of savoring a bit as well. =)

 In Chapter 5 now, and talking about e and logarithms, I wondered why it is again that e is a more natural base for logarithms than any other number. So I spent some time adding it up from the formula e = (1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)+(1/5!)+... and watched the digits slowly materializing 2.7182.... so I believe that much. =) Next I'm reading again how e originally came up in playing around with logs and powers. This book has that effect that it makes me think again about stuff that I haven't thought about since I was young. I would really like to feel I understood what we know of reality inside and out when I'm done. I want to see the whole chain starting from one cow, two cows on up to the standard model and beyond. It's always been an obsession of mine just to understand how things freaking work, what the universe is like, what nature is based on, and I have this feeling I could get much closer by going through this volume carefully. The title keeps reminding me of the Royal Road to Geometry, which Aristotle reportedly told Alexander the Great did not exist, so that's some kind of warning, hah!

 So far I've resisted the urge to jump ahead, except for reading the section called "beauty and miracles" near the very end. You have to admit that's an attractive section name! Alas, I understood it only in the broadest way, that beauty (mathematical elegance) and miracles (seemingly crazy mathematical coincidences such as all the complicated terms happening to drop out or whatever) act as a powerful but not unfailing guide so far to finding theories that fit how nature behaves. At that moment, my dear kitten Alai jumped up and sat right on the book, as if to say, "you want beauty and miracles? Just look at me!" As I pet him, I kept saying "beauty and miracles" affectionately.
 nonfiction science
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 James F
 1,379 reviews 86 followers
 January 1, 2016
 For the past year and a half I have been reading heavily in popular works on physics and astronomy, at various levels ranging from the superficial gosh-wow (Michel Kaku) through total beginner level to the somewhat more sophisticated (Brian Greene, Kip Thorne, Lee Smolin); but almost always I have been frustrated in my understanding by the lack of any mathematics to support the often metaphorical discussions. At the same time, I understood that the real mathematics of relativity, let alone quantum and string theory, would be way over my head (as when I borrowed, and immediately returned, one or two books by Penrose himself, as well as books by Wald, Susskind, etc.) So when I saw the description of this book, that Penrose intended to supply the necessary mathematics to understand the physics as he went along, I thought that it would be just what I wanted -- if it were possible. I was also rather skeptical, whether in fact it was possible, in something under 1100 pages; and as it proved, rightly so. Penrose does not succeed in making the math understandable; he explains something at a very simple level and then assumes that the reader understands far more than the author has actually explained, and when he gets to something especially difficult to comprehend, that's when he gives a footnote: show why this works. At the beginning, I read this pencil in hand, but it soon exceeded my abilities to work out the problems.

 I am not totally unmathematical (I say this because it is relevant to understanding the level of this book): I minored in math in college, and beyond the usual background in high school algebra and geometry, and physics (before the dumbing down of high school math and science circa 1970), I have taken two years of college calculus, a semester of calculus-based probability and statistics, several "fundamentals" courses, and a calculus-based (but entirely "classical") first-year physics course. Not a lot, really, but probably more than most non-math/science majors. And I have tutored high school and college students in math through early calculus for over ten years. So what did I understand of this book, with that background? The first six and a half chapters. Chapter six explains calculus in nineteen pages, and I'm fairly sure most of what he talks about was never included in my two years of calculus (maybe in a real analysis course?) Chapter seven was on complex analysis, and I understood about the first half. This was the model for the rest of the book -- I understood about the first half of each chapter, where he explains the basic concepts, and got lost when he tried to "make it clearer" through "the magic of complex numbers" (his favorite expression.) The same was true when he passed over into the physics of relativity, quantum theory, and the modern speculations about strings, twistors, etc. -- I understood about half of each chapter. (Actually the chapters on loop quantum gravity and twistors were totally out of my range from the beginning.) I would say that the minimum for really following him would be to already have taken at least a complex analysis course.

 Was the book a total loss, then? No. If I didn't learn the various fields of math he covers (vector and tensor calculus, some projective geometry and topology, etc.) I did learn what those fields deal with; if I didn't learn what I needed to understand the physics, I did learn what I would need to study to learn it, and perhaps most important to an autodidact who will never be able to afford any more formal education, what order I would need to study the various fields in. In short, for me (and probably for most readers who don't have a strong math/science background) this was not the "Road" but more of a roadmap; I didn't make the trip, but I got a feel for where the route passes through. At the least, I was inspired to review my high school and college math, and perhaps to try to go a little beyond where I stopped. At my age (nearing retirement) I will never get all the way to an understanding of the physics, but maybe I will keep my mind working a little longer for having read this.

 I should give a brief summary of what he is saying about the questions I have been reading about in other books: he is very skeptical of string theory, because of the higher dimensions (the problem of degrees of freedom, especially); he is somewhat more friendly to quantum loops and other alternatives; he is naturally most interested in his own theory of twistors, but admits that at present it doesn't have the solution either. He argues that to be consistent with general relativity, there must be significant modifications to standard quantum theory. I'm obviously not sufficiently informed to evaluate any of this.

 I would recommend the book for what it is, but not for what it claims to be, unless the reader has a real background in mathematics and physics.
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 Dan
 1,059 reviews 52 followers
 January 30, 2023
 3.5 stars

 This is a mathematical and physics tome of more than a thousand pages. It is essentially everything you should know about the universe by the Nobel Prize winner himself, Roger Penrose.

 Heavily formula based. Many of the later chapters were beyond my depth, unfortunately.

 Writing was okay. Would have liked to heard more narrative but I suspect Penrose's open mindedness kept him from deviating from established theory.

 3.5 stars
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 Yasiru
 197 reviews 117 followers
 February 23, 2012
 As accurate a title as can be for this tremendously ambitious behemoth. I very much enjoyed the masterful laying of a mathematical framework when first I came across it (the first dozen or so chapters if memory serves; hence the rating, as well as for the aforementioned ambition in the task- I think this is a right way to go, though popular expositors seldom venture down this route), as Penrose does it so efficiently (and naturally too, so that the layman wouldn't shove it aside in disgust after hardly a half dozen pages, and for the price even that handful of beginning chapters are worthwhile). Something of an idiosyncratic emphasis might be noted in these chapters, but it doesn't take away from the breadth of the account and can't really be faulted because it's setting things up for what follows.

 I never actually got to much of the 'meat' of it- which is the physics (and so unfortunately can't remark on it). I'd hoped to, but then I realised I was just putting it off out of apprehension that I'd find myself feeling the lack of formal first year physics at university (something I gleefully escaped as early as I could in favour of my chosen field- pure mathematics). This is probably an unfounded concern, since skipping ahead to chapter 17 on spacetime, I was able to follow the account, but nonetheless I closed the book at this point.

 Perhaps I'll revisit it sometime with a few other references handy should I need rescue. This would certainly be worthwhile if you can give this the time and energy required; you're sure to come out richer in knowledge, in a way almost no other popular account of science can impart.
 physics-and-other-science
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 Alex Lee
 894 reviews 104 followers
 September 17, 2015
 In this amazing book, Roger Penrose looks for a very fundamental issue.

 He is looking for a single metric to describe everything.

 This is not a unit of reality, however, although this is how he poses the issue.

 The problem with selecting a metric, as he shows us over and over, lies in how different metrics arise from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics will threaten to buckle. In many instances, the metrics (and their attendant relationships) will no longer be applicable. What this means, in the Kantian (and Badiouian sense) is that these relationships's applicability will become "undecidable". In some extreme cases, the relationships may even break down. For instance, black holes are a problem because the expressed relationships that emerge from physics experiments prove to be untenable in black holes (and the big bang) as these relationships decohere and infinities and zeros pop out everywhere.

 This search for a metric leads Penrose to reject string theory as a viable relationship form. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, weak force is a dimension. Each dimension is an independent mathematical vector of a different "inertial" influence. Additionally, the mathematics of string theory, as well as other theories, proves to be too illusionary. As with post-structural critiques of modernism, Penrose points out that the consistency of string theory relies on theoretical supplements/signs that are attached onto the positions of various types in order to maintain coherency. For instance, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions as well as its immanent affects proves to be unweldly to Penrose because the coherence of the relationships are maintained by theoretical enforcement rather than any direct correlation of math and physical experimentation.

 If Penrose was familiar with Badiou, Kant and Derrida, he would be able to recognize that the undecideability of supersymmetry and string theory result from these theoretical supplements. The supplements provide the missing pieces to cohere the theory, so physical experiments prove to be incomplete in their testing. As Penrose points out, string theorists in failing to find superpartners can always push the calibration of their theory to include these partners, just at higher energy levels, which can always lie beyond the ability of technology to generate.

 In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose falls fault to this when he theorizes that Quantum Field Theory can be modified (rather than the Einstein's general relativity) by changing the cut off metric. This is in line with all his discussions to "renormalize" the math so as to remove the variance accumulated by extending localized relations from beyond the area of origin on the manifold. We can always enforce a consistency of a given domain in two ways.

 1. To provide a "superpartner" to supplement the terms, to keep phenomenon visible to one another within the domain, as a motion of immanence, as Derrida suggests.

 Or.

 2. To encapsulate a domain by limiting its identity to its other. From there, we can radically reduce the other to zero, thereby hiding the limitations of a domain, as with Moffe & Laulau with their Hegemony or as with Badiou with a basic atomic "cut" to center the domain as with Being and Event II .

 Both of these strategies amount to the same kind of forced coherency by mapping a domain rigidly.

 Penrose does offer his own favorite solution; his Twistor theory, which removes the need for extra dimensions beyond 3 + 1. Additionally, he considers this theory by collapsing all the different vector differences held cosmically in string theory into immanent relations that are founded on the very "knots" of space, so that the pre-space twistors contain the information that wider "vibrations" are meant to express. Both theories are incompatible in this regard because of their huge difference in scale.

 And while Penrose admits that twistor theory adds nothing physically; that it's just another way of viewing a situation mathematically, he also realizes the need for us to see things differently than we have.

 It is this adherence to a particular view that causes all the problems in the first place. If you look at how these different views are constructed, you'll see the mathematicians switch from one domain to another through various class equivalences whenever it suits them. When they need to express vectors they will jump to a manifold model, or a more generic (abstract) deformation of an algebra. In other words, we lack enough views. So we supplement the one we have in an attempt to normalize them.

 Curiousier still is Penrose's tiny discussion of consciousness in which he attempts to "renormalize" consciousness in terms of objective reduction. He theorizes that the waveform reduction that collapses due to quantum gravity may be at the seat of consciousness's ability to complexly surject different sensory views into coherency. This suggestion is of the same kind as his forced synthesis of twistor theory. The satisfaction of trying to find a single metric, a single complex knot of relations that cannot be unraveled but contains all the "moves" is like a physicist trapped on a chess board recognizing the orthogonal formation of board, or as in Futurama the Professor discovering the smallest unit that constitutes the universe is the pixel.

 In a real way, Penrose seeks to calibrate physics to the mathematical domain. He doesn't want beautiful math that doesn't apply, that is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth of which the entirety of the physical is mapped; although mentality is generated from the physical and mathematical/Truth is generated from that.

 The Platonic ideologue he insists on lies on the equivalence of function, on the purity of the sameness of process from point to point of the same type. Never-mind that the subatomic particles we find today are largely generated from artificial means. Penrose would assume as sameness of process that forces a universalization, but that is the way metaphysics and science both work, to equate different phenomenon as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we see, all relations are born locally, within a limited scope. Their extension cosmically creates the basis for which we start to see a degradation of relation qua variance (pollution, or various forces of form-fitting). After all, we can have no irrationality without first being able to posit a rational sheet of complete consistency.

 Nonetheless, although this is a lengthy book it is still beautifully written. I wonder who Penrose's audience is, for he approaches much mathematical complexity in such a short time, talking about basic principles like polynomials and trigonometry before jumping into Lagrangian manifolds and so on. Still, if you hunger for complexity and abstraction, here it is. Much of his explanations of very complex concepts are very clear, although at times we could use more handholding. His pictures are also very interesting and complement his point nicely.

 Well worth the effort to read.
 2015 impressive mathematics
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 Enrique Oviedo
 232 reviews 12 followers
 December 5, 2020
 Un libro con un objetivo tan ambicioso como describir el estado del conocimiento científico que poseemos sobre la realidad profunda de la naturaleza y los caminos para avanzar en lo que nos falta por descubrir es realmente difícil de valorar.
 Este es el único libro científico que aparece entre los 100 primeros libros de la lista de Goodreads "Libros que te llevarías a una isla desierta". Creo que está ahí con todo merecimiento. Es un libro que admite muchas relecturas- Durante los casi dos meses que me ha llevado su lectura las cosas que leía me venían a la mente continuamente. Todo lo que plantea es interesante, estimulante y te expande la mente.
 El único problema con este libro es que en una isla desierta no hay Internet. Me explico: a pesar de sus más de 1.400 páginas, el libro es casi imposible de seguir solo con la información que en él aparece. He tenido que recurrir en muchísimas ocasiones a la web a buscar la información necesaria para "rellenar los huecos" de lo que estaba leyendo. El autor te lleva de la mano durante la exposición pero frecuentemente te suelta y te obliga a hacer un acto de fe en la argumentación o da por sentada la evidencia de un razonamiento matemático. He echado de menos enormemente enlaces a recursos en Internet donde se explique el detalle de las ideas expuestas o aparezcan resueltos los ejercicios que propone. En mi caso, solo cuando he podido seguir la línea argumental en detalle he tenido una imagen clara de lo que está leyendo.
 En cualquier caso, el esfuerzo de enfrentarse a la lectura de este libro es ampliamente recompensado por la ampliación de tus horizontes mentales.
 Resulta también fascinante el vislumbrar cómo funciona la mente de un científico como Roger Penrose, para mí, uno de los más grandes pensadores vivos.
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 Mohamed al-Jamri
 174 reviews 110 followers
 Shelved as 'half-read'
 April 14, 2016
 This book is not for those with no strong background in mathematics and physics and it is definitely not for lay readers.

 Except for the first 40 pages or so the book material was very sophisticated and hard to understand for me. Today I decided to stop as for the past 30 or so oages I could only understand little of what I was reading.

 I'm putting it on hold now and I may return to it later after establishing a strong base in mathematics and physics.
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 F Avery
 30 reviews
 January 19, 2013
 By his own admission in the preface, this is Penrose' attempt to popularize the current thinking in theoretical physics, including quantum mechanics, relativity, and unification theories such as string theories and quantum gravity. In the introduction he says (paraphrased) that he has intentionally gone for the more mathematical route, in spite of advice to the contrary, but he hopes that those without a mathematical bent can just skip the equations and get the gist of the concepts anyway.
 With due respect to the author, his attempt at “popularization” is a failure. I wonder who he thinks his target audience is when he goes to great pains to explain basic concepts such as imaginary numbers and why they aren't so mysterious and yet throws out higher level abstractions that take time even for a college graduate to feel comfortable with. His target audience seems to drift from the lay person on the street up to professional mathematicians and physicists.
 In my opinion this book of over 1000 pages replete with equations and complex diagrams would be good fodder for several graduate courses in mathematical physics. He introduces such abstractions as complex analysis, abstract algebra, manifolds, bundles on manifolds, tensor fields, Lie groups, Hilbert spaces, etc with just a few words of explanation and a lot of hairy equations, after which he marches on with advanced theoretical concepts and applications to physics. I studied most of those topics in graduate school to some degree, but I was especially comfortable with Hilbert spaces and complex analysis. And yet, it was all I could do to keep up with him. Perhaps it's the fact that I was in my early thirties then and had more functioning neurons, but this 63 year old brain found it hard to track his descriptions, let alone the equations. I confess that (in spite of considering myself an erstwhile mathematician) I often attempted to take the route he had advised for the non-mathematically inclined: just gloss over the equations and get the general concept. But his descriptions are mostly so down in the details that I found it difficult to get to the general concepts from the text alone.
 I also decided that I don't like his writing style much. It varies from overly verbose and redundant to cryptic and abstract in the extreme. And the edition I have was poorly edited: there were many mistakes such as unclosed parentheses, repeated words, missing words, and grammar mistakes. Given how turgid his prose is I don't envy the job of the editors, but it's still their job to find those kinds of obvious errors.
 The one good thing from all this is that I think I finally (kind of) understand tensors and tensor fields. For whatever reason I didn’t get into tensors when I studied differential geometry in the early 80's and I’ve found this to be a deficiency in my education over the years (e.g. understanding the field equations of general relativity). His description prompted me to study up on tensors and I found a couple of good websites with detailed descriptions and examples.
 In any case, I DO recommend the book if you have a knack for or interest in advance mathematics and theoretical physics. I DON’T recommend it if you want an easy read in popular science to make you feel smart :-).
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 David
 384 reviews 11 followers
 September 23, 2012
 Penrose examines the turn modern theoretical physics has taken in pursuit of multi-dimensional mathematical models to develop a unified model of the sub-atomic realm. His argument is not entirely mathematical, though he does have good arguments against unnecessary complexity from the point of view of the straightforward progress made by theoretical physics in discovering the mathematical elegance of relationships among various observed constants. His most profound argument against String Theory is a failure to make any predictions which could be tested by observation. He makes an eloquent argument for pursuing alternate models instead of mathematical physics being caught in what may ultimately prove to be a dead end. He proposes several ways forward, including his own twistor theory.

 Penrose reminds me of Feynman in his fresh thinking. Feynman's development of quantum-electrodynamics required thinking of observed phenomena in a new way. For those willing to scratch the surface of modern physics, Penrose provides a lucid primer. He even devotes nearly a third of the book to laying out the math so the reader can begin to understand what follows. At more than a thousand pages, this is a serious primer.

 I thank the friend who loaned me this book a few years ago and allowed me ample time to digest what I could. Yes, I did return it, but I may need to acquire my own copy.
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 Jimmy
 Author 5 books 199 followers
 July 20, 2010
 Not an easy read because of all of the math, but well worth the effort for those who can make it.
 science
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 Габриела Манова
 Author 2 books 95 followers
 Read
 June 7, 2017
 Най-накрая приключи.
 И само това да бях коригирала, щях да се гордея със себе си.
 и-з
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 Maarten
 18 reviews 4 followers
 September 6, 2019
 The story goes that Stephen Hawking was once told by a book publisher that every formula in his book would halve the amount of readers (or sales, almost the same thing, but not to a publisher). He was , of course, totally and utterly wrong. The Road to Reality contains about 1100 pages and, on average, there's about 9 formulas per page. That makes roughly 10,000 formulas. According to this publisher's law, that would halve the sales ten thousand times (2^(-10000)), so a rough estimate of the amount of readers left is around 5x10^(-3001), which is a number so absurdly and unimaginably small, you have to be a Belgian surrealist painter to be able to imagine it. Roger Penrose would be left with much, much less than a single quark of a reader. Judging by the amount of readers here, this is obviously not the case.

 What this publisher was pointing out, however, was that, in order to attract a lay public, you have to shun formulas, because they might chase them away and you wouldn't be able to teach anybody anything because there wouldn't be anyone left. Hawking followed the advice, wrote a book for the layman and, in my humble opinion, failed miserably. The layman didn't understand anything from his cryptic text, because they were missing several dozens of books of background information needed to understand most of the concepts. The more informed readers were chased away because of the lack of depth, the haphazard and disconnected way the concepts were presented and the absence of the mathematical beauty. It did sell well, so from this perspective, the publisher was undoubtedly right (and this was probably the only perspective he was interested in).

 This fiasco teaches us something very important: writing and reading about present-day physics is no small feat. Lots of background is needed (yes, mathematical as well). However, unfortunately, most writers listen to publishers and omit the formulas and lots of the difficult bits as well, so the task for the physics reader is greatly hindered.

 Luckily, Penrose is a kind old British gentleman, not afraid to take up the glove and rise to the challenge. The Road to Reality is his magnum opus, introducing the reader to modern physics (mostly cosmology and to a lesser degree quantum mechanics) , without oversimplification or the omission of essential formulas. He doesn't muck about either. If mathematics is what you need to understand it, mathematics is what you'll get. No less than 16 of the 33 chapters are devoted solely to mathematical foundations. After that, Penrose gives an overview of the established physics (mostly special and general relativity, quantum mechanics and some thermodynamics. The last few chapters are concerned with the more controversial topics, like string theory.

 The mathematical part is, to the best of my knowledge, quite complete. The established physics is concise and omits most things that aren't related to the aim of the book: present-day speculative cosmology. For the last part, Penrose focuses on string theory (currently still the most popular group of theories), loop quantum gravity (the most interesting contender) and twistor theory (Penrose's own field of research). His account of these theories is very honest, making no secret of his critiques on certain fields of research and warning the reader to take his interpretations with a pinch of salt and often pointing the reader towards books containing views conflicting with his own.

 Does this make The Road to Reality the ultimate physics book for the dauntless layman? Of course not. The task Penrose set himself is neigh impossible. One cannot replace several dozen textbooks by one, albeit bulky, volume, even if it is written by someone as erudite as him. A lot of his explanations are just too brief. He would need another two to three thousand pages to be able to explain everything thoroughly. Furthermore, the splitting of the maths and physics is different chapters is probably necessary, but it means Penrose refers a lot to previous chapters. Since I have a hard time exactly remembering some subtle mathematical notion from 400 pages ago, I needed to skip backwards and forwards a lot, making for quite a laborious read (not something to do while commuting by bus, for example). The subject itself is very slippery too. Current theories cannot be verified (yet) by experiments, so theoreticians are only guided by very abstract notions, such as mathematical beauty, or instincts honed by years of hard work. Such things are often very hard to convey to anyone not a specialist in that particular field, although Penrose does a good job, nonetheless.

 It is probably the closest you'll get to a textbook without actually reading a textbook. The Road to Reality trumps A Brief History of Time in many ways, but ultimately it cannot be avoided that one needs to read a lot more to truly understand physics, but that's not necessarily a bad thing (publishers will agree).
 natuurkunde
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 Rama Rao
 713 reviews 100 followers
 February 20, 2014
 Deciphering the laws of physics to create universal reality

 This is an exhaustive review of the laws of physics as related to physical reality with significant emphasis on the mathematical component. The author is an outstanding mathematical physicist of our times, and in this book of 1100 pages, he describes the concept of space, time, and matter (energy) in terms of classical physics, quantum physics, string theory and its derivatives.

 In physics, the behavior of objects is understood in terms of the action of a force; a vector quantity, which has both magnitude and direction. The force acts on a matter and produces a causative action that results in an effect. The cause - effect is one of the fundamental aspects of classical reality, but it gets fuzzy and uncertain at submicroscopic levels (quantum physical reality.) The main object of physical law is to describe the reality we observe. Our observation includes this universe that is made of space, time, matter, and energy. All objects are made of matter, which exists as complex structures composed of molecules, atoms and fundamental particles. Matter is also a form of energy and the two forms can interconvert as described by the Einstein's famous equation. The fundamental particles has certain physical properties and the manner in which energy (and force) is expressed is though their association with the so called force particles that are responsible for four fundamental forces that operate in nature, they are; electromagnetism, gravity, strong and weak nuclear forces. The four forces mediate matter-matter interaction and facilitate matter-energy conversions in spacetime and thus explain physical reality. The key to the understanding of nature and physical reality is to discover a theory that satisfactorily explains all the four forces and this theory must be experimentally verifiable. Unfortunately, this has not been achieved so far, but we have theories that can be verified but explains only three forces. One single physical theory that explains both quantum and classical realities have not been successful mainly because the nature of gravitational force (curved spacetime) is difficult to describe in a unified situation, since space and time at the most fundamental level are also quantized (exist in discrete quanta) and are they dynamic (not static background).

 To understand this book the reader is required to have undergraduate level physics and mathematics; the author explains in the introductory part of the book why he chose to include mathematics despite its negative impact on the book's marketing potential. It would suffice to say that the interplay between mathematical ideas and physical behavior played an important aesthetic role in the minds of great physicists, and Albert Einstein is one of the most important figures in being attracted aesthetically to a particular idea. You can skip chapters 1-16, and from chapters 17-30, general discussion about geometry of spacetime, quantum physics, quantum field theory, quantum cosmology and the standard model of particle physics is presented. I found the last four chapters to be most interesting.

 A brief summary is as follows: The unification of special relativity and quantum theory led to quantum field theory (QFT) which produced a minefield of infinities, but with some ingenuity, the infinity problem was circumvented leading to standard model of particle physics which is in good agreement with nature. The controversy between the quantum relativity group and the QFT side is that the latter group tries renormalizability or finiteness as the primary goal, but the former group likes to solve the conceptual difficulties between the two theories. The combination of two theories of particles physics into one framework to describe all interactions of subatomic particles, except due to gravity, is called standard model. These two theories are electroweak theory and quantum chromodynamics. They describe force interactions between particles in terms of exchange of intermediary particles. The author also engages the reader in an insightful discussion of many other theories.

 physics
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 SaЯRah Muhammad
 24 reviews 264 followers
 April 22, 2015
 This is an extraordinary book and certainly there is nothing else available on the market that is quite like it.

 Penrose is a pre-eminent mathematician whose work has affected my own thinking in deep ways. Often I've discovered, to my surprise, that some viewpoint which I learned from another source in fact derived ultimately from Penrose himself, the author of this other source having been, as it turns out, a student of Penrose. As an example I offer "Visual Complex Analysis" by Tristan Needham. I encountered this book in high school and so powerful was its exposition that it stuck with me all through college and beyond to the present day. I couldn't help but notice, while reading "The Road to Reality," that Penrose engaged in a similar revelry around complex numbers -- and so it was a pleasant surprise to see that Needham indeed had studied directly under Penrose! Despite having this book in my collection for a few years only recently did I discover the connection.

 With this tangential introduction out of the way, let me say at the outset that I cannot recommend this book to just anyone. It requires a great deal of mathematical acumen -- or perhaps, more accurately, a great deal of explicitly mathematical *interest*. You needn't be a mathematician, but you positively must delight in the opportunity of learning the mathematics of the universe. Even if you have a degree in mathematics you're likely to find something here you haven't encountered before -- for instance, I had not previously seen the notion of a hyperfunction which Penrose enthusiastically presents in connection with the Fourier transform.

 The book's mathematical explanations are quite idiosyncratic, and I think this reflects the depth of Penrose's intuition on the topics. It elevates this book from an encyclopedic reference to a personal outpouring of the author's vision of the world. Not only does the book feature unique topics that aren't commonly taught, the aforementioned hyperfunctions being an example, but even those which are commonly taught are explicated here in a unique manner. Penrose's style is unabashedly geometric, and so even partial differential operators on manifolds he almost always thinks of as vector fields. The book is filled with many beautiful hand-drawn diagrams showing everything from a fanciful vision of the creation of the cosmos to a field of one-forms on a surface to the conservation of electric charge in spacetime. And the book prominently features throughout his diagrammatic notation for tensor algebra, something again which I had never encountered elsewhere.

 I should say that this book approaches its physical topics from an exceptionally high level. You will probably not be able to learn electrodynamics from Penrose, not here. I don't recall the common form of Maxwell's equations even occurring in this book. Rather, he simply writes them down in the simplest, most beautiful, and most abstract form, using differential forms and exterior calculus. To delve in deeper, rather than expanding out these equations, he instead focuses on how they can arise as the curvature of a bundle connection via gauge theory. This is both stunningly beautiful and horrendously detached from practice.

 Despite the overwhelming emphasis on theory and mathematics, the book is quite adamant in insisting that physics still must be physics. Penrose is not optimistic about string theory, though he does give it some treatment towards the end for completeness. He's perhaps like Feynman in that regard -- he possess a deep appreciation for the mathematics and the theory, but at the same time is very uneasy with the lack of testability of much of modern theoretical physics. His own theory, twistor theory, is just as untestable, though he's honest about that.
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 Matt Heavner
 865 reviews 10 followers
 June 29, 2013
 This is quite a challenging read -- but definitely worth the effort! The first half is primarily "math" while the second half is "physics." Penrose did an amazing job of writing a guidebook to a great deal of the breadth of both of these fields. I felt there were some uneven sections -- I remember a great deal of discussion on Fourier transforms and thinking that if a whole section of discussion is needed there, how will the reader keep up through differential topology, twistor theory, diagrammatic and group theory notation, etc.. But overall, it was great. The writing was almost playful at times, especially as the book progressed. Penrose did a nice job of self-identifying his biases. I enjoyed the discussions of the relationship between math and reality (p 631 "What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description and then trying to regard that description as describing a 'reality'?"). The last two chapters of the book really explored this idea further.

 The discussion of string theory was especially understandable (and self-admittedly biased).

 It struck me as a bit funny that (especially later in the book) there was more and more reference to the "magic of complex numbers" and yet in one of the final sections there was an argument that there is nothing more or less confusing between real numbers and complex numbers).

 This book was extremely "hyperlinked"/self referential. At first all the links were "forward links" (necessarily..) and mostly I ignored them. As I got further into the books, I started following the "links" (both forward and backward) much more. I found myself using the index and really engaging with the text. As I started the review -- it takes some work and is definitely worth it!

 I plan to reread this book in a few years.
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 Michael
 12 reviews 2 followers
 February 9, 2009
 I desperately want to make it through this book. I might be crazy. I think part of my fascination with finishing it is to compensate for not finishing engineering school. I can tell you this... It would be a lot easier to read if I had attained my degree (and actually learned the material along the way). Nonetheless, this book opens in the most interesting and captivating fashion, which says a lot about a book that works to explain the universe by walking through the history of mathematics. A couple of years ago I saw a man reading it while on the treadmill at the gym. The book is 1000 pages long and after seeing the title I asked him about it. I asked him if one had to have a firm grasp on upper level mathematics to read it (which, despite going through Calculus 1-4, I do NOT). He said: "Oh no, I don't know much math but I am enjoying it anyhow". Well, it became apparent early on in the book that the guy at the gym was off his rocker (er, off his treadmill). After the opening attention grabber, the author details the beginnings of mathematics, the definitions of "proof", "theorem", and "postulates", and aims to start from "point A" and go through to what ever lies beyond mathematical "point Z". So, with an initial giddiness I started through the book. Soon I had a scratch pad handy. Then I was reading and re-reading sections to try and get a grasp before moving on. It was reminiscent of my struggles during my calculus classes while at Michigan Tech. I have a strong interest in the material and a desire to learn it but it hurts my little brain. In summary, I am still grappling with the first 100 pages, but would still highly reccommend this book, especially to those with an interest and aptitude for math & science. I'll keep at it.
 ~ Mike - February 2009
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Author  28 books13.4k followers     September 5, 2011   Many of my all-time favourite books make the list because they show you what it's like to be inside the mind of an extraordinary person. While you're reading them, Churchill's History of the Second World War and Yourcenar's Mémoires d'Hadrien let you be a great statesman at a pivotal moment in history. Simone de Beauvoir's autobiography, more than any other book I know, gives you the feeling of being a major literary figure. Polugayevsky's Grandmaster Preparation, which many chessplayers treat almost as a sacred text, is the only truly honest account I've seen of how a top Grandmaster thinks. Penrose belongs in this select company: I finally believe I have some idea, no matter how faint, of how a great mathematical physicist sees the universe. Like the other books, it's not an easy read. You can't build up this kind of picture without including a huge number of details; if you took them away, the whole texture of the world would disappear with them. Churchill needs the maps, troop movements and political networking. De Beauvoir has to assume (in my case, alas, incorrectly), that you're conversant with most of French literature. And if you removed the chess from Polugayevsky, there wouldn't be any story. In Penrose's case, it's mathematics and physics: he resolutely refuses to dumb it down, and includes a seriously frightening quantity of Greek letters. If it really were true that every equation halved your sales, he would not have sold a single copy. What saves him, and makes the book readable to non-experts like me who at least have some mathematical background, is his uniquely visual way of experiencing mathematics. Penrose can obviously hack the equations, but he also has to see them, and he is astonishingly resourceful at coming up with visualisations. The ones I liked most had to do with Special Relativity. You may recall this fairly well-known picture by Escher:   What I didn't know was that it illustrates the "hyperbolic geometry" which underlies Einstein's Special Theory. In Special Relativity, the speed of light is an absolute limit, so velocities can't simply be added: the correct formula for combining them is the one shown in the picture. You can add any number of fish together and never reach the edge; similarly, no matter how many time you add a velocity to itself, you never get to the speed of light. Believe it or not, the diagram exactly models the equation! And another geometrical argument he used here is nearly as beautiful. A great deal of nonsense has been written about the "Twins Paradox" (for example, by Robert Heinlein). Penrose's explanation is wonderfully concise and elegant. In Minkowski-space, a straight line is counterintuitively the longest distance between two points. The twin who flies out into space has a less straight world-line than his twin who stays at home, so he ages less. Thanks to Penrose, I can now see it. It turns out that theoretical physics is anything but a dry technical discipline: you come away feeling that these people are visionary poets who have chosen to write in mathematics rather than ordinary language. Blake is one comparison who came to mind, and I can't resist the temptation to juxtapose Blake's image of God:   with Penrose's:   If you're wondering what God is doing, it's actually pretty much the same as in Blake's version: the picture dramatizes the extremely low entropy of the Universe immediately after the Big Bang. I had not previously appreciated how remarkable this is, and the puzzle it represents is central to Penrose's exposition. Once again, the picture isn't gratuitous. He's illustrating, in a humorous way (the book is often funny), an extremely serious point. As I've said, it's not an easy read. It demands a great deal of concentration, and I think I must have spent at least two or three hours a day over the last month ploughing my way through it. A lot of that time, I was supposed to be doing other things, but I'm glad I ignored them and read Penrose instead. He's changed my way of looking at the world as much as Dante did when I read The Divine Comedy in 1999. Now, if only it were in terza rima with animated illustrations by Gustave Doré and Terry Gilliam. Then it would truly be perfect._____________________________________ We had another CERN physicist to dinner last night, an Australian post-doc who's working on validation of the Standard Model. I asked her if she'd read Road to Reality.  "I stopped reading popular science books when I was an undergraduate," she said apologetically.  I said it wasn't really a popular science book, and she opened it for a few seconds. "Hm, yes, it does seem to have quite a lot of equations," she muttered doubtfully, and then she put it down again.  Something seems to have gone slightly wrong with the marketing campaign for this book: laymen think it's a book for physicists, and physicists think it's a book for laymen. I'm reassured to see a fair sprinkling of reviews here from people who give every appearance of having read and enjoyed it.     life-is-dante linguistics-and-philosophy science               272 reviews380 followers     August 4, 2016   I am finished, finally. All the 1050+ pages of this ambitious behemoth - including many exercises. What a ride!... Finished? Well you are never finished with such a book, titled “The road to reality” but actually providing more than that: providing nothing less than a “road-map” to reality, and opening to the reader new beautiful vistas in modern mathematics and physics. I am sure that I will come back to this book in the future, as a source of inspiration and for future reference.Before I start, I must confess that it feels slightly ridiculous for me to critique such a monumental work by a crazy genius like Penrose, who clearly lives in a higher realm of consciousness than the large majority of us common mortals. Never mind – the best I can do is to describe my personal, deeply humbling experience in reading this amazing piece of intellectual prowess. Penrose is clearly the Mozart of mathematical physics: genius, craziness, wild imagination and pure technical virtuosity all combined into a unique intellect.  Let me start by highlighting some of the peculiarities of this book (due, in my personal opinion, much to editorial/commercial choices/pressures, and only partially to personal choices by the author himself). This is also important to the proper positioning of this book within the overcrowded (and of hugely varying quality) world of popular science books:  A) this book is sold as a science “popularization” (probably with the objective to attract as wide an audience as possible): in reality this book requires a significant amount of background knowledge in mathematical physics; in fact there are some sections where the equivalent of a full maths/physics degree would be required to fully appreciate all the subtleties of some of the subjects being treated. I would personally recommend, as a prerequisite, the following minimum:- calculus (including multivariate)- ordinary and partial differential equations (at least at rudimentary level)- complex analysis- linear algebra- basics of topology- ideally, differential geometry at basic level- in the physics area, some prior exposure to Maxwell's equations, the Lagrangian and Hamiltonian formalisms, the basics of quantum mechanics and relativity (at least special) would also be a great help. If a reader tried this book with no prior exposure to any such topics, I am afraid that it all might prove a very steep learning curve indeed. I had all the above pre-reqs, and still it was, for me, an occasionally demanding if not challenging book in terms of required focus, time and intellectual stamina. But this is also a strength of this book - one of its greatly rewarding aspects is that the author does not refrain from exposing the reader to real maths (some of the exercises can be pretty hardcore), and to get into the heart of modern physical theories such as QFT and GR, if you want the real thing, you simply can't avoid getting into some real maths.  B) this book is not really a textbook, or at least not an ordinary textbook: it lacks the necessary structure and flow, and (too) many important derivations are left as exercises. The depth of mathematical analysis and rigour are uneven, and they seems also highly dependent on the occasionally whimsical personal level of the author's interest in the subject. Moreover, the formal treatment of many subjects is highly original and something that, unless you have had some previous exposure to them, might be confusing and certainly not easily reconcilable with what standard textbooks present. But this is part of the beauty of this masterpiece.  C) this book, contrarily to what stated in the title, is not a “complete” guide to the laws of the Universe. While managing to concentrate so many sophisticated and fascinating subjects into a single book, and at a serious level of detail (which is no mean feat, and something quite unique), I think that Penrose should have written two books (one on the mathematical underpinnings, and a separate one on the physical aspects) rather than trying to concentrate such a massive amount of information in one single big book. This approach (admittedly less palatable from a commercial standpoint) would have allowed him to expand some important areas that he has unfortunately neglected in his otherwise magnificent book (such as finiteness and re-normalization issues in QFT) and which would have also allowed him to include other subject matters too – for example, the coverage of thermodynamics focuses mainly on the statistical view of the Second Law, neglecting all the other elements. But make no mistake - this book feels like a "War and Peace" of mathematical physics – a colossal enterprise that just keeps giving and giving, a treasure trove of original insights, beautiful hidden connections, amazing stories and revelations. A fantastic and detailed exploration of quantum physics, relativity, of the current trends in the attempts to unify the two, and of cosmology. An exhilarating intellectual adventure in the company of a crazy genius. Let me now make a few comments about the author's peculiar personal style and approach:- Penrose's prose is beautiful, even if considered from a purely literary perspective; often very clear even if sometimes a bit too concise; it usually flows very smoothly, and it occasionally even acquires some poetical undertones in sections where aspects of philosophy of science and philosophy of mathematics are treated with insightful passion.- Penrose relies heavily on a diagrammatical/pictorial/visual/topological representation of the concepts being treated. In doing so, many beautiful, eye-catching and highly informative hand-drawn diagrams/pictures are presented to the user. This approach generally works very well, but there are instances where (in my personal opinion) the most intuitive and simplest way to learn/teach a new concept is to present it analytically (in mathematical format), and where the purely visual approach might be quite limiting if not outright confusing. For example, the visual explanation of the concept of “covariant derivative”: while important and helpful, is in my opinion by itself not sufficient to get a real appreciation of the mathematical features of this entity: its analytical derivation, and its expression using the Christoffel symbols, would have actually better clarified its tensorial nature. - In order to condense as many subjects as possible within the constraints of the space allowed by one single book (even one of 1050+ pages) Penrose has left the derivation of many important results as “exercises”. The exercises are therefore very important, they are a must in order to get a full appreciation of the underlying theory, and some of them are beautiful and rewarding (like exercise 22.32, which entails a beautifully elegant derivation of the Laplacian in spherical coordinates, using the curved metric and covariant derivatives). But some others should not have been left as exercises, and they seem no more than an editorial cop-out: there is one exercise that is even asking the reader to complete a significant derivation step of the GR field equations! (thankfully there is a website where many exercises have been solved by other readers (the majority of them clearly with a professional background in mathematical physics) – see https://sites.google.com/site/vascopr... ).- I love Penrose's great intellectual honesty in not just debunking much of the hype behind String Theory and Multiverse Hypotheses in general, and in destroying the so-called “Strong Anthropic Principle”, but also in making very clear the speculative character of some of his own positions and theories. I also love his great originality and independence of mind, and his nuanced, multi-disciplinarian approach which includes aspects of philosophy of science and considerations of pure mathematical nature.- Penrose has reached such a higher, rarefied level of proficiency in mathematical physics that he must have completely forgotten how common humans think in relation to mathematical formalism. Just as an example: after getting into pretty advanced stuff such as hyperfunctions, and treating it like if it is the simplest thing on Earth, the author then refuses to get into a detailed definition of differentiability of a many variable function (which is quite simple, really) because "it is too technical"!! So his ideas of what is complex can occasionally be significantly at variance with what the common mortal might think.  Finally, let me add here some miscellaneous notes about selected individual chapters of this majestic book (it is a very incomplete list, only a severely reduced sample, as there is simply too much stuff in this book for me to be able to analyse in just one review):- In the first few chapters, after a fascinating introduction of overall philosophical character, Penrose briefly addresses some of the basic fundamentals of mathematics, including a short but intensely interesting discussion about the Axiom of Choice and its relationship to the Zermelo–Fraenkel set theory. A totally fascinating subject that unfortunately Penrose only touches, without developing into more detail. There is also a fascinating treatment of hyperbolic geometry, and of the number system/s. However, when dealing with the relationship between real numbers and reality, the author does not make any reference to important aspects such as computability and irreducible complexity, as for example addressed by the excellent work done by G.Chaitin.- The author then gets into one of the most beautiful and fascinating realms of mathematics - complex analysis. The treatment is concise but done well, and I completely share Penrose's enthusiasm and love for the aesthetically as well as functionally beautiful world of complex numbers, which he calls “magical” with good reason.- Another subject of interest treated are the fascinating quaternions, which extend the complex numbers and provide the uncommon and interesting features of a non-commutative division algebra. There are in the book a couple of minor missing things in relation to the algebraic structure of quaternions: an algebra is a vector space that must also be equipped with a bilinear product, and a ring (being also an abelian group under addition) must be provided with an additive inverse. Moreover, Penrose is dismissive of the utility of the quaternions in the development of physical theories – this is correct, but it must also be said that quaternions find important uses in Information technology applications, in particular for calculations involving three-dimensional rotations, computer graphics and computer vision.- Penrose could not have forgotten the extremely important Clifford/Grassmann algebras, which are foundational to the entire architectural structure of mathematics, and he didn't; they are treated well, but a bit too succinctly in my opinion, considering their importance.- Symmetry groups are treated really well, clearly and concisely. Very nice.- Manifolds and calculus on manifolds: all is treated quite well, but I would have found quite helpful some more analytical detail rather than a focus almost exclusively on the visual/topological approach. I confess that here, in order to get a proper detailed handle of tensor calculus and exterior calculus, I had to consult other more traditional, “textbook-type” sources.- Chapter 16 (Cantor's infinities, continuum hypothesis, Godel's incompleteness, Turing computability and similar) is OK and well written, and it would be utterly fascinating to a neophyte – but of course it could not have been detailed nor exhaustive, considering the complexity and width of such subjects.  - The “Physics” part proper starts with Chapter 17. Chapter 17 on spacetime, and chapter 18 on Minkowskian geometry (and special relativity of course) are succinct, but riveting and beautifully written. Just one small note: Penrose has a fetishism for non-standard, or uncommon, notational or representational choices, not always justified: for example, by using a non-standard metric tensor in page 434, Penrose gets himself into an error at the end of page 435 (c^4 should have been used rather than c^2) and I think that he would not have fallen into this typo, had he used the more standard and simple-to-use metric. - Chapter 19 (Maxwell and Einstein) are beautiful; Maxwell equations and Einstein field equations in tensorial/differential form are mind-blowing for their mathematical conciseness and beauty, and this is where the reader can start to see the value of the mathematical apparatus described in the previous chapters: things such as manifolds, tensors, exterior derivatives and bundle connections. Einstein's fields equations of general relativity are beautiful. Very rewarding. It all seems so neat and perfect, but then, the bombshell (at least to me, who was never told of such a thing!): the energy/momentum stress tensor does not account for the energy density of the gravitational field itself, and it seems that conservation of energy/momentum is non-local !- Chapter 20: Lagrangians and Hamiltonians: I must say that they are too hastily discussed - the derivation of the Euler–Lagrange equation (one of the most classic proofs in mathematics) is not treated, the Legrende transform to derive the Hamiltonian from the Lagrangian is not treated, the derivation of Hamilton's evolution equations is not treated either. Not very happy with this chapter.- The subsequent chapters on quantum mechanics are beautiful, and the description of the EPR issue is really nice. The derivation of Dirac's equations is equally beautiful. I also love Penrose's discussion and perspectives about the measurement paradox. Beautiful stuff indeed. An exception to the overall masterful treatment of Quantum Physics is chapter 26 (Quantum Field Theory) which is is a bit too qualitative - more like a "popularization" rather than a treatment at the same good level as done in the other chapters of this book – and unfortunately the important subject of re-normalization is treated only briefly and qualitatively. - The chapters on cosmology are very interesting and nicely written.- Chapter 29 is essentially about the measurement paradox and the various interpretations of quantum mechanics – succinctly but beautifully written.- The next chapters are essentially about the current unification attempts to reconcile QFT with GR. Penrose's FELIX experiment proposal (essentially testing the hypothesis of automatic quantum state-reduction as an objective gravitational effect) is utterly fascinating, but I feel that I should not bet any money on this daring hypothesis. - I must say though that I was disappointed by the second part of chapter 33 (twistor theory): in section 33.8 Penrose uses several verbose sentences to express mathematical relationships, rather than writing down the actual underlying equations - result: something quite close to incomprehensible. I also fail to get the underlying physical intuition. Pity, as the other 33 chapters and a half are mostly beautifully written, and generally very rewarding.- The last chapter (34) is beautifully written, and it deals primarily with aspects of philosophy of science and philosophy of mathematics.  To summarize: this is an immensely rewarding, even exhilarating book - a fantastic reading and learning experience. And it has opened my eyes on many aspects and connections that I was not aware of, and new beautiful vistas in modern mathematics (for example: tensor calculus, and exterior calculus in general) that I will now pursue in more depth. After reading this great book, I can tell you that I now feel that the majority of popular science books I have read are dull and superficial by comparison.It is not a perfect book by any means, but overall it is a great book, unique in its approach and contents. Not exhaustive, but with a huge and ambitious scope, virtually unrivaled in its category. It is much more than a “standard” popular science book. Very highly recommended, to be bought, studied, enjoyed and kept for future reference. 4.5 stars (rounded up to 5).  UPDATE: with link to a beautiful series of online lectures about Tensor Calculus and the Calculus of Moving Surfaces: https://www.youtube.com/playlist?list... (highly recommended to anybody interested in this subject).     owned science-and-maths               77 reviews180 followers     January 21, 2023   The story begins with me in the garage with my high school sweet heart. The one who had made the playground swing problem seem rather trivial through a guileless intuition which cast my cynical calculations in a kind of hideous antimony. An actor whose relaxed demeanor and gentle earnestness, served to effortlessly unweave the kinks in those rusty chains, and in so doing, spun intractable knots in my own heart. It was a union of opposites, me with my chin in my hand, and he with a wrench in his. There were no problems we could not troubleshoot in tandem. Our separate talents had even began to cross pollinate, with me sometimes starring up at the undercarriage of a vehicle and asking for a socket while he perused whatever theoretical oddities I was currently obsessed with. I could, with some confidence, suggest to people that their alternator was having a giggle, their radiator was taking the piss, their starter motor was an asshole, or, my favorite, “Your fuel economy is gobshite, bruv.” And he could clearly identify the value of switching his choice in the Monty Hall Problem, understand that some infinities are bigger than others, and comprehend the threat that a quantum computer would present to our current encryption protocols. This reciprocal exchange of mental dexterity continued to unfold one rainy day, with me sliding under a car on a rickety creeper (which I had damaged by repeatedly using it to luge down steep driveways at high speeds, causing one wheel to catch and be ground into an irregular half moon.), and Nicolas Kim Coppola (known professionally as Nicolas Cage) (ie. Nic Cage) flipping through the book I had carried in. He asked me what The Road to Reality was about. Paraphrasing, I said the following:Have you ever, while skidding down a vertiginous concrete pathway on a damaged creeper, felt the fixed vibrational frequency of healthy rotary friction give way to dissonant melodies which often presage the rapid, explosive disassembly of machinery under immense kinetic strain? Was all the blood in your superficial capillaries wrung out from clutching the sides of the sled in mortal terror, causing your knuckles to emerge from the dark like buds of white hibiscus and your pool-noodle arms to ripple like corded steel? Did your sweetheart, who you suspect must have reduced activity in his amygdala, (due to his performance in Ghost Rider: Spirit of Vengeance), leap from their stool and make to halt your (by now considerable) momentum using a bag of blood adumbrated by sticks of calcium (i.e. the vertebral column festooned in viscera and thinly veiled by contractile tissue that we call the human body)? During those tense moments you may have thought, in the heavily affected High English which is characteristic of all your poignant inner musings: Nicolas Cage, it is a pity that I can’t communicate with you more effectively. That our bandwidth is limited by verbal exchanges in which I must compress thoughts into packets of information and utter them as faithfully as I can in the hopes that you will receive and unpack them with minimal noise inserting itself during the transfer. Putting aside incidents in which my limbs have animated in the manner of an ecstatic Neil deGrasse Tyson, this is the extent of my ability to let you experience what it’s like to be me. I cannot understand your genius for seeing the good in every screenplay, and you cannot fathom the depths of my genius when it comes to nearly dying in bizarre ways. In those simple displays of affection where nothing is said, perhaps we say the most. And what of inhabiting the mind of a true genius, and more difficult still; the mind of brilliant theoretical physicist and math prodigy? With art, something primal touches the soul, so that even if you don’t understand the creative flourishes of virtuosos, you are moved and made aware of their power. Who could read Nabokov and not be humbled by its beauty and precision? Who could hear Hangar 18 by Megadeth and not respect how a guitarist’s flanges dance across wires like the legs of camel spiders on a heroic doses of methamphetamines? Who could see the Venus of Urbino by Titian and not want to bury their face in her gorgeous tummy and blow a gentle raspberry? And finally, who could hear Anton Chigurh request a ‘screwgie’ in No Country for Old Men and not be gripped by a palpable dread? But here the scientific genius faces a problem, in elucidating the purely conceptual matters of their field to a general public, they must conceal much of their brilliance. If they were to riff like Dave Mustaine and fill pages with the lateral movements of their mutant intellects, the majority of us could but collectively shrug before these strange symbols. But imagine if there were a book that managed the impossible. One that was simultaneously accessible to the laymen audience, but omitted none of the technical jargon which made it possible to appreciate the operations of their brilliant minds? Perfectly comprehensible to curious high school freshmen. What you hold in your hands, Nicolas Cage...” Sliding out from under the car and standing next to him. “This..” I say, taking the book gently in my hands. “Is NOT that fucking book!” Throwing it viciously to the ground and jabbing my finger at it. “THIS is madness, Nicolas Cage! This is fucking popsci for math and physics PHDs! Calculus, Fourier series, hyper functions, Riemann surfaces, Riemann mapping theorem, quaternions, Clifford and Grassmann algebras, transformation groups, Lie algebras, parallel transport, geodesics, curvature, exterior derivatives, calculus of manifolds, connections, fibre bundles.. In the first third of a book which contains, in its preface, words that indicate he wrote it for his innumerate aunt. Show me the numerically deficient aunt that made it through this with even the foggiest notion of what the hell was going on and I will crawl inside myself and subsist on my own incredulity until the stars grow cold.” Nicolas Cage, picking the book up and carefully inspecting it for damage, hands it back to me, saying, “It’s fine. You’ll understand it eventually. I know you will.” Begrudgingly I put the book under my arm and nod. I feel an insurgent grin dismantle the severity of my countenance. I silently curse his ability to mollify my tantrums so easily. I seize this renewal of levity to suggest we take the creeper out for some limit testing. “Wait!” I can now appreciate a lot this book. If you’re someone with a strong background in math and physics and you’re interested, I can’t recommend it highly enough. It may be the most wide-ranging book on theoretical physics I’ve ever seen, not merely summarizing material, but offering an in-depth treatment of many of the more sophisticated ideas of the subject. The first half of the book takes you through most of the mathematical techniques that physicists use today, gradually moving through things like, Riemann surfaces and complex mapping, hypercomplex numbers, manifolds of n dimensions, symplectic groups and tensors. Equations are curated magnificently on the basis of explanatory power. And here I would add that Penrose, perhaps owing to his genius, has a level of idiosyncrasy in his presentation that I don’t think I’ve witnessed since Feynman. It is quite obvious that what goes on in his brain is an intensely visual phenomena. All of his diagrams and drawings are incredibly helpful, especially if you too think in this fashion. The second half of the book is devoted to physics and the ascent is quite dizzying as we approach the various hopeful theoretical bridges we’re constructing in order to reconcile the discontinuities between our two most successful theories (general relativity and quantum field theory) and so you have discussions (it may be more appropriate, considering the sheer rhetorical heft with which Roger slings these ideas against the wall like wet pieces of bologna, to call it evisceration.) String Theory, M Theory, Loop Quantum Gravity, and Penrose’s horse in this race: Twistor Theory. If you do not have a background in these things, and don’t pursue high level mathematics recreationally, I would not recommend it to you as a comprehensive place to start. If you just want to keep it around and flip through it to occasionally augment your understanding with some clever illustrations, or you simply wish to marvel at it as an enduring artifact of the human intellect, by all means. But if you’re planning to work through it from front to back, caveat emptor. This is one of those rare gems that has brought me very close to experiencing the intuitive ease with which a mathematical genius operates. A beautiful work of staggering breadth and depth.                   816 reviews44 followers     February 12, 2016   Dave Langford, SF&amp;F critic and reviewer, in his long-since defunct column for White Dwarf magazine, once said that, "There is a tendency to over-praise big books simply because one has got through them." I agree that this tendency exists but note that Langford gave no reason for it. I think the reason is more or less macho intellectual pride; look at me! I read this honking great saga! It must be great or I'd have to admit wasting my time! And I need to show off my intellectual credentials! Now imagine that the book is not only huge, but really difficult because, say, it's dense with obscure references (e.g. Ulysses) or full of mathematics and not kiddie maths, either...the temptation must be even worse.Hence I'm going to start my review with a couple of gripes: This book, which is full of maths, much of which would make your average undergrad scientist grunt with the strain at the very least, as well as physics to post-grad level in places, has no glossary of technical terms. There is ample cross-referencing and an index but these are no substitute. When you want to know, Clifford Algebra, which one was that again? (Because you've met ordinary algebra, complex algebra, Clifford Algebras, Lie Algebras and Grassman Algebras...), going back and reading through an entire section again to find out, is a bit annoying - a list of definitions at the back would have helped enormously. Admittedly this would have made a big book even bigger but it would have made it much more user-friendly. Gripe number two is in a similar vein; Penrose fails to supply a list of the upper and lower case Greek alphabet symbols and their names or a similar list for obscure mathematical symbols, such as del and scri. Given that nobody without training in Greek or in science is going to know these and such a list would only take up one page, its omission is egregious. This leads neatly into a topic that has been dicussed quite a bit here on Goodreads - namely, who is this book aimed at? What is it's purpose? Firstly I would point out that the subtitle "A Complete Guide to the Laws of the Universe" is not really true: Classical Thermodynamics is barely seen as we rush straight into the statistical view of the Second Law. Of the other three Laws of Thermodynamics, Zero is never mentioned and the others barely name-checked. I doubt many physicists would consider that all the basic theories have been covered in such a circumstance. But I think this is a marketing problem; I don't believe Penrose ever intended to write such a "Complete Guide."  In the preface Penrose talks about wanting, with this book, to make cutting edge physics available to people who struggle to understand fractions. Now, this can only be taken as a joke, considering what one is up against only in chapter 2, but I would guess that Penrose genuinely wants to have the widest possible audience for his book whilst not compromising his aims. What are those aims? In my view he wants to give his personal views on the state of cosmology and fundamental physics but to be able to do it at an advanced technical and mathematical level and additionally to give his own philosophies regarding the nature of thought, science, maths and...Nature! This means that he wanted to deliver Chapters 27 - 33 on the physics/cosmology, bracketed by Chapters 1 and 34 of philosophising. The entirety of the rest of the book is simply there in order to equip readers to understand what he says in those six technical chapters! This requires 15 Chapters of maths and ten Chapters of physics/cosmology... Looked at this way, the book begins to reflect the genius and madness of the author: Many of the explanations in earlier stages of the book left me thinking, why do it that way? That's not the easiest way to understand this if you've never come across it before! He also goes straight to very general mathematical principles, missing out intermediate levels of abstraction that might make what comes later easier. He chooses to emphasise the geometrical/topological view of everything, which, it might surprise one to know, is not always the easiest way to understand things. Many of the choices of what to emphasise and what to ignore seem odd...that is until one gets to the late stages of the book. Upon arrival at Chapters 27 - 33 (i.e. what I think Penrose really wants to talk about) one can see that everything that has gone before has been put together in order to provide the most efficient route to understanding - hardly a page has been wasted. All those strange choices of what to emphasise, all the peculiar, non-standard explanations when easier explanations exist, all the leaping to the most general mathematical ideas, all the things missed out, all these things are done so that the points he wants to discuss can be followed without wasting time or space in what is a 1000+p book as it stands. The necessary skill, thought and effort required to do this impress me enormously. Inevitably this means that most of what is covered in the book of "standard" physics has been explained better (by which I mean more readily comprehensibly), even at a mathematical level, elsewhere - but not in one volume! The consequence of this is that Penrose's widest possible audience may not be all that wide: although he suggests one could read the book and ignore every equation in it, (something I often do when reading technical literature!) I suspect one would rapidly become bored and disenchanted. The unavoidable fact is that the greater your mathematical capabilities, the more you will get from this book and additionally, the more maths and physics you know before starting, the more you will gain from this book.  Further, the more you are willing to study the book the more you will gain. Manny approached it by reading 3 hours per night until done. I would suggest that the nearer to that approach you can get the better off you will be, even though I failed miserably to do so. There are numerous excercises scattered through-out, which I did not attempt, but I would suggest that if you are determined to attempt them, you should read the remainder of each chapter as soon as you hit a hard problem, then go back and look at the problems again. (And note the solutions web address given in the preface!) So what did I gain from the unavoidable slog of this book? The general philosophising of Chapters 1 and 34 struck me as a waste of time; I either thought what was being espoused was obviously clap-trap or obviously true - and for me the questions he raises mostly aren't interesting to me anymore. (They were back when I hadn't reached my own conclusions yet.) Others, may feel very differently, however - and many would not agree about which parts are claptrap! The remainder offered me quite a bit, however. For instance, a frankly embarressing mis-understanding of the EPR paradox I was labouring under was corrected! (Something of a body-blow to me as it is undergrad physics!) On the other hand, Penrose makes an astounding mistake at one point, where he gets himself horribly messed up with basic (high school) probability theory and time-reversal. (Pretty good combination to the head from me!) This is a good reminder that there is no argument from authority in science: just 'cos Penrose says it, doesn't make it right! This wrong argument is then used to go on to explain a completely freaky (and I suspect wrong) prediction about basic quantum theory. I am not clear that the example, which is definitely wrong, invalidates his whole line of reasoning, though; it may be that other examples show the general argument to be correct. Then Penrose delivers the knock-out punch: Conservation of energy/momentum/angular momentum in General Relativity is non-local! Not only that but it has only been proved to be true at all in a subset of cases! Seriously, how could I have never known this before?! (Non-physicists may well have no clue why I am so thunder-struck by this revelation, but it is not far short of learning that there's a whole continent you'd never heard of before.) It's completely gob-smacking. And I can't see how I didn't get told as an undergrad. Further, Penrose's main purpose was achieved; I have a much better understanding of the main approaches to tackling the outstanding problems in cosmology/fundamental physics than I did before and along the way I gained some insights I previously lacked. Two examples are the Higgs boson explanation of the origin of mass and spinors. The Higgs boson theory is barely touched upon and is one of the rare examples of something being included that is not strictly necessary later. I wish there had been more about it, whilst recognising precisely why there is not. What material there is made the theory seem much less arbitrary than it had previously. Spinors are a mathematical concept that feature heavily in the book, mainly because they feature extremely strongly in Penrose's Twistor Theory of quantum gravitation. Penrose gives an assessment of his own theory that I respect enormously and cannot praise highly enough; he expresses clearly what it it can acheive and equally clearly and forthrightly what it cannot. Every weakness and limitation is mentioned and explained. The only time I have previously come across a scientist giving such an honest and complete assessment of the weaknesses of his own theories in a popular account is when I read Charles Darwin's Origin of Species. I cannot express how much respect Penrose earns from me by doing this. Suffice to say that most popular science books will make out that the author's ideas are obviously and unassailably correct. Further, many technical papers fail to match this level of dispassionate critical assessment. But back to the spinors; they feature in the now well established Dirac Equation for a relativistic electron but the (non-standard) way Penrose shows this and explains their connection with the left-handedness of the Weak nuclear force and how they link to the Higgs boson ideas are fascinating. However I am not clear about them in one (crucial) regard: are they real? Penrose says they are. I am not sure (because my understanding is still muddy) and I find (somewhat to my horror!) that even though I've read all 1050p of the main text, all of Chapters 2-17 twice and many individual sections several more times, I am still not done with this book! I have to go back and see if I can make sense out of these spinors. Also, I owe Manny a discussion of Inflationary Cosmology: I'm going to have to read the relevant chapter again in order to provide it. Wish me luck as I delve back into the very deep waters of this book!  Cosmology, Early Universe Symmetry Breaking and Inflation So, Manny requested my views on the above topics: blame him!I must say at the outset that I am no expert in this field and in fact Manny has read much more about modern cosmology than I have, so I’m not sure how much value should be placed on the following; it’s a pretty naïve collection of speculations and intuitions.  Early Universe Electro-weak Symmetry Breaking (EUSB)  The current theory of the weak nuclear force and the electromagnetic force relies on a “broken” symmetry. That is to say all the relevant particles and their interactions were more symmetrical when their temperature was higher; so high that one has to look back to shortly after the Big Bang to find anything with a high enough temperature. Penrose gives the (standard) analogy of a lump or iron cooling down; at some critical temperature, the atoms go through a phase change and instead of having randomly aligned magnetic fields, these fields all line up in one direction. This creates the macroscopic magnetic field but in the process reduces the symmetry of the iron. It used to look the same in every direction but now it has an obviously different look, depending on the direction the magnetic field is pointing. So the idea is something similar happened when the universe cooled down below a critical value and the weak nuclear force and the electromagnetic force now look different because of the reduction in symmetry. But the lump of iron in fact won’t spontaneously have all its atoms line up in exactly the same direction unless it is cooled very slowly. Instead, “domains” develop. Inside a domain all the atoms are lined up the same direction but each domain has its own direction, which is why any old lump of iron is in fact not a macroscopic magnet. All the fields from the microscopic domains, pointing in different directions tend to cancel each other out. Which leads to weirdness when talking about the particles and forces of the universe doing the same thing: there are equivalents of the directions of the magnetic domains that the cooling particles could drop into that are different from what we observe. So the fundamental interactions would look different in a different domain. And the universe did not cool slowly, so it is much more likely than not that such “domains” did form if the theory is true. Now the boundaries of these domains would look and behave very strangely. In fact one type of boundary predicted by the theory, Cosmic Strings, can lead to something really bizarre: time travel! That is, technically, space-like movement into the past. Well, I just don’t believe time travel into the past is actually possible, which means I don’t believe cosmic strings exist which means I think there’s something wrong with current electro-weak theory. However all the “low” energy density tests done show electro-weak theory to do very well indeed, thanks! So I’m in a bind; the high-energy prediction of a low energy theory that works really well predicts something I don’t believe. What to do? Well, it is often possible to write a theory in more than one way, mathematically, so I would search for a different mathematical description of the low energy theory that did not rely on the EUSB idea, thus getting rid of the unwanted cosmic strings and parts of the universe that are radically different from ours altogether. I don’t know if this is possible. There has been one claim that a cosmic string has been observed but I don’t know if any corroboration of the claim exists. If they do, then electro-weak theory as it stands gets an extra-ordinary boost.  Inflation Penrose states that the initial motivation for the idea of cosmological inflation was to “explain” why magnetic monopoles are not observed but exist anyway. Magnetic monopoles are neat as they would explain why electrical charge comes only as integer multiples of a fundamental value (though not what the value is). The trouble is, nobody has ever seen one and if they were formed at all it would have been with such concentration that they would have been easily spotted by now. Unless inflation had reduced their concentration radically by expanding the universe at a ridiculous rate…Well, this seems to me to be only half the problem; the other half is demonstrating that monopoles must have formed and that they did so prior to inflation and not afterward. Later, people suggested that inflation could explain homogeneity and flatness. Homogeneity is the fact that wherever we look the in the universe the matter seems to be distributed in a similar way (i.e. stars, galaxies, clusters, super-clusters…). Flatness is the idea that the universe is, over-all, expanding at a rate just high enough to prevent it collapsing again because of the gravity of all the stuff in it. Penrose presents cogent arguments as to why inflation actually cannot explain homogeneity. They seem indisputable to me. That the universe started off in an extremely low entropy state seems an unavoidable fact. Why was it like that? I don’t know. It’s a big mystery.Inflation cannot solve the problem of EUSB either, but hey! it’s a hypothesis and it can make predictions, so astronomers should try to see if they can prove it wrong or not. As far as I have gathered, the observational status of inflation is ambiguous. My feeling is that the whole idea is very arbitrary: a field occupying the whole universe must exist in order to provide the opportunity for inflation to occur. No hint of a carrier-boson for said field has ever been found. I don’t know if theory can predict anything at all about such a particle, apart from it must have integer spin. There is talk of a second inflation occurring because it seems that some astronomical objects are not only moving away from us but accelerating away from us. This suggests to me that whilst there may in fact have been inflation in the early universe, current theory is nowhere near adequate to explain it: why then? Why again now? What causes the transition? It could be a purely random event where the field transitions from one state to another quantum mechanically but to do so the new state must allow an immediate drop of energy in the field. How can one decide what the possible energy levels of the field are? Or if we are in the ground state now or not? The theory also has implications for the nature of the vacuum i.e. it is different before and after an inflation period starts. The vacuum in the quantum mechanical sense seems to me not to be understood at all well. I think that if inflation has ever happened it indicates that a deep theory explaining the nature of the vacuum is required.  The Anthropic Principle This gets dragged up a lot in discussions of cosmology. It’s annoyingly persistent. It comes in a weak and a strong form. Starting with the weak form (WAP): Many adherents claim that the WAP has predictive power and is therefore in some sense “correct” i.e. some deep law of the universe. What it states is that there is sentient life therefore…X. X is a prediction of some phenomenon. The most famous example is a certain energy level of the Carbon nucleus. The argument went, we have life because we have heavy atoms so there must be a way of fusing lighter atoms to make heavier ones but to make any atom heavier than carbon, carbon itself must have this specific energy level…and it does! Triumph for the WAP! Except that is rubbish, because the argument doesn’t rely on the existence of life at all; it is easy to imaging a lot of heavy atoms floating about but no life. The real argument, stripped of inessential guff, is simply: there are atoms heavier than carbon – there must be this energy level of the carbon nucleus for that to happen. Life, let alone human sentience doesn’t feature at all. All WAP arguments fail in this manner: it turns out that life is inessential to the argument.Then there is the strong anthropic principle (SAP): This states either the universe was fine-tuned for the existence of human sentience to be possible or there are in fact a huge number of universes that are somehow different from each other so ours is just a statistical freak. This assumes that the only possible way that sentience could occur is if physics follows the laws we see. I don’t buy this at all: are people seriously claiming that they know what all the possible emergent ramifications of some grand set of all possible sets of physical laws are and only a tiny fraction of them could sustain sentience? It seems to me we don’t even know all the ramifications of the laws of the observed universe yet, let alone any other one. But there is some sort of prediction here; there might be other universes. Maybe that is a testable proposition. I don’t know.  Spinors and Spin I re-read the material on the Dirac Equation and spinors a while ago but I've only just got round to discussing it. The discussion is moved to the comments due to the character limit on reviews!     non-fiction physics science               222 reviews434 followers     December 27, 2018   Its the greatest science book ever written in the whole world, since the beginning of the time. Its certainly not popular science, its hardcore science and maths, written for general audience.                  704 reviews277 followers     August 19, 2011   Penrose, Penrose, Penrose. Oh how I LONG to know thee. I am becoming minorly obsessed with you and your work. I am pacing for crying out loud. I am running myself in circles. Opening, closing, referencing, coming back, straining my eyes as if that will make me see the world that you do. Why do you elude me so? Why does your tongue speak as if attached to the left temporal lobe itself? I catch glimpses of this reality you see. I feel myself drawn to it in longing for truth and understanding. For some reason I feel that to understand you, truly and completely I would find some kind of wholeness within myself. Oh someone save me I am in love. I am falling madly and passionately in love with physics. It has been coming on a long time, this slow fever. This lingering low hum, that is exploding in tiny bursts. As with lovers of old your elusive and coquettish nature has wooed my heart oh physics. I want so badly to truly understand, not some superficial knowledge, but some deep personal connective enlightenment. Cosmic if you will. I pledge to re attend school. Career be damned I have to know you, and I can't know you without the mathematical background to do so. I can't truly understand you until I can follow this terse and sometimes insipid language of higher calculus. May the forces of this universe help me, I will not die until I know this form that physics takes. This is my pledge.     science               Author  1 book698 followers     May 15, 2011   Penrose came to GT and gave an open lecture on cosmic parameters and cosmological arguments from the 2nd Law of Thermodynamics (chapter 27 in this book, one of the most ambitious and impressive -- if incomplete, a bit uneven, and just as taxing as you've heard -- catechisms I've ever read), and a closed lecture on twistor theory (chapter 33), and signed my copy! w00t! I shook Sir Roger's hand as trillions of neutrinos passed through us both, completely undetected, our entangled R-type state evolution leaving an indelible imprint on all our lightcones forevermore at the cost of a little more entropy, order traded for disorder in the guise of order, orderly.     autographed important incredibly-large               317 reviews227 followers      Want to read  November 15, 2009   I have a suspicion that Penrose hasn't spoken to a undergraduate in 30 years. His notion of "introductory material" is not just wrong, its downright strange.The famed mathematician devotes several pages to discussing the addition of fractions then breezes through holomorphic functions and Reimann spheres. I'll return to this book in a year or two when I have the mathematical background to qualify as a "non-mathematician."     priority               594 reviews252 followers     March 1, 2022   UPDATE 2022: Several years later I found this work, including Feynman's lectures, to be a much better use of time, and thanks to it (and COVID) came to understand fundamental physics. These are the "years' worth of secondary sources" mentioned in the review: I could now comprehend the book. https://www.susanrigetti.com/physics  _______________³¹⁴⁸⁸⁵⁹_______________t me start off by saying (its relevance will soon be revealed) I have a bachelor of science in applied mathematics and a PhD-ABD in another strongly quantitative discipline* (both are top-50 schools, and I wasn't in the bottom 50% of the class), and after the first 300 or so pages (out of 1200) the math in this book (and it's at least 40% or more straight math, not text, and often without text explaining the math) is way above my head and is left often undefined in the text. The author doesn't even do the courtesy of pointing the reader to textbooks where these concepts, such as pseudo-Riemannian geometry and anti-de Sitter spaces and Seiberg-Witten manifolds, are defined and can be learned. The book fails in its promise and purpose to be a self-contained guide to the current mathematical- or theoretical-physical understanding of the universe. It is far from accessible to the layman (I have postgraduate training in math and I was a good student and its inaccessible to me), and to grasp the concepts in this book, I'd have to spend probably a year of free time and a thousand or more dollars in secondary sources (if I bought them used and cheap). I bought this book to get a $20 overview (like Collier's 'A Most Incomprehensible Thing' for the theories of relativity [I prefer the original 'invariance'], which was technical but self-contained and comprehensible; reading that is the only thing that gave me any knowledge at all of tensors, which this book is chock full of): what I got was in essence a 1200 page bibliography without the authors being noted and without the important works being starred. This is a very ambitious book which fails utterly in execution. The author goes from explaining what complex and irrational numbers are and why they are useful (this is freshman high school math) in the introduction, accompanied by an apology for the necessity of using as difficult a concept as logarithms, to pseudo-Riemannian geometry (this is postgraduate pure math) 200 pages later. No joke. Penrose spends about five pages defining all of classical statics and dynamics, and then assumes that you understand classical mechanics. This same breakneck pace is kept up throughout, which is how he manages to range from logarithms and complex numbers to doctoral-level mathematics in 500 or 600 pages. Once he goes out of the pure math and back to applied math (i.e., physics proper) it gets a little easier but I'd still not recommend trying to tackle this book unless you're a graduate in maths or a self-taught prodigy in pure maths. The book promises to be a self-contained guide to the best mathematical understanding of the universe we have, but it ends up more like the author just stuck the important theorems in with a minimum of explanation (he does hit almost all of them: one thing that struck me as unnecessarily erudite - showing off - and odd was the statement of Maxwell's field equations, which is mathematically simple and elegant, in terms of tensors, which are very, very difficult), so it's a complete guide if you already know all of the math (in which case you don't need the book): it's much more of a refresher and quick reference for people who already are familiar with and understand (or at one time understood) the concepts the author represents. Required prerequisites: understanding of linear algebra (Lie, Poisson, Frobenius), TENSORS (and more tensors), several varieties of noneuclidean geometry (Minkowski, de Sitter, Riemann), scalars, topology and n-manifolds, group theory (Lie groups), gauge theory, etc., or the willingness to learn these from expensive secondary sources, because Penrose will not teach you them here and the arguments of the book are incomprehensible without them. Without them, one would be reduced to skimming the 20% of the book that is text (especially the final chapter, which is comprehensible to any semieducated layman) and taking the author's word for the rest of it. Just about the only thing he explains in full is twistor theory (his own invention). I still have to award two stars for the obvious intensity and depths of erudition which Penrose funneled in to this work, but only two because it doesn't even partially fulfill its stated purpose or self-description. *Redacted to protect the privacy of a member of Vagabond of Letters.     dont-own               2,377 reviews18.8k followers     April 6, 2021   What is reality? How come that mathematics is so handy describing it? And often more astutely that our eyes? What are the laws governing it all? Are we getting it all right? What if we are trying for the wrong questions and answers? These and many other questions are what the 2020 Nobel Prize winner Roger Penrose's giving the reader a taste of working on: string theory, physics, the mindboggling quantum effects... - all through the prizm of mathematical apparatus.                  1,015 reviews1,164 followers      Read  June 30, 2011   So we had a physicist around to dinner the other day and thrust this at him. I can't call T---- by his real name, let's just say he rhymes with a dip made with chickpeas and tahini. The reason I can't call him by his real name is that he works at a place that starts with C and rhymes with a complete lack of humour. He likes his job, I don't want to get him sacked for reading Penrose.He flicks through it and the first thing I note is that physicists take about 5 nanoseconds to read what it takes ordinary mortals eons to get through. He starts with the cover, of course. 'Reviewed in the Financial Times?' A disparaging snort follows. 'Ah,' he says after the third nanosecond. 'He's written this type of science book.' I like that. I have no idea what it means, but I like it. After four nanoseconds he is up to page 1050 or thereabouts. He reads out a question from it and says 'That is a good question. I don't know the answer.' Slaps book shut. Really, I mostly get the impression that real physicists like him just wish those other ones would just stop it. Stop with all the philosophical 'should we be worried about this?' stuff. Let's just get on with it p-lease. And he says 'You didn't say the dinner invitation came with a catch.' I say 'But I didn't say it didn't, did I?' I am seriously thinking of reading this while skipping every page that doesn't have only words on it. Seriously.     haven-t-read-but science-fiction science-sort-of               28 reviews25 followers     June 27, 2008   this book RULES. it is a sort of primer on the mathematics required to really understand quantum physics. of course, that is a pretty huge pile of stuff, and this is a damn huge book. it moves faaast too: the entire theoretical foundations of single-variable calculus takes up one chapter. the reader is rapidly pulled through pretty heavy cram sessions in multivariable calculus, algebraic topology, real analysis... everything you need! and yet, it does not feel at all dense, because roger penrose is one of the great living stylists in mathematical writing: even a healthy dose of equations can't obstruct the fluidity of his prose, the lucidity of his explanations, or the enthusiasm of his presentation. i took classes in some of these topics and felt like penroses's single chapters did at least as much for me. other topics i was only cursorily familiar with, and this was felt like a rocket-fuel-grade introduction. there are even some really really nice excercises, mainly in the form of proofs (the fun kind of excercise). exhaustive theoretial math books are rare but they do exist; what makes this one actually work (in contrast to some dogmatic behemoth like the classic whitehead &amp; russell) is that penrose is actually directed towards a somewhat taangible goal: educating a casually geeky, intellectually curious layperson about quantum physics, and leaving nothing out. for whatever reason, it works.i brought this thing along as my only book on an 8-week tour, and it was perfect: a quick dose of clearly, beautifully written, brain twisting math a couple times a day. YES!                   89 reviews44 followers     February 27, 2019   wow... I actually managed to read it, 1050 pages, every single one of them.But can I really say that I'm done with this book? I don't think so... Although it took me a year and a half to read it, I didn't even understand a significant part of it. Since I'm a physics student I understood most of it on some very basic level, but I'm pretty sure I'll have to open this book again and again to take a peek at some of the awesome ideas put here by Penrose. Did I say awesome? That's a huge understatement. I meant incredibly brilliant, original, profound and refreshingly sober! Sir Roger Penrose is the reason why I came to love physics as much as I do and he's probably the main reason why I chose theoretical physics and why I'd like to be a mathematical physicist.  You, sir, are a huge inspiration... Thank you! I don't want to write anything else because I don't think I could give this book a truly proper review, you should simply try to read it... and if you manage to do it, I hope you'll understand what I mean.     informal-but-technical mathematics philosophy           January 5, 2011   Amazing. While I can not exactly call Road to Reality a popularization of general relativity and quantum theory, it is a peerless introduction to and review of those topics. I have a PhD in mathematics, and studied physics and math as an undergraduate, and there was plenty for me to learn from this book. There are very few people in the world who would not learn much from reading it.Many years ago, I read Penrose's Emporer's New Mind which was good as far as it went, but earned my derision with doubtful, hand-waving arguments for quantum origins of consciousness. Knowing Penrose is no dummy, I permitted a friend to convince me his work deserved another chance. I am very glad to have read RtR, even though the process took me most of 2010. I now have a far better understanding of mathematical physics than I could have achieved with any other reading list. I did not complete most of the exercises; I suspect that if I had, then (A) I would not have finished until 2012, and (B) the exercises would have been sufficient to bring me to a fairly professional level of competence. Kudos to Mr. Penrose for including them. The book begins with quite a few chapters of mathematics, quickly progressing to advanced undergraduate topics such as calculus on manifolds. In some ways I liked Penrose's clear treatment and drawings better than, say, Michael Spivak's beautiful but sparse texts. In order to provide a foundation for his chapters on physics, more mathematics is interspersed where necessary. Penrose introduces complex manifolds, continuous groups (Lie groups), and principal bundles. This machinery is all truly essential to the physics, and it was enlightening to see it collected in a single place, however briefly explained. It is especially useful because most graduate students in physics or math end up missing a formal introduction to one or more of these topics. The grand themes in RtR are the two major 20th century discoveries of general relativity and quantum theory. Penrose is particularly interested in probing how the two may be made consistent. He covers some of the cosmological work that treats both (e.g. Hawking radiation from black holes), and then discusses theories that seem to join them, including various level of detail on spin foams, string theory and M-theory, loop quantum gravity and his own invention, twistors. A great strength of this magnum opus is Penrose's ability and willingness to discuss philosophical and aesthetic issues of the physics. Four of these stand out. First, I quite like his perspective on the futility of obtaining unified theories by (more-or-less) trying to guess a tractable Lagrangian. Second, his detailed treatment of entropy, especially the universe's original low-entropy state with respect to gravity and the cosmological implications, was really fascinating. Third, Penrose seriously considers the various interpretations available for (apparent) collapse of the quantum wavefunction. His bias is toward objective collapse (environmental collapse), rather than being spookily dependent on "observation" by a conscious observer, and I agree with him that far. He suggests that general relativity, being the only other physical theory we have of similar stature to quantum theory) may somehow provide the mechanism. This is not an assertion but merely a suspicion on his part, and personally I lend it little credence. I do agree with him that general relativity is likely to remain a permanent Newtonian-style large-scale limit of the physics, while quantum theory seems ripe for some kind of fundamental reinterpretation. Finally, Penrose revels in the aesthetics of what he labels complex number magic. That is, he considers the interesting ways in which physical reality is so well described not just by mathematics but specifically by complex analytic structures, a simple example being the phases of quantum wavefunctions. His fascinating twistors are the coolest example of this, where he changes the physical perspective utterly. No longer are points in spacetime the essential quantities; rather the physics is on the manifold of (potential) light rays. A spacetime point is a confluence of rays, and the interesting part is how fundamentally a point can be represented by, and treated as, a Riemann sphere (a compactified 1-dimensional complex line). As an ex-complex-manifolds guy, this was wonderful stuff to me. I will conclude by noting that Penrose even redeemed, somewhat, his handwaving arguments from New Mind. I now understand that he is essentially pointing out that our conscious observations of physical phenomena are (or appear to be) collapsing the wavefunction. Since there must be a mechanism for that collapse, Penrose is arguing that something fundamental about conscious minds (as opposed to highly sophisticated computers) is triggering it. I still don't agree, because I believe consciousness is computational and emergent from complex systems, but his point no longer seems so silly.     favorites               148 reviews112 followers     July 8, 2011   This book is too sprawling to wait and review all at once at the end, so I've decided to do it little by little as I go along.I thought the  prologue sucked, but immediately after that it became deeply fascinating, so don't get discouraged. I guess I should say why I hated it, though. It seemed as though he was judging former times and societies through a "presentist" lens, as though all people have always and only been scientists since the start of time, only they were really bad at it back then. It's kind of a scientist's way of ignoring everything else about reality besides science, and made me a bit nauseated, thinking "oh no I hope he's not going to be this dumb all the way through." Luckily, he quickly transitioned to extreme brilliance, in which he's jaw-droppingly continued since then. Even though he's talking so far about seemingly simple stuff, he keeps knocking me for a loop with his deep insights which I've never considered before.Only in  chapter 3 so far, and discussing integers, irrational numbers, and the real numbers. I keep having to stop and think hard about the things he's saying. He asks the question if we lived in a universe where things were an amorphous soup would the integers exist there. He also points out that calculus (and stuff like momentum, velocity, and many of our physical concepts depend on calculus) is defined on the real numbers. If it turns out that the universe is discrete at the tiniest level, this math won't apply anymore (except as an approximation). However, he also observes that the real numbers first invented in Euclid's day when we had physical evidence spanning only some 15 orders of magnitudes (the smallest to largest distances known) are still going strong now when our knowledge spans something like 150 orders of magnitude, so they aren't doing too badly! These are the notions of someone who has thought deeply about how math and physics are intertwined. I keep being dumbstruck with things he casually asks about things that are ostensibly simple which I've known forever but never thought to ask that. Really important stuff. He is breathtakingly brilliant! I'm so glad I'm reading this book!Aside: The more I read the more sure I am that Platonic essences exist independent of the nature of physical reality, and independent of their instantiation in some physical reality. Spent some time going over familiar ground in the complex plane. It's been long enough since I studied or used this stuff that it's quite enjoyable and satisfying to do that. I think I've settled on the slow savoring method of reading this book rather than the quick devour. This review's going to be very long, but I hope it'll admit of savoring a bit as well. =) In  Chapter 5 now, and talking about e and logarithms, I wondered why it is again that e is a more natural base for logarithms than any other number. So I spent some time adding it up from the formula e = (1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)+(1/5!)+... and watched the digits slowly materializing 2.7182.... so I believe that much. =) Next I'm reading again how e originally came up in playing around with logs and powers. This book has that effect that it makes me think again about stuff that I haven't thought about since I was young. I would really like to feel I understood what we know of reality inside and out when I'm done. I want to see the whole chain starting from one cow, two cows on up to the standard model and beyond. It's always been an obsession of mine just to understand how things freaking work, what the universe is like, what nature is based on, and I have this feeling I could get much closer by going through this volume carefully. The title keeps reminding me of the Royal Road to Geometry, which Aristotle reportedly told Alexander the Great did not exist, so that's some kind of warning, hah! So far I've resisted the urge to jump ahead, except for reading the section called "beauty and miracles" near the very end. You have to admit that's an attractive section name! Alas, I understood it only in the broadest way, that beauty (mathematical elegance) and miracles (seemingly crazy mathematical coincidences such as all the complicated terms happening to drop out or whatever) act as a powerful but not unfailing guide so far to finding theories that fit how nature behaves. At that moment, my dear kitten Alai jumped up and sat right on the book, as if to say, "you want beauty and miracles? Just look at me!" As I pet him, I kept saying "beauty and miracles" affectionately.      nonfiction science               1,379 reviews86 followers     January 1, 2016   For the past year and a half I have been reading heavily in popular works on physics and astronomy, at various levels ranging from the superficial gosh-wow (Michel Kaku) through total beginner level to the somewhat more sophisticated (Brian Greene, Kip Thorne, Lee Smolin); but almost always I have been frustrated in my understanding by the lack of any mathematics to support the often metaphorical discussions. At the same time, I understood that the real mathematics of relativity, let alone quantum and string theory, would be way over my head (as when I borrowed, and immediately returned, one or two books by Penrose himself, as well as books by Wald, Susskind, etc.) So when I saw the description of this book, that Penrose intended to supply the necessary mathematics to understand the physics as he went along, I thought that it would be just what I wanted -- if it were possible. I was also rather skeptical, whether in fact it was possible, in something under 1100 pages; and as it proved, rightly so. Penrose does not succeed in making the math understandable; he explains something at a very simple level and then assumes that the reader understands far more than the author has actually explained, and when he gets to something especially difficult to comprehend, that's when he gives a footnote: show why this works. At the beginning, I read this pencil in hand, but it soon exceeded my abilities to work out the problems.I am not totally unmathematical (I say this because it is relevant to understanding the level of this book): I minored in math in college, and beyond the usual background in high school algebra and geometry, and physics (before the dumbing down of high school math and science circa 1970), I have taken two years of college calculus, a semester of calculus-based probability and statistics, several "fundamentals" courses, and a calculus-based (but entirely "classical") first-year physics course. Not a lot, really, but probably more than most non-math/science majors. And I have tutored high school and college students in math through early calculus for over ten years. So what did I understand of this book, with that background? The first six and a half chapters. Chapter six explains calculus in nineteen pages, and I'm fairly sure most of what he talks about was never included in my two years of calculus (maybe in a real analysis course?) Chapter seven was on complex analysis, and I understood about the first half. This was the model for the rest of the book -- I understood about the first half of each chapter, where he explains the basic concepts, and got lost when he tried to "make it clearer" through "the magic of complex numbers" (his favorite expression.) The same was true when he passed over into the physics of relativity, quantum theory, and the modern speculations about strings, twistors, etc. -- I understood about half of each chapter. (Actually the chapters on loop quantum gravity and twistors were totally out of my range from the beginning.) I would say that the minimum for really following him would be to already have taken at least a complex analysis course. Was the book a total loss, then? No. If I didn't learn the various fields of math he covers (vector and tensor calculus, some projective geometry and topology, etc.) I did learn what those fields deal with; if I didn't learn what I needed to understand the physics, I did learn what I would need to study to learn it, and perhaps most important to an autodidact who will never be able to afford any more formal education, what order I would need to study the various fields in. In short, for me (and probably for most readers who don't have a strong math/science background) this was not the "Road" but more of a roadmap; I didn't make the trip, but I got a feel for where the route passes through. At the least, I was inspired to review my high school and college math, and perhaps to try to go a little beyond where I stopped. At my age (nearing retirement) I will never get all the way to an understanding of the physics, but maybe I will keep my mind working a little longer for having read this. I should give a brief summary of what he is saying about the questions I have been reading about in other books: he is very skeptical of string theory, because of the higher dimensions (the problem of degrees of freedom, especially); he is somewhat more friendly to quantum loops and other alternatives; he is naturally most interested in his own theory of twistors, but admits that at present it doesn't have the solution either. He argues that to be consistent with general relativity, there must be significant modifications to standard quantum theory. I'm obviously not sufficiently informed to evaluate any of this. I would recommend the book for what it is, but not for what it claims to be, unless the reader has a real background in mathematics and physics.                   1,059 reviews52 followers     January 30, 2023   3.5 starsThis is a mathematical and physics tome of more than a thousand pages. It is essentially everything you should know about the universe by the Nobel Prize winner himself, Roger Penrose. Heavily formula based. Many of the later chapters were beyond my depth, unfortunately.  Writing was okay. Would have liked to heard more narrative but I suspect Penrose's open mindedness kept him from deviating from established theory.  3.5 stars                   197 reviews117 followers     February 23, 2012   As accurate a title as can be for this tremendously ambitious behemoth. I very much enjoyed the masterful laying of a mathematical framework when first I came across it (the first dozen or so chapters if memory serves; hence the rating, as well as for the aforementioned ambition in the task- I think this is a right way to go, though popular expositors seldom venture down this route), as Penrose does it so efficiently (and naturally too, so that the layman wouldn't shove it aside in disgust after hardly a half dozen pages, and for the price even that handful of beginning chapters are worthwhile). Something of an idiosyncratic emphasis might be noted in these chapters, but it doesn't take away from the breadth of the account and can't really be faulted because it's setting things up for what follows. I never actually got to much of the 'meat' of it- which is the physics (and so unfortunately can't remark on it). I'd hoped to, but then I realised I was just putting it off out of apprehension that I'd find myself feeling the lack of formal first year physics at university (something I gleefully escaped as early as I could in favour of my chosen field- pure mathematics). This is probably an unfounded concern, since skipping ahead to chapter 17 on spacetime, I was able to follow the account, but nonetheless I closed the book at this point. Perhaps I'll revisit it sometime with a few other references handy should I need rescue. This would certainly be worthwhile if you can give this the time and energy required; you're sure to come out richer in knowledge, in a way almost no other popular account of science can impart.     physics-and-other-science               894 reviews104 followers     September 17, 2015   In this amazing book, Roger Penrose looks for a very fundamental issue.He is looking for a single metric to describe everything. This is not a unit of reality, however, although this is how he poses the issue. The problem with selecting a metric, as he shows us over and over, lies in how different metrics arise from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics will threaten to buckle. In many instances, the metrics (and their attendant relationships) will no longer be applicable. What this means, in the Kantian (and Badiouian sense) is that these relationships's applicability will become "undecidable". In some extreme cases, the relationships may even break down. For instance, black holes are a problem because the expressed relationships that emerge from physics experiments prove to be untenable in black holes (and the big bang) as these relationships decohere and infinities and zeros pop out everywhere. This search for a metric leads Penrose to reject string theory as a viable relationship form. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, weak force is a dimension. Each dimension is an independent mathematical vector of a different "inertial" influence. Additionally, the mathematics of string theory, as well as other theories, proves to be too illusionary. As with post-structural critiques of modernism, Penrose points out that the consistency of string theory relies on theoretical supplements/signs that are attached onto the positions of various types in order to maintain coherency. For instance, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions as well as its immanent affects proves to be unweldly to Penrose because the coherence of the relationships are maintained by theoretical enforcement rather than any direct correlation of math and physical experimentation. If Penrose was familiar with Badiou, Kant and Derrida, he would be able to recognize that the undecideability of supersymmetry and string theory result from these theoretical supplements. The supplements provide the missing pieces to cohere the theory, so physical experiments prove to be incomplete in their testing. As Penrose points out, string theorists in failing to find superpartners can always push the calibration of their theory to include these partners, just at higher energy levels, which can always lie beyond the ability of technology to generate. In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose falls fault to this when he theorizes that Quantum Field Theory can be modified (rather than the Einstein's general relativity) by changing the cut off metric. This is in line with all his discussions to "renormalize" the math so as to remove the variance accumulated by extending localized relations from beyond the area of origin on the manifold. We can always enforce a consistency of a given domain in two ways. 1. To provide a "superpartner" to supplement the terms, to keep phenomenon visible to one another within the domain, as a motion of immanence, as Derrida suggests. Or. 2. To encapsulate a domain by limiting its identity to its other. From there, we can radically reduce the other to zero, thereby hiding the limitations of a domain, as with Moffe &amp; Laulau with their Hegemony or as with Badiou with a basic atomic "cut" to center the domain as with Being and Event II. Both of these strategies amount to the same kind of forced coherency by mapping a domain rigidly. Penrose does offer his own favorite solution; his Twistor theory, which removes the need for extra dimensions beyond 3 + 1. Additionally, he considers this theory by collapsing all the different vector differences held cosmically in string theory into immanent relations that are founded on the very "knots" of space, so that the pre-space twistors contain the information that wider "vibrations" are meant to express. Both theories are incompatible in this regard because of their huge difference in scale. And while Penrose admits that twistor theory adds nothing physically; that it's just another way of viewing a situation mathematically, he also realizes the need for us to see things differently than we have. It is this adherence to a particular view that causes all the problems in the first place. If you look at how these different views are constructed, you'll see the mathematicians switch from one domain to another through various class equivalences whenever it suits them. When they need to express vectors they will jump to a manifold model, or a more generic (abstract) deformation of an algebra. In other words, we lack enough views. So we supplement the one we have in an attempt to normalize them. Curiousier still is Penrose's tiny discussion of consciousness in which he attempts to "renormalize" consciousness in terms of objective reduction. He theorizes that the waveform reduction that collapses due to quantum gravity may be at the seat of consciousness's ability to complexly surject different sensory views into coherency. This suggestion is of the same kind as his forced synthesis of twistor theory. The satisfaction of trying to find a single metric, a single complex knot of relations that cannot be unraveled but contains all the "moves" is like a physicist trapped on a chess board recognizing the orthogonal formation of board, or as in Futurama the Professor discovering the smallest unit that constitutes the universe is the pixel. In a real way, Penrose seeks to calibrate physics to the mathematical domain. He doesn't want beautiful math that doesn't apply, that is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth of which the entirety of the physical is mapped; although mentality is generated from the physical and mathematical/Truth is generated from that. The Platonic ideologue he insists on lies on the equivalence of function, on the purity of the sameness of process from point to point of the same type. Never-mind that the subatomic particles we find today are largely generated from artificial means. Penrose would assume as sameness of process that forces a universalization, but that is the way metaphysics and science both work, to equate different phenomenon as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we see, all relations are born locally, within a limited scope. Their extension cosmically creates the basis for which we start to see a degradation of relation qua variance (pollution, or various forces of form-fitting). After all, we can have no irrationality without first being able to posit a rational sheet of complete consistency. Nonetheless, although this is a lengthy book it is still beautifully written. I wonder who Penrose's audience is, for he approaches much mathematical complexity in such a short time, talking about basic principles like polynomials and trigonometry before jumping into Lagrangian manifolds and so on. Still, if you hunger for complexity and abstraction, here it is. Much of his explanations of very complex concepts are very clear, although at times we could use more handholding. His pictures are also very interesting and complement his point nicely. Well worth the effort to read.     2015 impressive mathematics               232 reviews12 followers     December 5, 2020   Un libro con un objetivo tan ambicioso como describir el estado del conocimiento científico que poseemos sobre la realidad profunda de la naturaleza y los caminos para avanzar en lo que nos falta por descubrir es realmente difícil de valorar.Este es el único libro científico que aparece entre los 100 primeros libros de la lista de Goodreads "Libros que te llevarías a una isla desierta". Creo que está ahí con todo merecimiento. Es un libro que admite muchas relecturas- Durante los casi dos meses que me ha llevado su lectura las cosas que leía me venían a la mente continuamente. Todo lo que plantea es interesante, estimulante y te expande la mente.El único problema con este libro es que en una isla desierta no hay Internet. Me explico: a pesar de sus más de 1.400 páginas, el libro es casi imposible de seguir solo con la información que en él aparece. He tenido que recurrir en muchísimas ocasiones a la web a buscar la información necesaria para "rellenar los huecos" de lo que estaba leyendo. El autor te lleva de la mano durante la exposición pero frecuentemente te suelta y te obliga a hacer un acto de fe en la argumentación o da por sentada la evidencia de un razonamiento matemático. He echado de menos enormemente enlaces a recursos en Internet donde se explique el detalle de las ideas expuestas o aparezcan resueltos los ejercicios que propone. En mi caso, solo cuando he podido seguir la línea argumental en detalle he tenido una imagen clara de lo que está leyendo.En cualquier caso, el esfuerzo de enfrentarse a la lectura de este libro es ampliamente recompensado por la ampliación de tus horizontes mentales.Resulta también fascinante el vislumbrar cómo funciona la mente de un científico como Roger Penrose, para mí, uno de los más grandes pensadores vivos.                  174 reviews110 followers      Shelved as 'half-read'  April 14, 2016   This book is not for those with no strong background in mathematics and physics and it is definitely not for lay readers.Except for the first 40 pages or so the book material was very sophisticated and hard to understand for me. Today I decided to stop as for the past 30 or so oages I could only understand little of what I was reading. I'm putting it on hold now and I may return to it later after establishing a strong base in mathematics and physics.                   30 reviews     January 19, 2013   By his own admission in the preface, this is Penrose' attempt to popularize the current thinking in theoretical physics, including quantum mechanics, relativity, and unification theories such as string theories and quantum gravity. In the introduction he says (paraphrased) that he has intentionally gone for the more mathematical route, in spite of advice to the contrary, but he hopes that those without a mathematical bent can just skip the equations and get the gist of the concepts anyway.With due respect to the author, his attempt at “popularization” is a failure. I wonder who he thinks his target audience is when he goes to great pains to explain basic concepts such as imaginary numbers and why they aren't so mysterious and yet throws out higher level abstractions that take time even for a college graduate to feel comfortable with. His target audience seems to drift from the lay person on the street up to professional mathematicians and physicists. In my opinion this book of over 1000 pages replete with equations and complex diagrams would be good fodder for several graduate courses in mathematical physics. He introduces such abstractions as complex analysis, abstract algebra, manifolds, bundles on manifolds, tensor fields, Lie groups, Hilbert spaces, etc with just a few words of explanation and a lot of hairy equations, after which he marches on with advanced theoretical concepts and applications to physics. I studied most of those topics in graduate school to some degree, but I was especially comfortable with Hilbert spaces and complex analysis. And yet, it was all I could do to keep up with him. Perhaps it's the fact that I was in my early thirties then and had more functioning neurons, but this 63 year old brain found it hard to track his descriptions, let alone the equations. I confess that (in spite of considering myself an erstwhile mathematician) I often attempted to take the route he had advised for the non-mathematically inclined: just gloss over the equations and get the general concept. But his descriptions are mostly so down in the details that I found it difficult to get to the general concepts from the text alone. I also decided that I don't like his writing style much. It varies from overly verbose and redundant to cryptic and abstract in the extreme. And the edition I have was poorly edited: there were many mistakes such as unclosed parentheses, repeated words, missing words, and grammar mistakes. Given how turgid his prose is I don't envy the job of the editors, but it's still their job to find those kinds of obvious errors.The one good thing from all this is that I think I finally (kind of) understand tensors and tensor fields. For whatever reason I didn’t get into tensors when I studied differential geometry in the early 80's and I’ve found this to be a deficiency in my education over the years (e.g. understanding the field equations of general relativity). His description prompted me to study up on tensors and I found a couple of good websites with detailed descriptions and examples. In any case, I DO recommend the book if you have a knack for or interest in advance mathematics and theoretical physics. I DON’T recommend it if you want an easy read in popular science to make you feel smart :-).    owned               384 reviews11 followers     September 23, 2012   Penrose examines the turn modern theoretical physics has taken in pursuit of multi-dimensional mathematical models to develop a unified model of the sub-atomic realm. His argument is not entirely mathematical, though he does have good arguments against unnecessary complexity from the point of view of the straightforward progress made by theoretical physics in discovering the mathematical elegance of relationships among various observed constants. His most profound argument against String Theory is a failure to make any predictions which could be tested by observation. He makes an eloquent argument for pursuing alternate models instead of mathematical physics being caught in what may ultimately prove to be a dead end. He proposes several ways forward, including his own twistor theory. Penrose reminds me of Feynman in his fresh thinking. Feynman's development of quantum-electrodynamics required thinking of observed phenomena in a new way. For those willing to scratch the surface of modern physics, Penrose provides a lucid primer. He even devotes nearly a third of the book to laying out the math so the reader can begin to understand what follows. At more than a thousand pages, this is a serious primer. I thank the friend who loaned me this book a few years ago and allowed me ample time to digest what I could. Yes, I did return it, but I may need to acquire my own copy.                   Author  5 books199 followers     July 20, 2010   Not an easy read because of all of the math, but well worth the effort for those who can make it.     science               Author  2 books95 followers      Read  June 7, 2017   Най-накрая приключи.И само това да бях коригирала, щях да се гордея със себе си.    и-з               18 reviews4 followers     September 6, 2019   The story goes that Stephen Hawking was once told by a book publisher that every formula in his book would halve the amount of readers (or sales, almost the same thing, but not to a publisher). He was , of course, totally and utterly wrong. The Road to Reality contains about 1100 pages and, on average, there's about 9 formulas per page. That makes roughly 10,000 formulas. According to this publisher's law, that would halve the sales ten thousand times (2^(-10000)), so a rough estimate of the amount of readers left is around 5x10^(-3001), which is a number so absurdly and unimaginably small, you have to be a Belgian surrealist painter to be able to imagine it. Roger Penrose would be left with much, much less than a single quark of a reader. Judging by the amount of readers here, this is obviously not the case.What this publisher was pointing out, however, was that, in order to attract a lay public, you have to shun formulas, because they might chase them away and you wouldn't be able to teach anybody anything because there wouldn't be anyone left. Hawking followed the advice, wrote a book for the layman and, in my humble opinion, failed miserably. The layman didn't understand anything from his cryptic text, because they were missing several dozens of books of background information needed to understand most of the concepts. The more informed readers were chased away because of the lack of depth, the haphazard and disconnected way the concepts were presented and the absence of the mathematical beauty. It did sell well, so from this perspective, the publisher was undoubtedly right (and this was probably the only perspective he was interested in). This fiasco teaches us something very important: writing and reading about present-day physics is no small feat. Lots of background is needed (yes, mathematical as well). However, unfortunately, most writers listen to publishers and omit the formulas and lots of the difficult bits as well, so the task for the physics reader is greatly hindered. Luckily, Penrose is a kind old British gentleman, not afraid to take up the glove and rise to the challenge. The Road to Reality is his magnum opus, introducing the reader to modern physics (mostly cosmology and to a lesser degree quantum mechanics) , without oversimplification or the omission of essential formulas. He doesn't muck about either. If mathematics is what you need to understand it, mathematics is what you'll get. No less than 16 of the 33 chapters are devoted solely to mathematical foundations. After that, Penrose gives an overview of the established physics (mostly special and general relativity, quantum mechanics and some thermodynamics. The last few chapters are concerned with the more controversial topics, like string theory. The mathematical part is, to the best of my knowledge, quite complete. The established physics is concise and omits most things that aren't related to the aim of the book: present-day speculative cosmology. For the last part, Penrose focuses on string theory (currently still the most popular group of theories), loop quantum gravity (the most interesting contender) and twistor theory (Penrose's own field of research). His account of these theories is very honest, making no secret of his critiques on certain fields of research and warning the reader to take his interpretations with a pinch of salt and often pointing the reader towards books containing views conflicting with his own. Does this make The Road to Reality the ultimate physics book for the dauntless layman? Of course not. The task Penrose set himself is neigh impossible. One cannot replace several dozen textbooks by one, albeit bulky, volume, even if it is written by someone as erudite as him. A lot of his explanations are just too brief. He would need another two to three thousand pages to be able to explain everything thoroughly. Furthermore, the splitting of the maths and physics is different chapters is probably necessary, but it means Penrose refers a lot to previous chapters. Since I have a hard time exactly remembering some subtle mathematical notion from 400 pages ago, I needed to skip backwards and forwards a lot, making for quite a laborious read (not something to do while commuting by bus, for example). The subject itself is very slippery too. Current theories cannot be verified (yet) by experiments, so theoreticians are only guided by very abstract notions, such as mathematical beauty, or instincts honed by years of hard work. Such things are often very hard to convey to anyone not a specialist in that particular field, although Penrose does a good job, nonetheless. It is probably the closest you'll get to a textbook without actually reading a textbook. The Road to Reality trumps A Brief History of Time in many ways, but ultimately it cannot be avoided that one needs to read a lot more to truly understand physics, but that's not necessarily a bad thing (publishers will agree).     natuurkunde               713 reviews100 followers     February 20, 2014   Deciphering the laws of physics to create universal realityThis is an exhaustive review of the laws of physics as related to physical reality with significant emphasis on the mathematical component. The author is an outstanding mathematical physicist of our times, and in this book of 1100 pages, he describes the concept of space, time, and matter (energy) in terms of classical physics, quantum physics, string theory and its derivatives.  In physics, the behavior of objects is understood in terms of the action of a force; a vector quantity, which has both magnitude and direction. The force acts on a matter and produces a causative action that results in an effect. The cause - effect is one of the fundamental aspects of classical reality, but it gets fuzzy and uncertain at submicroscopic levels (quantum physical reality.) The main object of physical law is to describe the reality we observe. Our observation includes this universe that is made of space, time, matter, and energy. All objects are made of matter, which exists as complex structures composed of molecules, atoms and fundamental particles. Matter is also a form of energy and the two forms can interconvert as described by the Einstein's famous equation. The fundamental particles has certain physical properties and the manner in which energy (and force) is expressed is though their association with the so called force particles that are responsible for four fundamental forces that operate in nature, they are; electromagnetism, gravity, strong and weak nuclear forces. The four forces mediate matter-matter interaction and facilitate matter-energy conversions in spacetime and thus explain physical reality. The key to the understanding of nature and physical reality is to discover a theory that satisfactorily explains all the four forces and this theory must be experimentally verifiable. Unfortunately, this has not been achieved so far, but we have theories that can be verified but explains only three forces. One single physical theory that explains both quantum and classical realities have not been successful mainly because the nature of gravitational force (curved spacetime) is difficult to describe in a unified situation, since space and time at the most fundamental level are also quantized (exist in discrete quanta) and are they dynamic (not static background).  To understand this book the reader is required to have undergraduate level physics and mathematics; the author explains in the introductory part of the book why he chose to include mathematics despite its negative impact on the book's marketing potential. It would suffice to say that the interplay between mathematical ideas and physical behavior played an important aesthetic role in the minds of great physicists, and Albert Einstein is one of the most important figures in being attracted aesthetically to a particular idea. You can skip chapters 1-16, and from chapters 17-30, general discussion about geometry of spacetime, quantum physics, quantum field theory, quantum cosmology and the standard model of particle physics is presented. I found the last four chapters to be most interesting.  A brief summary is as follows: The unification of special relativity and quantum theory led to quantum field theory (QFT) which produced a minefield of infinities, but with some ingenuity, the infinity problem was circumvented leading to standard model of particle physics which is in good agreement with nature. The controversy between the quantum relativity group and the QFT side is that the latter group tries renormalizability or finiteness as the primary goal, but the former group likes to solve the conceptual difficulties between the two theories. The combination of two theories of particles physics into one framework to describe all interactions of subatomic particles, except due to gravity, is called standard model. These two theories are electroweak theory and quantum chromodynamics. They describe force interactions between particles in terms of exchange of intermediary particles. The author also engages the reader in an insightful discussion of many other theories.      physics               24 reviews264 followers     April 22, 2015   This is an extraordinary book and certainly there is nothing else available on the market that is quite like it.Penrose is a pre-eminent mathematician whose work has affected my own thinking in deep ways. Often I've discovered, to my surprise, that some viewpoint which I learned from another source in fact derived ultimately from Penrose himself, the author of this other source having been, as it turns out, a student of Penrose. As an example I offer "Visual Complex Analysis" by Tristan Needham. I encountered this book in high school and so powerful was its exposition that it stuck with me all through college and beyond to the present day. I couldn't help but notice, while reading "The Road to Reality," that Penrose engaged in a similar revelry around complex numbers -- and so it was a pleasant surprise to see that Needham indeed had studied directly under Penrose! Despite having this book in my collection for a few years only recently did I discover the connection. With this tangential introduction out of the way, let me say at the outset that I cannot recommend this book to just anyone. It requires a great deal of mathematical acumen -- or perhaps, more accurately, a great deal of explicitly mathematical *interest*. You needn't be a mathematician, but you positively must delight in the opportunity of learning the mathematics of the universe. Even if you have a degree in mathematics you're likely to find something here you haven't encountered before -- for instance, I had not previously seen the notion of a hyperfunction which Penrose enthusiastically presents in connection with the Fourier transform. The book's mathematical explanations are quite idiosyncratic, and I think this reflects the depth of Penrose's intuition on the topics. It elevates this book from an encyclopedic reference to a personal outpouring of the author's vision of the world. Not only does the book feature unique topics that aren't commonly taught, the aforementioned hyperfunctions being an example, but even those which are commonly taught are explicated here in a unique manner. Penrose's style is unabashedly geometric, and so even partial differential operators on manifolds he almost always thinks of as vector fields. The book is filled with many beautiful hand-drawn diagrams showing everything from a fanciful vision of the creation of the cosmos to a field of one-forms on a surface to the conservation of electric charge in spacetime. And the book prominently features throughout his diagrammatic notation for tensor algebra, something again which I had never encountered elsewhere. I should say that this book approaches its physical topics from an exceptionally high level. You will probably not be able to learn electrodynamics from Penrose, not here. I don't recall the common form of Maxwell's equations even occurring in this book. Rather, he simply writes them down in the simplest, most beautiful, and most abstract form, using differential forms and exterior calculus. To delve in deeper, rather than expanding out these equations, he instead focuses on how they can arise as the curvature of a bundle connection via gauge theory. This is both stunningly beautiful and horrendously detached from practice. Despite the overwhelming emphasis on theory and mathematics, the book is quite adamant in insisting that physics still must be physics. Penrose is not optimistic about string theory, though he does give it some treatment towards the end for completeness. He's perhaps like Feynman in that regard -- he possess a deep appreciation for the mathematics and the theory, but at the same time is very uneasy with the lack of testability of much of modern theoretical physics. His own theory, twistor theory, is just as untestable, though he's honest about that.                   865 reviews10 followers     June 29, 2013   This is quite a challenging read -- but definitely worth the effort! The first half is primarily "math" while the second half is "physics." Penrose did an amazing job of writing a guidebook to a great deal of the breadth of both of these fields. I felt there were some uneven sections -- I remember a great deal of discussion on Fourier transforms and thinking that if a whole section of discussion is needed there, how will the reader keep up through differential topology, twistor theory, diagrammatic and group theory notation, etc.. But overall, it was great. The writing was almost playful at times, especially as the book progressed. Penrose did a nice job of self-identifying his biases. I enjoyed the discussions of the relationship between math and reality (p 631 "What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description and then trying to regard that description as describing a 'reality'?"). The last two chapters of the book really explored this idea further.The discussion of string theory was especially understandable (and self-admittedly biased). It struck me as a bit funny that (especially later in the book) there was more and more reference to the "magic of complex numbers" and yet in one of the final sections there was an argument that there is nothing more or less confusing between real numbers and complex numbers). This book was extremely "hyperlinked"/self referential. At first all the links were "forward links" (necessarily..) and mostly I ignored them. As I got further into the books, I started following the "links" (both forward and backward) much more. I found myself using the index and really engaging with the text. As I started the review -- it takes some work and is definitely worth it! I plan to reread this book in a few years.                   12 reviews2 followers     February 9, 2009   I desperately want to make it through this book. I might be crazy. I think part of my fascination with finishing it is to compensate for not finishing engineering school. I can tell you this... It would be a lot easier to read if I had attained my degree (and actually learned the material along the way). Nonetheless, this book opens in the most interesting and captivating fashion, which says a lot about a book that works to explain the universe by walking through the history of mathematics. A couple of years ago I saw a man reading it while on the treadmill at the gym. The book is 1000 pages long and after seeing the title I asked him about it. I asked him if one had to have a firm grasp on upper level mathematics to read it (which, despite going through Calculus 1-4, I do NOT). He said: "Oh no, I don't know much math but I am enjoying it anyhow". Well, it became apparent early on in the book that the guy at the gym was off his rocker (er, off his treadmill). After the opening attention grabber, the author details the beginnings of mathematics, the definitions of "proof", "theorem", and "postulates", and aims to start from "point A" and go through to what ever lies beyond mathematical "point Z". So, with an initial giddiness I started through the book. Soon I had a scratch pad handy. Then I was reading and re-reading sections to try and get a grasp before moving on. It was reminiscent of my struggles during my calculus classes while at Michigan Tech. I have a strong interest in the material and a desire to learn it but it hurts my little brain. In summary, I am still grappling with the first 100 pages, but would still highly reccommend this book, especially to those with an interest and aptitude for math &amp; science. I'll keep at it.~ Mike - February 2009
The Road to Reality: A Complete Guide to the Laws of th…
https://www.goodreads.com/book/show/10638.The_Road_to_Reality
https://www.amazon.com/Surely-Youre-Joking-Mr-Feynman/dp/0393355624/ref=as_li_ss_tl?dchild=1&keywords=Surely+You%E2%80%99re+Joking,+Mr+Feynman&qid=1606593411&sr=8-1&linkCode=sl1&tag=abakcus-20&linkId=0e1a583756cd8d2ee16131cd87082f0e&language=en_US
“Surely You’re Joking, Mr. Feynman!”: Adventures of a Curious Character: Feynman, Richard P., Leighton, Ralph, Gates, Bill: 9780393355628: Amazon.com: Books
2018-02-06
Richard P Feynman
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<div><div><p><h3>Reviews with images</h3></p></div><div><div><div><div><p></p></div><div><p>An ok experience with this used book</p><div><p>Surely You're Joking Mr. Feynman!By Richard P. FeynmanFirst Edition, Paperback.Size (Roughly): 20.5 x 13.5 x 2.8 centimeters.Book sold by "bellwetherbooks" on Amazon.Announced in "Like New" condition with the next description: LIKE NEW/UNREAD!!! Text is Clean and Unmarked! Has a small black line on edge of pages. Tracking is not available for orders shipped outside of the United States.No tracking information given by the seller as offered, it arrive a few days later than it should've had. Not properly a textbook, this is a pop science book, meaning is not trying to properly teach to anything.A good book by Feynman whatsoever.Nice book</p></div></div></div><p></p></div><div><p>Sorry we couldn't load the review</p></div></div></div>
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 “Surely You’re Joking, Mr. Feynman!”: Adventures of a Curious Character Paperback – February 6, 2018

 by Richard P. Feynman (Author), Ralph Leighton (Editor), Bill Gates (Introduction)
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 One of the most famous science books of our time, the phenomenal national bestseller that "buzzes with energy, anecdote and life. It almost makes you want to become a physicist" ( Science Digest ).

 Richard P. Feynman, winner of the Nobel Prize in physics, thrived on outrageous adventures. In this lively work that “can shatter the stereotype of the stuffy scientist” ( Detroit Free Press ), Feynman recounts his experiences trading ideas on atomic physics with Einstein and cracking the uncrackable safes guarding the most deeply held nuclear secrets―and much more of an eyebrow-raising nature. In his stories, Feynman’s life shines through in all its eccentric glory―a combustible mixture of high intelligence, unlimited curiosity, and raging chutzpah.

 Included for this edition is a new introduction by Bill Gates.

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 1. Book 1 of 2
 Feynman Series
 2. Print length
 400 pages
 3. Language
 English
 4. Publisher
 W. W. Norton & Company
 5. Publication date
 February 6, 2018
 6. Dimensions
 5.5 x 1.1 x 8.3 inches
 7. ISBN-10
 0393355624
 8. ISBN-13
 978-0393355628
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 1. I learned there that innovation is a very difficult thing in the real world.
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 Editorial Reviews

 Review

 "A storyteller in the tradition of Mark Twain. Feynman proves once again that it is possible to laugh out loud and scratch your head at the same time."
 ― K. C. Cole, New York Times Book Review

 "Quintessential Feynman―funny, brilliant, bawdy…enormously entertaining."
 ― The New Yorker

 "Books like this are temptations―to give up reading and devote life to rereading…The book is a litmus paper: anyone who can read it without laughing out loud is bad crazy."
 ― Los Angeles Times Book Review

 "A chain reaction is not a bad analogy for Feynman’s life. From a critical mass of gray matter it goes off in all directions, producing both heat and light."
 ― Time

 "Feynman is legendary among his colleagues for his brilliance and his eccentricity…It’s not hard to smile all the way through."
 ― Newsweek

 About the Author

 Richard P. Feynman (1918–1988) was a professor at Cornell University and CalTech and received the Nobel Prize for physics in 1965. In 1986 he served with distinction on the Rogers Commission investigating the space shuttle Challenger disaster.

 Ralph Leighton lives in northern California.

 Product details

 * Publisher ‏ : ‎ W. W. Norton & Company; Reissue edition (February 6, 2018)
 * Language ‏ : ‎ English
 * Paperback ‏ : ‎ 400 pages
 * ISBN-10 ‏ : ‎ 0393355624
 * ISBN-13 ‏ : ‎ 978-0393355628
 * Item Weight ‏ : ‎ 2.31 pounds
 * Dimensions ‏ : ‎ 5.5 x 1.1 x 8.3 inches
 * Best Sellers Rank: #9,485 in Books ( See Top 100 in Books )
 + #26 in Scientist Biographies
 + #34 in Physics (Books)
 * Customer Reviews:
 4.5 4.5 out of 5 stars 11,956 ratings
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 1. Richard P. Feynman

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 Richard P. Feynman was born in 1918 and grew up in Far Rockaway, New York. At the age of seventeen he entered MIT and in 1939 went to Princeton, then to Los Alamos, where he joined in the effort to build the atomic bomb. Following World War II he joined the physics faculty at Cornell, then went on to Caltech in 1951, where he taught until his death in 1988. He shared the Nobel Prize for physics in 1965, and served with distinction on the Shuttle Commission in 1986. A commemorative stamp in his name was issued by the U.S. Postal Service in 2005.

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 3. Ralph Leighton

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 Ralph Leighton (born 13 November 1949) is a biographer, film producer, and friend of the late physicist Richard Feynman. He recorded Feynman relating stories of his life. Leighton has released some of the recordings as The Feynman Tapes. These interviews became the basis for the books Surely You're Joking, Mr. Feynman! and What Do You Care What Other People Think?, which were later combined into the hardcover anniversary edition Classic Feynman: All the Adventures of a Curious Character. Leighton is an amateur drummer and founder of the group Friends of Tuva. In 1990 he wrote Tuva or Bust! Richard Feynman's Last Journey.

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  An ok experience with this used book
  Surely You're Joking Mr. Feynman!By Richard P. FeynmanFirst Edition, Paperback.Size (Roughly): 20.5 x 13.5 x 2.8 centimeters.Book sold by "bellwetherbooks" on Amazon.Announced in "Like New" condition with the next description: LIKE NEW/UNREAD!!! Text is Clean and Unmarked! Has a small black line on edge of pages. Tracking is not available for orders shipped outside of the United States.No tracking information given by the seller as offered, it arrive a few days later than it should've had. Not properly a textbook, this is a pop science book, meaning is not trying to properly teach to anything.A good book by Feynman whatsoever.Nice book
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  LA in Dallas
  5.0 out of 5 stars A lot of ham, but absolutely no baloney
  Reviewed in the United States on December 17, 2023
  Verified Purchase
  Here's a bit of advice if you're thinking of reading "Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character. First watch a 15 min video called "My friend Richard Feynman" by Leonard Susskind. In it Susskind talks about Feynman. He doesn't skip over Feynman's faults, but it is obvious that Susskind knew and truly loved Feynman. Nothing you can do in 15 min will give you a better understanding of Feynman's character. The words "A lot of ham, but absolutely no baloney" are a quote from Susskind's video.

  I read Surely You're Joking shortly after it came out in 1985, as did several of my coworkers. There were differing opinions. I enjoyed it. To me it reads as if Feynman believed he could get away with expressing his unfiltered thoughts publicly. Some of those thoughts were of the inside kind that most people know better than to say out loud. If Feynman thought he could get away with this, he was right! The book was a best-seller, and some of us, at least, interpreted as an extremely intelligent and entertaining man expressing the thoughts that many of his tribe are secretly afraid to share.

  Here's my advice to readers of Surely You're Joking. As you read, you will encounter bits that strike you as reprehensible. When that happens, try to think hard about them from Feynman's point of view. In many, perhaps most, such cases you will decide that the passages in question are really as reprehensible as you first thought. But in others you may realize they are not. Let me give an example. In the chapter "Los Alamos from Below" he talks about how he learned that the atomic bomb was going to be tested.

  'After we’d made the calculations, the next thing that happened, of course, was the test. I was actually at home on a short vacation at that time, after my wife died, and so I got a message that said, “The baby is expected on such and such a day.”'

  I overheard two of my coworkers expressing their outrage at this casual, apparently callous mention of his wife's death. They clearly thought he should have expressed more pain. My thought was "A man who had felt less, might." (Bonus points if you recognize the quote!) After all, he's talking about Los Alamos with a friend 40 years after the events in question. It would not be sensible to derail the conversation with a eulogy for Arlene.

  In fact, the sequel "What Do You Care What Other People Think?": Further Adventures of a Curious Character contains a chapter entitled “What Do You Care What Other People Think?” about his love for and marriage with Arlene. Ralph Leighton, who compiled these recollections, describes it as follows

  "The story of Arlene, from which the title of this book was taken, was painful for Feynman to recount. It was assembled over the past ten years out of pieces from six different stories. When it was finally complete, Feynman was especially fond of this story, and happy to share it with others."

  So, give the guy a break, OK?

  An entertaining book, but perhaps too unfiltered for many readers.
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  Alano
  5.0 out of 5 stars Magical
  Reviewed in the United States on April 21, 2024
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  I feel as though the author is sitting next to me and sharing his stories. Magical. And, through that he instills the joy of being constantly curious about any thing and everything!
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  Xiangqin Cui
  4.0 out of 5 stars Great book, good read! Would not recommend for school projects though.
  Reviewed in the United States on May 22, 2020
  Verified Purchase
  The book is a great piece of literature that demonstrates the lack of necessity for there to be a continuous progression of story in books today. Surely You're Joking Mr. Feynman! is an excellent collection of stories from throughout Richard Feynman's Life, and is a great tale of in a way, what everyone could be if we all just had a little bit of a more creative mind. He doesn't have any particular special trait that makes him a great person, it's just that he is curious, and that leads him down the great paths in life that he goes down, from his house as a child fixing radios, to great schools such as MIT and Princeton. I find in particular that his open-mind leads to a lot of friends and opportunities, such as being curious enough that he joined a biology class in grad school while knowing little in the way of biology. The places where he goes is a demonstration of sorts of Richard Feynman's progression as a character. he begins as a child and progresses to MIT, where it's clear he knows more, but his knowledge is not fully developed. After, progressing to MIT, then to Princeton, then to work for the US developing the nuclear bomb, where it is clear he has gained a lifetime of experience and knowledge. I find his collection of stories remarkable, as he tells about his experiments from watching his dreams, to understanding how ants find their paths. I could not recommend this book for school projects, however, as the stories have extremely connection to each other. I would still recommend this book as a read though, as it is fantastic to hear about how he learned to deal with the fact that one of his first lectures was in front of Einstien, and other fascinating tales. His style is interesting, one I have never seen before, and if you have seen any of his lectures, you will know what I am referring to. In his stories, he never gives all of the details away at once, only what is required. As Bill Gates once put it, "you feel like you are discovering alongside him". This style of teaching is evident in his story, as when he talks, he talks about the story slowly so that you don't know what will happen until the very end. Again, he represents as a human what everyone could be, just if only they had a little more creativity, and the mind and passion to pursue those traits to whatever path they lead down. I thoroughly believe everyone should read this book, as it is both international, and entertaining
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  Edward Melmed MD
  5.0 out of 5 stars One really great book
  Reviewed in the United States on March 18, 2024
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  Young people above all should read this book. Inspiring. Funny. Great
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  ukalltheway
  5.0 out of 5 stars Great read!
  Reviewed in the United States on March 19, 2024
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  This was an enjoyable book to read and understand the life of a scientist. Was encouraged to read it through the Freakonomics podcast. Hope you decide to read it as well.
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  Victorina Shandarin
  5.0 out of 5 stars It’s a great book by a genius scientist. He tells stories about his life and science with humour
  Reviewed in Canada on December 15, 2023
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  We own this book - my husband is a scientist and this is one of his favourite books.
  I ordered 2 books: for my grandson and a friend.
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  Moni
  5.0 out of 5 stars Excelente libro
  Reviewed in Mexico on June 21, 2022
  Verified Purchase
  Es un excelente libro, que si o si debería estar en tu librero. Es una lectura bastante ligera y entretenida. Obviamente debes tener en cuenta la época y los prejuicios de la misma.
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  Moni
  5.0 out of 5 stars Excelente libro
  Reviewed in Mexico on June 21, 2022
  Es un excelente libro, que si o si debería estar en tu librero. Es una lectura bastante ligera y entretenida. Obviamente debes tener en cuenta la época y los prejuicios de la misma.
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  Pratiksha Mehta
  5.0 out of 5 stars Love the way it is written
  Reviewed in India on April 22, 2024
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  This book express how Feynmen ji was. The language used is just the same as he expresses in real life. That is the most fun thing for me. If you love peoples expert in learning read this book because Feynman ji was not only a physicist, he also was an artist in the field of sketching, music.
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  Espurs
  5.0 out of 5 stars brilliant and funny
  Reviewed in the United Kingdom on March 15, 2024
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  How one man can do so much in his life, his curiosity had no bounds
  Great read it won’t disappoint
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  Vitaly
  5.0 out of 5 stars Muy bien
  Reviewed in Spain on December 27, 2023
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  Muy interesante
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Reviews with images           An ok experience with this used book  Surely You're Joking Mr. Feynman!By Richard P. FeynmanFirst Edition, Paperback.Size (Roughly): 20.5 x 13.5 x 2.8 centimeters.Book sold by "bellwetherbooks" on Amazon.Announced in "Like New" condition with the next description: LIKE NEW/UNREAD!!! Text is Clean and Unmarked! Has a small black line on edge of pages. Tracking is not available for orders shipped outside of the United States.No tracking information given by the seller as offered, it arrive a few days later than it should've had. Not properly a textbook, this is a pop science book, meaning is not trying to properly teach to anything.A good book by Feynman whatsoever.Nice book        Sorry we couldn't load the review
“Surely You’re Joking, Mr. Feynman!”: Adventures of a Curious Character: Feynman, Richard P., Leighton, Ralph, Gates, Bill: 9780393355628: Amazon.com: Books
https://www.amazon.com/Surely-Youre-Joking-Mr-Feynman/dp/0393355624/ref=as_li_ss_tl?dchild=1&keywords=Surely+You%E2%80%99re+Joking,+Mr+Feynman&qid=1606593411&sr=8-1&linkCode=sl1&tag=abakcus-20&linkId=0e1a583756cd8d2ee16131cd87082f0e&language=en_US
https://www.amazon.com/Alan-Turing-Enigma-Andrew-Paperback/dp/B00I60WA5E/ref=as_li_ss_tl?dchild=1&keywords=Alan+Turing:+The+Enigma&qid=1589181960&s=books&sr=1-2&linkCode=sl1&tag=abakcus-20&linkId=ff7b88f1c9503b94849885be475df3e4&language=en_US
Amazon.com
2014-01-01T00:00:00Z

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