Reading the Comics, May 1, 2019: Not Perfectly Certain Edition

There’s several comics from the first half of last week that I can’t perfectly characterize. They seem to be on-topic enough for my mathematical discussions. It’s just how exactly they are on-topic that I haven’t quite got. Some weeks are like that.

Dave Whamond’s Reality Check for the 28th circles around being a numerals joke. It’s built on the binary representation of numbers that we’ve built modern computers on. And on the convention that “(Subject) 101” is the name for an introductory course in a subject. This convention of course numbering — particularly, three-digit course numbers, with the leading digit representing the year students are expected to take it — seems to have spread in American colleges in the 1930s. It’s a compromise, as many things are. As college programs of study become more specialized there’s the need for a greater number of courses in each field. And there’s a need to give people some hint of the course level. “Numerical Methods” could be a sophomore, senior, or grad-student course; how should someone from a different school know what to expect? But the pull of the serial number, and the idea that ’01’ must be the first in a field, is hard to resist.

Woman looking at college classroom doors: English 101 and then Computers 101 0101001 101010100 0110110011 100100100.
Dave Whamond’s Reality Check for the 28th of April, 2019. Essays which include Reality Check should be gathered at this link.

Anyway, the long string of zeroes and ones after the original ‘101’ is silliness and that’s all it has to be. The number one-hundred-and-one in binary would be a mere “1100101”, which doesn’t start with the important one-oh-one, and isn’t a big enough string of digits to be funny. Maybe this is a graduate course. The number given, if we read it as a single long binary number, would be 182,983,026,468. I’ve been to schools which use four-digit course codes. Twelve digits seems excessive.

Man carrying a large numeral 8 walks to a man sitting on a recliner in a field. The man with the eight asks, 'Is this nine?' The sitting man says, 'No. Eight.' The man with the eight says, 'I've got the wrong number'. And he walks away, carrying the 8, in a silent final panel.
John Deering’s Strange Brew for the 29th of April, 2019. Other appearances by Strange Brew are at this link.

John Deering’s Strange Brew for the 29th circles around being an anthropomorphic numerals joke. At least it is a person using a large representation of the number eight. I’m not sure how to characterize it, or why I find the strip amusing. It’s a strange one.

Cop, presenting a handcuffed 2, 3, 5, and 7 to his supervisor at the Vice Squad: 'We're breaking up the numbers racket. These are some of the prime suspects.'
Thaves’s Frank and Ernest for the 1st of May, 2019. This is the first time in maybe a month that I’ve written about Thaves’s strip. But last time, and other earlier appearances, of Frank and Ernest should be gathered at this link.

Thaves’s Frank and Ernest for the 1st is, finally, a certain anthropomorphic numerals joke. With wordplay about prime numbers being unavoidably prime suspects. … And when I was a kid, I had no idea what “numbers rackets” were, other than a thing sometimes mentioned on older sitcoms. That it involved somehow literally taking numbers and doing … something … that the authorities didn’t like was mysterious. I don’t remember what surely hilarious idea the young me had for what that might even mean. I suspect that, had I seen this strip at the time, I would have understood this wasn’t really whatever was going on. But I would have explained to my parents what a prime number was, and they would put up with my doing so, because that’s just what our relationship was.

Fish standing at a podium with a laptop, and behind, a screen with a string of overlapping circles. It says to the other: 'These are Venn diagras for my presentation. And no, I'm not tooting.'
Dave Whamond’s Reality Check for the 1st of May, 2019. And it’s a bit odd to have two Reality Check strips in the same essay. But I’m glad to have the strip back at all, since I discovered I had somehow lost the comic for a couple of months.

Dave Whamond’s Reality Check for the 1st is more or less the Venn Diagram joke for this essay. It’s a bit of a fourth-wall-breaking strip: the joke wouldn’t really work from the other goldfish’s perspective. Anyway, only two of those figures are proper Venn diagrams. The topmost figure, with five circles, and the bottommost, with three, aren’t proper Venn diagrams. Only some of the possible intersections between sets exist there. They are proper Euler diagrams, though.

Person giving a presentation: 'As this slide indicates, the most popular pies are apple, chocolate, and pumpkin.' The slide is a pie chart, showing (in decreasing popularity) apple, chocolate, pumpkin, pecan, cherry, lemon meringue, coconut cream, banana cream, key lime, and blueberry. Caption; 'Metadata'.
Wayno’s WaynoVision for the 1st of May, 2019. This appears to be the first time I’ve mentioned this comic. Well. This and any future essays mentioning WaynoVision should be at this link.

Wayno’s WaynoVision for the 1st is the pie-chart joke for the essay. It’s not as punchy as that Randolph Itch strip I kept bringing back around. But it’s on the same theme, mixing the metaphor of the pie chart with literal pies.

There’s one more Reading the Comics post before I’ve got all last week’s strips covered. That, I hope to have published and available at this link for Tuesday.

Reading the Comics, April 24, 2019: Mic Drop Edition Edition

I can’t tell you how hard it is not to just end this review of last week’s mathematically-themed comic strips after the first panel here. It really feels like the rest is anticlimax. But here goes.

John Deering’s Strange Brew for the 20th is one of those strips that’s not on your mathematics professor’s office door only because she hasn’t seen it yet. The intended joke is obvious, mixing the tropes of the Old West with modern research-laboratory talk. “Theoretical reckoning” is a nice bit of word juxtaposition. “Institoot” is a bit classist in its rendering, but I suppose it’s meant as eye-dialect.

Cowboys at the 'Institoot of Theoretical Reckoning'. One at the whiteboard says, 'Well, boys, looks like this here's the end of the line!' The line is a long string of what looks like legitimate LaTeX
John Deering’s Strange Brew for the 20th of April, 2019. Other appearances by Strange Brew, including ones less diligent about making the blackboard stuff sensible, are at this link.

What gets it a place on office doors is the whiteboard, though. They’re writing out mathematics which looks legitimate enough to me. It doesn’t look like mathematics though. What’s being written is something any mathematician would recognize. It’s typesetting instructions. Mathematics requires all sorts of strange symbols and exotic formatting. In the old days, we’d handle this by giving the typesetters hazard pay. Or, if you were a poor grad student and couldn’t afford that, deal with workarounds. Maybe just leave space in your paper and draw symbols in later. If your university library has old enough papers you can see them. Maybe do your best to approximate mathematical symbols using ASCII art. So you get expressions that look something like this:

  / 2 pi  
 |   2
 |  x cos(theta) dx - 2 F(theta) == R(theta)
/ 0

This gets old real fast. Mercifully, Donald Knuth, decades ago, worked out a great solution. It uses formatting instructions that can all be rendered in standard, ASCII-available text. And then by dark incantations and summoning of Linotype demons, re-renders that as formatted text. It handles all your basic book formatting needs — much the way HTML, used for web pages, will — and does mathematics much more easily. For example, I would enter a line like:

\int_{0}^{2\pi} x^2 \cos(\theta) dx - 2 F(\theta) \equiv R(\theta)

And this would be rendered in print as:


There are many, many expansions available to this, to handle specialized needs, hardcore mathematics among them.

Anyway, the point that makes me realize John Deering was aiming at everybody with an advanced degree in mathematics ever with this joke, using a string of typesetting instead of the usual equations here?

The typesetting language is named TeX.

Wavehead, at lunch: 'You know if I were the other shapes I'd be like, 'listen, circle, you can have a perimeter or a circumference, but you can't have both'.'
Mark Anderson’s Andertoons for the 21st of April, 2019. When do I ever not discuss this comic? All the essays at this link are about Andertoons, at least in part.

Mark Anderson’s Andertoons for the 21st is the Mark Anderson’s Andertoons for the week. It’s about one of those questions that nags at you as a kid, and again periodically as an adult. The perimeter is the boundary around a shape. The circumference is the boundary around a circle. Why do we have two words for this? And why do we sound all right talking about either the circumference or the perimeter of a circle, while we sound weird talking about the circumference of a rhombus? We sound weird talking about the perimeter of a rhombus too, but that’s the rhombus’s fault.

The easy part is why there’s two words. Perimeter is a word of Greek origin; circumference, of Latin. Perimeter entered the English language in the early 15th century; circumference in the 14th. Why we have both I don’t know; my suspicion is either two groups of people translating different geometry textbooks, or some eager young Scholastic with a nickname like ‘Doctor Magnifico Triangulorum’ thought Latin sounded better. Perimeter stuck with circules early; every etymology I see about why we use the symbol π describes it as shorthand for the perimeter of the circle. Why `circumference’ ended up the word for circles or, maybe, ellipses and ovals and such is probably the arbitrariness of language. I suspect that opening “circ” sound cues people to think of it for circles and circle-like shapes, in a way that perimeter doesn’t. But that is my speculation and should not be mistaken for information.

Information panel about numerals, including a man who typed every number from one to a million, using one finger; it took over 16 years, seven months. Puzzle: add together every number that, written as a word, consists of three letters; what's the total?
Steve McGarry’s KidTown for the 21st of April, 2019. It’s rare that this panel is on-topic enough for me to bring up, but at least a few KidTown panels are discussed here.

Steve McGarry’s KidTown for the 21st is a kids’s information panel with a bit of talk about representing numbers. And, in discussing things like how long it takes to count to a million or a billion, or how long it would take to type them out, it gets into how big these numbers can be. Les Stewart typed out the English names of numbers, in words, by the way. He’d also broken the Australian record for treading water, and for continuous swimming.

Bub: 'I don't like crosswords because I'm not good at word stuff. I'm much better at math. That's why I like sudoku.' Betty: 'What math? There's no adding or subtracting or multiplying in sudoku.' Bub: 'That's my favorite kind of math.' Betty: 'If you were better at word stuff, you'd know you're confusing math with logic.'
Gary Delainey and Gerry Rasmussen’s Betty for the 24th of April, 2019. I don’t seem to have discussed this comic before. This and future appearances by Betty should be at this link.

Gary Delainey and Gerry Rasmussen’s Betty for the 24th is a sudoku comic. Betty makes the common, and understandable, conflation of arithmetic with mathematics. But she’s right in identifying sudoku as a logical rather than an arithmetic problem. You can — and sometimes will see — sudoku type puzzles rendered with icons like stars and circles rather than numerals. That you can make that substitution should clear up whether there’s arithmetic involved. Commenters at GoComics meanwhile show a conflation of mathematics with logic. Certainly every mathematician uses logic, and some of them study logic. But is logic mathematics? I’m not sure it is, and our friends in the philosophy department are certain it isn’t. But then, if something that a recognizable set of mathematicians study as part of their mathematics work isn’t mathematics, then we have a bit of a logic problem, it seems.

Come Sunday I should have a fresh Reading the Comics essay available at this link.

Reading the Comics, November 7, 2018: Shorthand and Reruns Edition

There’s two types of comics for the second of last week’s review. There’s some strips that are reruns. There’s some that just use mathematics as a shorthand for something else. There’s four strips in all.

John Deering’s Strange Brew for the 6th uses mathematics as shorthand for demonstrating intelligence. There’s no making particular sense out of the symbols, of course. And I’d think it dangerous that Lucky seems to be using both capital X and lowercase x in the same formula. There’s often times one does use the capital and lowercase versions of a letter in a formula. This is usually something like “x is one element of the set X, which is all the possible candidates for some thing”. In that case, you might get the case wrong, but context would make it clear what you meant. But, yes, sometimes there’s no sensible alternative and then you have to be careful.

Person upstairs: 'I don't understand how Lucky keeps getting out.' Lucky, the dog, is downstairs, writing out plans: 'V_1 Q_q = X'^4 y / B(4) x^2'
John Deering’s Strange Brew for the 6th of November, 2018. The mathematics is all fine but have they considered they never did close the patio door?

Randy Glasbergen’s Glasbergen Cartoons for the 6th uses mathematics as shorthand for a hard subject. It’s certainly an economical notation. Alas, you don’t just learn from your mistakes. You learn from comparing your mistakes to a correct answer. And thinking about why you made the mistakes you did, and how to minimize or avoid those mistakes again.

Student, to teacher: 'If we learn from our mistakes, shouldn't I make as many mistakes as possible?' On the blackboard is the problem 473 x 17.
Randy Glasbergen’s Glasbergen Cartoons for the 6th of November, 2018. The strip is a rerun, but I have no information to date when it’s from.

So how would I do this problem? Well, carrying out the process isn’t too hard. But what do I expect the answer to be, roughly? To me, I look at this and reason: 473 is about 500. So 473 x 17 is about 500 x 17. 500 x 17 is 1000 times eight-and-a-half. So start with “about 8500”. That’s too high, obviously. I can do better. 8500 minus some correction. What correction? Well, 473 is roughly 500 minus 25. So I’ll subtract 25 times 17. Which isn’t hard, because 25 times 4 is 100. So 25 times 17? That’s 25 times 16 plus 25 times 1. 25 times 16 is 100 times 4. So 25 times 17 is 425. 8500 minus 425 is 8075. I’m still a bit high, by 2 times 17. 2 times 17 is 34. So subtract 34 from 8075: it should be about 8041.

Student taking a test: 'Which of these is a right triangle?' (Figures a, b, and c.) Maria's answer: 'c is right. a is left. b is middle.'
John Zakour and Scott Roberts’s Maria’s Day for the 7th of November, 2018. Kind of curious whether this is meant to have one correct answer or an unspecified number of correct answers, since both ‘b’ and ‘c’ look plausibly like right triangles to me.

John Zakour and Scott Roberts’s Maria’s Day for the 7th is a joke built on jargon. Every field has its jargon. Some of it will be safely original terms: people’s names (“Bessel function”) or synthetic words (“isomorphism”) that can’t be easily confused with everyday language. But some of it will be common terms given special meaning. “Right” angles and “right” triangles. “Normal” numbers. “Group”. “Right” as a description for angles and triangles goes back a long way, at least to — well, says 15th century. But EtymologyOnline says late 14th century. Neither offers their manuscripts. I’ll chalk it up to differences in how they interpret the texts. And possibly differences in whether they would count, say, a reference to “a right angle” written in French or German rather than in English directly.

Literary Calendar. Several jokes, including: Saturday 7pm: an infinite number of chimpanzees discuss their multi-volume 'Treasury of Western Literature with no Typos' at the Museum of Natural History. Nit picking to follow.
Richard Thompson’s Richard’s Poor Almanac rerun for the 7th of November, 2016.

Richard Thompson’s Richard’s Poor Almanac for the 7th has been run before. It references the Infinite Monkey Theorem. The monkeys this time around write up a treasury of Western Literature, not merely the canon of Shakespeare. That’s at least as impressive a feat. Also, while this is a rerun — sad to say Richard Thompson died in 2016, and was forced to retire from drawing before that — his work was fantastic and deserves attention.

This and every Reading the Comics post should be at this link. Essays discussing topics raised by Strange Brew are at this link. The essays discussing Glasbergen Cartoons are at this link. Essays which mention Maria’s Day, are at this link. And essays featuring Richard’s Poor Almanac are at this link.

My Fall 2018 Mathematics A-To-Z averages two new posts a week, through the end of December. Thanks again for reading.

Reading the Comics, March 24, 2018: Arithmetic and Information Edition

And now I can bring last week’s mathematically-themed comics into consideration here. Including the whole images hasn’t been quite as much work as I figured. But that’s going to change, surely. One of about four things I know about life is that if you think you’ve got your workflow set up to where you can handle things you’re about to be surprised. Can’t wait to see how this turns out.

John Deering’s Strange Brew for the 22nd is edging its way toward an anthropomorphic numerals joke.

Man, to woman at candlelit dinner: 'I can still remember the cute little number you were wearing the day we first met.' He's wearing the number 72102; she, 67350.
John Deering’s Strange Brew for the 22nd of March, 2018. I like to think she was wearing something from the Gary Larson collection.

Brant Parker and Johnny Hart’s Wizard of Id for the 22nd is a statistics joke. Really a demographics joke. Which still counts; much of the historical development of statistics was in demographics. That it was possible to predict accurately the number of people in a big city who’d die, and what from, without knowing anything about whether any particular person would die was strange and astounding. It’s still an astounding thing to look directly at.

The Duke: 'Sire, I have worked out some amazing statistics, here.' The King: 'Let's hear them.' The Duke: 'My figures show that the odds against a short man outliving a tall man are 5 to 1.' The King: 'Have the royal basketball team report to the gallows.'
Brant Parker and Johnny Hart’s Wizard of Id for the 25th of March 1968, and rerun the 22nd of March, 2018. That’s an interesting demographic the Kingdom of Id has there. Just saying.

Hilary Price and Rina Piccolo’s Rhymes with Orange for the 23rd has the form of a story problem. I could imagine turning this into a proper story problem. You’d need some measure of how satisfying the 50-dollar wines are versus the 5-dollar wines. Also how much the wines affect people’s ability to notice the difference. You might be able to turn this into a differential equations problem, but that’s probably overkill.

The Pop^Cork Quiz. Hostess with bottles of wine. Caption: 'If Laura owns 5 bottles of 50-dollar wine and 5 bottles of 5-dollar wine, how many bottles of 50-dollar wine must she serve in order to switch to the 5-dollar wine without anyone noticing?'
Hilary Price and Rina Piccolo’s Rhymes with Orange for the 23rd of March, 2018. Fortunately, one of Laura’s guests brought Jesus of Nazareth along as his `plus one’.

Mark Anderson’s Andertoons for the 23rd is Mark Anderson’s Andertoons for this half of the week. It’s a student-avoiding-the-problem joke. Could be any question. But arithmetic has the advantages of being plausible, taking up very little space to render, and not confusing the reader by looking like it might be part of the joke.

Kid at the blackboard, pondering 72 / 8: 'I know the answer, I'm just letting the suspense build.'
Mark Anderson’s Andertoons for the 23rd of March, 2018. Yeah, don’t try this with your thesis committee. Word to the wise.

John Zakour and Scott Roberts’s Working Daze for the 23rd has another cameo appearance by arithmetic. It’s also a cute reminder that there’s no problem you can compose that’s so simple someone can’t over-think it. And it puts me in mind of the occasional bit where a company’s promotional giveaway will technically avoid being a lottery by, instead of awarding prizes, awarding the chance to demonstrate a skill. Demonstration of that skill, such as a short arithmetic quiz, gets the prize. It’s a neat bit of loophole work and does depend, as the app designers here do, on the assumption there’s some arithmetic that people can be sure of being able to do.

Ed: 'The trick to making an easy quiz app is to come up with questions anybody could get right.' Rita: 'One plus one. Well, that's easy. It's two. No, wait. It's a trick question. It's eleven. Right? Unless ... ' Roy, thinking: 'This is going to be harder than we thought.'
John Zakour and Scott Roberts’s Working Daze for the 23rd of March, 2018. Ask your friend who does web stuff about Javascript and addition. You won’t understand the results but that’s all right; neither do they.

Teresa Burritt’s Frog Applause for the 24th is its usual bit of Dadist nonsense. But in the talk about black holes it throws in an equation: S = \frac{A k c^3}{4 G \hbar} . This is some mathematics about black holes, legitimate and interesting. It is the entropy of a black hole. The dazzling thing about this is all but one of those symbols on the right is the same for every black hole. ‘c’ is the speed of light, as in ‘E = mc2‘. G is the gravitational constant of the universe, a measure of how strong gravity is. \hbar is Planck’s constant, a kind of measure of how big quantum mechanics effects are. ‘k’ is the Boltzmann constant, which normal people never heard of but that everyone in physics and chemistry knows well. It’s what you multiply by to switch from the temperature of a thing to the thermal energy of the thing, or divide by to go the other way. It’s the same number for everything in the universe.

Woman's legs emerging from a portable hole, in three panels. The caption: 'Help! I'm defying the laws of gravity while also being sucked into a black hole that's supposed to be invisible --- except when the hole is in a comic strip!' (And on the side, S = Akc^3/4G h-bar.) 'Holy Hawking! As the space-time continuum continuums, I'm being warped into a state of striped-pants disreality teetering on a crummy fulcrum of fugly shoes. And even if I shout, 'I've fallen in a black hole and I can't get out', I'll forever be sinking deeper into a lamer surreality that never reaches the tendency pit of analyticity.'
Teresa Burritt’s Frog Applause for the 24th of March, 2018. Honestly surprised I didn’t see talk about striped-pants direality in Zippy the Pinhead first.

The only thing custom to a particular black hole is ‘A’, which is the surface area of the black hole. I mean the surface area of the event horizon. Double the surface area of the event horizon and you double its entropy. (This isn’t doubling the radius of the event horizon, but you know how much growth in the radius it is.) Also entropy. Hm. Everyone who would read this far into a pop mathematics blog like this knows that entropy is “how chaotic a thing is”. Thanks to people like Boltzmann we can be quantitative, and give specific and even exact numbers to the entropy of a system. It’s still a bit baffling since, superficially, a black hole seems like it’s not at all chaotic. It’s a point in space that’s got some mass to it, and maybe some electric charge and maybe some angular momentum. That’s about it. How messy can that be? It doesn’t even have any parts. This is how we can be pretty sure there’s stuff we don’t understand about black holes yet. Also about entropy.

This strip might be an oblique and confusing tribute to Dr Stephen Hawking. The entropy formula described was demonstrated by Drs Jacob Bekenstein and Stephen Hawking in the mid-1970s. Or it might be coincidence.

Reading the Comics, August 5, 2017: Lazy Summer Week Edition

It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.

Tom Thaves’s Frank and Ernest for the 30th of July is an anthropomorphic-symbols joke. The tick marks used for counting make an appearance and isn’t that enough? Maybe.

Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.

Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.

Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.

John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.

Dana Simpson’s Ozy and Millie rerun for the 2nd name-drops multiplication tables as the sort of thing a nerd child wants to know. They may have fit the available word balloon space better than “know how to diagram sentences” would.

Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.

Dad: 'How many library books have you read this summer, Hammie?' Hammie: 'About 47.' Zoe: 'HA!' Dad: 'Hammie ... ' Hammie: 'Okay ... two.' Dad: 'Then why did you say 47?' Hammie: 'I was rounding up.' Zoe: 'NOW he understands math!'
Rick Kirkman and Jerry Scott’s Baby Blues for the 5th of August, 2017. Hammie totally blew it by saying “about forty-seven”. Too specific a number to be a plausible lie. “About forty” or “About fifty”, something you can see as the result of rounding off, yes. He needs to know there are rules about how to cheat.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th is a rounding-up joke that isn’t about herds of 198 cattle.

Stephen Bentley’s Herb and Jamaal for the 5th tosses off a mention of the New Math as something well out of fashion. There are fashions in mathematics, as in all human endeavors. It startles many to learn this.

Reading the Comics, June 24, 2017: Saturday Morning Breakfast Cereal Edition

Somehow this is not the title of every Reading The Comics review! But it is for this post and we’ll explore why below.

Piers Baker’s Ollie and Quentin for the 18th is a Zeno’s Paradox-based joke. This uses the most familiar of Zeno’s Paradoxes, about the problem of covering any distance needing infinitely many steps to be done in a finite time. Zeno’s Paradoxes are often dismissed these days (probably were then, too), on the grounds that the Ancient Greeks Just Didn’t Understand about convergence. Hardly; they were as smart as we were. Zeno had a set of paradoxes, built on the questions of whether space and time are infinitely divisible or whether they’re not. Any answer to one paradox implies problems in others. There’s things we still don’t really understand about infinity and infinitesimals and continuity. Someday I should do a proper essay about them.

Dave Coverly’s Speed Bump for the 18th is not exactly an anthropomorphic-numerals joke. It is about making symbols manifest in the real world, at least. The greater-than and less-than signs as we know them were created by the English mathematician Thomas Harriot, and introduced to the world in his posthumous Artis Analyticae Praxis (1631). He also had an idea of putting a . between the numerals of an expression and the letters multiplied by them, for example, “4.x” to mean four times x. We mostly do without that now, taking multiplication as assumed if two meaningful quantities are put next to one another. But we will use, now, a vertically-centered dot to separate terms multiplied together when that helps our organization. The equals sign we trace to the 16th century mathematician Robert Recorde, whose 1557 Whetsone of Witte uses long but recognizable equals signs. The = sign went into hibernation after that, though, until the 17th century and it took some time to quite get well-used. So it often is with symbols.

Mr Tanner: 'Today we'll talk about where numbers come from. Take zero, for instance ... Quincy, do you know who invented the zero?' Quincy: 'I'm not sure, Mr Tanner, but from the grades I get it must have been one of my teachers.'
Ted Shearer’s Quincy for the 25th of April, 1978 and rerun the 19th of June, 2017. The question does make me wonder how far Mr Tanner was going to go with this. The origins of zero and one are great stuff for class discussion. Two, also. But what about three? Five? Ten? Twelve? Minus one? Irrational numbers, if the class has got up to them? How many students are going to be called on to talk about number origins? And how many truly different stories are there?

Ted Shearer’s Quincy for the 25th of April, 1978 and rerun the 19th of June, starts from the history of zero. It’s worth noting there are a couple of threads woven together in the concept of zero. One is the idea of “nothing”, which we’ve had just forever. I mean, the idea that there isn’t something to work with. Another is the idea of the … well, the additive identity, there being some number that’s one less than one and two less than two. That you can add to anything without changing the thing. And then there’s symbols. There’s the placeholder for “there are no examples of this quantity here”. There’s the denotation of … well, the additive identity. All these things are zeroes, and if you listen closely, they are not quite the same thing. Which is not weird. Most words mean a collection of several concepts. We’re lucky the concepts we mean by “zero” are so compatible in meaning. Think of the poor person trying to understand the word “bear”, or “cleave”.

John Deering’s Strange Brew for the 19th is a “New Math” joke, fittingly done with cavemen. Well, numerals were new things once. Amusing to me is that — while I’m not an expert — in quite a few cultures the symbol for “one” was pretty much the same thing, a single slash mark. It’s hard not to suppose that numbers started out with simple tallies, and the first thing to tally might get dressed up a bit with serifs or such but is, at heart, the same thing you’d get jabbing a sharp thing into a soft rock.

Guy Gilchrist’s Today’s Dogg for the 19th I’m sure is a rerun and I think I’ve featured it here before. So be it. It’s silly symbol-play and dog arithmetic. It’s a comic strip about how dogs are cute; embrace it or skip it.

Zach Weinersmith’s Saturday Morning Breakfast Cereal is properly speaking reruns when it appears on For whatever reason Weinersmith ran a patch of mathematics strips there this past week. So let me bundle all that up. On the 19th he did a joke mathematicians get a lot, about how the only small talk anyone has about mathematics is how they hated mathematics. I’m not sure mathematicians have it any better than any other teachers, though. Have you ever known someone to say, “My high school gym class gave me a greater appreciation of the world”? Or talk about how grade school history opened their eyes to the wonders of the subject? It’s a sad thing. But there are a lot of things keeping teachers from making students feel joy in their subjects.

For the 21st Weinersmith makes a statisticians joke. I can wrangle some actual mathematics out of an otherwise correctly-formed joke. How do we ever know that something is true? Well, we gather evidence. But how do we know the evidence is relevant? Even if the evidence is relevant, how do we know we’ve interpreted it correctly? Even if we have interpreted it correctly, how do we know that it shows what we want to know? Statisticians become very familiar with hypothesis testing, which amounts to the question, “does this evidence indicate that some condition is implausibly unlikely”? And they can do great work with that. But “implausibly unlikely” is not the same thing as “false”. A person knowledgeable enough and honest turns out to have few things that can be said for certain.

The June 23rd strip I’ve seen go around Mathematics Twitter several times, as see above tweet, about the ways in which mathematical literacy would destroy modern society. It’s a cute and flattering portrait of mathematics’ power, probably why mathematicians like passing it back and forth. But … well, how would “logic” keep people from being fooled by scams? What makes a scam work is that the premise seems logical. And real-world problems — as opposed to logic-class problems — are rarely completely resolvable by deductive logic. There have to be the assumptions, the logical gaps, and the room for humbuggery that allow hoaxes and scams to slip through. And does anyone need a logic class to not “buy products that do nothing”? And what is “nothing”? I have more keychains than I have keys to chain, even if we allow for emergencies and reasonable unexpected extra needs. This doesn’t stop my buying keychains as souvenirs. Does a Penn Central-logo keychain “do nothing” merely because it sits on the windowsill rather than hold any sort of key? If so, was my love foolish to buy it as a present? Granted that buying a lottery ticket is a foolish use of money; is my life any worse for buying that than, say, a peanut butter cup that I won’t remember having eaten a week afterwards? As for credit cards — It’s not clear to me that people max out their credit cards because they don’t understand they will have to pay it back with interest. My experience has been people max out their credit cards because they have things they must pay for and no alternative but going further into debt. That people need more money is a problem of society, yes, but it’s not clear to me that a failure to understand differential equations is at the heart of it. (Also, really, differential equations are overkill to understand credit card debt. A calculator with a repeat-the-last-operation feature and ten minutes to play is enough.)

Reading the Comics, April 15, 2017: Extended Week Edition












