Social Dimension

Subscribe to WIRED Magazine

Software Clones: Genetic Variation and Technology


Andy Murray/Flickr

In biology, we desire genetic variation. Genetic variation is the raw material for natural selection: some gene types are beneficial and result in more offspring, thereby getting selected for, while others are not and end up getting weeded out of the population over time. Having genetic differences in a population allows for selection to happen.

But genetic variation is also an insurance policy of sorts: if the members of a species are too similar, then if something terrible happens, such as a deadly disease or a big environmental catastrophe like an ice age, it doesn’t just affect an individual, it can affect the entire population; since there is no variation, there might be no gene types that might provide protection against the unforeseen calamity and the entire population could be eliminated.

This same thing can happen in complicated technological systems and is related to what is known as systematic risk. These are the risks, especially in finance, that can cause a monstrous cascade, affecting the entire system being examined, i.e. the entire economy. This can be due to the explicitly interconnected nature of a system, but also due to implicit similarities. Specifically, when systems that appear complex and diverse are actually made up of very similar components, anything that affects one of them can end up affecting them all. For example, in the financial world, imagine if numerous trading firms independently converged on similar trading strategies. While they might happily make money, unaware of their similar mechanisms for profit, if there is a weakness in the methods—which are often highly automated—it will affect them all simultaneously and cause massive problems.

This type of problem also extends to the software world. Computer programs are identical and consist of a vast monoculture: every copy of Microsoft Windows version X is exactly the same, like clones. This makes for an incredibly attractive target for those who wish to compromise these systems. One approach, being worked on by Michael Franz, a computer scientist, at University of California, Irvine, is to automate a method of genetic diversity for software. Franz has developed something known as a multicompiler, a piece of software that modifies how computer code is generated. In general, a compiler converts a computer program—written by coders—into efficient machine code that can be run on a computer. But Franz’s multicompiler doesn’t yield identical instructions for the machine every time. Instead, it makes a series of tiny choices that yield different, yet ultimately equivalent, instructions. These differences are not detectable to the user, but can give us a kind of computational genetic diversity, making software more robust to attacks. This kind of approach could be used in the future to help prevent accidental failures that are the result of technological monocultures.

Making technology more “biological” is one of those techniques we pay lip service to and something that can even be great to do. In this case, actually creating more genetic variation in our software could help prevent massive problems.

Monty Hall, Erdos, and Our Limited Minds

The Monty Hall problem is a well-known mathematical brainteaser. But I find it intriguing not for how to solve it, but for how widespread having trouble with it is.

Based off of a television game show, the Monty Hall problem begins with a contestant finding herself in front of three doors. She is told that behind one of them is a car, while behind the other two there are goats. Since it is presumed that contestants want to win cars not goats, if nothing else for their resale value, there is a one-third chance of choosing the car and winning.

But now here’s the twist. After the contestant chooses a door, the game show host has another door opened and the contestant is shown a goat. Should she stick with the door she has originally chosen, or switch to the remaining unopened door?

There are many ways to examine this, but it turns out that it is always better to switch. Many people assume that the probability remains the same—it’s fifty-fifty so switching doesn’t matter—but they are wrong. There is a higher probability of the car being behind the door when you switch (here is a detailed discussion but I like to think about it based on an extreme version, one with 100 doors. One has a car and the others all have goats. You choose a door. The host opens 98 other doors, showing all goats. Should you switch? Of course! The host has done the work of almost certainly finding of the car for you.)

Anyway, I’m not concerned with the particulars of the problem but rather with how people respond to it. Namely, many listeners, even highly-trained mathematicians, are initially confused by the probabilities. In fact, until I learned of the extreme version with 100 doors, I didn’t really understand why switching is better either.

In fact, Paul Erdős, one of the most prolific and foremost mathematicians involved in probability, when initially told of the Monty Hall problem also fell victim to not understanding why opening a door should make any difference. Even when given the mathematical explanation multiple times, he wasn’t really convinced. It took several days before he finally understood the correct solution.

This problem is one of those situations—albeit rare—where someone can be shown an entire chain of logic, surveying the whole problem and its solution, and yet still have it bump up against their intuition. Of course, there is nothing inherently useful about our intuitions. Forged by evolution in situations completely different millions of years ago, our brain’s cognitive abilities are very often irrational, and when dealing with highly sophisticated tasks, we must overcome our intuition in order to understand them properly.

But seldom is this seen so clearly as in the Monty Hall problem. From Wikipedia:

When first presented with the Monty Hall problem an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter (Mueser and Granberg, 1999). Out of 228 subjects in one study, only 13% chose to switch (Granberg and Brown, 1995:713). In her book The Power of Logical Thinking, vos Savant (1996, p. 15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying “… no other statistical puzzle comes so close to fooling all the people all the time” and “that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer”. Pigeons repeatedly exposed to the problem show that they rapidly learn always to switch, unlike humans (Herbranson and Schroeder, 2010).

Stressing that last line again, that pigeons “rapidly learn always to switch, unlike humans,” shows how unstable the pedestal is upon which humanity places itself. Our cognitive powers are great, but we certainly are far from perfect.

The Ages of Whales and Technological Change


Wikimedia/Public Domain

There are many animals that are old. Tortoises can live over 150 years and the tuatara—a New Zealand reptile—can live for over 100 years. But my favorite example of a long-lived creature is the bowhead whale. It’s fascinating to me not just because whales are interesting, but specifically because of how we learned that this species of whale could live for more than 100 years. From Wikipedia (emphasis mine):

Bowheads were once thought to live 60 to 70 years, similar to other whales. However, discoveries of 19th century ivory, slate, and jade spear points in freshly killed whales in 1993, 1995, 1999, and 2007 triggered research based on structures in the whale’s eye, suggesting at least some individuals reached 150–200 years old (another report claimed a 90-year-old female was still fertile). The amino acid racemization process has provided the scientific basis for these claims. This process is controversial and has failed to correlate well with other dating methods.


In other words, we can use the rate of change in harpoon technology to explore how old some bowhead whales are. There are some whales that have survived attacks from harpoons manufactured in the same city where Moby Dick begins: New Bedford.

Increasingly, the technological and the natural are becoming intertwined. We see this in the discussion around terming the current stretch of time the Anthropocene, based on humanity’s effect on our planet and its geology. The systems we are building weave together ecosystems and infrastructure, neurology and software, data centers and weather. Everything is increasingly interconnected.

We are also seeing the advent of long-term datasets, what I term long data. At last we have the convergence of these trends: evidence of long-term historical change in technology, through an exploration of biology, and vice versa. This is reminiscent of how radiocarbon dating requires knowledge of historical nuclear testing, as well as other human activities. Or how the Industrial Revolution affected insect evolution.

Technology and biology can be physically interconnected, along the lines of cyborgs. But they can also be connected with long data, through a deep knowledge of our technological and biological history.

The Invention of the Equals Sign


Seth Goodman/Flickr/CC

The use of ‘=’ to mean ‘equals’ is one of those minor advances in mathematics that we take for granted. It’s so small that we don’t really think about it. But Joseph Mazur, the author of Enlightening Symbols A Short History of Mathematical Notation and Its Hidden Powers, has thought about ‘=’ as well as the other symbols with which we pepper our calculations. Mazur has this to say on the history of the equals sign:

The ideas of algebra brought on the symbols, not the other way around. Robert Recorde had written the words “is equal to” almost two hundred times in his book Whetstone of Witte (1557) before noticing that he could easily “avoid the tedious repetition” of those three words by designing the symbol = to represent them. The initial incentive was the need to abbreviate, but once the equal symbol was in place, something else took over. The concise character of the symbol came with an unintended benefit: it enabled an unadorned picture in the brain that could facilitate comprehension.

In other words, how we represent mathematical ideas affects how we think about them. So the timeline below is not just interesting, but perhaps shows how we have changed our very thoughts about mathematics over time:

Quantitative Biology and Quantitative Football

I’ve written before about how mathematics can be used to unify lots and lots of different disciplines. Well, here’s another great example from an article (behind paywall) from 2007. It’s about how Stephen Oh, the co-founder of AccuScore, brought his knowledge of population genetics to sports:

So in 2002, Oh began writing code that simulated football teams instead of human genomes. Genes were replaced with players; mutation rate and selection pressure became the probability that a pass would be completed or that a player would run for a touchdown. Each generation became a discrete “play” in a game. The rules of American football, in which each play depends cleanly on the ones before it, lent themselves to modelling the game this way. And so the idea behind Accuscore was born.

I love this kind of thing.

From 53 kilobytes of RAM in 1953

“In March of 1953 there were 53 kilobytes of high-speed random-access memory on planet Earth.” This line from George Dyson’s Turing’s Cathedral makes it clear how far we have come since computing’s dawn. My own laptop now has more than 100,000 times the RAM of the entire planet less than a century ago. While I couldn’t find estimates for the current global RAM (a related discussion is here), separately, it has been estimated that humanity’s technologies could, as of 2007, carry out a total of 6.4 × 1018 instructions per second, a phenomenal speed.

While everyone knows that technology grows at an exponential rate, we often have a certain blindness when it comes to the speed of changes and what these changes mean. Two researchers have put our current computational powers in perspective, with the kind of comparisons that I am a sucker for:

To put our findings in perspective, the 6.4 × 1018 instructions per second that humankind can carry out on its general-purpose computers in 2007 are in the same ballpark area as the maximum number of nerve impulses executed by one human brain per second (1017). The 2.4 × 1021 bits stored by humanity in all of its technological devices in 2007 is approaching an order of magnitude of the roughly 1023 bits stored in the DNA of a human adult, but it is still minuscule as compared with the 1090 bits stored in the observable universe. However, in contrast to natural information processing, the world’s technological information processing capacities are quickly growing at clearly exponential rates.

Such a journey from our humble beginnings sixty one years ago.

When Extrapolation Fails Us: Incorrect Mathematical Conjectures

It is well-known that our intuition is not perfect. We are predictably irrational in a huge number of ways in our everyday lives. But what about something a bit more sophisticated? Are there times when we use our reason—our ability for extrapolation and prediction—and still fail, because things are simply too complicated. This sort of situation seems to be embodied in a Quora question that I recently came across: What is an example of a conjecture that was proven wrong for “very large” numbers?

Essentially, the questioner was interested in situations where a mathematical conjecture appeared true, but fails only with the application of advanced computational power as cases far beyond human abilities are tested.

And there are a lot of these. One of the more famous examples is the Pólya conjecture. This conjecture states that given a number N, the fraction of numbers less than N that have an even number of prime factors is always less than the fraction that have an odd number of prime factors. This seems to be true. Until that is, you get to 906,150,257. Our intuition failed.

Another example is a conjecture from Euler:


Euler’s equation: x4 + y4 + z4 = w4


2,682,4404 + 15,365,6394 + 18,796,7604 = 20,615,6734


As Singh notes, “The moral of the story is that you cannot use evidence from the first million numbers to prove absolutely a conjecture about all numbers.”

These instances are fascinating. They show that large numbers are not infinity and trends do not indicate proof. Our human brains are powerful but we must increasingly work in concert with machines, to help us place bounds on our intuition.

Computational Theology


Wikimedia/Public Domain

There is a burgeoning field within philosophy known as computational philosophy. This term covers a large amount of work being done, including everything from computationally discovering connections between different philosophical topics to artificial intelligence and the philosophy of mind. One fun example is how automated search methods found a connection between a medieval philosophical idea and a modern one. (In this case, the weird but fascinating outdated idea of “divine illumination” is connected to “mental representation” through “the medieval problem of universals.”)

One of my favorite examples of computational philosophy is in metaphysics. During the Middle Ages, it became fashionable to attempt proofs for God’s existence. And the most famous of these (and most logically strange and not compelling) is Anselm‘s ontological argument for the existence of God. Essentially, the argument revolves around assuming that God is the most perfect being imaginable and since existence is more perfect than non-existence, God must exist (here’s the argument in more detail).

Since then, others have come and refined the argument as well as criticized it. But one of the most intriguing variants of this argument comes from computational theology.

In computer science and mathematics, there is a long tradition of computational proof: using a computer program to derive mathematical proofs from a series of axioms. So two philosophers decided to connect this to Anselm. When they set out to have a computer program prove the ontological argument, not only were they successful, they actually made his argument more elegant. As described in Wikipedia:

Paul Oppenheimer and Edward Zalta used an automated theorem prover—Prover9—to validate Anselm’s ontological thesis. Prover9 subsequently discovered a simpler, formally valid (if not necessarily sound) ontological argument from a single non-logical premise.

Separate from whether the proof “works,” it’s quite impressive that a computer program was able to distill this argument to its simplest form, allowing one to examine it as clearly as possible. In this case, the entire argument rests on the premise “if the conceivable thing than which nothing greater is conceivable fails to exist, then something greater than it is conceivable”, which the authors find wanting. But as the philosophers wrote in their paper:

Anselm’s ontological argument has come in for criticism ever since it was first proposed. But we think that the focus on finding flaws in the argument may have hindered progress in logically representing the argument in its most elegant form. We hope to show that computational techniques offer a new insight into Anselm’s ontological argument and demonstrate that there is much beauty inherent in its logic.

While in many cases machines are making discoveries that are increasingly complicated, this is not always the case. As seen here, computers can help us find the beauty in our own, sometimes flawed, arguments.

Measuring Inbreeding in the Greek Gods

In population genetics, there is a method of measuring how inbred a certain individual is, known as the inbreeding coefficient. Previously, I used to this technique to examine the amount of inbreeding in the X-Men and was intrigued to find that there wasn’t any.

However, it’s an entirely different matter when it comes to mythology. In mythological tales, there is a great deal of incest. As you can see below, the family tree of the Greek gods is a rather convoluted one:

And here, unlike in the case of superheroes, there is quite a bit of inbreeding. For example, using the calculated coefficients of the ancient Pharaohs as a template, it seems that Ares has an inbreeding coefficient of 37.5%. This is due to the fact that his parents—Zeus and Hera—are siblings, as well as his grandparents with each other. Zeus has an inbreeding coefficient of 25%. I don’t know which Greek god has the highest coefficient, so please feel free to share calculations in the comments.

Of course, whether the superhuman powers along with complete dysfunction and strange behavior of the Greek gods is a genetic result of this inbreeding is left as an exercise to the mythological geneticist.

The Mathematics of Novelties and Innovations



Our lives are filled with encounters with novelty. Whether it’s reading a new word or learning some new facts, these kinds of experiences are what makes life interesting. And often, these encounters lead us to find other new things; ever looked up one thing on Wikipedia and then discovered over an hour has passed as you have clicked from article to article, having fallen down the Wikipedia rabbit hole?

Well, are there mathematical regularities behind how we encounter novelties? And are these encounters similar to how we encounter innovations more generally?

Recently, a team of applied researchers (including Steven Strogatz, my graduate school advisor) set out to examine this. Their paper is very engaging and well-written so I really just recommend you go check out the whole thing, but here are some excerpts:

The notion that one new thing sometimes triggers another is, of course, commonsensical. But it has never been documented quantitatively, to the best of our knowledge. In the world before the Internet, our encounters with mundane novelties, and the possible correlations between them, rarely left a trace. Now, however, with the availability of extensive longitudinal records of human activity online, it has become possible to test whether everyday novelties crop up by chance alone, or whether one truly does pave the way for another.

The larger significance of these ideas has to do with their connection to Kauffman’s theoretical concept of the ‘‘adjacent possible’’, which he originally discussed in his investigations of molecular and biological evolution, and which has also been applied to the study of innovation and technological evolution. Loosely speaking, the adjacent possible consists of all those things (depending on the context, these could be ideas, molecules, genomes, technological products, etc.) that are one step away from what actually exists, and hence can arise from incremental modifications and recombinations of existing material. Whenever something new is created in this way, part of the formerly adjacent possible becomes actualized, and is therefore bounded in turn by a fresh adjacent possible. In this sense, every time a novelty occurs, the adjacent possible expands. This is Kauffman’s vision of how one new thing can ultimately lead to another. Unfortunately, it has not been clear how to extract testable predictions from it.

They conclude that the statistical features of the datasets that they look at are consistent with the idea of the continually expanding adjacent possible:

All four of our datasets displayed the same statistical patterns, both for the rates at which novel events occur and for the statistical signatures of triggering events. Two of the data sets involved innovations (the creation of brand new pages in Wikipedia and the introduction of brand new tags in, while the other two involved novelties that do not qualify as innovations (the first appearance of a word in a text, or the first time a user listens to an existing song). The fact that we observe the same statistical signatures for novelties and innovations strengthens the hypothesis that they could be two sides of the same coin, namely, manifestations of correlations generated by the expansion of the adjacent possible.

Read the rest to find out more about how they examined this.