This weekend, I came across Granville Sewell’s article “[A Mathematicians View of Evolution][sewell]“. My goodness, but what a wretched piece of dreck! I thought I’d take a moment to point out just how bad it is. This article, as described by the [Discovery Institute][diref], purportedly shows:
>… that Michael Behe’s arguments against neo-Darwinism from irreducible
>complexity are supported by mathematics and the quantitative sciences,
>especially when applied to the problem of the origin of new genetic
I have, in the past, commented that the *worst* math is no math. This article contains *no math*. It’s supposedly arguing that mathematics supports the idea of irreducible complexity. Only there’s no math – none!
The article claims that there are *two* arguments from mathematics that disprove evolution. Both are cheap rehashes of old creationist canards, so I won’t go into much depth. But it’s particularly appalling to see someone using trash like this with the claim that it’s a valid *mathematical* argument.
The First Argument: You can’t make big changes by adding up small ones.
>The cornerstone of Darwinism is the idea that major (complex) improvements can
>be built up through many minor improvements; that the new organs and new
>systems of organs which gave rise to new orders, classes and phyla developed
>gradually, through many very minor improvements.
This is only the first sentence of the argument, but it’s a good summary of what follows. There are, of course, several problems with this, but the biggest one coming from a mathematician is that this asserts that it’s impossible to move a large finite distance by taking small finite steps. This is allegedly a mathematician making this argument – but that’s what he’s claiming: that it’s impossible for any large change to occur as a result of a large number of small changes.
It also incorrectly assumes a *directionality* to evolution. This is one of the requirements of Behe’s idea: that evolution can only *add*. So if we see a complex system, the only way it could have been produced by an evolutionary process is by *adding* parts to an earlier system. That’s obviously not true – and it’s not even consistent with the other creationist arguments that he uses. And again, as a mathematician, he *should* be able to see the problem with that quite easily. In mathematical terms, this is the assertion that evolution is monotonically increasing in complexity over time. But neither he nor Behe makes any argument for *why* evolution would be monotonically increasing with respect to complexity.
So there’s the first basic claim, and my summary of what’s wrong with it. How does he support this claim?
>Behe’s book is primarily a challenge to this cornerstone of Darwinism at the
>microscopic level. Although we may not be familiar with the complex biochemical
>systems discussed in this book, I believe mathematicians are well qualified to
>appreciate the general ideas involved. And although an analogy is only an
>analogy, perhaps the best way to understand Behe’s argument is by comparing the
>development of the genetic code of life with the development of a computer
>program. Suppose an engineer attempts to design a structural analysis computer
>program, writing it in a machine language that is totally unknown to him. He
>simply types out random characters at his keyboard, and periodically runs tests
>on the program to recognize and select out chance improvements when they occur.
>The improvements are permanently incorporated into the program while the other
>changes are discarded. If our engineer continues this process of random changes
>and testing for a long enough time, could he eventually develop a sophisticated
>structural analysis program? (Of course, when intelligent humans decide what
>constitutes an “improvement”, this is really artificial selection, so the
>analogy is far too generous.)
Same old nonsense. This is a *bad* analogy. A *very* bad analogy.
First of all, in evolution, *we start with a self-reproducing system*. We don’t start with completely non-functional noise. Second of all, evolution *does not have a specific goal*. The only “goal” is continued reproduction.
But most importantly for an argument coming from a supposed mathematician: he deliberately discards what is arguably *the* most important property of evolution. In computer science terms (since he’s using a programming argument, it seems reasonable to use a programming-based response): parallelism.
In evolution, you don’t try *one* change, test it to see if it’s good and keep it if it is, then go on and try another change. In evolution, you have millions of individuals *all reproducing at the same time*. You’re trying *millions* of paths at the same time.
In real evolutionary algorithms, we start with some kind of working program. We then copy it, *Many* times; as many as we can given the computational resources available to us. While copying, we randomly “mutate” each of the copies. Then we run them, and see what does best. The best ones, we keep for the next generation.
What kind of impact does parallelism have?
As an experiment, I grabbed a rather nifty piece of software for my mac called [Breve Creatures][breve]. Breve is an evolutionary algorithms toolkit; BC uses it to build moving machines. The way it works is that it produces a set of random assemblies of blocks, interconnected by hinges, based on an internal “genetic code”. For each one, it flexes the hinges. Each generation, it picks the assemblies that managed to move the farthest, and mutates it 20 times. Then it tries each of those. And so on. So Breve gives us just 20 paths per generation.
Often, in the first generation, you see virtually no motion. The assemblies are just random noise; one or two just happen to wiggle in a way that makes them fall over, which gives that a tiny bit of distance.
Typically within 20 generations, you get something that moves well; within 50, you get something that looks amazingly close to the way that some living creature moves. Just playing with this a little bit, I’ve watched it evolve things that move like inchworms, like snakes, like tripeds (two legs in front, one pusher leg in back), and quadrapeds (moving like a running dog).
In 20 generations of Breve, we’ve basically picked a path to successful motion from a tree of 2020 possible paths. Each generation, we’ve pruned off the ones that weren’t likely to lead us to faster motion, and focused on the subtrees that showed potential in the tests.
Breve isn’t a perfect analogy for biological evolution either; but it’s better than Sewell’s. There’s two important things to take from this Breve example:
1. Evolution doesn’t have a specific goal. In the case of Breve Creations, we didn’t say “I want to evolve something that walks like a dog.” The selection criteria was nothing more than “the ones that moved the furthest”. Different runs of BC create very different results; similarly, if you were to take a given species, and put isolated two populations of it in similar conditions, you’d likely see them evolve in *different* ways.
2. Evolution is a process that is massively parallel. If you want to model it as a search, it’s a massively parallel search that prunes the search space as it goes. Each selection step doesn’t just select one “outcome”; it prunes off huge areas of the search space.
So comparing the process to *one* guy randomly typing, trying *each* change to see how it works – it’s a totally ridiculous analogy. It deliberately omits the property of the process that allows it to work.
The Second Argument: Thermodynamics
>The other point is very simple, but also seems to be appreciated only by more
>mathematically-oriented people. It is that to attribute the development of life
>on Earth to natural selection is to assign to it–and to it alone, of all known
>natural “forces”–the ability to violate the second law of thermodynamics and
>to cause order to arise from disorder.
Yes, it’s the old argument from thermodynamics.
I want to focus on one aspect of this which I think has been very under-discussed in refutations of the thermodynamic argument. Mostly, we tend to focus on the closed-system aspect: that is, the second law of thermodynamics says that in a *closed system*, entropy increases monotonically. Since the earth is manifestly *not* a closed system, there’s nothing about seeing a local decrease in entropy that would be a problem from a thermodynamic point of view.
But there’s another very important point. Entropy is *not* chaos. An system that seems ordered is *not* necessarily lower entropy than a system that seems chaotic. With respect to thermodynamics, the real question about biology is: do the chemical processes of life result in a net increase in entropy? The answer? *I don’t know*. But neither does Sewell or the other creationists who make this argument. Certainly, watching the action of life: the quantity of energy we consume, and the quantity of waste we produce, it doesn’t seem *at all* obvious that overall, life represents a net decrease in entropy. Sewell and folks like him make the argument from thermodynamics *never even try* to actually *do the math* and figure out if if the overall effect of any biological system represents a net increase or decrease in entropy.
For someone purportedly writing a *mathematicians* critique of evolution, to argue about thermodynamic entropy *without bothering to do the math necessary to make the argument* is a disgrace.