As it happens, I've been thinking about mathematical anti-evolutionism a lot lately.

Sometime over the summer, though I can't find the exact post, I mentioned that I had been working on an article about mathematical arguments against evolution. I finished it in the fall, and it has recently been accepted for publication in the journal *Science and Education*. The article is currently in production, but I don't how long the process will take.

The main point of the article is that while anti-evolutionists deploy mathematics in a large variety of ways, ultimately all of their arguments are just small variations on a few basic themes. First, they are all based on modeling evolution as a combinatorial search. We treat some modern, complex, biological structure as a target of the search. The argument concludes by invoking some piece of mathematics that is meant to demonstrate the unreasonableness of known evolutionary mechanisms locating the target.

The sorts of mathematics that get invoked are themselves of two basic sorts. You either carry out a probability calculation of some sort, or you invoke a general principle. Examples of the former strategy are found in the simplistic creationist arguments in which the precise sequence of amino acids in, say, a hemoglobin molecule, is viewed as a combinatorial string selected at random from a set of equiprobable possibilities, Dembski's arguments about specified complexity, and Michael Behe's probability arguments in *The Edge of Evolution.* Examples of the latter strategy are arguments based on the second law of thermodynamics, No Free Lunch theorems, or Conservation of Information theorems.

(Technically, the second law argument might be considered to be based on physics and not mathematics, but it is of a sufficiently mathematical character that I think it deserves inclusion here. In the article, space restrictions prevented me from discussing the second law argument in detail, so I just mention it in passing. Maybe that should be a separate article!)

Once this basic framework is recognized, it becomes easy to zero in on critical weak spots in their arguments. The probability arguments invariably fail because they are based on reducing probability calculations to combinatorics, which is never justified in any non-trivial biological application. The general principle arguments fail either because of basic empirical considerations, or because the principle at issue is simply irrelevant to the issue at hand.

For example, applying Dembski's machinery of specified complexity to biology requires that one calculate the probability of evolving a structure like a flagellum given many millions of years in which to work. Since he has suggested no plausible way of carrying out such a calculation we're done here. The second law argument on the other hand, leaving aside the minutiae put forth by its defenders, plainly runs afoul of empirical considerations. Known evolutionary mechanisms demonstrably have the power to create novel functionalities in organisms and to change relative frequencies of genes. That is sufficient to show that there is nothing thermodynamically impossible in what evolutionists are saying. Again, we're done here.

Of course, I don't mean to say that these observations constitute a complete catalog of all that is wrong with these arguments. There is plenty else to criticize. For example, Dembski's notion of “specification” is hopelessly vague, and people like Granville Sewell makes childish errors in their discussions of the second law. My point is simply that to the extent that our only goal is to refute the challenge these arguments are said to pose to evolution they can be dismissed very quickly with just a few basic points.

A further goal of the article is to trace the history of modern mathematical anti-evolutionism back to the famous Wistar conference of 1966. That was the conference whose proceedings were published under the title, “Mathematical Challenges to the Neo-Darwinian Theory of Evolution.” The challenges came primarily from Muuray Eden and Marcel-Paul Schutzenberger. I argue that their arguments exemplify the two main strategies that are used, and established the framework in which modern mathematical anti-evolutionism is presented. They both modeled evolution as a combinatorial search. Eden pursued the “calculation” strategy, and based his argument mostly on the observation that the set of abstractly possible proteins is many orders of magnitude larger than the set of proteins found in modern organisms. Schutzenberger pursued the “general principle” strategy. He argued by analogizing genes to computer code, and put forth the principle that random changes in formal languages degrade meaning. I discuss both arguments in considerable detail, explain why they are wrong, and show how they fit cleanly into my rubric of mathematical anti-evolutionism.

The final point I make is that in modern anti-evolutionist discourse, the mathematics never really contributes anything to the discussion. As I pointed out in yesterday's post, Dembski's arguments about specified complexity as applied to evolution are complete parasitic on prior ID arguments, for example, Michael Behe's claims about irreducible complexity. If Behe's claims were correct they would all by themselves be a powerful argument against evolution. A probability calculation would do nothing to make them stronger. Since Behe's claims are not correct, no calculation based on them is going to be relevant. Likewise for Behe's *Edge of Evolution* calculations. It is the assumption that the evolution of certain bio-molecular systems require numerous simultaneous mutations that is doing all the work in his argument. The numerology Behe slathers on top of that dubious assumption serves only to obfuscate. And so it goes.

Anyway, that's a very quick summary. The finished article is actually quite long, at a little over eleven thousand words. Even after writing at such length I'm painfully aware of everything I had to leave out. Hopefully, though, I've managed to say something new. One thing I noticed during my time schmoozing at creationist conferences is that mathematical arguments are rhetorically very powerful. It's easy to bamboozle folks with a few equations and Greek letters. Mathematical research can often seem esoteric and rarefied, so it's nice to be able to write about something with practical import for a change.

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Interested to read about the 'random changes to computer code' argument as work has since been done on evolving code rather than writing it by making - random changes to computer code. Strangely enough computer scientists expect to get better code as a result, not degraded meaning.

i'm ignorant of the mathematics the anti's actually use, but I doubt they properly take into account the immense number of, um, incidences of random events at which weird things might happen. I'm not saying this very well. But given how many 'interesting' molecules, say, there might be on the earth's surface, over a couple of billion years ... that's a lot of opportunities for some beneficial mutation to happen. Say 10^6 molecules per cc of surface area .. do the math ... earth surface area = 10^8 square kms = 10^20 square cms x depth of kilometre on average = 10^25 cc say, times the 10^6 or whatever molecules per cc to 10^31 and say lifespan of opportunity is one second, that over two billion years is 10^40 or whatever possible points at which something interesting could happen. Just saying it is a very very large number ...

@2 - the Kitzmiller day 12 morning trial transcript provides a good example of the sort of calculation you're doing. Behe's on the stand, and the defense attorney doing the cross-examination points out that the number of prokaryotes in one ton of soil is seven orders of magnitude larger than the population Behe considered in his published attempt to claim some mutational event couldn't happen. Fun reading.

I've a new post on Ewart, Dembski and Marks and their attack on my genetic algorithm for solving Steiner's problem at nmsr.org. They basically rationalize that difficult problem into the much simpler Minimum Spanning Tree problem, then attack the latter via the argument that a "trivial random search" produces answers "as good" as the Steiner solutions (not). Online here:

http://www.nmsr.org/weaselsnew.htm

(I can't post on Panda's Thumb until the server gets fixed.)

More interesting stuff.

sean s.

I loved 'Among the Creationists' and wish you were implanted at every convention and gathering that was held to report back... I wonder if there could be a follow-up book simply with more real-world encounters, interspersed with “harder” science examples such as this between. Would be great to bounce between the math and the personalities over and over…

I think that Dembski's original (pre-2005) Complex Specified Information argument was an exception to your statement that the math adds noting to ID/creationist arguments. He actually had a Law of Conservation of Complex Specified Information (LCCSI) that supposedly established that natural evolutionary forces could not put CSI into the genome if it was not already there. Alas for him, it turns out that he compared apples to oranges and then you make that apples to apples the whole thing collapses. But it was an attempt to really use math to do the heavy listing.

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Wow, a Meta-typo. Good going, Joe!

Hi Joe.

But he has no way of showing that anything in the genome is an instance of CSI. Such a showing requires a probability calculation, and as far as we can glean from Dembski's writing such a calculation requires presupposing the correctness of Behe's irreducible complexity arguments.

But if Behe is right, then no probability calculation is necessary. Since Behe is wrong, no calculation based on his argument is relevant.