# The Futility of Anti-Evolutionary Mathematics

Let me thank Joe Felsenstein for mentioning my new book *The Failures of Mathematical Anti-Evolutionism*, which is now available from Cambridge University Press. The original intention was for a book discussing mathematics and evolution more generally, with just one section devoted to anti-evolutionary nonsense. But when that section ran into the hundreds of pages with no end in sight, we decided just to make the whole book a response to the nonsense.

Mathematics has considerable propaganda value for anti-evolutionists since it can be used to confuse a lay audience into thinking that something profound has been said. It also offers the possibility of an in-principle argument. If the numbers say evolution is impossible then that is the end of the story, regardless of any circumstantial evidence drawn from paleontology, genetics, anatomy, and so on.

In the book, I analyze all of the main threads of mathematical anti-evolutionism and explain why none of them work at all. Along the way I explain how to think clearly about probability, information, combinatorial search, and thermodynamics. However, it is worth noting that even without wading into the technical details, we have a right to be deeply skeptical of the whole project. After all, the ingredients of the evolutionary process are all just empirical facts. Genes really do mutate, sometimes leading to new functionalities, and natural selection really can string together these novelties into directional evolutionary change. If evolution can account for small changes over human timescales, it’s hard to believe that an abstract mathematical argument will fundamentally rule out larger changes over longer time scales.

Indeed, as soon as you look into the details of their arguments you realize that the mathematics invariably plays only a ceremonial role in their discourse. The equations and theorems never really contribute anything; it’s always something else that does the work.

For example, consider Dembski’s notion of complex, specified information. Recall that in this context, “complex” means low probability, while “specified” means that there is a recognizable pattern. In his book *No Free Lunch*, Dembski attempted to apply this notion to the bacterial flagellum. He based his probability calculation on the assumption that an “irreducibly complex” system (meaning, roughly, that the system requires all of its parts to function) cannot evolve gradually. Interestingly, Michael Behe devoted a whole book to defending this assumption, and he certainly didn’t seem to think that an additional probability calculation was needed to strengthen his argument. If the assumption is correct, then it’s all by itself a strong argument against evolution, and the probability calculation is irrelevant. Since the assumption is patently false, any calculation based on its truth is irrelevant.

Behe himself presented some probability calculations in his book *The Edge of Evolution*. This time his argument was that certain evolutionary novelties, such as choloroquine resistance in the malaria parasite, require multiple simultaneous mutations because there is no selectable function until all the mutations are in place. To bolster this argument, he presented some highly dubious calculations meant to show the probability of such mutational sequences was extremely low. But here again the calculation was irrelevant. It was the assumption that whole mutational sequences were required all at once that was doing all the work. Once again, if that assumption is correct then no probability calculation is needed, but since it is not the calculations were irrelevant.

Sometimes the anti-evolutionists invoke a mathematical principle rather than carry out a calculation. They go on at length about the “No Free Lunch” (NFL) theorems, for example. These are legitimate mathematical results that establish the non-existence of a universally successful search algorithm. Dembski, sometimes with various coauthors, has argued that since evolution is in some way analogous to a combinatorial search, these theorems imply that any success that it has can only result from intelligent tailoring of nature’s fitness landscapes to the “algorithm” of natural selection. But once again the theorem plays only a rhetorical role in the argument. Since nature’s fitness landscapes arise ultimately from the laws of physics, Dembski and his collaborators are really just asking why the universe has just the properties it does. It’s a reasonable question, but it’s not one biologists need to worry about, and it’s not one to which the NFL theorems make any contribution toward answering.

The pattern occurs again in their invocations of the second law of thermodynamics. The second law—the real thing as opposed to the asinine caricatures about randomness and disorder—is a mathematical inequality that precisely quantifies the permissible amount of entropy change that can result from a thermodynamic process. If you are not using any of the mathematical machinery of thermodynamics, if instead you are just making vague statements to the effect that the second law rules out the possibility of organisms growing more complex over time, then there is no reason to bring up thermodynamics at all. Everyone agrees that the growth in complexity over time requires a special sort of explanation. Scientists believe they have such an explanation while the anti-evolutionists demur, but the important point is that the resulting argument has nothing to do with thermodynamics.

It requires writing at book length to discuss the myriad conceptual and scientific errors of mathematical anti-evolutionism, and if you are interested in exploring that topic, then I know a good book you can read. But even without all that effort you can be certain that their arguments amount to nothing. If someone claims he can refute evolution with a back-of-the-envelope probability calculation or by invoking some abstract principle or theorem, then you can, with total confidence, dismiss the claim out of hand.

*Jason Rosenhouse is a professor of mathematics at James Madison University and the author of Among the Creationists: Dispatches From the Anti-Evolutionist Front Line, as well as books on the mathematics of Sudoku and the Monty Hall problem. His latest book, The Failures of Mathematical Anti-Evolutionism, is available from Cambridge University Press. Matt Young will be the moderator of this thread.*