[The following is a copy of a book review, written by the present author, which appeared in the Reports of the National Center for Science Education.]

*The Failures of Mathematical Anti-Evolutionism*, Cambridge University Press, 2022, 292 pages. Reviewed by David H. Bailey

Although modern science has uncovered a universe that is far vaster and more awe-inspiring than ever imagined before, some writers, mostly of the creationist and intelligent design schools, prefer instead to combat science, particularly on traditional topics such as evolution. One common line of argumentation is that certain biological structures are so unlikely, according to simple back-of-the-envelope reckonings based on probability or information theory, that they could never have been produced by a purely natural, “random” evolutionary process, even assuming millions of years of geologic time. Thus evolutionary theory must be false.

Biologists have never taken these writings seriously, mainly because the empirical evidence for evolution is so overwhelming. Mathematicians and statisticians have never taken these writings seriously, mainly because they have deemed them unworthy of detailed refutation. As a result, there has been a dearth of reliable, readable information on the topic.

Mathematician Jason Rosenhouse’s new book *The Failures of Mathematical Anti-Evolutionism* addresses this specific topic. Rosenhouse is very well-qualified for the task. He has previously published *Among the Creationists: Dispatches from the Anti-Evolutionist Front Line*, describing his experiences attending numerous creationist and intelligent design conferences. He has also published several books explaining probability paradoxes to a mainstream audience. His books clearly demonstrate a talent for science writing.

His new book respectfully but firmly explains why various anti-evolution arguments based on probability and information theory are without merit. Many of these are some variation of what Rosenhouse terms the “Basic Argument from Improbability”: (a) identify a complex biological structure; (b) model its evolution as a random selection from a large space of equally probable outcomes; (c) use elementary combinatorics to enumerate this space; and then assert that the resulting “probability” is too remote for the structure to have evolved.

As Rosenhouse observes, such arguments fall to several well-known fallacies: First of all, they presume that all outcomes are equally probable, which is utterly false in real-world biology — some structures are very likely to appear, while vast numbers of others are not biologically possible at all. Further, these arguments presume that the structure appeared via a single-shot “random” selection among all combinatorial possibilities, whereas real biological structures arose from a long string of earlier steps over the eons, each useful in an earlier context. Finally, these arguments ignore the crucial role of natural selection in finding a “path” through biological space.

In general, such arguments are dead ringers for the post-hoc probability fallacy, namely reckoning a probability after the fact, and then claiming that the event could not have happened naturally. As Rosenhouse explains, we should not be surprised at a seemingly improbable outcome, because some outcome had to happen.

Rosenhouse illustrates this type of fallacious reasoning with the following story (pg. 128-129):

Suppose you and a friend are in the downtown area of a major American city, and you both decide you want a slice of pizza. You pick a direction and start walking. Within just two blocks you find a pizza parlor. Your friend now says, “Incredible! The surface of the Earth is enormous, and almost none of it is covered with pizza parlors. Yet somehow we were able to find one of the few places on Earth that has a pizza parlor. How can you explain something so remarkable?

As Rosenhouse explains, the surface area of the Earth is irrelevant because it was only necessary to search the tiny portion near their location, which, because it is in a major city, has numerous pizza parlors. Rosenhouse then points out that the Basic Argument from Improbability “is guilty of precisely the same oversights, except applied to protein space rather than to the surface of the Earth.” He adds that “the mathematical model on which the [improbability] argument relies is far too unrealistic to produce meaningful results.”

Rosenhouse also addresses arguments based on information theory, entropy and the Second Law of Thermodynamics. Although such arguments are superficially more sophisticated than probability arguments, in the end he finds them equally vacuous — they either rely on intuitive lines of thinking that do not stand up to rigorous analysis, or else they feature profound-looking mathematical analyses, which, because they are based on deeply flawed idealistic models, are irrelevant.

Rosenhouse’s book is a major step forward, and will be greatly appreciated in the community. But as Rosenhouse himself acknowledges, much remains to be done. Hopefully his nicely crafted book will serve as a template for additional contributions in this arena.