The Failures of Mathematical Anti-Evolutionism: Review

Book cover
The Failures of Mathematical Anti-Evolutionism by Jason Rosenhouse, Cambridge University Press, 2022, 274 pp.

Jason Rosenhouse’s newest book, The Failures of Mathematical Anti-Evolutionism, is a mathematics book, not a book on evolution, and not a book on creationism or theology. Though the author plainly believes in – no: though the author plainly accepts evolution, his main purpose is to show that the mathematical arguments of anti-evolutionists are flatly wrong, rather than to defend evolution explicitly.

Jason Rosenhouse is an American author who has written several books, including Among the Creationists: Dispatches from the Anti-Evolutionist Front Line. His experience as a mathematician and of actually wading into the swamp of creationism make him uniquely qualified to have written the present book.

Joe Felsenstein has posted an annotated table of contents, and Prof. Rosenhouse himself has presented an essay The futility of anti-evolutionary mathematics on PT; I will not try to duplicate either of those. Additionally, if you want to get a feeling for some of the more egregious nonsense, you might want to read Has Michael Egnor shown that everything is intelligently designed?, also by Joe Felsenstein. I cannot make, um, head or tail of Dr. Egnor’s argument, except that he seems to think that if you use tossing coins in an illustrative manner, then you must think that the coins themselves were formed by natural causes.

One of the things I took away from this book – and which I thought should have been stressed more – was Prof. Rosenhouse’s distinction between Track-1 and Track-2 explanations. This very important distinction is not shown in what looked like an otherwise comprehensive index.

A Track-1 explanation is “our intuitive understanding,” a descriptive explanation, possibly written in plain English. A Track-2 explanation is a rigorous mathematical exposition, including precise definitions and proved theorems. Track 1 is not definitive; as I would put it, Track 1 gives you a hunch and guides you toward developing a mathematical proof. Track 2 is the rigorous mathematical proof itself. You need both tracks, because, if you stick to Track 1, you will find it too easy to make “logical oversights.” If you cannot prove something rigorously, then you have not proved it at all.

Creationists typically develop a Track-1 explanation, then simply rephrase it as a Track-2 explanation, but they do not prove anything rigorously. They might, for example, note that proteins are extremely complex and therefore so improbable that they could not have arisen by chance. They then apply combinatorial analysis and indeed calculate what they set out to calculate: that proteins almost certainly did not originate by chance. No one thinks that they did. Rather, they originated by a complex sequence of processes that cannot be modeled as a simple combinatorics problem, à la the famous tornado in a junkyard.

In other words, the creationists’ supposed Track-2 explanation is mere window dressing that repeats the Track-1 explanation using mathematical notation in place of words. Indeed, as we see as we progress through the book, all the creationists’ mathematics, bar none, is sophisticated gobbledygook designed to appear rigorous to people who would not understand a word of it. That the purveyors of such window dressing accept it as proof is testament to the power of confirmation bias.

Much of intelligent-design creationism relies on irreducible complexity, the claim that a system has well matched, interacting parts, all of which are essential to the functioning of the system. That is, if any one of the parts is broken or removed, the system will not function. Professor Rosenhouse explains how the claim is false by showing how an eye might evolve step by step until it consists of well matched, interacting parts, all of which are critical to its functioning. But where he jabs the knife in and twists it is in this quotation:

It is clever marketing to refer to these systems as "irreducibly complex." A more accurate description is "easily broken," and his [Michael Behe's] argument could then be rephrased like this: "The prevalence of easily broken systems in nature is strong evidence of intelligent design." In that form the argument is not terribly persuasive.

What is not to like about a book that comes up with gems like this one?

Or this one, after discussing Kelvin’s estimate of the age of the earth and the possibly spurious “proof” that a bumblebee cannot fly:

If copious physical evidence suggests that something has occurred, but someone's mathematical model says the thing is impossible, then it is probably the model that is wrong.

Following a section on “The perils of long-term modeling,” he notes similarly:

We have copious physical evidence that modern life forms are the end results of a lengthy evolutionary process.… And since no mathematical model could possibly include enough of nature's complexity to be convincing, we are not worried that a few back-of-the-envelope calculations will provide a good reason for abandoning that hypothesis [that is, the theory of evolution].

A section called “The basic argument from improbability” explains in some detail why simple combinatorial analysis is not a good model for the evolution of proteins. I cannot go into detail, but Prof. Rosenhouse notes that, given enough opportunity, even improbable events actually happen (an occurrence with odds of one million to one, for example, happens eight times a day in New York), so it is not enough to say that a particular protein is so improbable that a special explanation is required. Those who favor what Prof. Rosenhouse calls the Basic Argument from Improbability provide no argument in favor of a special explanation, but merely (blindly, if I may say so) apply combinatorial analysis where it is completely inapt.

Later in the same chapter, Prof. Rosenhouse takes on William Dembski’s concept of complex specified information. There is too much to discuss here, but I will note that Dembski requires us to distinguish designed “patterns” from undesigned. Professor Rosenhouse notes, however:

We know what mountains look like when we do not carve faces into them, and that makes it easy to recognize Mount Rushmore as something designed. This background knowledge is precisely what we lack in the biological context. No one has intuitions about what will arise after billions of years of evolution starting from a relatively simple sort of life.

Indeed, one of the main stumbling blocks in Dembski’s analysis is that he thinks we can recognize design in the same way that Mr. Justice Stewart thinks he can recognize obscenity.

There is more about Dembski, including his misapplication of the No Free Lunch theorems, which is well worth reading. I liked the chapter on thermodynamics as well, though the editor in me feels obliged to point out that heat is transferred, not necessarily </i>radiated</i>. Professor Rosenhouse notes that the second law of thermodynamics does not preclude increases or decreases of entropy. He correctly inveighs against conflating entropy with order and disorder, but perhaps confusingly sometimes uses disorder as an analogy to entropy. The analogy is often useful, but it is important to recognize that it is only an analogy and proves nothing; Prof. Rosenhouse notes that a jagged chunk of ice looks less orderly than a smooth pool of water, but its thermodynamic entropy is actually less.

If you want to use thermodynamics to describe evolution, you have to perform a rigorous Type-2 analysis. How, asks Prof. Rosenhouse, do you calculate the change in entropy between an ancestral organism and an elephant? How do you apply the laws of thermodynamics to the theory of evolution? No one knows.

Reviewer’s quibbles. The book is well prepared and very readable. I found only a few errors, such as “adaption” and “few 1,000” (and Watt where it should have been watt, but that is getting really picky). The entropy of the ice is calculated incorrectly (p. 241); the correct calculation is left as an exercise for the reader, who is advised to remember that it is necessary to extract heat from the water before it will freeze. I thought the book possibly could have used a few more figures, but I did not particularly care for Figure 5.2, which lacks axis labels and looks too much like a graph of some quantity as a function of time; in fact, it represents some kind of protein space in 2 dimensions. Figure 6.1 also lacks axis labels; it is drawn with very thick curves whose thickness is not explained. The discussion of a thrown ball on p. 65 is not incorrect but seems to imply that the ball’s velocity increases linearly with time, a property I wish were true of my forehand drive. Finally, I was a bit put out by Prof. Rosenhouse’s disparagement, several times, of high school math classes. I do not remember exactly enjoying high school math, but I certainly recognized its importance and was not terrifically bored. An editor should have caught that.

Acknowledgment and disclosure. Jason Rosenhouse very kindly sent me a review copy of the book. He and I are members of the PT “Crew.” We communicated once as I was preparing this review.

Dr. Dembski has responded to Prof. Rosenhouse’s book here.