One name that was unfamiliar to me was brought up several times amidst the panoply of purported “criticisms” and “debunkings” of Probability Zero that are presently being flung around by hundreds of evolutionary enthusiasts, very few of whom have actually read the book. That name is Jason Rosenhouse, the author of Failures of Mathematical Anti-Evolutionism, published by Cambridge University Press in 2022.
Anti-scientific misinformation has become a serious problem on many fronts, including vaccinations and climate change. One of these fronts is the persistence of anti-evolutionism, which has recently been given a superficially professional gloss in the form of the intelligent design movement. Far from solely being of interest to researchers in biology, anti-evolutionism must be recognized as part of a broader campaign with a conservative religious and political agenda. Much of the rhetorical effectiveness of anti-evolutionism comes from its reliance on seemingly precise mathematical arguments. This book, the first of its kind to be written by a mathematician, discusses and refutes these arguments. Along the way, it also clarifies common misconceptions about both biology and mathematics. Both lay audiences and professionals will find the book to be accessible and informative.
I read it, of course, in order to see if he had somehow anticipated my own demonstration of the mathematical impossibility of evolution by natural selection, selective sweeps, neutral sweeps, genetic drift, ILS, biased gene conversion, and every other imagined mechanism, but, as it turns out, he hadn’t. Nothing that he addresses in his book has anything whatsoever to do with my own mathematical work on the subject. Rosenhouse’s book has two primary objectives. First and foremost, he was attempting to defuse the anti-evolutionary work of the Intelligent Design community, beginning with Michael Behe and William Dembski. Since I’m not familiar with their work and since their work does not overlap with mine, I’ll leave it to the latter to address Mr. Rosenhouse’s critique.
Rosenhouse’s book is objectively bad. It purports to be a critique of mathematics as used by ID proponents and of my mathematical work in particular. Yet it betrays a lack of comprehension throughout. It makes a virtue of misrepresentation.
I’m not in a position to have an opinion one way or the other. However, what I can say is that Dembke’s summary is consistent with the parts of the book that addressed something I do know, and which concern Rosenhouse’s attempt to mitigate the serious damage to the mathematical credibility of evolutionary theory that resulted from the 1966 Wistar Symposium, which I have read and to which I devoted an entire chapter of PZ. To put it charitably, Rosenhouse systematically misrepresents the entire debate between the mathematicians and the biologists, and falsely claims that the mathematical issues raised by the mathematicians there were successfully addressed by the biologists present.
His account of Wistar is simply not accurate. It is a systematic misrepresentation of the transcript of the Symposium in three different ways: factual errors, strategic omissions, and interpretive falsehoods and distortions. Here is a systematic analysis of Rosenhouse’s description of the symposium:
Factual Errors
- “Only two posed challenges to evolution’s fundamental soundness.”
Rosenhouse claims only Eden and Schützenberger challenged evolution, and that Ulam “was not challenging the fundamental soundness of the theory.” This is flatly contradicted by the transcript. Ulam explicitly states: “What I am going to do will come to Eden’s conclusions.” He also says, in the discussion, “In contrast to the tone of the discussion I took, personally, I believe that the numbers I took are very optimistic”—meaning he believes the real situation for neo-Darwinism is worse than his model suggests, not that he was merely sketching a neutral mathematical exercise. Rosenhouse’s selective quotation of Ulam’s modest throat-clearing about “schematic thinking” and “a starting point for discussion” is a textbook example of mistaking courtesy for agnosticism. Ulam was just being polite. He was not even remotely neutral on the fundamental soundness of evolution. - “Schützenberger’s presentation is muddled.”
The transcript appears muddled because it was OCR’d and the scanning was very bad. Schützenberger’s argument is perfectly clear: he introduced three topological spaces, argued that the mapping between the first and second is the unsolved problem, and concluded that “there is a considerable gap in the neo-Darwinian theory of evolution, and we believe that this gap cannot be bridged within the current conception of biology.” Rosenhouse treats the garbled OCR as evidence of confused thinking. This is either dishonest or lazy. He could have checked a physical copy of the proceedings like I did. - The attribution of the “stepping-stone” argument to the biologists.
Rosenhouse constructs an elaborate analogy involving truffle hogs, river crossings, stepping stones and presents it as though it captures what the biologists actually said at Wistar. It does not. No biologist at the conference presented a stepping-stone model of protein evolution. No biologist calculated the density of functional proteins in the neighborhood of any existing protein. No biologist demonstrated that the local search space is sufficiently dense to support the model. Rosenhouse invented the analogy in 2022 and projected it backward onto a 1966 transcript where it does not appear. This is the classic Fictional Defender move we’ve seen from both the Neo-Darwinists and the Neo-Kantians: constructing a more defensible version of the position than any past figure ever actually articulated, then declaring that this post-facto invented defense answers the challenge to the original’s case. - Ulam’s quote about Eden is misrepresented.
Rosenhouse quotes Ulam saying that Eden’s comments “refer to a random construction of such molecules and even those of us who are in the majority here, the non-mathematicians, realize that this is not the problem at all.” He uses this to claim Ulam was criticizing Eden. But the transcript shows Ulam was agreeing with Eden’s broader point while noting that the first five minutes of Eden’s talk addressed a preliminary issue that was not the central problem. Ulam immediately goes on to develop his own argument about rates that reaches the same conclusion Eden reached. Rosenhouse presents Ulam as an ally of the biologists. The transcript shows him as an ally of Eden.
Strategic Omissions
- Wald’s complete irrelevance is never acknowledged.
Rosenhouse does not mention that George Wald’s formal presentation on “The Problems of Vicarious Selection” had absolutely nothing to do with the mathematical challenges. Wald talked about luminescent bacteria on deep-sea fish and the mating habits of eels and lampreys. This was one of the “formidable talents” assembled to respond to the mathematicians, and his response was to give a paper on an entirely different subject. Rosenhouse presents the biologists as having answered the challenges effectively. He omits the fact that one of his star witnesses didn’t even show up to the fight. - Lewontin’s admission is buried.
Rosenhouse quotes Lewontin’s point about enzyme changes as though it settles the matter. He does not mention Lewontin’s admission, under direct questioning from Schützenberger, that he cannot justify the continuity assumption that small genetic changes typically produce small phenotypic changes. The transcript records Lewontin saying, “That is a very good question. I don’t know.” This is the single most important exchange in the entire symposium, because the continuity assumption is what makes hill-climbing selection work. Without it, the entire stepping-stone model that Rosenhouse constructed collapses. He omits it entirely. I, of course, specifically cited it in Probability Zero. - Wald’s observation that supported Eden is omitted.
Wald stated that he was “hard put to find a single instance” where a single amino acid change in hemoglobin did not “change markedly the properties.” This is relevant to Eden’s argument about the ruggedness of the fitness landscape—if nearly every single-residue change has significant functional consequences, then the space is rugged, not smooth, and local search is unreliable. Rosenhouse omits this because it directly contradicts his stepping-stone narrative. - Crosby’s support for the mathematicians is left out.
Rosenhouse quotes Crosby’s exasperated comment about “gorgeous unreality” as though it refutes the mathematicians. He does not mention that in the discussion of Eden’s paper, Crosby actually supported Eden’s argument, noting that each intermediate stage “has got to be capable of existing viably” and that frame-shift mutations “decrease enormously the possibility of intermediate stages being viable.” Crosby was frustrated with what he felt were oversimplifications in Ulam’s model; he was not dismissing the mathematical challenge as a whole. - No biologist produced a single calculation.
This is the single most important omission in the entire chapter. Rosenhouse never acknowledges that not one biologist at the conference produced a single calculation that contradicted the mathematicians’ conclusions, because acknowledging it would destroy his thesis. Eden calculated the size of sequence space. No one calculated a smaller space. Ulam calculated a rate. No one calculated a faster rate. Schützenberger asked for a mechanism. No one demonstrated one. The biologists asserted, objected, analogized, and hand-waved. They did not even attempt to do the math. Rosenhouse’s entire chapter is structured to conceal this fact.
Falsehoods and Distortions
- The Kansas/New Jersey analogy is backwards.
Rosenhouse argues that Schützenberger’s computer-program analogy fails because computer languages are like Kansas (words widely scattered) while the genetic code is like New Jersey (words densely packed). His evidence is that there are 64 codons and all of them code for something. This is true at the codon level, but it is irrelevant to Schützenberger’s argument, which was about proteins, not codons. Every codon codes for an amino acid or a stop, but that does not mean every protein is functional. The question is not whether every three-letter word in the genetic language means something, but whether every 250-letter sentence is grammatical. The answer is overwhelmingly no. Eden had already shown this: the space of 250-residue proteins is ~10^325, and the number of functional proteins that have ever existed is ~10^52. Rosenhouse attacked a strawman of his own construction, refuted an argument Schützenberger was not making, and claimed to have refuted Schützenberger. - Waddington’s summary is presented as authoritative.
Rosenhouse quotes Waddington’s summary as “exactly right” and as proof that the biologists won the argument. But Waddington’s summary is a diplomatic statement of the biologists’ position, not a demonstration that the position is correct. Waddington asserts that “the meaningful section” of explored sequence space “is quite large in comparison with all the things that could conceivably be made out of it in single steps.” This is an empirical claim. He provides no data to support it. He provides no calculation. He simply asserts it. Rosenhouse treats this assertion as though it were a proof. It is not. It is the claim that required proving, and no one at Wistar even tried to prove it. - Mayr’s “adjust the figures” quote is reinterpreted in a false context.
Rosenhouse devotes enormous effort to providing context for Mayr’s statement that “somehow or other by adjusting these figures we will come out all right.” He tries to claim that Mayr was making the sophisticated point that Ulam’s model was too simple to be useful. But the transcript shows Mayr was simply retreating to the argument from existence. “We are comforted by knowing that evolution has occurred” is not a mathematical rebuttal. It is not even a scientific argument. It is a profession of blind faith. Mayr was asserting that the numbers must work out because the conclusion is already known. It was nothing more than an appeal to hope in help that would never arrive. - The “biologists were right” framing is unsupported by the transcript.
Rosenhouse attempts to paint the picture that the biologists successfully answered the mathematicians at Wistarr. The transcript proves the opposite. The biologists offered qualitative objections (things are more complicated than your model), anecdotal counterexamples (hemoglobin variants survive single changes), conceptual reframings (you’re modeling it wrong), and existential assertions (evolution happened, so the math must work). None of these constitute a quantitative refutation. None of them even began to solve the problems the mathematicians identified. And the mathematicians themselves did not accept the biologists’ responses as adequate, and the closing remarks by the host of the symposium made it clear that he did not believe the biologists’ collective response was adequate or that the situation had been resolved.
In my second post on Failures of Mathematical Anti-Evolutionism later this week, I’ll review whether Jason Rosenhouse provided any evidence of his claim in the book that the Wistar mathematicians’ various anti-evolutionary arguments were successfully refuted during the sixty years since the end of the Symposium or not.