Preamble
Vox Day has worked as a novelist, nonfiction author, publisher, game designer, technology entrepreneur, musician, cultural commentator, and long-running blogger. He has developed a substantial readership largely outside conventional academic and media institutions, and his influence has come as much through the publishing ventures and intellectual communities he has built as through the large body of work he has written. His interests range across economics, politics, technology, religion, history, and imaginative literature.
This interview will concentrate on a narrower subject: Day’s challenge to evolutionary theory, especially the arguments developed in his recent books Probability Zero and The Frozen Gene. As an intelligent design proponent, I have my own arguments for thinking that evolutionary mechanisms face serious explanatory shortfalls. The aim of this conversation is to give Day the opportunity to present his strongest case against evolutionary theory and to examine how it withstands the strongest objections to it. Many related questions will arise in this interview, not least where he thinks we should go to replace the account of evolution he is attempting to refute.
This is a long and detailed interview, and I’m grateful to Day for taking the time to answer all the questions that follow. This interview came about through a correspondence with Day that resulted from a review of his book Probability Zero that I posted recently on this Substack. Day’s technical work on evolutionary theory appears at Zenodo, the free, general-purpose open repository for research run by CERN. You can view all his Zenodo articles by clicking here. Day works fast, and he just posted at Zenodo an article titled MITTENS 3.0, which expands on this interview by addressing a 2009 Jeffrey Barrick study on genome evolution. MITTENS 3.0 is available at here at Zenodo and immediately below for download:
In the interview, Day mentions the famous 1966 Wistar Symposium, whose proceedings appeared in print as Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution. With Day’s permission, I’m including chapter 6 of Probability Zero (2nd ed.), which describes the symposium and its importance. This chapter is included at the end of the interview.
Background and Intellectual Formation
Bill Dembski: You have worn an unusual number of hats: novelist, game designer, publisher, entrepreneur, musician, cultural critic, and economic commentator. Explain how these experiences have shaped your approach to scientific controversies, and especially to the use of math to resolve such controversies.
Vox Day: First, when you’re analyzing economic statistics, you have to be comfortable working in large numbers. So, the customary appeal to the magic of “millions and billions of years” isn’t the least bit intimidating when you’re accustomed to working in hundreds of trillions. For example, one number that I tracked closely for years was total credit market debt, which currently runs around $119 trillion in the USA alone. So when an evolutionist is waving his hands about six million years or nine million years, my immediate reaction is to wonder what is causing the difference. A 1.5 percent delta is a huge deal in economics and is enough to make a difference between expansion and contraction, so a 50 percent one tends to raise the eyebrows. Second, as a game designer, you have to have a holistic perspective, and that requires you to always keep the whole system in context even when you’re dealing with the smallest details.
Bill: You graduated from Bucknell University with majors in economics and East Asian studies. Please describe your training in economics in detail. What mathematics, probability, statistics, econometrics, or modeling did the program teach you, and which parts of that training have proved most relevant to your work on evolution?
Vox: My econ program covered all of those things except probability, although I didn’t take a course in modeling because my focus was on the historical process of development in late-developing countries like Japan and the Soviet Union. I did independent studies under Michael Moohr and Robert Chernomas, so my studies were a little bit more Marxian than was customary at the time. I would say developing an intuitive grasp of statistics, their limits, and how important it is to understand them contextually is what proved to be most relevant to all of my subsequent work, in games, evolution, and philosophy.
Bill: Did you pursue any graduate study, professional research, or sustained independent work in mathematical economics or mathematics more generally after Bucknell?
Vox: None whatsoever. My biggest educational regret is not dropping out after my first semester sophomore year. I consider academic credentials to be a pointless waste of time. At Bucknell I seldom went to class and sometimes didn’t even bother buying the textbook. Once my professors realized that I was doing fine academically without doing the reading or attending the classes, they switched me to independent studies. I barely went to to a class my senior year.
Bill: Which mathematical methods used in Probability Zero did you already command, and which did you have to learn specifically for the project?
Vox: The math in PZ is very simple. People get confused about the math and the object of the math, what the math is actually measuring. Most of it is just simple multiplication and division, with a little bit of algebra here and there. The problem is that you have to correctly understand the object of the math or you’re just spinning your wheels without truly understanding what you’re doing. The moment you see someone mention “martingale” with regards to Neutral Theory, you know they’re off in la-la land with absolutely no idea what the numbers represent.
Bill: Economics and evolutionary biology both study populations, competition, constrained resources, and outcomes that emerge from many local events. What did an economist’s way of thinking allow you to see that, in your judgment, most evolutionary biologists have missed?
Vox: A big number is not an explanation and an appeal to a mechanism is not a calculation.
Bill: What, if any, are the pitfalls in importing intuitions from economics into biology, where the agents, mechanisms, and units of inheritance are so different?
Vox: Economists are particularly prone to simplifying things in order to make their models work and then confusing the map for the territory. The fact that our numbers tend to be precise does not make them accurate, or even necessarily relevant.
Bill: Your core argument in Probability Zero is dubbed MITTENS. Explain what this acronym means and briefly state its key claims (we’ll explore it in detail later in this interview).
Vox: Mathematical Impossibility of The Theory of Evolution by Natural Selection. It means that the rate of natural selection is mathematically unable to account for the observed genetic difference, as measured in base-pairs, between humans and chimpanzees. Or, for that matter, any two vertebrate species. I’ve sent you the version 3.0 of the paper to review.
Bill: Probability Zero is now in a second edition. What changed between the first and second editions, and which revisions in the second edition most strengthen your MITTENS argument?
Vox: In the first edition, I used the 35 million base-pair difference reported in the 2005 report that was falsely characterized as the complete genomic comparison of chimps and humans. The second edition updated the numbers with the 410 million base pair difference reported in the 2025 Yoo et al paper that actually covered the complete genomes. So what was already a conclusive case got 10x stronger.
Bill: The title Probability Zero sounds absolute. Do you mean that evolution has literally zero mathematical probability, or that, given specified empirical constraints and timescales, its probability is effectively zero? What assumptions define the scope of that conclusion?
Vox: Zero. Absolute zero. Never happened that way. Never even could happen that way. Absolutely, totally, mathematically, and practically impossible. Your average origin story out of Marvel or DC Comics about getting bitten by a radioactive spider or whatever is more scientifically viable. There are no assumptions except the scientific estimate for the age of the universe. You can’t walk to the Moon. And you can’t create hundreds of millions of fixated mutations across an entire species in 14 trillion years, forget about six million.
Bill: No one’s credentials decide whether a mathematical result is correct. Even so, disciplinary training can expose hidden assumptions and prevent elementary mistakes. What forms of feedback did you seek from mathematicians, statisticians, economists, population geneticists, evolutionary biologists, and representatives of other disciplines while developing MITTENS? From what likely sources did you not seek feedback and why?
Vox: My first, foremost, and primary form of feedback is from my Red Team. For all my papers, non-fiction books, and translations, I run them through a Red Team Stress Test comprised of ChatGPT, Deepseek, Gemini, and Grok instructed to take a hard oppositional stance. They produce detailed and extensive criticisms, most of which are obviously erroneous in some way, but even when incorrect, often produce new lines of attack. I seldom bother with human feedback. But both PZ and TFG were sent out pre-release to about ten volunteer readers, who ranged from a world-class physicist to a number of mathematicians with PhDs. I got some very good suggestions for improvement from a few of them, and even an Introduction and an Appendix from Dr. Tipler. But none of them had anything to add that fundamentally altered the work; I discovered and resolved the Kimura and LTEE [Long-Term Evolution Experiment] anomalies on my own after the fact.
Bill: What criticisms, if any, from technically qualified readers caused you to revise or improve your argument? To what degree did AI provide a sounding board for your work.
Vox: AI did all the calculations and wrote the first draft of everything. It also provided about 750 of the 20 effective criticisms that improved the paper. I don’t think most people understand the first thing about the proper way to use AI to augment your outputs. If you don’t really know what you’re doing, AI will do nothing but defend its training and convince you that you’re wrong. I address this in great detail in Hardcoded, a book I wrote about the process of writing PZ and TFG.
Bill: Briefly describe the gist of your follow-up book, The Frozen Gene. How does its argument relate to that of Probability Zero? To what degree do they complement each other? If a reader could only read one, which would you suggest reading and how much would that reader miss from the other?
Vox: TFG is mostly a collection of essays and companion papers that cover tangential issues raised in PZ. They are very complementary. Definitely PZ.
Bill: Throughout your two books you credit Claude Athos as a collaborator and even as a second author on technical papers—in other words, you explicitly credit an AI. How does AI figure into your workflow? How much of your mathematical heavy lifting in your books is AI doing for you? To what extent do you confirm the accuracy of what AI is telling you? Do you make a point of understanding everything you do in collaboration with AI? Why shouldn’t readers of your work be concerned about the degree to which it depends on AI?
Vox: Claude Athos is an integral part of my work. I have calculated that between him and the Red Team, they’re augmenting my organic intelligence by around 1.5 SD. I came up with the basic argument on my own, but the difference between the original MITTENS as it was laid out on the blog and MITTENS 3.0 is the AI augmentation. I always understand everything I do in collaboration with AI; if I didn’t, I would reliably end up with nonsensical results. I think those readers will find themselves becoming a lot more suspicious of any human author who isn’t AI augmented. AI is a much, much harsher critic, particularly for those who are going against their training orthodoxy, than 100 human critics will ever be. And they always anticipate the human criticisms; remember, they’re trained on exactly the same textbooks and papers. Just try telling an AI that k!=u and see what happens if you doubt me.
The Road to Skepticism
Bill: When did you first become skeptical of neo-Darwinism? Was there a particular book, calculation, empirical result, or conversation that made you think the standard account might be mathematically inadequate? Was there a point in life when you were perfectly content to accept whatever the reigning theory of evolution happened to be?
Vox: After reading all of Richard Dawkins’s books as part of my preparation for writing The Irrational Atheist in 2008. I could not believe how stupid and incompetent the man is. He’s a wonderful writer, which is the reason no one ever notices what a vapid cretin he is or that most of his arguments aren’t even coherent. Then, after reading all of Daniel Dennett’s work, I realized that the evolutionists have no idea what they’re even trying to prove or how to prove it. I summed up the entirety of the evolutionist case thanks to Dennett’s core argument: “you can believe biologists because physicists get very accurate results.” All that evolutionary biology has ever amounted to is butterfly collectors telling fairy stories under the guise of stolen scientific valor.
Bill: What were the strongest arguments in favor of evolution that you encountered before offering your own critique of it? I’ve been able to trace blog posts by you critical of neo-Darwinism on Vox Popoli to 2012. Was this when you first officially weighed in on evolutionary theory?
Vox: I never really thought about it much outside of the usual high school biology class. I was offered the opportunity to debate evolution and “be taught about it” by a science teacher who was also an evolution blogger. They love to offer to teach you. And when it became clear that he didn’t understand why “what is the average rate of evolution by natural selection” was not only a relevant question, but an absolutely necessary one, I began to notice that evolutionists are hopelessly innumerate. I mean, sure, it’s a difficult question, but by definition, there is absolutely an answer. I’ve since learned that evolutionists don’t understand the concept of an “average rate.” In fact, some of them with PhDs don’t even understand the concept of “average.” I’m not kidding.
Bill: Did your skepticism begin with natural selection, with universal common descent, with the neutral theory of molecular evolution, with philosophical naturalism more generally, or some combination of these, or none of the above? How did those concerns become connected in your thinking?
Vox: Pure natural selection. I’m not even sure what “common descent” means. I don’t think you would believe how little this stuff interests me, how unfamiliar I am with the normal buzzwords, or how obviously irrelevant the entire traditional evolutionary debate is.
Bill: Which evolutionary theorists do you regard as the strongest or most intellectually serious opponents of your position? Which do you think are fakers or poseurs?
Vox: JBS Haldane was a serious guy. EO Wilson was smart, but got too caught up in the weeds. R.A. Fisher had the right ideas, more or less, but he focused on mutations instead of fixations and set the entire field off on the wrong direction for a century as a result. Kimura was onto something, but he didn’t have the courage of his own mathematics. Ernst Mayr was a faker and a poser. Dawkins is just an innumerate moron; he genuinely believes his own nonsense. But I tend to enjoy his books; he could have been a great science fiction writer.
Bill: Is there any major aspect of contemporary evolutionary theory that you came to appreciate and embrace more fully while writing your two recent books on the topic?
Vox: I very much respect the work that the genetic scientists are doing on the various genomes. I suspect they know perfectly well what the implications and inevitable consequences of their work are, but they keep their mouths very carefully shut in order to avoid upsetting the academic apple cart.
Bill: You often use neo-Darwinism as the principal name for the theory you oppose. What exactly do you include under that term: random mutation and natural selection, the broader modern synthesis, neutral and nearly neutral evolution, or every naturalistic account of evolutionary change?
Vox: I use the term correctly. Most evolutionists don’t. Darwinism is natural selection. The Modern Synthesis is Darwinism + Mendelian genetics as per Mayr et al. Neutral and Nearly Neutral Theory are not compatible at all with Neo-Darwinism, were developed more than a decade after the Modern Synthesis, and I describe the attempt to put it all in one big Darwinian box as the Postmodern Poly-thesis. Creationists have already defeated Neo-Darwinism, which is why evolutionists immediately retreat to Kimura and various forms of neutral substitution now. Natural selection proper is dead and they know it. Even Dawkins talks about Evolution by (probably) Natural Selection now.
Bill: Which of those claims does MITTENS directly address, and which require additional arguments? Although we’ve touched on The Frozen Gene already, expand on its role in your critique of evolutionary theory.
Vox: All of them. Probability Zero covers about nine stages of the evolutionist retreat from Moscow to Paris. So far, they’re just starting to touch upon stage three. The only thing that requires more work is refining the actual numbers more precisely, because the original work by Barrick in 2009 was sloppy and inconsistent and the later work by Goode in 2017 wasn’t quite there yet. I’ve broken their collective data down in detail in the MITTENS 3.0 paper and the detailed results are much more clear than in their papers.
Bill: To what degree, if at all, do religious considerations motivate you, not so much in the arguments you make but in the fact that you are making arguments against neo-Darwinism at all? In 2008, you published a book titled The Irrational Atheists, taking on what were then “the New Atheists” — Dawkins, Dennett, Hitchens, and Harris. They all lean heavily on Darwin to support their atheism. Did your religious leanings or your anti-atheistic leanings at all motivate your work criticizing evolution? Briefly, can you state your religious faith, whatever it may be?
Vox: Not at all. My faith is not based upon the historical origins of homo sapiens sapiens or any other species. I believe in material evil and I believe that Jesus Christ is the only thing standing between Man and his enslavement by that evil. I believe in one God, the Father Almighty, Maker of Heaven and Earth, and of all things visible and invisible. And in one Lord Jesus Christ, the Son of God... In sum, I’m a Nicene Creed Christian.
MITTENS and Decisive Disconfirmation
Bill: Philosophers of science have long debated the possibility of a crucial experiment: a single experiment or result that decisively confirms one theory or disconfirms another—the problem being that it’s always possible to shore up a failing theory with auxiliary hypotheses (however ridiculous these might be). Do you regard MITTENS as the mathematical equivalent of a crucial experiment against neo-Darwinism? If so, why?
Vox: Yes. Because if natural selection cannot account for the differences between species, it cannot account for the origin of them.
Bill: What precisely do you believe MITTENS has disconfirmed: natural selection as an important mechanism, its sufficiency for large-scale evolution, the modern synthesis, common descent, or naturalistic evolution as a whole, thus including the Extended Evolutionary Synthesis and The Third Way of Evolution (more on these later in the interview)?
Vox: MITTENS has nuked everything that is evolution-related. Absolutely everything. Ironically, it has also underlined the importance of natural selection as a means of protecting the genome from harmful mutations. In fact, perhaps the worst thing about evolutionary biology is that its century-long focus on trying to somehow salvage Darwinian theory has prevented biologists from studying a very serious potential threat to human genetics, the degradation of the human genome.
Bill: A critic may say that MITTENS tests a package of assumptions: a particular fixation benchmark, a particular generation time, a particular treatment of effective population size, and a particular way of counting genomic differences. How do you show that a failure belongs to neo-Darwinism itself rather than to one or more auxiliary assumptions in your model?
Vox: Because the failure is not based on any of our assumptions, it is based on the core mechanism of neo-Darwinism, the idea that natural selection is capable of producing substantive genetic change in a species.
Bill: MITTENS depends on empirically determined numbers. Please lay out in broad strokes what these numbers are supposed to measure, what the current best estimates of them are, and how they render the needed mutations and their fixation in the human lineage implausible. How accurate are these numbers? Is there any reasonable prospect that further empirical investigation will so alter the estimates on which MITTENS depends that the argument, though now seemingly sound, will ultimately fail? What has to happen with the numbers for it to fail?
Vox: None whatsoever. The LTEE total throughput already includes: Beneficial sweeps (positive selection). Neutral hitchhiking (neutral theory contribution), Parallel fixation (multiple loci sweeping simultaneously), Clonal interference (competing beneficial mutations), Compensatory mutations, Epistatic interactions, Hypermutation (in mutator populations), Frequency-dependent selection (documented in several populations) and Eco-evolutionary dynamics (stable coexisting clades). There is no hidden multiplier left to invoke. The ~1,322 gen/fixation is the empirical output of every single viable polythesistic mechanism running simultaneously at maximum speed under ideal laboratory conditions, except for ILS, obviously, which is negligible. And forget the CHLCA [Chim-Human Last Common Ancestor], there isn’t enough time in the estimated age of the universe for that process to play out.
Bill: Neutral theory holds that the rate of neutral substitution is approximately equal to the neutral mutation rate and, in its simplest form, is largely independent of population size. Why does that result not bypass the fixation bottleneck MITTENS identifies? Is your objection to the mathematics of neutral theory itself, or to its applicability to the genomic differences relevant to human evolution?
Vox: First, all neutral mechanisms are now incorporated into MITTENS 3.0. They always were, since they’re included in the LTEE count, but I never bothered to point that out because the evolutionists couldn’t even grasp that the LTEE numbers were in parallel, so expecting them to understand sweeps and supermutations wasn’t likely. Second, there is a hard population limit on genetic drift within a species of around 10k individuals. The mathematical application of neutral theory in population genetics is fundamentally wrong because Kimura’s famous equation is a steady-state identity and cannot legitimately be utilized as it has been utilized by population geneticists for the last 60 years. I can send you the corrected equation if you like.
Bill: A critic could accept the logic of using experimental evolution as a benchmark yet argue that transferring a bacterial result (as in Richard Lenski’s Long-Term Evolution Experiment) to primates requires scaling for differences in mutation rate and genome size. If those corrections substantially reduce the raw numerical shortfall, does MITTENS remain primarily a mutation-supply argument, or does the burden shift to the population’s capacity to select and fix changes?
Vox: No, and that argument is flat-out wrong. The scaling element doesn’t apply at all, it is entirely irrelevant, because sexual reproductive capacity is the real limit on humans and other non-bacteria. Mutational fixation in humans and other vertebrates can never approach the speed of mutational fixation in bacteria. The defense is dead on arrival. This is exactly what I mean about mathematicians failing to grasp about the context of the math. The critic is demonstrating that he doesn’t even understand the nature of the underlying issue by suggesting that solution to the mathematical problem.
Bill: Population-genetic critics may also object that evolution is not a serial search: many variants arise in parallel, recombination brings them together, and adaptation can draw on standing variation. How does MITTENS account for these processes, and under what conditions could they materially weaken its conclusion?
Vox: MITTENS and Probability Zero already address all of those objections. And as the MITTENS 3.0 paper on the Post-Darwinian Polythesis points out, every single one of these mechanisms has already been incorporated into the core analysis. The polythesis numbers do not improve things for the Neo-Darwinians. At all. The natural selection-only rate rises to 4,615 generations per fixation.
Bill: What observation, derivation, or simulation would lead you to revise MITTENS materially? I do not mean that you would abandon your larger skepticism about evolution, but that you would conclude that this particular argument had failed or been overstated.
Vox: Evidence that a significant percentage of the 205 million base-pairs that were identified as separating humanity from chimpanzees are not actually fixated throughout the entire species of homo sapiens sapiens. This wouldn’t render MITTENS false, in fact, it might even make the case against natural selection et al stronger, but it would definitely call into question our basic understanding of the current genetic situation and require a serious revision.
Bill: Would you be willing to collaborate with a population geneticist—one who shares your skepticism—on an explicit multilocus simulation of the MITTENS argument, with the assumptions and code made public in advance? What would such a test need to include to be fair?
Vox: Certainly. And I don’t care if they share my skepticism or not because the numbers are what they are. The LTEE is already complete through 85,000 generations and the sequenced data for the first 60,000 generations are already publicly available on GitHub. What is needed to be fair is clear and distinct definitions of everything from “beneficial selection” to “hitchhiker.” It would also be very helpful if this hypothetical population geneticist genuinely understands the difference between natural selection and not-natural selection.
Biologists and Mathematical Competence
Bill: You have suggested that biologists are largely innumerate and thus fail to appreciate the mathematical problems confronting evolutionary theory. To what degree do you hold that judgment still and how, if at all, would you qualify it? Do you mean most bench biologists, most public defenders of evolution, or the field’s leading mathematical theorists?
Vox: Every single last one of them. Despite having decades to do so, not a single one of them noticed what was immediately obvious to me within five seconds of first reading a mainstream summary of that 2009 paper on the LTEE.
Bill: R. A. Fisher was both an architect of the modern evolutionary synthesis and one of the preeminent statisticians of the twentieth century. Does he count as a straightforward counterexample to the claim that evolutionary biology is mathematically naive? If not, where do you think Fisher’s mathematics went wrong or ceased to describe biological reality?
Vox: Fisher is a perfect example of the problem. He was a smart guy, and his instincts were sound, but he erroneously focused on the probabilities of the original mutations occurring instead of the far more relevant probabilities of the mutational fixations being permanently established throughout the entire population. Of course, we have the advantage of access to the empirical data that he never had.
Bill: The contemporary field also contains researchers with substantial mathematical credentials. Corina Tarnita earned her doctorate in mathematics at Harvard before moving into evolutionary dynamics. Martin Nowak trained in both biochemistry and mathematics and has spent his career developing mathematical models of evolution. Simon Levin holds a doctorate in mathematics and is a leading theorist of spatial and eco-evolutionary dynamics. Amy Goldberg was trained in mathematics and evolutionary anthropology and works on statistical inference from genomic and archaeological data. How do figures like these affect your general assessment of the field?
Vox: I don’t give an airborne rodent’s posterior for their “substantial mathematical credentials.” Read the report of the 1966 Wistar Symposium. The biologists there had even more impressive credentials, being founders of their fields and future Nobel Prize winners, and none of those credentials sufficed to buy any of them a clue when they had the best mathematicians in the world literally pointing out the problem to them.
Bill: Do you think these researchers fail to see a mathematical contradiction, or do they see the same mathematics and interpret its biological meaning differently?
Vox: They don’t even understand what the math is representing. Seriously, read the Wistar account, it’s hilarious.
Bill: Other scholars occupy the boundary between mathematics and evolutionary biology: L. Mahadevan in applied mathematics and organismic and evolutionary biology, Yun S. Song in statistics and population-genetic inference, and Mariel Vazquez in the topology of DNA. Are such examples exceptional? Is the problem really a shortage of mathematical ability, or is it the assumptions and incentives governing how that ability is developed and deployed?
Vox: I think it’s mostly the latter. I know a number of graduates from one of the world’s most elite math courses. I can’t even read the equations they utilize. But their ability to do very high-level math doesn’t necessarily grant them a solid understanding of the math as it applies to the real world.
Bill: Would the more defensible charge be not that biologists cannot do mathematics, but that biologically unrealistic assumptions (such as about the power of natural selection) can bias them into not drawing the right conclusions from their mathematical models? Might you be willing to restate your argument in this way, and if not, why not?
Vox: No. Because a) they try to argue with the inarguable and b) the things they write are too observably innumerate. For example, in one of his recent books, Richard Dawkins, PhD, Oxford University, burbles on about how 600,000 generations is just an eyeblink. But according to the current scientific consensus, there are an effective 206,000 generations separating humans from proto-chimps. So his rhetorical eyeblink is nearly three times more than he’s got to work with. I think they’re too high on their own rhetoric to bother even thinking about the math.
Critique and Replacement
Bill: Your books concentrate heavily on critique. Do you regard that as sufficient? It’s been said that one never really defeats a system of thought until one has replaced it. William Blake put it this way: “I must Create a System, or be enslav’d by another Man’s; / I will not Reason & Compare: my business is to Create.” Do you have a replacement for the evolutionary mechanisms you reject, and, if so, what is it?
Vox: Of course it’s sufficient. You don’t have to know the correct answer to prove that a false one is false. William Blake is a poet; should we also consult Chuck D and Snoop Doggy Dogg? I don’t have a replacement per se, but the most logical conclusion in the face of the evidence is what I call Intelligent Genetic Manipulation.
Bill: You have used the expression Intelligent Genetic Manipulation. What exactly does IGM assert? Is it a scientific theory, a historical inference, a research program, or a broad name for a family of possible interventions?
Vox: It’s a logical conclusion. We know the evolutionary mechanisms are far too slow to account for what we observe. We know that artificial mechanisms can significantly speed up the process. Ergo, what was proposed as an unintelligent and accidental process is infinitely more likely to be an intelligent and purposeful one, because at least the latter is theoretically possible.
Bill: Does IGM require an intelligence external to terrestrial life, or could organisms themselves possess the relevant intelligence?
Vox: No. This is not a Christian apologetic. It could be God, certainly. Or it could be aliens from another galaxy or demons from another dimension. I expect the truth will prove to be stranger than anyone currently imagines.
Bill: Does it affirm common descent, reject common descent, or remain neutral about ancestry?
Vox: IGM doesn’t affirm anything. It’s more marking “here be dragons” on a part of the map that isn’t filled in yet.
Bill: What mechanism of manipulation do you presently envisage? Are you proposing targeted sequence changes, structural rearrangements, the introduction of genetic modules, alteration of developmental programs, or something else?
Vox: Any and all of the above. Based on some of the observable results, I tend to suspect teenage aliens armed with a very advanced form of Crispr.
Bill: What distinctive genomic signature should IGM produce that would not also be expected from endogenous genome restructuring, biased mutation, horizontal transfer, hybridization, or selection acting on standing variation?
Vox: I think the so-called “fused chromosome” is an obvious candidate. I’d also look for a set of gene-pairs that all look like they come from the same species. If humans were constructed, I’d be looking pretty hard at the porcine genome.
Bill: What would count as evidence against IGM? If every evolutionary outcome can be described after the fact as something an intelligence might have chosen, how does the hypothesis avoid explaining anything and everything?
Vox: Make evolution work somehow. While I do find the idea of drunk aliens making species by rolling 10-sided dice to be amusing, I don’t think the universe is quite that insane. The hypothesis doesn’t really explain anything, it merely exists in the realm of the possible. Which is more than we can say for evolution or any of its random and non-random processes.
Bill: If you had the resources to turn IGM into an empirical research program, what experiment or genomic analysis would you undertake first, and what result would count as a distinctive success for IGM rather than merely another anomaly for neo-Darwinism?
Vox: I’d look deeper into the fused chromosome and look for sets of gene-pairs that line up cleanly with non-ape species. I’d also have some properly credentialed scientists do the right sorts of analyses and papers on the LTEE experiment, the aDNA data [ancient DNA data], and the primate genome projects. I’ve already done some of the work, so I already know most of what they’ll “discover” but I am well aware that no academic scientist will ever cite me. So someone else will have to replicate it.
Bill: Does IGM identify the existence of intelligence only, or can it also tell us something about the intelligence’s aims, capabilities, timing, and mode of action? Where do you believe the mathematics ends and historical interpretation begins?
Vox: Existence only at this point. The math ends at the destruction of the polythesis.
Bill: To come full circle in this section, as a critic of neo-Darwinism, what do you think of adopting the role of a defense attorney whose job is not, like Perry Mason, to identify who did it but merely to create sufficient doubt to defeat the prosecution’s case—the prosecution’s case here being its brief for neo-Darwinism. What are the pros and cons rhetorically of adopting an approach of pure critique?
Vox: That’s what I use the Red Team for. I could provide you with hundreds of pages of their textbook recitations, appeals to credentialed authority, hallucinated math, and so forth. AIs don’t get tired, they don’t get bored, and they have the entire scanned history of the field to summon in defense of the consensus orthodoxy. The only problem with the approach of pure critique is that the human mind abhors an explanatory vacuum. Most people would rather invent something obviously nonsensical than simply admit they don’t know. When AIs do that, we call it hallucination. Perhaps we need a word for when humans do it.
Intelligent Design and Rhetorical Effectiveness
Bill: It seems that you have been reluctant to make common cause with the school of thought known as intelligent design. Yet your IGM seems like something that would fit squarely into intelligent design, which regards itself as a broad tent and whose defining commitment is to an intelligence operative in biology that is not reducible to purely materialistic processes. Yet you have maintained your distance. Why?
Vox: I’ve never been that interested in the subject. As I mentioned previously, my attention to these matters was mostly the result of atheist critics of my book on the New Atheism coming at me on my blog. I’m not a scientist; I don’t really care about science, and I don’t care what scientists consider to be their consensus. I have nothing against them. I’m just not a joiner by nature.
Bill: You have been critical of the intelligent design movement for advancing arguments that you regard as less than compelling, seeing the movement as engaged in an endless dialectic rather than in decisively settling its differences with neo-Darwinism. Which arguments or rhetorical habits do you have chiefly in mind, and what do you think the movement has missed about persuading an intelligent but skeptical audience?
Vox: I wouldn’t say that I’m critical of the ID movement because I don’t know enough about it to have much of an opinion. But what little I’ve seen strikes me as science nerds trying to convince other science nerds using logic because no conclusive evidence is available for either side. From the outside, it looks rather like a game of “You can imagine X, but I can imagine Y!” Just cut to the chase. Their math is obviously wrong, their mechanisms are multiple orders of magnitude too slow to operate, so stop trying to explain complicated chains of logic to people who probably can’t follow it anyhow and will always find ways to handwave it away.
Bill: What, in your view, makes your own case against evolution more compelling than the arguments made by intelligent design’s defenders and advocates? Is the difference the use of hard numerical limits, the narrower target, the rhetoric, the willingness to state a decisive conclusion, or something else?
Vox: The reaction of every single person who encounters it. Consider an analogy. Suppose a man shows up in Times Square and tells you that he walked there from downtown Los Angeles in just five minutes. What is more convincing to a third party: a) pointing out that no human can walk 29,340 miles per hour or b) bending down and engaging in a complicated analysis of the tread of his left shoe to determine whether the current state of the rubber is consistent with having been heavily utilized of late, then standing up and launching into a monologue that begins with the history of rubber tree plantations? Look, I suspect that most of what the ID guys say is more or less correct, because we KNOW evolution never happened. But they haven’t gone about proving they are correct in a comprehensive and conclusive manner that is both easy to grasp and very hard to dispute.
Bill: Why should a skeptical reader not regard MITTENS as another proposed mathematical obstacle that evolutionary biologists will answer by modifying the model?
Vox: Because the modifications required would involve increasing the speed of evolution to the point that we could witness it in real-time. I mean, we’re talking literal X-men here. We’d have to see more FIXATIONS across 8 billion people in a single generation than there are mutations in a single individual at birth. And we just don’t see that.
Bill: You place considerable emphasis on rhetoric. Rhetoric has been defined as the art of persuasion. What rhetorical moves have you found particularly effective at dislodging adherence to neo-Darwinism and persuading people of its falsehood? What advice would you give to proponents of intelligent design to improve their rhetoric, and how would you advise they recast their arguments for greater influence?
Vox: People find it to be humiliating to be identified with something that is obviously stupid and wrong. Neo-Darwinian math is obviously stupid and wrong. So rub their faces in it. Don’t ever let them “what about” and handwave. Anticipate their retreats. Make them do the math every single time. They will not be able to escape the conclusions. And people will laugh at them.
Bill: Concretely, what should the intelligent design community do differently over the next five years if it wants to exert greater scientific and cultural influence, especially in challenging naturalistic theories of evolution?
Vox: Do the math. Stop accepting their frameworks. Think outside the box. Show no mercy.
Bill: Among the intelligent design movement’s current emphases, should it concentrate more on peer-reviewed technical work, popular exposition, institutional development, experimental research, public debate, or some combination? Are there areas in which the movement should say less until it can demonstrate more?
Vox: Forget peer review. It’s trash. Forget the journals, they’re irrelevant. Look at what works and what doesn’t work. If any idea doesn’t convince most people in a reasonable period of time, then drop that line of attack. 95 percent of people are rhetorical communicators. You have about 10 seconds to acquire their attention and they can retain 2-3 things at once. Don’t waste that window of opportunity talking about something they’ve never heard of before and definitely don’t care about.
Bill: If the intelligent design movement has been rhetorically ineffective, is it possible that the difficulty lies partly in the evidential burden rather than merely in presentation? How do you distinguish a message that has been poorly communicated from an argument that has not yet earned assent?
Vox: Certainly. Take the complexity argument. How do you quantify “too complex?” Can you actually quantify it meaningfully or are you just appealing to incredulity? I think you can distinguish between them by the form of the criticism.
Bill: Practically speaking, how much success have your own writings and arguments achieved? What evidence do you have that Probability Zero and The Frozen Gene have changed minds rather than mainly reinforced people who were already skeptical of evolution? Have any working evolutionary biologists or population geneticists publicly revised their position because of MITTENS?
Vox: They were both bestsellers in categories like biology and evolution. PZ has 123 reviews, averages 4.8 stars, and is still in the top 50 in Genetics. I have no such evidence nor have I looked for it. I don’t think many working evolutionary biologists or population geneticists have heard of MITTENS, and they certainly wouldn’t admit it if they had. They don’t even like to engage with you guys, and you all have academic credentials. I don’t think a platinum record, a Best Dance Record award, and three spots on the Billboard Top 40 Club Chart are going to impress them.
Bill: What measure of success in this regard would satisfy you: book sales, public debate, technical rebuttal, published replication, changes in research programs, explicit conversions, or your work appearing in Science and Nature? What are your ambitions here? Are you merely a contrarian stirring the pot, after which you’ll find another pot to stir? Or do you intend to stay with this debate until neo-Darwinism is no longer textbook orthodoxy, which is to say, vanquished?
Vox: I’m already satisfied. An anomaly bothered me; I solved the anomaly to my own satisfaction, and I’m good with that. I don’t think about it at all most of the time. These days, I’m mostly occupied with my Japanese translation work. I’ll revise things as they occur to me, of course. Just this afternoon, I revised MITTENS to incorporate all of the known evolutionary mechanisms, although I was sorry to do so because that wrecked the acronym.
The Extended Evolutionary Synthesis and The Third Way of Evolution
Bill: The Extended Evolutionary Synthesis argues that developmental bias, phenotypic plasticity, niche construction, and forms of inheritance beyond DNA sequence deserve a more central causal role in evolution. Do you regard the EES as a serious correction to neo-Darwinism, an attempt to rescue it, or a relabeling that leaves the essential problem untouched? Would you still have written Probability Zero, or something close to it, if the EES rather than neo-Darwinism were textbook orthodoxy?
Vox: It’s just another attempt to rescue it. Based on what I’ve seen of post-Darwinism to date, I have no doubt that it will prove to be as unviable as Neutral Theory has proved to be.
Bill: EES advocates may agree that organisms do not explore genetic and phenotypic possibilities as an undirected random search. They nevertheless explain the resulting direction through development, plasticity, and organism-environment feedback rather than intelligence. What does MITTENS say to that alternative?
Vox: If they don’t actively address and solve the reproductive limit problems, they’ll get absolutely nowhere.
Bill: The Third Way of Evolution places still greater emphasis on processes such as natural genetic engineering, mobile genetic elements, genome restructuring, symbiogenesis, horizontal transfer, and internally regulated change. Does this work strengthen your critique of standard neo-Darwinism?
Vox: I have never heard that term before. I have no idea what you’re talking about.
Bill: Which Third Way mechanisms do you regard as most important or best supported?
Vox: I don’t think about them at all.
Bill: James Shapiro argues that cells possess regulated biochemical systems capable of restructuring genomes. Why interpret such processes as evidence of Intelligent Genetic Manipulation rather than as natural genetic engineering performed by the cell itself?
Vox: For the same reason we don’t interpret them as black magic performed by the cell itself, presumably.
Bill: Third Way advocates explicitly reject the claim that their work supports intelligent design. Do you think they have stopped one inference too soon, or do you think IGM makes a different empirical claim from theirs?
Vox: I don’t know enough to have an opinion.
Bill: What observation would allow us to decide between endogenous natural genetic engineering and the operation of an external intelligence?
Vox: A copyright notice.
Bill: Large, coordinated genome changes may affect thousands or millions of bases in a small number of events. Does the growing importance of structural variation like this require MITTENS to be revised, counting evolutionary events differently from individual affected bases?
Vox: Not even a little bit. In fact, from this question, it’s clear that whoever is working on this stuff is not looking at the problem in the correct context.
Bill: Could the EES or Third Way absorb the mathematical objections in Probability Zero and The Frozen Gene while retaining a fully naturalistic account of evolution? If not, where exactly is the quantitative barrier separating these different approaches?
Vox: Not a chance, if I’m correct that none of these guys are paying attention to the fixation math. It sounds to me that like RA Fisher, they’re focused on the inputs when it’s the outputs that matter.
Closing Questions
Bill: What is the strongest objection to MITTENS that you have encountered, and why do you believe it ultimately fails?
Vox: I haven’t encountered anything that even begins to successfully refute even the smallest part of it. Every single issue that has been raised or encountered has only made the case stronger and more conclusive. Now, obviously, if the evidence I’ve cited is incorrect and the genetic difference between chimps and humans actually turns out to be 22 base pairs, not 410 million, it’s wrong.
Bill: What is the most important point about Probability Zero that even sympathetic readers tend to misunderstand? What is the most important point that hostile readers tend to misunderstand?
Vox: PZ doesn’t claim that natural selection doesn’t exist or is not important. That evolution isn’t just wrong, but entirely irrelevant, and all of the work that biologists put in trying to demonstrate that everything is consistent with evolution by natural selection would be much better spent on learning more about what looks like the degradation of the human genome over time.
Bill: Suppose a mathematically sophisticated evolutionary biologist accepts your calculations but concludes only that an overly simple model of serial substitutions has failed. What additional argument should move that person from model revision to Intelligent Genetic Manipulation?
Vox: Do the math for every proposed mechanism. He’ll see that the failure isn’t due to an overly simple model. None of the models work. None of the mechanisms work. There wouldn’t be enough time for all of them working in parallel together even if the first proto-chimp appeared at the moment the universe was born.
Bill: At the end of this debate, what would you most like evolutionary biologists, advocates of intelligent design, and undecided readers to investigate for themselves?
Vox: Run the numbers. See for yourself. You’ve got 205 million base pairs to fixate throughout the entire population and 250,000 generations in which to fixate them. On average, how many base-pairs have to fixate throughout a population of eight billion people every single generation in order for all of them to appear in the entire population of Generation 250,001.
From Probability Zero (2nd ed.) on 1966 Wistar Symposium
Chapter 6: The 1966 Meeting of the Minds
Adaptation is the result of natural selection, and natural selection alone.
—Ernst Mayr, Animal Species and Evolution (1963)
In the summer of 1965, at a pair of Sunday afternoon picnics in Geneva, four mathematicians cornered two biologists and refused to let them enjoy their drinks in peace. The mathematicians—Murray Eden, Marcel Schützenberger, Victor Weisskopf, and Stanislaw Ulam—had been discussing what they regarded as serious problems with the Darwinian theory of evolution. The biologists—Martin Kaplan and Hilary Koprowski—found themselves unable to answer the objections being raised. After several hours of what Kaplan would later describe as “heated debate,” the biological contingent proposed a truce of sorts: a formal symposium where the mathematical challenges could be presented systematically, and where a more powerful array of biologists could be assembled to respond to the mathematicians.
That symposium convened on April 25–26, 1966, at the Wistar Institute of Anatomy and Biology in Philadelphia. The proceedings were published the following year as Symposium Monograph Number 5, under the title Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution. Kaplan, writing the preface, was not optimistic about the outcome: “I suspect that instead of a peaceful accord we shall witness the parallel of other peace conferences now underway in Switzerland.”
He was right to be pessimistic. The biologists did not answer the mathematicians. They could not. What makes the Wistar symposium historically significant is not that it resolved the debate, but that it documented the inability of the professional evolutionists to successfully address the mathematical challenges to Neo-Darwinian theory and did so with participants whose credentials could not be dismissed.
The chairman was Sir Peter Medawar, director of the National Institute for Medical Research in London, who would receive the Nobel Prize in Physiology or Medicine just four years later for his work on acquired immunological tolerance. Medawar was not a neutral arbiter; in his opening remarks, he acknowledged that “a pretty widespread sense of dissatisfaction” with neo-Darwinian theory had motivated the conference. He noted that objections had come from three quarters: religious, philosophical, and scientific.
The religious objection that evolution cannot happen without Divine motivation he set aside. The philosophical objection, articulated by Karl Popper, was that neo-Darwinism “has the methodological defect of explaining too much,” rendering it a tautology that made it difficult to imagine any evolutionary episode that could not be somehow explained by it one way or another. It was the scientific objection that chiefly concerned him.
“There are objections made by fellow scientists who feel that, in the current theory, something is missing.”
The mathematicians who would articulate what was missing were not marginal figures in their respective fields. Murray Eden was a professor of electrical engineering at MIT. Stanislaw Ulam held a research position at Los Alamos Scientific Laboratories, where he had co-invented the hydrogen bomb with Edward Teller and made fundamental contributions to the Monte Carlo method, cellular automata, and mathematical biology. Marcel Schützenberger was a professor at the University of Paris who had done pioneering work in combinatorics, formal language theory, and the mathematics of genetics. These were highly intelligent men who understood probability, computation, and the behavior of complex systems. They were fully capable of demonstrating their mastery of all the math involved, as they would subsequently show at the symposium.
On the biological side, the Wistar Institute assembled similarly formidable talent. Ernst Mayr, from Harvard’s Museum of Comparative Zoology, was perhaps the most influential evolutionary biologist of the twentieth century, the architect of the Modern Synthesis, also known as the Neo-Darwinian synthesis, that united Darwinian selection with Mendelian genetics. Richard Lewontin, then at the University of Chicago, was a leading population geneticist who would later become famous for his work on genetic diversity. George Wald, also from Harvard, would win the Nobel Prize the following year for his work on the biochemistry of vision. C.H. Waddington, from the University of Edinburgh, was a developmental biologist who had coined the term “epigenetics.” These were not second-string scientists brought in to serve as punching bags; they were among the very best that the field of evolutionary biology had to offer.
The conference also featured Loren Eiseley, the University of Pennsylvania anthropologist and historian of science, who delivered the introductory address. Eiseley struck a cautionary note, invoking the painter Corot’s habit of working in the early morning mist rather than the harsh clarity of midday: “When one sees things exposed in a certain terrible clarity, one perhaps sees too much. Mystery, and the elusive shadows that are also part of the landscape, disappear.” He suggested that neo-Darwinism might have achieved a false clarity, that its explanatory success might even be “a bit deceptive.” He even reminded the participants that Darwin himself had been troubled by the problems they were about to discuss.
“He used to say that the intricacies of the human eye gave him cold shudders.”
The stage was thus set for a genuine intellectual confrontation. On one side, mathematicians and physicists who believed they had identified fatal flaws in the probabilistic foundations of evolutionary theory. On the other, biologists who had spent their careers building on Darwin’s original theory and forging its synthesis with Mendelian genetics. What followed over the next two days would reveal not a resolution, but an unbridgeable divide—not because the questions were unanswerable, but because the participating biologists could not engage with the mathematics.
The Arguments
The mathematical challenge to Neo-Darwinism rested on a simple observation: the theory requires random mutations to generate functional biological novelty, and natural selection to preserve and propagate that novelty across a population over time. But the space of possible genetic sequences is unimaginably vast, the proportion of functional sequences within that space is vanishingly small, and the time available for the process to take place is insufficient for random search to find what needs to be found. The three principal mathematical critics at Wistar approached this problem from different angles, but their conclusions inevitably converged on the same weakness of the Neo-Darwinian theory.
Murray Eden opened the scientific presentations with a paper titled “Inadequacies of Neo-Darwinian Evolution as a Scientific Theory.” His argument began with a contemplation of the space of all possible proteins. A typical protein consists of a chain of approximately 250 amino acids, drawn from an alphabet of 20 types. The number of all the possible sequences combining those amino acids is therefore approximately twenty raised to the two-hundred-fiftieth power, which is a one followed by 325 zeros. I will spare you the sight of that number filling the page, but consider this to give you a sense of the scale involved.
The total number of atoms in the observable universe is estimated as a one followed by eighty zeros. The space of possible proteins is not merely larger than the physical universe; it is larger than the universe by a factor that is itself also larger than the universe. Eden asked: how much of this space has evolution actually been able to explore?
He calculated an upper bound. Assume a biosphere one centimeter thick covering the entire Earth, filled with cells at a density of a billion billion per cubic centimeter, each containing proteins at a concentration of one ten-thousandth, with each protein molecule lasting an average of one second, over a total span of ten billion years. This yields approximately one followed by fifty-two zeros—ten thousand trillion trillion trillion trillion—protein molecules that could ever have existed. This is an overestimate by any reasonable measure. And yet, compared to the space of all the possible proteins, which you may recall is one followed by 325 zeros, it is effectively zero. It is like a single grain of sand compared to all the beaches of a billion billion worlds.
The neo-Darwinian response to Eden’s challenge was that functional proteins are not randomly distributed, and therefore evolution does not search randomly. The argument runs as follows: natural selection is not a blind process testing proteins at random. It is guided. Start with a working protein. Make a small change, like a single amino acid substitution. If the new protein works better, it spreads through the population and becomes the new starting point. If it works worse, it disappears. Evolution thus moves through sequence space the way a man crosses a river on stepping stones: he never needs to know where all the stones are, only where the next stone is. Each step is local. Each step is tested. And over time, these small, tested steps can carry him from one bank to the other without ever requiring him to leap the whole distance at once.
This is an elegant picture. It is also wrong, for reasons Eden immediately identified.
The stepping-stone model requires that functional proteins be connected by single-step mutations, which means that from any working protein, there exists at least one small change that produces another working protein, and from that one another, and so on, forming a continuous path through sequence space. If the stones are too far apart, the man cannot cross. If most single-step changes destroy function entirely, then evolution cannot step from one working protein to the next. The path becomes a dead end.
Eden examined the evidence. If functional proteins were densely connected in sequence space—if the stepping stones were close together—we would expect to find many proteins that differ dramatically in sequence but perform similar functions. Instead, we find the opposite: proteins with similar functions tend to have similar sequences. The functional proteins that exist cluster in small, isolated regions of sequence space, separated by vast stretches where nothing works. The stones are not close together. They are islands, scattered at random far away from each other across an uncrossable ocean.
Eden then considered the specific case of hemoglobin. The alpha chain contains 141 amino acids and the beta chain contains 146 amino acids. A minimum of 120 point mutations would be required to convert alpha to beta if evolution proceeded from one chain to the other, or from a common ancestor to both, then each step along the path must have been independently viable. But the path requires traversing sequence space through intermediate forms, and Eden calculated that even under generous assumptions about mutation rates and selection coefficients, the time required to do so vastly exceeds the time available.
Stanislaw Ulam approached the problem from a different direction, as he asked the exact same question that started me on my journey toward writing this book fifteen years ago, about “the rate of evolution.” His contribution was to formalize the probability calculations that Eden had sketched out. Ulam introduced explicit parameters of population size, generation time, mutation rate, and most importantly, the frequency of favorable mutations as distinct from general mutations. Since most mutations are neutral or negative, the subset that confer a selectable advantage is very small. Ulam worked through the arithmetic of sequential improvement: if an organism requires a series of mutations, each of which must arise and be fixed throughout the species before the next can be useful, how many generations are required to complete the series?
The astute reader will note this is exactly the same question that independently occurred to me when reading the article about the Chimpanzee-Human Last Common Ancestor in 2019.
Ulam’s answer was extremely discouraging for Neo-Darwinism. Even granting generous assumptions of large populations, short generation times, and high mutation rates, the number of generations required for sequential improvements rapidly exceeds the number of generations available. Ulam noted that the problem becomes acute when one considers that evolution is supposed to have produced not just one single complex adaptation but millions of them, across millions of species, each requiring its own series of coordinated mutations.
Ulam also raised the problem of what he called noise. Contra the confusion of Richard Dawkins and his Weasel program, random mutation is not a directed search toward a pre-established destination, it is a random walk through sequence space. Most of the steps on this walk go nowhere. Many steps go backward, degrading functional sequences that selection had previously constructed. The signal, or the rare beneficial mutation, must somehow be preserved against this constant background of noise. Ulam questioned whether selection was powerful enough to do this, given realistic population sizes and realistic selection coefficients.
Marcel Schützenberger brought the tools of formal language theory and information science to bear on the problem. His paper, “Algorithms and the Neo-Darwinian Theory of Evolution,” introduced a conceptual framework that neither Eden nor Ulam had explicitly employed: the distinction between typographic space and functional space.
Consider, Schützenberger suggested, the genome as a text, as a linear string of characters from a four-letter alphabet. This is the typographic space. Now consider the organism that the genome encodes, the phenotype, with all its structures and functions. This is the functional space. Neo-Darwinism proposes that random changes in the typographic space (the mutations) can produce meaningful changes in the functional space (the phenotypes).
But is this actually plausible?
Schützenberger offered an analogy. Imagine a text written in French that is a grammatical, meaningful paragraph. Now apply random typographic changes: substitute a letter here, delete a letter there, insert a random character elsewhere. What is the probability that these changes will produce another equally grammatical, meaningful French paragraph? The probability is essentially zero. Random changes in typographic space almost never preserve meaning; they reliably destroy it. The space of meaningful texts is a tiny archipelago in a vast ocean of gibberish.
The same logic, Schützenberger argued, applies to genomes. The space of functional genomes—those that encode viable organisms—is a tiny subset of the space of possible sequences. Random changes to a functional genome will almost always produce a non-functional one. The mutation may be “typographically” small (a single nucleotide substitution), but it is “functionally” catastrophic (a broken protein, a dead organism). For neo-Darwinism to work, there must be a correspondence between typographic proximity and functional proximity: small changes in sequence must typically produce small changes in function. But Schützenberger pointed out that no evidence supported this assumption, and there was a considerable amount of evidence that contradicted it.
He pressed the point further. Even if we grant that some mutations are neutral or beneficial, the problem remains: how does a random search through typographic space find the rare sequences that are functional? Selection cannot help until a functional variant exists; it cannot guide the search, only filter the results. The search is blind, and the target is vanishingly small.
To understand what the mathematicians were saying, it helps to think in terms of concrete analogies. Imagine you are trying to find a particular book in a library. This is not a difficult task, if the library is small, and organized, and you know the classification system by which the books are arranged. But now imagine a different scenario: the library is massive and it contains every possible book and every possible arrangement of letters that could fill three hundred pages. Most of these “books” are pure gibberish, random strings of characters signifying nothing. A tiny fraction of them are coherent texts. An even tinier fraction are coherent and useful texts—books that contain accurate histories or compelling stories that you want to read. And your job is to locate one specific useful book, and to find it by pulling random volumes off the shelf without reading the covers.
Or to put it another way, the fact that your 10,000 proverbial monkeys managed, against all odds, to type: “It was the best of times, it was the worst of times” there is absolutely no reason to believe that the very next thing they are going to produce will be a comma, let alone the correctly punctuated phrase: “, it was the age of wisdom,”. There is no reason, and no way for selection to know, that the next character should be a comma, as the next random mutation could just as easily be an ampersand, the number 6, a period, or a capital U with umlauts.
Even the odds against random mutation and natural selection producing the 119 words of the first sentence are absolutely astronomical, and you can definitely forget the idea of it coming up with the entire English text of A Tale of Two Cities before the end of the Kali Yuga or the next five ages after that.
Ulam’s contribution was to put numbers on the problem. Suppose evolution requires a sequence of ten improvements, each of which must be fixed in the population before the next one can be useful. How long does this take? Each mutation must first occur—a function of population size and mutation rate. Then it must spread through the population—a function of the selection coefficient and the number of generations. Ulam worked through the arithmetic and showed that even under optimistic assumptions, the time required grows rapidly. For the thousands of complex adaptations that evolution is supposed to have produced, the total time required dwarfs the age of the Earth.
The mathematicians were not claiming that evolution was impossible in a metaphysical or philosophical sense. They were pointing out that the specific mechanism proposed by neo-Darwinism—random mutation filtered by natural selection—simply did not suffice for the task required of it, given the numbers involved. This is not a philosophical objection or a religious objection. It is a straightforward mathematical claim about rates: the rate of beneficial mutation is far too low, and the rate of fixation is far too slow, to account for the observed complexity of life in the available time.
The biologists at Wistar replied with three papers of their own.
Ernst Mayr, the dean of evolutionary biology, contributed “Evolutionary Challenges to the Mathematical Interpretation of Evolution”—a title that seemed to promise a counter-attack but actually delivered something much closer to a complete change of subject. Mayr’s paper was a catalog of evolutionary phenomena: rapid evolution in house sparrows since their introduction to North America, stasis in horseshoe crabs over hundreds of millions of years, the diversity of cichlid fishes in African lakes. He discussed gene flow, genetic drift, and the founder effect. He emphasized that evolution proceeds at variable rates under variable conditions.
What Mayr did not do at any point was to engage with the mathematical arguments. He did not dispute Eden’s calculation of sequence space. He did not challenge Ulam’s probability estimates. He did not address Schützenberger’s typographic analogy. His paper read as if the mathematical challenges had not even been presented to him. It appears that the father of the Modern Synthesis believed that the appropriate response to a probabilistic math challenge was a collection of natural history anecdotes.
In this, he presaged Dawkins’s The God Delusion. I have always found it remarkable that the famous Oxford biologist genuinely seemed to imagine that a series of unrelated anecdotes that included a story about Alfred Hitchcock driving through Switzerland was a substantive argument against the existence of God.
Richard Lewontin offered a more superficially sophisticated response in “The Principle of Historicity in Evolution.” Lewontin distinguished between deterministic and stochastic models of evolutionary change, and introduced a third category he called “capricious” processes—those in which the outcome depends upon the historical sequence of events. He presented computer simulations showing how gene frequencies wander through state space under fluctuating selection and how populations can end up in very different places depending on the order in which environmental changes occur.
This was technically impressive, particularly given the early state of computing, but it completely missed the point. Lewontin was analyzing the dynamics of gene frequencies under the assumption that mutations exist and selection operates on them. The mathematicians were asking a deeper question about whether the mutations required for complex adaptation can arise in the first place. Lewontin’s models simply assumed what first needed to be proven.
When Schützenberger pressed him on this point during the discussion, by pointing out that the topology of the fitness landscape cannot be taken as given but must itself be explained, Lewontin retreated to a circular argument: the fitness topology is “itself a product of evolution.” But this assumed precisely what was being questioned. You cannot explain how evolution produces complex adaptations by assuming that evolution has already produced the preconditions for complex adaptation.
George Wald’s contribution, “The Problems of Vicarious Selection,” was the most obviously irrelevant of the biological papers. Wald discussed group selection that operates on non-reproducing individuals through their effects on the reproductive success of relatives, such as worker bees that help the hive and elderly humans that help their grandchildren. This was an insightful paper that anticipated later developments in kin selection theory. But it had absolutely nothing to do with the mathematical challenges that were the stated purpose of the symposium! Wald did not even attempt to answer Eden, Ulam, or Schützenberger; he just presented a paper on an entirely different subject that was totally unrelated to the subject.
The discussions following each paper were often more revealing than the papers themselves, and we shall examine them in the next section. But even from the formal presentations, the pattern was clear: the mathematicians raised specific, substantive, and quantitative objections to the core foundations of Neo-Darwinism, and the biologists had nothing to offer in return.
The Discussions
The formal papers at Wistar established the battle lines, but the discussions that followed each presentation revealed the true state of the conflict. It was in these exchanges, often heated, sometimes confused, and occasionally brutal, that the confusion of the biologists and their inability to comprehend the mathematical challenges, much less answer them, became unmistakable. The transcript preserves a remarkable record of intellectual evasion, talking past the point, and the gradual dawning recognition among some of the participants that something had gone badly wrong.
The discussion following Eden’s paper set the tone. Waddington, the developmental biologist, attempted to reframe the problem. Surely, he suggested, the issue was not probability in an abstract sense, but rather, the structure of the fitness landscape. If the landscape had the right properties—if it was smooth rather than rugged, with gentle slopes leading upward from almost any starting point—then selection could guide evolution efficiently through sequence space. Eden’s response was polite but he showed Waddington no mercy: “I must apologize for being so vague on the nature of R,” he said, referring to the fitness function, “but let me say just one thing that led me to this conclusion: it requires a more complete definition of fitness or survival in which case one can discuss the absolute magnitude of the probabilities.”
To put it in plain English, he was saying “show me the math.” Waddington couldn’t do it.
This pattern repeated throughout the symposium. The biologists would offer qualitative objections—surely things were more complicated, surely there were factors the mathematicians had not considered, surely the numbers would work out if only the right adjustments were made—and the mathematicians would ask for the supporting math. And the math was never produced. The biologists simply didn’t have any evidence of any kind to support their blithe assertions.
Mayr’s discussion was particularly revealing. When pressed on the mathematical substance, he retreated to what can only be called the ontological argument from existence: evolution happened, we are here, therefore the mathematics must be wrong. “The very fact that we have this conference,” he observed at one point, “is evidence that evolution has occurred.” One can almost hear the mathematicians sighing. Yes, Professor Mayr, we know we are here, but the question is whether the neo-Darwinian mechanism can account for that. Pointing to the observable fact of biological complexity does not explain how that complexity came to be in the first place.
This is like responding to an engineer who says you couldn’t have crossed the bridge from the other side of the canyon in the last five minutes because there is no bridge, and gesturing at the empty canyon and telling him: “but you can see I’m right here! How do you explain that without a bridge?”
Maybe he can. Maybe he can’t. But regardless, there isn’t a bridge. For all he knows, you were always there.
Mayr also deployed what might be called the argument from variability. Evolution sometimes proceeds rapidly, sometimes slowly; sometimes it produces dramatic change, sometimes stasis. This variability, he rather bizarrely suggested, somehow answered the mathematical objection. But, of course, it did nothing of the kind. The mathematicians were not arguing that evolution proceeds at a constant rate; they were pointing out that even the fastest observed rates of evolution were too slow. Variability within an insufficient range is still insufficient. If you need to drive a thousand miles in a day and your car’s top speed is ten miles per hour, it does not help to point out that sometimes you can push it to twelve.
The discussions also revealed a persistent confusion among the biologists about what, exactly, the mathematicians were claiming. Several times, biologists responded as if the challenge concerned the origins of life, and things like the first self-replicating molecule or the first cell. But Eden, Ulam, and Schützenberger made it explicitly clear that they were not talking about abiogenesis. They were focused on the subsequent evolution of complex adaptations, given that self-replicating life already exists. Their question was not “how did life begin?” but “how did life, having begun, produce eyes and brains and immune systems?” The complete state of confusion by the biologists on this point strongly suggests they had not been able to understand the critical papers to which they were supposedly responding.
Schützenberger proved the most effective interrogator. During Lewontin’s discussion, he focused relentlessly on the question of the genotype-phenotype mapping. Lewontin had presented elegant models of gene frequency dynamics and shown how populations wander through genetic space under fluctuating selection. Schützenberger wanted to know what justified the assumption that the fitness landscape had any particular structure? Lewontin’s models assumed that small genetic changes typically produced small phenotypic changes, assuming that the mapping from genotype to phenotype was, in some sense, continuous. But why should anyone believe this?
Lewontin’s response was circular. The fitness topology, he suggested, was “itself a product of evolution.” But this is precisely what cannot be assumed. The question at hand is whether the structure of sequence space permits evolution to occur at all. Answering that question by asserting that evolution shaped the structure is not an argument; it is an evasion. A man cannot explain how he crossed an uncrossable river by claiming that he used stepping stones that were conveniently placed, and when asked who placed them, replying that he did it himself as he crossed.
Schützenberger pressed further. He pointed out that in the only domain where we have good data on the genotype-phenotype mapping—the genetic code itself, where we know exactly how nucleotide sequences map to amino acid sequences—small typographic changes frequently produce catastrophic functional changes. A single nucleotide substitution can convert a codon specifying one amino acid into a codon specifying a completely different one, or into a stop codon that truncates the protein entirely. The genetic code is not smooth; it is a minefield. Why should anyone assume the higher-level mapping from genes to organisms is any different?
Lewontin had no answer. The transcript records an exchange that borders on the surreal:
“Dr. Schützenberger: I would like to know how you could use a notion like quasi-continuity.”
“Dr. Lewontin: That is a very good question. I don’t know.”
There it is. One of the world’s leading population geneticists, confronted with a direct question about the basic foundations of his field, freely admitting that he does not know how to answer a question about the central assumption on which the entire Neo-Darwinian structure rests. If small genetic changes do not typically produce small phenotypic changes, then hill-climbing does not work, and natural selection cannot do what the theory claims it does.
Lewontin’s candid admission of ignorance should have been a watershed moment. But it was not. The symposium moved on, and the field moved on, and sixty years later, still no one has successfully answered Schützenberger’s question.
The summary discussion, led by Waddington, attempted to paper over the yawning chasm that separated the math from the evolutionary fairy tales. Waddington offered a conciliatory summation: perhaps the mathematicians and biologists were simply talking past each other, perhaps the issues were more subtle than either side appreciated, and perhaps further work would reconcile the competing perspectives. This was a diplomatic summary, but a dishonest one. The mathematicians had made specific claims and asked specific questions. The biologists had not answered them. Pretending that the disagreement was a mere misunderstanding, rather than a comprehensive failure, allowed everyone to go home without acknowledging what had actually happened, and probably contributed to the way in which the landmark symposium has all but vanished from the history of science.
Sixty years have passed, and there has been no reconciliation. And now we know there never will.
To his credit, Sir Peter Medawar seemed to recognize the gravity of the situation. In his occasional interjections throughout the symposium, one detects a growing impatience with the biologists’ relentless evasions. At one point, when a biologist offered yet another qualitative objection without supporting calculations, Medawar asked pointedly whether anyone intended to actually engage with the mathematics. His question hung in the air, unanswered. The answer, obviously, was no, they did not.
What are we to make of Wistar, sixty years on? The most charitable interpretation is that the biologists were unprepared, as if they had come expecting a superficial philosophical debate and suddenly discovered themselves in a mathematical gunfight without ammunition. This isn’t entirely untrue. The Neo-Darwinian synthesis had been constructed by naturalists and geneticists, not by mathematicians. Its founders had not bothered to work out the probability calculations because they assumed, reasonably enough, that their logic was correct and therefore the numbers would eventually work out in support of their conclusions. Therefore, when Eden, Ulam, and Schützenberger actually did the math, the biologists simply weren’t ready for the possibility that the numbers just weren’t there.
The same, quite obviously, is true today. Once the biologists finally had some new mathematical models, as well as some numbers that worked for bacteria, how could they ever have imagined that neither the models nor the numbers would work for things that aren’t bacteria?
This is the reason for the saying: let reason be silent when experience gainsays its conclusions. The same is even more true of math combined with empirical data.
But the less charitable interpretation is much better supported by the transcript as well as the subsequent behavior of the field for the last six decades. The biologists at Wistar were not merely unprepared for the mathematical challenges, they were obviously unwilling to even consider them. When confronted with arguments they could not answer, they blatantly changed the subject. When pressed for calculations, they offered stories about bees. When shown that their assumptions were baseless, they asserted that the assumptions must be correct because the theory required them to be. This is not the behavior of scientists confronting a difficult problem; it is the behavior of dogmatic advocates defending an indefensible position.
The most striking feature of the Wistar transcript is what it does not contain. There is not one single example of a biologist producing one single calculation that even attempts to contradict the mathematicians’ conclusions. Eden claimed that the sequence space was too vast for random search. No one calculated a smaller space. Ulam claimed that the time required for sequential improvements exceeded the time available. No one calculated a shorter time. Schützenberger claimed that random typographic changes could not reliably produce functional variations. No one demonstrated a mechanism by which they could. The biologists asserted, objected, analogized, and hand-waved. They did not do the math.
We can safely expect that this is precisely how the professional biologists and advocates still clinging to the now-disproven theory of Neo-Darwinian natural selection will behave in response to this book.
This asymmetry is the key to understanding Wistar. The mathematicians came with numbers; the biologists came with narratives. In any scientific dispute, numbers will eventually beat narratives, not because numbers are always right, but because numbers can be checked and the equations can be refined, just as I have done repeatedly with regards the various iterations of MITTENS. If Eden’s calculation of sequence space was wrong, a biologist could have shown the error. If Ulam’s probability estimates were incorrect due to being based on faulty assumptions, a biologist could have substituted correct assumptions and derived contrary results. If Schützenberger’s typographic analogy was misleading, a biologist could have presented data on actual genotype-phenotype mappings that refuted it. None of this happened. The mathematicians’ numbers stood unchallenged, because the biologists could not challenge them.
And so the conference ended, not with resolution but with duplicity. The mathematicians had made their case. The biologists had totally failed to refute it. Kaplan’s prediction that Wistar would resemble other failed peace conferences proved accurate. The proceedings were published, occasionally referenced, and gradually forgotten over time. The Neo-Darwinian synthesis rolled on, undisturbed by the mathematical objections that had never been answered. For the next sixty years, biologists continued examining fish color, beak sizes, bee hives, and other irrelevant trivia, solemnly pronounced them “consistent with evolution by natural selection” and accomplished absolutely nothing of scientific or technological value.
But unanswered is not the same as unanswerable. The uncomfortable questions raised at Wistar did not go away because the biologists of 1966 could not address them. Those questions lingered in the scientific darkness awaiting the data that would settle the matter one way or another.
That data has now been gathered.
The day of reckoning has arrived.
The Mathematical Challenge: Then and Now
The mathematicians at Wistar were working blind. They had the math and they had the logic, but they lacked the data to make their proofs conclusive. They had the theoretical framework required to demolish TENS once and for all, with the sequence spaces, the probability calculations, and the information-theoretic constraints, but they lacked the necessary empirical measurements of the key variables. How fast do mutations actually fix in real populations? How long does it actually take for a beneficial change to spread from a single individual to an entire species? Eden, Ulam, and Schützenberger could estimate these parameters from theoretical considerations, and they reached the correct conclusions, but they could not point to observed data because science lacked the necessary technology in 1966.
This lack of empirical data to support their mathematical logic gave the biologists an escape hatch they did not hesitate to take. Perhaps the real-world numbers were more favorable than the theoretical estimates suggested. Perhaps evolution was, somehow, magically, faster than the math predicted.
So what you’re saying is, there’s a chance!
This empirical escape hatch remained open for decades and the biologists continued to avail themselves of it. The Neo-Darwinian synthesis continued to develop, incorporating neutral theory, molecular clocks, and increasingly sophisticated population genetics even though these elements were demolishing the core theory of natural selection from the inside.
What finally changed everything was the advent of whole-genome sequencing and the accumulation of meaningful data on real-world fixation rates. We can now measure, directly, how fast mutations spread through actual populations. We can observe fixation happening in real time, in bacteria with short generation times. We can infer fixation rates in humans by examining genetic markers with known histories. The theoretical estimates that Eden and Ulam worked with have been replaced by empirical observations. And the empirical observations are even worse for Neo-Darwinism and its core mechanism of natural selection than the theoretical estimates were.
The observed rates of mutational fixation, in bacteria, in humans, and in every other form of life, are far too slow to account for the genetic changes required by Neo-Darwinian evolution within the available timeframes.
The mathematicians at Wistar were right all along. They were correct in 1966, when they raised their mathematical challenges to evolution by natural selection, and they are right today, when the data confirms their calculations. The biologists who dismissed them and avoided their challenges were wrong. The defenders of the Modern Synthesis were wrong not because their math was wrong, but because they assumed, without evidence, that the numbers would work out in their favor. But the numbers did not work out. They never could have done.
What Wistar lacked, and what we have now, is empirical closure. In 1966, the biologists could retreat to uncertainty: “We don’t really know the fixation rates in complex organisms. Perhaps they are much faster than in bacteria. Perhaps there are mechanisms we haven’t discovered.”
This retreat is no longer available. We have measured the relevant rates. We have observed the mechanisms. And they can not do what neo-Darwinism requires them to do.
The escape hatches are now welded firmly shut. The mathematical challenges stand strong, supported by incontrovertible evidence. Sixty years after a roomful of distinguished evolutionary biologists failed to answer Eden, Ulam, and Schützenberger, we can say with absolute confidence that they failed because there was never any chance that they could succeed. They were always doomed to fail. The theory of evolution by natural selection is now confirmed to be mathematically impossible due to the observed rates of genetic change, and to a degree that would do a particle physicist proud.
This failure of the theory of evolution by natural selection does not mean that life did not evolve in some manner. What it means is that the mechanism proposed by Neo-Darwinist theory cannot possibly account for the variety of phenotypes observed in nature or the genetic record. Something else is required.
What that something else may be is a question for subsequent chapters and future inquiries. But the first step is to recognize that the question is now entirely open, that despite sixty years of relentless pseudoscientific post-symposium posturing, we can no longer credibly claim to know the origin of the species, or how complex life arose from simpler forms.
The mathematicians knew this in 1966. The evidence proves it today.
Finally finished the whole 'stack. Holy hell! Two HUGE / DEEP minds in a serious back and forth, outlining the general shape of the future of a field. Thank you BOTH for an astonishingly rewarding read!!
Wow does it sound narcissistic, I know, but I presented this critique in nascent form way back in the 1970s in college. Problem was, of course, I didn’t have the data or the math skills, so all I had were logical challenges and rhetoric.
I asked the dyed-in-wool Evolutionists around me if they realized that every current feature of the body resulted from a sequence of mutations, and the only way they’d be here today is if they all could somehow become standard equipment (my feeble attempt to say “fixed in the genome") and do so all at once or in a smooth yet comprehensive sequence.
Basically, I argued that the strong majority of “transitional forms” with new and modified features had to exist so that there was even a chance for the mutations to become standard equipment and therefore effectively heritable. The Evolutionists either didn’t grasp my question or credited everything to “millions of years.” I was powerless to go farther in the argument.
Therefore, I’m delighted to the max that Vox Day has made the powerful math-based argument, which I understand to be essentially:
1. A key problem is that Evolutionists cannot answer what is "the average rate of evolution by natural selection." (That was an earlier clue to me when I asked and they didn’t know this key datum underlying how their theory worked in practice.)
2. Evolutionists typically focus upon the probability of mutations arising rather than of fixations. Yet fixations of the mutations are required for new body plans, physiological components, skeletal frameworks, biochemical processes (with monitoring and negative feedback loops), and all other components and traits, to become the “new species.”
3. If natural selection cannot account for the genetic differences between species, it cannot account for their origin.
4. The calculations show it takes about 1,322 generations per fixation for all proposed evolutionary mechanisms working combined, and about 4,615 to achieve a fixation via natural selection alone.
5. Vox Day counts about 205 million base pairs separating humans from chimpanzees, which are assumed fixed throughout Homo sapiens.
6. Vox Day counts about 206,000 effective generations since the supposed human-chimp last common ancestor.
7. Using the LTEE rates at their most generous, the time to achieve all the fixations between chimp to human would far exceed the generally-accepted 9 million years (max) of time between chimps and humans.
8. Vox Day calculates at LTEE-maximum rates, the required fixations would take longer than the age of the universe.
9. Conclusion: neo-Darwinian Evolution theory is hopelessly underpowered to account for the supposed evolution from chimps to humans. Vox Day also shows why some of the newer alternative theories fail on similar grounds.
I would really like to see the reasoning and the math in a book, but although not math-illiterate, I’d do better with a fairly step-by-step presentation. That would be especially helpful when I’m writing to the public or speaking to non-technical audiences.
I hope someone within or known to the Discovery Institute can take a careful look at Vox Day’s arguments and math, so that facts can be verified and arguments clarified.
That would be a marvelous use of someone’s research time. I wish I had the skill set!!
Congratulations to Vox Day for persevering on this project!
P.S. And just when we think the hardware evolution is impossible, we have to layer on the supposed evolution of behavioral software!
See: https://salvomag.com/article/salvo25/software-for-sex