There is a massive difference between the innumerate Evo-Avengers committing one mathematical error after another in trying, and failing, to criticize Probability Zero and the analyses of the possibility of evolution by various means proposed it contains, and a critical review by an actual mathematician, in this case, Dr. Ola Hössjer, a Professor of Mathematical Statistics at Stockholm University
1. Introduction
On September 16, 2026, I wrote a Substack guest-post review of the first edition of Vox Day’s book Probability Zero. In this book, Day presents an argument for the Mathematical Impossibility of The Theory of Evolution by Natural Selection (MITTENS). Since Day updated his argument in the second edition of Probability Zero, I am here writing a more extensive follow-up review based on the second edition of Probability Zero and some other written material of Vox Day.Recall that Vox Day in Probability Zero bases his arguments for the mathematical impossibility of blind evolution on genetic comparisons between humans and chimpanzees. Day claims that the time available since the supposed Chimpanzee-Human Last Common Ancestor (CHLCA) population lived is not enough to explain the genetic differences between humans and chimpanzees today. These arguments are on one hand based on population genetics (the mathematical framework for evolutionary theory) and on the other hand the outcomes of the 60,000 generations Long-Term Evolutionary Experiment (LTEE) for E. coli bacteria, conducted by Richard Lenski and his collaborators.
In the second edition of Probability Zero, Vox Day has updated some estimates of the genetic differences between humans and chimps, based on a recent Nature study from 2025, where the complete genomes of six great ape species, including chimpanzees, were sequenced. These new data made it possible to compare the human and chimpanzee genomes in more detail. Whereas previous comparisons between human and chimp DNA, based on incompletely sequenced data, revealed a 1.2% difference between the two genomes, in this more recent analysis from 2025 a much larger 14% difference was found. Whereas most of this 14% difference refers to insertions, deletions and larger structural variations, the single nucleotide variant (SNV) differences, along those parts of the human and chimpanzee genomes that can be aligned, still account for about 1.2%. Not surprisingly,
these new data with a 14% DNA difference make it even harder to explain the genetic differences between humans and chimps by means of blind evolution.In this second blog post, I will discuss some of the mathematical challenges that the theory of evolution faces. My arguments are not a full review of Day’s work. They are based on that material from the second edition of Probability Zero, the accompanying book The Frozen Gene and several other articles by Vox Day that are relevant for assessing whether blind evolution can explain common ancestry between human and chimps. My first review of Probability Zero was largely positive, and this impression remains after having read more of Day’s work. I agree with many of his conclusions, and the points where we differ are not important for the main arguments. Compared to my first blog post, in this second article I will focus more on mathematical and population genetic details. To keep the text accessible to a wider audience, most of the mathematics appear in footnotes.
2. Basic parameters
I will follow the assumptions in the second edition of Probability Zero, that the genomes of humans and chimps are about 𝐿 = 3 · 109 (3 billion) nucleotides long, that the supposed CHLCA population lived 𝑇 = 6.3 · 106 (6.3 million) years ago, with a generation time of 𝑇𝑔𝑒𝑛 = 25 years after the split along the human lineage, corresponding to 𝐺 = 𝑇𝑔𝑒𝑛 = 252, 000 generations. These generations are partially overlapping, and Day estimates that the fraction of individuals that are replaced in each generation is 𝑑 = 0.8, the so-called turnover rate. This implies that the effective generation length 𝑇𝑔𝑒𝑛 𝑑 = 25 0.8 = 31 of years corresponds to an expected lifetime, and that 𝐺𝑒𝑓𝑓 = 252, 000 · 0.8 = 201,600 effective generations elapsed from the CHLCA population until today. The number of SNV differences between humans and chimps is roughly 1.2% of 3 billion, or 35 million. If half of these SNVs (17.5 million) first appeared as point mutations (single nucleotide mutations) in one individual along the human lineage and then spread to the whole population (so called fixations of these mutations), the required number of fixations along the human lineage for evolutionary theory to explain is 𝐹𝑟𝑒𝑞 = 17.5 million. I will assume that the probability of a point mutation for humans
is 𝜇 = 1.2 · 10−8 per nucleotide and generation (the so-called pointwise mutation rate).In this second blog post, I will mainly concentrate on the 1.2% (or 35 million) SNVs differences between humans and chimps, or the 17.5 million required fixations along the human ancestral lineage. Then at the end I will also comment on the remaining 12.8% genetic differences between the two species. This will reinforce Vox Day’s conclusion that no known mechanism of blind evolution can explain common ancestry between humans and chimpanzees.
Prof. Hössjer has put the whole paper on Zenodo, where you can read the whole thing if you are mathematically inclined. But, I can assure both you and the skeptical biologists and population geneticists, he is far from the only mathematician to have critically reviewed my work. In addition to providing early version of both PZ and TFG to ten mathematicians and physicists prior to the publication of the first editions, none of whom were Prof. Hössjer, with whom I was hitherto unfamiliar, I’ve recently received a 36-page paper from one of those pre-release reviewers who is presently checking some of my post-PZ math on relictation and the mathematical boundaries of Kimura’s time equation.
I hasten to point out that none of this means there aren’t legitimate mathematical challenges to my assertion of evolution’s mathematical impossibility. There are, they will be presented, they must be analyzed in full, and they will be. Like any good iterative designer, I’m methodically working through those potential challenges at increasingly higher resolution and greater levels of detail as the various equations are better understood and refined. Of course, it only falls to me to do so because the scientists in the relevant fields have proven to be too innumerate to grasp the obvious legitimacy of even the earliest, crudest forms of the proof.
The demonstration of mathematical impossibility may yet be wrong. It is not, and it can never be, irrelevant.
Is it still theoretically possible that I’m wrong and that the post-modern polythesis will somehow survive my mathematical analysis? In theory, yes. I can currently construct one analogous model based on real empirical evidence that may or may not be directly applicable to the chimp-human divergence that would, in theory, produce enough base pairs to satisfy the observed shortfall. But only one, while all of the other constructed models point the other direction, and we now have an entire matrix of comprehensive divergences that the polythesis model has to somehow satisfy perfectly to even hope to remain in play.
It’s a little ironic that all of this work will be performed and published outside the relevant scientific fields, but that’s what happens when the evolutionary biologists are too lazy and innumerate to join in all the big boy games.