Dennis McCarthy has absolutely no idea how absolutely hopeless the case has gotten for evolution by natural selection. Believing in evolution is now much more far-fetched and implausible than believing the Earth is flat or that it is held up by a turtle supporting four elephants.
[This was one of my more popular efforts, and I think it provides a nice intro to the evidence supporting evolution:]
I believe this is one of my more important posts—not only because it explains evolution in simple, intuitive terms, making clear why it must be true, but because it directly refutes the core claims of Vox Day’s best-selling book Probability Zero: The Mathematical Possibility of Evolution by Natural Selection. Day’s adherents are now aggressively pushing its claims across the internet, declaring evolution falsified. As far as I am aware, this post is the only thorough and effective rebuttal to its mathematical analyses currently available….
Here is the problem: What Vox Day calculated—(1/20,000)20,000,000 —are the odds that a particular group or a pre-specified list of 20 million mutations (or 20 million mutations in a row) would all become fixed. In other words, his calculation would only be accurate if the human race experienced only 20 million mutations in total over the last 9 million years—and every one of them then became fixed. And, yes, hitting a lottery (with odds 1/20,000) 20 million times in a row would indeed essentially be probability zero.
But our evolutionary history does not require that an exact group of 20 million mutations become fixed—only that some 20 million out of an enormous pool of candidate mutations become fixed.
Here’s the correct analysis. Using Vox Day’s numbers, in a population of 10,000 humans, we would expect, on average, 50,000 new mutations per year. And over the course of 9 million years, this means we would expect:
50,000 x 9 million = 450 billion new mutations altogether.
So out of 450 billion mutations, how many mutations may we expect to achieve fixation? Well, as Vox Day noted, each mutation has a probability of 1/20,000 in becoming fixed.
450 billion x 1/20,000 = 22.5 million fixed mutations.
And that is a pretty close approximation to the 20 million fixed mutations that have been observed. Change the assumptions¹ and the estimate moves. But under Vox’s own assumptions, the result is the opposite of “probability zero”: it’s basically what you’d predict.
First, Dennis was completely, absolutely, and hopelessly wrong about literally everything he said in that original post, because he doesn’t understand big numbers, genetic drift, or how probability works. That’s not his fault, not very many people do. Including, as it turns out, the population geneticists.
But what is his fault is that he didn’t even notice that I had to release a new edition of Probability Zero because it turned out that the “complete mapping of the human and chimpanzee genomes” completed in 2005, and upon which all of the numbers in the book were based, was not, in fact, the complete mapping of the human genome or the chimpanzee genome, neither of which were published until 2025.
And when Yoo et al published the genuinely complete mappings of all the great apes, that 35 million difference between the two species was considerably expanded. This is from the Introduction to the Second Edition.
In fact, the genetic difference between chimps and humans turned out to be 13.8 percent, with 410 million base pairs separating the two lineages since the Chimpanzee-Human Last Common Ancestor. This 10x increase in the number of observed differences between the two genomes has had, as you might expect, a tremendous impact on the arguments I presented in the first edition of this book. In fact, it made them approximately ten times more conclusive.
Not only that, but subsequent work on Kimura’s substitution equation rendered McCarthy’s attempt to escape to Neutral Theory and genetic drift not only highly improbable to the point of effective impossibility, but flatly impossible. I was wrong. Genetic drift in humanity didn’t stop relatively recently, as I calculated in The Frozen Gene. In fact, it hasn’t occurred in humans for millions of years, because no genetic drift can take place in any population that has exceeded 10,000 individuals at any point in its existence.
You can read more about that in my paper The Hard Limits of Fixation Through Genetic Drift, which was written a few months ago after discovering a Portuguese mathematician’s analysis of Kimura’s equation and his identification of the way in which that equation has been systematically misunderstood and misapplied by Kimura and others for the last sixty years.
Kimura’s neutral substitution rate, k = μ, is a steady-state identity: it holds only after a population has held one size for the roughly 4Nₑ generations a neutral allele needs to drift from a single copy to fixation. That transit has never been checked against the number of generations that species lineages have actually had. Checking them yields a hard ceiling on population size, X = (Vₖ + 2)·G/16 — reproductive variance and lineage generations alone, with no mutation rate, no coalescent quantity, and no fitted constant. For a large, long-lived vertebrate the effective ceiling falls to about ten thousand individuals. Above it, a neutral allele’s chance of fixing within the generations its lineage will ever have is not merely small but exponentially small, of order exp(−π²Nₑ/G) — for humans at current size, about one in ten to the seventy-eight-millionth. Humans number more than eight billion, the better part of a million times over the line; the African elephant, endangered at four hundred thousand and falling, is still forty times too abundant for drift to complete to fixation. No vertebrate population is simultaneously large enough to persist as a species and small enough to fix a neutral allele by drift. What substitution these abundant populations show is not produced at their current size; it is residual drainage from the smaller populations they descend from. The domain of k = μ is confined to demographic conditions that no non-endangered species is capable of meeting.
Evolution isn’t just dead, it is absolutely, hopelessly, and completely mathematically impossible. It’s absolutely and observably retarded to continue to believe in evolution, as that is tantamount to admitting that you can’t comprehend basic multiplication or grasp the concept of a number larger than ten thousand. It is more reasonable by far to believe that a black pygmy woman wrote the entire Shakespeare canon in Africa than to believe that evolution by natural selection or genetic drift ever produced one single vertebrate species in the entire history of the planet Earth.
What part of “mathematically impossible” is so hard to understand?
DISCUSS ON SG
