Category: Uncategorized

They Didn’t Read the Book

A regular here jumped on the grenade for everyone who, like myself, lacked the fortitude to sit through three-and-a-half hours of two people discussing a book that neither of them had bothered to read, and thereby gleaned the following information from the recent video by Dr. Erika and Dr. Hanson.

  • Erika: “Will doesn’t include in his presentation how d is actually calculated, but I suspected it was probably in Vox’s book. So I just texted one of my several friends who are reading through the book right now and sort of yucking it up with me via text messages over it, and I was like, ‘Hey, does anybody have the definition for his selection coefficient d?’ And my friend said that on page 153, in the chapter titled ‘The Overlapping Generations Problem,’ d is defined as the fraction of the population replaced per time unit…”
  • Dr. Hanson: “So because of all of that, I don’t foresee any population geneticist, one, even knowing who Vox is, or two, being like bothering with ever reading a book that’s probably mostly written by AI.”
  • Erika: “That’s just based off of what Will presented to us. Of course, Vox has a book floating around out there. I wonder—I wonder if maybe I should read it and then, like, make fun of it with some of my friends? Like, go through some of the more in-depth claims, or I should say extraneous claims, that exist in that book. That might be fun…”
  • Erika: “There’s no doubt in my mind that Vox is going to respond to this video, and he’s probably going to say something to the tune of, ‘You didn’t answer all of the points that I made in my book. All you did was address Will Duffy’s points.’ And it’s like, yes, that was the priority of this video.”
  • Erika: “It’s also worth noting that in some places he has complained that people who criticize him actually haven’t read his book… So all of those things together put an evil little idea in my head. I was talking to Zach and a couple other of my friends who have relevant formal training in areas in and surrounding this exact topic, and we kind of just thought to ourselves, ‘Man, what if we just did read the book? What if we read it and then got together and critiqued the book as a whole, and we can each bring our favorite parts of the book to this round table together and we can sort of atomize it?’ …You can expect that to come within a couple of weeks, a week maybe, of this video. We’re just going to actually go through Probability Zero, and it’s probably going to take a long time.”

Interesting. I was pretty confident that Erika hadn’t read the book, but I was under the impression that Dr. Hanson had read the 2nd edition, specifically, on the basis of some of his comments. Believe it or not, I have no problem whatsoever with evolutionists attempting to critique Probability Zero or The Frozen Gene without bothering to read them first. It’s their credibility and their careers on the line, not mine. And they certainly make my job as the author significantly easier, because I have neither the reason nor the responsibility to respond to any critique by anyone who hasn’t read the book he is purporting to critique and isn’t even addressing the relevant details.

So that’s my initial response to their 210 minutes of not discussing my book: they didn’t read it and they didn’t discuss it, they simply discussed what they imagined it must be. Although perhaps someone should warn Erika what happened to the last female critic who thought that reading through one of my books and critiquing it would be fun.

But talking about the book without reading it is absolutely fine, so long as that’s made clear, which both of them obviously did. I have never paid attention to their videos before and they have yet to give me any reason to start doing so. I might as reasonably respond by talking about The Refutation of Kant and providing proof of the amphiboly in das Ding an sich, as that’s another of my books they also haven’t read. Or, for that matter, the Amorran formations in A Throne of Bones.

This isn’t to say that their video is worthless. To the contrary, it gives us a very clear picture of the current state of the field’s mainstream understanding of itself as well as how it is unprepared to defend this particular front. Now, perhaps this evolutionary round table Erika is assembling will do better. It certainly should do better on the basis of actually having a target at which to shoot. And when I respond, I will respond in detail to every material criticism of my mathematical disproof of evolution by any, all, and every mechanism, including natural selection, raised in both of the videos. While I am aware that Erika and Dr. Hanson spent some time discussing me on a personal level, I didn’t even bother reading that part of the transcript.

I’ve been getting attacked personally for 25 years now. I don’t care. I’m a former Wax Trax! recording artist and my own fans and Vile Faceless Minions refer to me as Supreme Dark Lord. So I think the mainstream narrative of me being a Very Bad Man has been sufficiently established that we can all just take it as given and get on with the substantive discussion. I mean, what part of “downright evil” is hard to understand?

  • “Vox Day is one sick puppy.” —Dr. P.Z. Myers, PhD
  • “Vox Day is a fascist mega-dickbag and less a human being than one long sequence of junk DNA.” —Dr. Phil Sandifer, PhD
  • “I consider Vox Day one step, either direction, from certifiable.” —Mike Resnick, science fiction author, 38-time Hugo Award nominee
  • “I think I have made my disgust with Vox Day and his Rabid Puppies clear.” —George R. R. Martin, fantasy author, 19-time Hugo Award nominee
  • “Vox Day rises all the way to ‘downright evil’. ” —Patrick Nielsen Hayden, Manager of Science Fiction, Tor Books, 15-time Hugo Award nominee
  • “Vox Day is a real bigoted shithole of a human being.” —John Scalzi, three-time SFWA President and science fiction author, 9-time Hugo nominee
  • “Vox Day and his followers made it impossible for me to remain silent, keep calm, and carry on.” —Connie Willis, science fiction author, 24-time Hugo Award nominee
  • “The real burning question is, ‘what will Vox Day attack next?’” —Charles Stross, science fiction author, 15-time Hugo Award nominee

Well, at least we have the answer to Charles Stross’s question, as St. Darwin is truly dead. And thanks to one of my readers, we can even add to the collection:

  • “Vox Day is one of the worst people I have covered in this channel. He is unambiguously a raging racist, giga-misogynist and clinical narcissist (no hyperbole).”—Erika Whatever her name is, Youtuber and armchair psychiatrist

My only thought is that she never covered Richard Dawkins, Stephen Gould, Steven Pinker, Ed Boyden, Marc Hauser, Martin Nowak, David Sloan Wilson, George Church, or any of the other big-name evolutionists who used to hang out with Jeffrey Epstein? Well, I suppose she did say only “one of the worst”. I’ll just have to do better.

Despite being a recently diagnosed clinical narcissist, I don’t need their attention. I never sent out a single press release for the book. I’ve done zero book signings and no public events. There was no book launch party. You can even see from my publication history that I almost entirely stopped paying attention to evolution from February to September. So whether they engage or not makes very little difference to me. If and when they do, I’ll address the critiques and any mistakes they identify. If they don’t, then the work stands as it is until someone can come along and actually show that it doesn’t.

DISCUSS ON SG

Back to the 70s

It’s not often that I find myself wishing I was back in Minnesota. But seeing College GameDay there, watching the Michigan game and seeing the Golden Gophers reclaim the Little Brown Jug at home for the first time since 1977 definitely felt like a heartwarming blast from the past. I didn’t attend that game, but I attended several around that time – one game against Indiana is particularly strong in my memory – and it was so long ago that Tony Dungy, the retired Super Bowl-winning coach of the Colts and the Buccaneers, was the Gophers’ quarterback at the time.

Anyhow, congrats to all the Gophers and Gophers alumni for defeating the Wolverines at their new home.

College football is so much better with a) the playoffs, b) NIL preventing the big boys from stocking all the best players four-deep and c) all the new outdoor stadiums. I’m watching it again for the first time in decades.

And now that the Gophers are reclaiming the Little Brown Jug, can another Super Bowl appearance for the Vikings be far behind? Young Nasty University does look a lot like the Purple People Eaters of yore.

DISCUSS ON SG

PZ on PZ

Hey, the old wannabe Fifth Horseman of the New Atheism is back! They’re mostly dead now and he’s been irrelevant for at least a decade, but apparently if there is one thing that is going to wake him up and get that weary old ticker thumping again, it’s the unholy marriage of William Dembski and myself. Which is really a terribly dramatic way to describe an interview, but whatever.

Vox has an undergraduate degree in economics and East Asian studies from Bucknell University, a small private liberal arts college. He does not have a science degree, and by his own admission he did not exactly apply himself to his studies….Any student who tells me that their achievement was developing an intuitive grasp of a subject is bullshitting me. Then he confirms it: Vox Day was a slacker who learned nothing in college.

He wishes he dropped out after his first semester, he seldom went to class, and didn’t bother reading the textbook — and he probably thinks that means he must have been a genius, rather than a lazy goof. It doesn’t speak well of Bucknell or his professors that they decided to get rid of him by putting him in a program of independent studies, rather than flunking him. I sorta sympathize with them. You get attached to your students and want to help them succeed, so you coach them through and design a limited curriculum that matches their abilities to allow them to finish the program. I guess we’re doing the students no favor if that just means their ego is stoked.

So if he has no background in or comprehension of biology, how did he write MITTENS? He explains it all: Apparently the proper way to use AI is to hammer its outputs through multiple iterations until it tells you the answer you want to hear.

He really does think he has disproven all of evolution all by himself, with a paper that contains all of 11 citations (a number I’d find unacceptable in an undergrad student paper that was much more narrow in its scope). Even worse, 7 of those citations are to the LTEE, and contradict his conclusions, and 2 are to ape genome sequencing papers whose authors would be surprised to learn how their work is being distorted. At least he has 2 that reinforce his argument, sorta, but they’re both also written by Vox Day.

So this is an argument made by an unqualified buffoon who churned it out of a battery of AIs, written with negligible knowledge of the scientific literature, and rubber-stamped by a couple of biased dorks from the Discovery Institute.

I’m definitely archiving this, because I very much want to have PZ on the record stating that I did everything by myself, with only a battery of AIs and an unacceptable number citations in an undergrad student paper. It’s going to be really fun to know that he is struggling to accept the reality that the man he has sincerely believed to be “an unqualified buffoon” has always been a world-class genius of historic levels, far more significant in the course of human intellectual development than sweet St. Darwin himself, who somehow managed to cripple Man’s correct understanding of his own origins for 167 years and counting.

Science was born free and everywhere it is in chains. I can’t do much about physics or sociology, but at least I can set the geneticists and biologists free.

The thing that I am finding so terribly amusing about all of this is that these scientific charlatans are so uncurious and so prone to posturing and resting on their credentials that it literally never occurs to them that I am nothing like them. It never occurs to them that maybe my professors weren’t stroking my ego, or making sure a lazy goof got his degree, but rather, catering to a student they regarded as “a brilliant fuckup”. Which is a direct quote from my favorite professor, by the way.

It never occurs to them to wonder why I wish I had dropped out of college. Jensen Huang knows. More than anyone, he’s the primary beneficiary of my return to university. But if you don’t understand why, that’s another story for another day.

And most of all, it never occurs to them that anyone might use AI creatively in a productive manner, one that observably augments human intelligence and makes things possible that were not previously possible. I’m not, of course, referring to the disproof of evolution by natural selection, since that was a piece of cake so obvious that I cannot believe anyone with half a brain capable of performing long division is still seriously trying to defend it. I never needed any AI assistance or augmentation for that.

Being the first man in history to solve the Agrippan Trilemma and other little puzzles like the Hard Problem of Consciousness, to say nothing of refuting Kant’s critique of pure reason, on the other hand, definitely required a bit of an artificial boost.

Anyhow, I just want PZ to remember every little thing he ever said about me in this regard as the horror gradually dawns in him as more and more people start actually doing the relevant math and confirming it for themselves. Because I won’t. I don’t think about him at all. I genuinely thought Pharyngula shut down years ago.

And here’s the more important thing for him to contemplate. If he was wrong about me, well, that’s going to sting a little. But it’s not really that big a deal in the cosmic scheme of things. But if he was wrong about Jesus Christ, on the other hand, that’s a much more serious problem. So if the former turns out to be true, however unlikely, maybe take another, closer, look at the latter.

UPDATE: Oh, Sweet St. Kimura, PZ doesn’t know the difference between a mutation and a fixation.

  • COMMENTER: Bill Dumbski [sic] is a nobody, full of himself. Every person born has about 100 mutations that neither of their parents had. But being willfully ignorant does have its advantages.
  • PZ: No, no — according to Vox, we are born with at most 1 mutation, and it’s going to be shared with the entire population, eventually. Don’t you know math?

DISCUSS ON SG

The Scholars Revolt

All across France, schools are burning due to scholarly unrest over the quality of their educations. Or something.

High schools across France have closed, thousands of teenagers have been arrested, and hundreds of people have suffered injuries as unrest over conditions in the lycée system has spread and erupted into violence in recent days. Roughly 3,000 people have been arrested since the protests began nearly two weeks ago outside of Paris, with nearly 2,000 being detained on Thursday alone, the French interior ministry announced.

As demonstrations have at times escalated into violent clashes, 170 students and 65 school staff members have been injured, according to education minister Édouard Geffray. Nearly 400 police officers have also reportedly suffered injuries.

And the protests showed no signs of abating on Friday, when roughly 900 demonstrations took place around France, according to police. More than 500 French schools remained closed as students set fires, blockaded schools, and clashed with riot police around the country.

Oh, those unruly French! Truly, somethings just never change… What a pity no one can discern the reason for this scholarly dissatisfaction!

DISCUSS ON SG

Better than a PhD

If you spend the next four minutes watching the video at the link, you will know more about the actual state of evolutionary science than pretty much every single evolutionary biologist and population geneticist on the planet, regardless of how many years they have spent obtaining their credentials and working in the field. You will definitely know more factual information about the subject than Richard Dawkins, Sam Harris, and the earthly remains of Daniel Dennett combined.

I’m neither exaggerating nor joking. That’s how dreadful the state of the science is. Erika and her pet population geneticists would learn more from that four minutes of video than everything they have learned in however many years of graduate education. Besides, this is about their level. They’re certainly not going to read the book, let alone the relevant papers.

Please don’t forget to pick up your complimentary PhD in Evolutionary Biology on the way out.

DISCUSS ON SG

Sign Up Now for Unlimited

Over the last seven weeks, Castalia House has translated approximately 10 million words from over 100 foreign language works into English. Most of these works have never before been translated into English, including the complete ouvres of major authors like Benito Perez Galdos, Eiji Yoshikawa, Zénaïde Fleuriot, Naoki Sanjugo, and Nomoro Kido. They also include never-before-seen military analyses of historic Japanese battles like Sekigahara, Nagashino, and the Korean Campaign published by the General Staff of the Imperial Japanese Army, to say nothing of never-before-translated biographies of historic Japanese figures and long-lost Spanish Church histories.

At some point in the next two weeks, Castalia House will launch Castalia Unlimited, which is designed to be a significant improvement on Kindle Unlimited. It is not a store. We will not offer single books for sale there and we are not attempting to compete with Amazon. What we will offer is a steady and relentless supply of high-quality literature from the public domain of every major literary language on Earth, including English, although the widespread availability from free sites like Project Gutenberg is why we will not focus on English originals. And while we had no intention of making it exclusive, due to the new Amazon KDP publishing limits, we anticipate a growing number of books that will be exclusively available at CU.

You can now sign up and register for an account at Castalia Unlimited. All you need to do is provide a username, and email address, and a password, and we’ll send you back an email to confirm your email address. When the site goes live, you’ll be the first to be notified. And while I’m not going to say anything more about it at the moment, I will say to be sure to sign up if you’re a subscriber to Library, History, Libraria, Cathedra, or Chateau… you are not likely to regret it.

Also, be sure to check your spam and your junk folders if the confirmation email hasn’t arrived within five minutes or so. And finally, not only are print editions coming, they are already here.

Never before translated, coming soon to bookstores near you.

DISCUSS ON SG

Someone Has a Sense of Humor

That, or I really need to place more blind trust in my mathematical intuition. Thus spake Red Team Grok: The ~1,580–1,590 generations per fixation (pooled, strict whole-population definition) is the appropriate figure for “normal” LTEE populations. That is the rate observed in populations that still have intact DNA-repair systems.

The all-population rate of ~132 generations per fixation is real, but it is dominated by the seven hypermutator populations. Those populations have broken mismatch repair (or oxidative-damage repair), are accumulating mutations at ~100× the ancestral rate, show the genomic decay documented by Couce et al., and in several cases exhibit intervals of net loss of high-frequency alleles. They are not healthy, steady-state evolving populations; they are populations that have traded genome maintenance for short-term mutational supply. Calling their throughput “the fastest experimental rate ever measured” without strong qualification is therefore misleading if the intended comparison is to ordinary evolutionary processes.

This is why the source papers (and your own earlier summaries) routinely separated or excluded the hypermutators when stating a representative rate. The corrected data do not change that logic; they simply make the separation cleaner.

Recommended reporting:

  • Primary: Non-mutator pooled rate ≈ 1,587 generations per whole-population fixation (5 populations, 189 fixations).
    Secondary / completeness: When hypermutators are included, the overall rate falls to ~132 generations per fixation (12 populations, 5,496 fixations). This figure is driven by populations with defective DNA repair and should not be treated as a general benchmark for intact systems.
  • That framing is accurate, consistent with prior literature practice, and avoids inflating the apparent speed of ordinary fixation by averaging in genomic-cancer lineages.

The data tables and the analysis are both available at Zenodo: Fixation in the LTEE: Whole-Population Fixation Counts at 500-Generation Resolution

DISCUSS ON SG

Repent, Richard

Richard Dawkins put his faith in Charles Darwin, not in Jesus Christ. It wasn’t just the wrong bet, it was a very foolish one:

On Oct 2 it will be 20 years since The God Delusion was published. Coincidentally, books by Sam Harris, Dan Dennett, and Christopher Hitchens came out at around the same time. This led someone (not any of the four of us) to invent “New Atheism” as a “project”. We wrote our books independently without collusion, and as far as we were concerned there was no such project. It was sad that the old arguments needed to be restated. Even sadder, they still need to be re-stated, in 2026.

They don’t need to be restated. They were demolished in 2009 by The Irrational Atheist. Ever notice that no one claims religion causes war anymore, Richard? Yeah, that wasn’t The New York Times or Nature. They were literally quoting me. Ever notice that no one cites the Red State argument anymore? Also me.

Not all physicists accept the premise of the fine-tuning argument. See Victor Stenger’s The Fallacy of Fine-Tuning. Some suggest that it works only if you twiddle one knob at a time. If you turn several knobs together, there could be a very large number of combinations of settings that yield biologically promising universes.

Other physicists, including Martin Rees himself, point out that the currently favoured theory of universe inflation predicts the existence of a multiverse embracing huge numbers of universes. A small minority of these universes happen to have their knobs set to biology-favouring values. We obviously have to be sitting in one of that minority, because here we are – the so-called anthropic principle.

As a biologist, I lack authority to enter this debate. I agree with Paley that the biological argument from design was the big one. Darwin’s solution has correspondingly huge significance. It inspires confidence that the relatively minor cosmological version will in due course yield.

Darwin’s solution has no significance. Darwin is irrelevant. It’s now logically, mathematically, and empirically proven that evolution by natural selection never happened. It couldn’t have ever happened and it didn’t happen. The scientific case is closed, Richard Dawkins just doesn’t know it yet.

Christians don’t just know some hymns, or think it might be a rather nice idea if people loved their neighbours a bit more. Christians believe. They believe that a man called Jesus died to redeem our sins and walked three days later. If, like me, you reject such tosh, you are not a Christian.

I pay God the compliment of taking the hypothesis of his existence seriously. If verified, God would be the most exciting hypothesis in the entire history of science. A universe conceived and designed by a superhuman intelligence would be a totally different kind of universe from the one which, in my opinion, we actually inhabit. At a stroke, the whole of science would have to be rewritten, from the bottom up.

That “tosh” is exactly what we believe. And rewriting the whole of science is exactly what we’re doing. Starting with evolutionary biology.

DISCUSS ON SG

Snikker-Snak

Since Erika isn’t a sufficiently big girl to defend her own field of science from a game designer with no academic or scientific credentials at all, I’m reliably informed that she’s going to have DOCTOR ZACH HANCOCK white-knight for her and offer his no doubt Very Serious and Very Credentialed Critique of Probability Zero.

That’s right, THE DOCTOR. ZACH HANCOCK! I’m sure you’re all aquiver with dread and awe.

And since Dr. Hancock, like the intrepid Brian, is a POPULATION GENETICIST, it should be very amusing to watch him demonstrate that he doesn’t know the first thing about the math that serves as the sand beneath his science. But I’m anticipating we’re going to hear all about ISLANDS and DEMES and STEPPING STONES, which should not only offer us an expanded vocabulary, but entirely new ways of amusing ourselves at the expense of midwits in labcoats who never realized there was rather more to understanding science than memorizing the textbook.

It truly amazes me that these people never, ever, stop to consider who and what they’re dealing with. First, they claim that I’m a white supremacist… and they think that’s some sort of sign that I don’t know the math? Correct me if I’m wrong, but I seem to recall a certain group of Aryan supremacists who were very, very good with math, so much so that the US science community imported a whole collection of them in the middle of the 20th Century for one reason or another.

Second, they know I’m a game designer. Not only that, but a game designer who is very heavily involved with artificial intelligence. And yet, they keep being surprised that I know what they’re going to say on the subject before they say it. Which is amusing, considering that I can already tell what Zach Hanson will have for lunch next Thursday with a 87 percent chance of success.

If you doubt that these credentialed scientists are really as dumb and innumerate as I’ve been pointing out, consider this lunatic trying to correct someone who is explaining the concept of an AVERAGE to him. Like JFG, he literally doesn’t understand what an AVERAGE RATE is.

“When dealing with average rates, it really doesn’t matter if particular fixations happen parallel or in sequence. We could have 25 fixations in sequence over a timeframe, or we could have 20 parallel and five in sequence over the same timeframe. The average is the same “

This is mathematically false.

No. It’s not mathematically false. It’s not false at all. It’s literally what an average rate means!

If you drove ten miles and it took you an hour, then it makes no difference if you were driving sixty miles an hour part of the time or you were stopped part of the time, or even if you turned around and drove back home to pick up something you forgot. The AVERAGE RATE of 10 MPH covers all of those possibilites and more.

And don’t forget, we already know how many of those fixations happened in parallel and how many did not because the data is available in 500-generation slices. For example, Ara+2 had 66 fixations in 60,000 generations. At 909 generations per fixation, this was one of the fastest still-viable populations. There were 14 fixation events and every single one of them was sequential. The smallest gap between fixations was 1,500 generations. The largest gap was 9,500 generations.

So there were zero parallel fixations in 60,000 generations. None whatsoever. That’s not theory. That’s the actual empirical evidence from the most famous experiment in evolution. And to answer the obvious question how you can get 66 fixations out of 14 fixation events, the answer is simple: sweeps. Each selective serial fixation carried along an average of 5.3 neutral mutations to fixation with it.

I ran the numbers across all 12 of the populations to make sure this wasn’t an anomaly. There were ZERO parallel events, none in any of the five viable populations and none in the seven hypermutating populations. The smallest gap between fixation events was the 1,500 generations in Ara+2. The largest gap was 10,500 generations in Ara-6.

In fact, what we’re seeing here is empirical evidence for what I mathematically demonstrated with the Bernoulli Barrier. Which means the third edition of Probability Zero is going to be a doozy.

DISCUSS ON SG

The Education of a Population Geneticist

I think it’s funny that Brian Mansfield thinks I’m afraid to discuss evolution with anyone. Fine, Brian, you are herewith challenged to either a) a written debate on population genetics and neutral theory, or alternatively b) a discussion on Rebekah Davis’s channel. We’ll see who lacks what you describe as “the balls”.

“Vox Day tries to refute this on his web site but doesn’t have the balls to do it here.“

My account has been blocked on YouTube for seven years. For me to create a new account and post there would be a violation of their terms. I’m also personally banned from setting foot on Google’s Mountain View campus as it happens. So I will refute his woefully outdated critique and attempt to bring him up to date on the state of the art of his own field here. Anyone reading this is welcome to post this in its entirety in response to his comment.

“The only Kimura ‘equation’ I have mentioned is the probability of fixation of a new neutral allele — 1/2N — so he seems very confused.”

Yes, and that’s the problem. 1/2N is the fixation probability. It tells you the chance that a given neutral mutation will eventually fix, given unlimited time. It contains no time variable. It says nothing about when. The Kimura equation Brian should have used is Kimura’s equation for fixation time: 4Nₑ generations for a neutral allele, or t ≈ (2/s) × ln(2Nₑ) for a beneficial one. Without the time equation, his calculation has no temporal constraint. The fixation time equation is the Kimura equation that Brian omitted, and that’s the equation that produces the result he calls “ludicrous” because it’s the one that forces time back into a calculation from which it was omitted.

Everything Brian says depends upon k = μ applying, and he has obviously never examined the domain conditions under which that identity actually applies. It doesn’t apply over changes in either time or population. It also doesn’t apply to any sexually-reproducing species above approximately 10,000 census. Even setting aside the mathematical domain problem, comparing Bergeron’s (2023) pedigree-measured mammalian mutation rate against the required substitution rate from Yoo et al. (2025) gives k = 32.3μ, not k = μ. Brian doesn’t know the related literature and he hasn’t done the relevant math.

“For Vox Day to say that ‘genetic drift doesn’t happen in any population over 10,000’ is incomprehensibly stupid. Genetic drift happens in every population and his claim otherwise is mystifying. Population size only affects which alleles are effectively neutral.”

It’s only mystifying to those who don’t understand the relevant math and haven’t taken the limits of reproduction into account. What Brian is revealing here is that he doesn’t understand population genetics at all beyond the idealized textbook version. Population size absolutely imposes a hard limit on genetic drift. What he’s doing here is appealing to k = μ again, failing to realize it has been mathematically, empirically, and logically proven to be inapplicable to any real-world population, across more than 100 species.

“Empirically, each human zygote has about 100 new mutations. The question is how many of these are expected to drift neutrally to fixation — that is, they are neutral and they segregate independently of a selected variant.”

The question is not how many mutations are expected to appear or to drift to fixation under irrelevant steady-state assumptions. The question is how many can actually complete the journey to population-wide ubiquity within the available generations, given the actual population size and its history. Expected value under k = μ and realized completions under finite time are totally different quantities. Brian is treating the first as though it answers the second.

“If even just 2 of these 100 are neutral — which is certainly way under the actual proportion — then in a population of size N there are about 2×N new neutral alleles introduced each generation. The probability of fixation of each one is 1/2N. So, the expectation is that there will be on average 1 neutral fixation every generation if just 2% of new mutations are neutral.”

This is k = μ. Input rate × fixation probability = expected output. The algebra is correct. It is also an asymptotic steady-state identity that holds only when the fixation pipeline has been running at constant population size for at least 4Nₑ generations. For humans at variance Nₑ, that’s billions of generations. The pipeline is not full. The identity does not apply. He has derived the delivery rate of a full pipe without checking whether the pipe is full. I have actually checked the pipeline using the ancient DNA data. The empirical evidence supports my math, not his error-filled textbook assumptions. And he’s obviously not aware of Franco Chalub’s 2022 solution of the Neutral Kimura equation with two integral constraints or its implications.

“Day’s calculation of just six fixations over 9 million years is ludicrous. To get this he erroneously takes the time to fixation of a neutral allele, which is very slow. I assume this is the ‘time-related’ equation he refers to.”

The Probability Zero derivation does not use neutral fixation time. It uses Kimura’s fixation time for beneficial mutations: t ≈ (2/s) × ln(2Nₑ), at s = 0.001 (the empirical mean for beneficial mutations in humans from Zeng et al. 2021). This is faster than the neutral time of 4Nₑ, not slower. He assumed which equation was being used without reading the derivation, and he assumed incorrectly.

“This is simply incorrect. It assumes that one allele needs to get fixed before the next one can be considered. But, of course, that is nonsense and thousands of alleles are drifting around independently at the same time.”

The MITTENS calculation does not assume sequential fixation. The LTEE rate of 1,322 gen/fix is a total throughput measurement — the aggregate output of twelve independent populations running every evolutionary mechanism simultaneously, including concurrent sweeps, neutral hitchhiking, and clonal interference. It is the net output after parallel fixation has already occurred. There is no sequential assumption to remove, because the rate was never derived from one.

The Probability Zero derivation at s = 0.001 does compute a per-fixation time, but dividing total generations by per-fixation time to get maximum achievable fixations is not an assumption of sequential processing. It is also a throughput calculation, the same arithmetic you use when you ask “how many jobs can a machine complete in eight hours if each job takes twenty minutes?” The machine can run multiple jobs simultaneously, but total output is still bounded by total time divided by per-unit processing time, adjusted for parallelism. The LTEE rate is the parallelism-adjusted rate.

“His entire premise is a farce and the use of fixation time is an error. The only thing I can guess is that Day seems to think that only 1 allele can be undergoing fixation at any time because if an allele reaches fixation then there are no other alleles in the population.”

He is guessing because he has not read the argument. The Hard Limits paper explicitly addresses the parallel fixation objection under the heading “The Second Objection: Fixations Run in Parallel,” devotes several pages to it, derives the transient fill fraction F(T) = exp(−π²Nₑ/T), and demonstrates that even multiplying by every mutation at every site in every individual across every generation produces an expected number of completed fixations with tens of millions of zeros after the decimal point. The objection he imagines is devastating is the one the paper conclusively refutes.

“So there can be a fixation event every generation at one of these loci, followed by another the next generation at a different locus and so on.”

Only if the pipeline is full. This is the critical point. A pipeline with a 4Nₑ-generation transit delivers one fixation per generation at steady state — that’s k = μ. But reaching steady state requires the pipeline to have been loaded for 4Nₑ generations at constant population size. For humans at variance Nₑ, the transit time is on the order of 10¹⁰ generations. The human lineage has had 252,000 generations. The pipeline isn’t partially empty. It’s functionally nonexistent and empirically confirmed to be empty. The one-per-generation delivery rate he’s invoking is the far-end output of a pipe that hasn’t been fed long enough to deliver anything.

“It would be a remarkably stupid mistake for Day to make, but it is all I can think of that would allow him to get to his impossible conclusion of 6 fixations over 9 million years.”

It is all he can think of because he isn’t aware of the problems with the textbook and he hasn’t read the paper that specifically addresses them. The six-fixation figure (now seven at updated parameters) comes from the beneficial fixation time at s = 0.001, not from neutral drift. The parallel fixation objection is addressed explicitly and closed with a quantitative proof. He has constructed his own version of the argument that would indeed be stupid, attributed it to me, and then refuted his own construction. This is textbook strawmanning.

“The real number is closer to the number I provided, but of course it depends on the real fraction that have been neutral in ancestral populations, which is certainly much higher than the low end estimate I give here.”

His number comes from k = μ. k = μ requires a full pipeline and a steady-state. The pipeline cannot fill above the drift ceiling. His number is zero at any census population above ~10,000. The fraction of neutral mutations is irrelevant to an identity that doesn’t hold.

“And his formula for the probability of 20 million changes is set up to calculate the probability of just one set of 20 million fixations, another colossal blunder on his part.”

There is no blunder at all. Either the specific fixations matter — in which case the Darwillion applies — or they’re interchangeable — in which case they’re neutral noise that can’t explain the observed functional divergence. And furthermore, the drifting of 20 million neutral substitutions is blocked by the Hard Limit and the fact that k != μ in humans.

UPDATE: This was Brian’s response, in its entirety. Feel free to post my explanation:

Vox’s response was basically an assumption that at the time of split between humans and chimps the ‘pipeline’ as he calls it was empty. Somehow, all segregating alleles disappeared? The ‘pipeline’ would have been full from the X generations preceding that point in time. He seems to be saying that it gets reset somehow. That would certainly change things but it is biologically preposterous.

That’s absolutely wrong. The pipeline was full, but it was much shorter. Back then, at the ancestral census of ~100,000, the pipe was 4Nₑ ≈ 228,000 generations long. So the very few fixations we have observed in the last 7,000 years are the last little drops of ancestral leakage. Mutations keep starting at the entrance at rate μ; that never stops. The problem is they can’t traverse the pipe. Some mutations made it through. As the population grows, the pipe grows with it. At census 1 million, the pipe was 2.28 million generations long. At census 8 billion, it’s 29 billion generations long.

So all those new mutations that the evolutionists find so exciting are entering a pipe that is getting longer much faster than they can travel through it. They will never reach the far end. The far end only delivers what was loaded when the pipe was short enough to traverse, which is the ancestral fill. Once that drains out, nothing replaces it. That’s the Hard Limit of genetic drift: the pipe lengthens with population size, and for any population above ~10,000 census, the pipe is already longer than the species can be expected to survive. The only population-wide fixations that complete are those that got in when the population was small. Everything that loads after the population crossed the hard limit is still in transit in the pipe, and will remain in transit until the lineage goes extinct or speciates into something else. And all of this is based soundly on Kimura’s equation: but the correct equation, not the steady-state identity.

Due to his erroneous insistence that k = μ applies over time regardless of population size, Brian is arguing that the pipe always stays the same length no matter the size of the population. It doesn’t. It grows with the population.

UPDATE: You guys would do better to simply past what I wrote than trying to interpret what you don’t quite understand.

he says the “pipeline” was not full based on ancient DNA data.

Brian’s comment was about the status of the pipe in ancestral times. At the time of the CHLCA split, we can assume that it was full and 228,000 generations long, so fixations can be reached around now. But the ancestral evidence shows that only very few fixations have taken place in the last 7,000 years, even when limited to a mostly European subset of the population. So what the ancestral data is confirming that already the pipe is far too long, because it shows absolutely no advancement from low-percentages to middle-percentages, or middle-percentages to high. Only a relatively small number of fixations have taken place in 280 generations because those mutations were already in most of the modern European population from their common ancestors.

If he wishes to check the evidence for himself, he can review Allele Frequency Trajectories in the European Ancient DNA Record.

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