Never Argue with a Gamma
There is absolutely no point to it
My recent publication of Probability Zero: The Mathematical Impossibility of Evolution by Natural Selection has been a case study in the complete inutility of arguing with Gamma males. Again and again, we see the same behaviors:
Self-appointed authorities
Incorrect references to the relevant literature
Obvious failure to understand the literature and authorities cited
Refusal to engage directly with the object being criticized
Unreasonable demands of the party being criticized
Baseless accusations of the other party’s nonexistent failures
Groundless criticism of the other party’s motivations
Overeliance on credentials
Here is one, belated and particularly egregious example of what had already been demonstrated by at least three other Gammas before one SacredCowKilla - there is a Gamma red flag if you’ve ever seen one - deigned to adjust his secret crown and step into the fray.
1) There is no “absolute limit” on fixation. There’s a formula which is dependent on effective population size and selection coefficient; and the numbers could be massaged to produce 1,600 generations; that doesn’t necessarily imply that that is the case with the population in question.
2) Under the “neutral theory,” long-run substitutions at neutral sites is approximately equal to the neutral mutation rate. Large numbers of substitutions can accumulate can accumulate without requiring each to be positively selected.
3) Neutral theory isn’t abandoning selection, it just partitions the genome into components where selection is strong/weak/drift; and modern evo theory uses both.
4) Parallel adaptation is not abandonment of selection, it’s commonly accepted in modern evo theory. Soft sweeps explicitly describe scenarios where multiple copies of beneficial variants rise concurrently under selection.
5) Hitchhiking has been demonstrated empirically.
and then as far as sensationalist claims:
A) There was a lot less math in biology back in the 60s. This has been changing and basically with the advent of genomic tools, biology has “as much math” as any of the other STEM fields.
B) Biologists not doing math is just objectively false. Biomathematics exists as a field, genomics exists as a field, population dynamics, evo theory, systems biology, etc.
Vox Day (author of the book)
You’re flat-out wrong. Every single objection you have made is incorrect.
Biologists can’t do math. They can’t even understand what the math is for. You haven’t read the book, so you are opining in ignorance. You will shudder in embarrassment for the entire field of biology when you read the chapter on the 1966 Wistar Symposium.
Furthermore, I am the only person who has ever analyzed the Harvard aDNA data with 17,000 genomes going back 7000 years in this context. I know what I’m talking about. No one else does.
SirHamster (individual who has read the book)
1. There absolutely is a fixation limit. Every member of the population who doesn’t have the gene has to die for fixation to occur. Fixation rate is limited by that death rate.
2. Neutral theory is addressed in the book. If there is no selection on neutral mutations, then there is no selection on harmful mutations and the population goes extinct. Selection is in effect and limits the rate of genetic propagation and fixation of neutral mutations.
3. Neutral theory exists because selection demonstrably cannot account for the genetic differences that exists. The book points out that even when both are applied, the numbers do not add up and evolution by random mutation, natural selection, drift, etc etc is mathematically disproven.
4. Parallel fixation looks outside of selection to power evolutionary change. But parallel fixation is accounted for in the measured fixation rates and it’s still not enough. .
5. Hitchhiking is addressed in the book. It does not add enough genetic fixation to change the mathematical impossibility of evolution.
A. The book goes over mathematical arguments against evolution from 1966. Biology has failed to provide an answer to those challenges for 60 years. It’s still failing to answer the math.
B. See A. Until the math in Vox’s book is addressed, biologist math is a joke.
1. Fixation is an allele-frequency outcome driven by differential reproduction and lineage survival across generations, not by mass death of non-carriers; it refers to an allele reaching frequency 1 through reproductive asymmetry rather than population-wide turnover.
2. Neutral theory does not assume the absence of selection; it holds that most fixed mutations are neutral or nearly neutral, while deleterious mutations are removed by purifying selection and neutral mutations can fix via genetic drift, so selection and drift coexist within the framework.
3. Population-genetic models do yield closed-form solutions, but these equations describe expected values under specified assumptions rather than deterministic evolutionary trajectories, and they do not imply implausible replacement dynamics or mathematical inconsistency.
4. Empirical measurements of parallel fixation are inherently contingent on timescale, population structure, and initial genetic conditions, with observed parallelism reflecting shared constraints, standing variation, and similar selective landscapes rather than a fundamental limit on evolutionary change.
5. Genetic hitchhiking operates multiplicatively through linkage, increasing the fixation probability of linked neutral or weakly selected alleles in proportion to selection strength and linkage, while recombination bounds the effect locally even as repeated hitchhiking events can substantially restructure genomic regions over time.
A. From where I’m standing, it’s done fairly well. So far, most biomath predictions hold out, assuming you give it the correct inputs.
B. If Mr. Beale wishes to submit a paper for review, he should do so. There are several journals dedicated to biomathematics. There, his paper would be subject to peer review. Otherwise I fail to see how his claims could be challenged.
You’re literally retarded. Peer review is both a) totally worthless and b) far less effective than AI stress-testing. The rigor in Probability Zero exceeds the rigor in any biology book ever published. Run the numbers yourself. Doesn’t matter which AI you use. They’ll all tell you the same thing: the case is closed.
1. That’s a non-sequitor. There are limits on any physical process. The rate that mutations are fixated in the population has to be limited by reproduction and death rates.
2. If selection applies, then it’s reproductive advantage driving the spread of genes through the population. But drift ignores reproductive advantage and that means selection is not applied. There is no selection term in the drift equation.
3. There are 40 million base-pair differences between human-chimpanzees, which is supposed to have taken place over 9 million years. 20 million of those changes can be attributed to human evolution. Natural selection with parallel fixation can account for 127 genetic changes in those 9 million years, leaving 19.999873 million changes unaccounted for. The problem is that the models cannot explain the observed data. The models are falsified by the scientific data.
4. This is avoiding the scientific data and retreating to word-salad. Methods for genetic fixation are imagined without observation or measurement. Fantasy is not science.
5. You wrote a lot of words while avoiding any numbers. Vox’s book covers hitchhiking and even does the math for you, since you won’t. Yes, it exists. No, it cannot salvage the math against evolution by natural selection.
A. You haven’t answered the math. Patting yourself on the back is not an answer.
B. You can challenge his claims by reading the book, understanding the math, and then demonstrating the math is wrong. You don’t need peer review to challenge wrong math.
1) The limit is generation time and effective population size, not mass death rate.
2) Fokker-Planck uses both, for instance. It really depends on which model you’re using. Some use it, some don’t.
3) My back of the envelope math suggests 32-43 million substitutions over 9 million. Checks out to me.
4) That’s untrue. Viral evolution immediately comes to mind.
5) I will admit that I haven’t read the book. If I did, I would refute these claims on Amazon and such. I am only responding to the claims made in the article. Also, calling it word-salad is an insult. Don’t stoop to Mr. Beale’s level and keep it polite. I have done back of the envelope math, and Mr. Beale’s claims are wrong and sensationalist. In attacking Dr. Dawkins (a bloviating popularizing fool), Mr. Beale has stooped to his level.
A) Most of the math I did was back of the envelope. It’s good enough for an argument over the Internet.
B) Frankly, it’s not a good use of my time. Mr. Beale has devolved to shit-flinging and insults (and I’m willing to fire back). I have responded to the claims made in the article. I have done the math based on these claims. If you are willing to share the mathematical claims, provided I have the free time I will respond to them. But I really do not see why Mr. Beale’s claims can be submitted to a topical journal and be analyzed by a cohort of biomathematical scholars. If his claims are precise and accurate, then the community would need to force to re-examine themselves. If his claims are not, then people who have the time for a detailed analysis would report that. Seems fairly straightforward.
Like
1. No. You don’t know what you’re talking about.
2. It doesn’t matter which model you’re using. Moran admits it’s impossible. Wright-Fisher and Kimura treat humans as amoebas. And they all screw up because ancient effective population size is one-third the number they erroneously treat as a constant.
3. You’re a retard and your math isn’t even close. You are ignoring the Law of Large Numbers because you know nothing about probabilistic math. The retreat to drift doesn’t exist.
4. Viral evolution doesn’t apply.
5. Again, you’re a retard. You would never, ever, accept the standard of arguing from complete ignorance the other way, and yet you engage in it.
A) No, it’s not. Your “argument” doesn’t even rise to the level of a sub-100 IQ high school dropout who at least has the brains to check ChatGPT.
B) The community will be forced to re-examine itself. Peer review is less accurate than a coin toss. Of course a retard like you would trust it despite the reproducibility crisis.
You’re both retarded and lazy. Not an effective combination.
1) Not a rebuttal. Take the cock out of your mouth.
2) You’re the retard. It absolutely does matter what model you use. For the purpose of modeling, humans ARE no different than amoeba. What is your source on the population estimate?
3) Would you like to substantiate your claims?
4) If you think the principles of viral evolution don’t apply to eukaryotic evolution, you’re an imbecile and should stick to whining about how you never won a Nebula or Hugo.
5) Except I have. None of the books written by say, Dawkins, are worth the paper they’re printed on. But that doesn’t magically make your book good. Nor am I responding to the arguments presented in the book - I’m responding to the arguments presented in the interview. Which are objectively wrong AND you keep being objectively wrong.
A) The fact that you think ChatGPT is in any way reliable as an authoritative source is indicative of your level of understanding.
B) Don’t misunderstand me. I am all for calling out fake scientists and false claims. In that sense, I actually agree with you. But again, if you’re trying to expose them for the frauds that they are, why not do it in an intelligent way, instead of making wild (and incorrect) claims. Write it up as an article, challenge the math directly, and publish it. It WILL get responses from the scientific community. Write it under a pseudonym if you’re worried about your reputation preceding you.
Anyway, I’m done with this conversation. You clearly have a chip on your shoulder, you can’t verify your math, you argue like a sophomore, and so on. The ONE thing I will agree with you is that bad science should be called to task, but there’s a smart way to do it and a dumb way, and you’re dead set on your path.
You want some math? Fine. Here is one little piece of the puzzle. I very much doubt you will be able to follow it.
1. Introduction
The mathematical challenge to neo-Darwinian evolution has long centered on time constraints. The genetic divergence between humans and chimpanzees—approximately 40 million fixed differences across both lineages—must have accumulated within approximately 9 million years since their hypothesized common ancestor (Chimpanzee Sequencing and Analysis Consortium 2005). At observed fixation rates, sequential accumulation of these differences is mathematically impossible (Day 2025).
Defenders of the neo-Darwinian framework frequently invoke parallel fixation as an escape from this constraint. The argument is intuitive: if many mutations can fix simultaneously rather than sequentially, total genetic change can accumulate faster.
Day and Athos (2025a) identified one constraint on parallel fixation: the reproductive ceiling. The total selection differential across all segregating beneficial mutations cannot exceed the maximum reproductive output of the organism. For humans, this limits parallel fixation to approximately 100 simultaneous events.
Here we identify a second, independent constraint that is purely statistical in nature: the Law of Large Numbers. This constraint does not depend on reproductive biology but arises from fundamental probability theory. As we demonstrate, it imposes an even more severe limitation on parallel fixation than the reproductive ceiling alone.
2. The Variance Problem
2.1 Selection Requires Variance
Natural selection operates on variation. For selection to change allele frequencies, there must be individuals with different genotypes, and those genotypes must differ in fitness. The greater the fitness variance in the population, the faster selection can operate; if all individuals have identical fitness, selection halts entirely regardless of which alleles they carry.
This principle is formalized in Fisher’s Fundamental Theorem of Natural Selection: the rate of increase in mean fitness equals the additive genetic variance in fitness (Fisher 1930). When variance is zero, evolution stops.
2.2 The Law of Large Numbers
The Law of Large Numbers (LLN) is a foundational theorem in probability theory. It states that as the number of independent random trials increases, the sample mean converges to the expected value, and the relative variance decreases.
Consider an analogy. If you flip a coin 10 times, substantial variation in outcomes is expected—some people will get 3 heads, others 7. If you flip a coin 157,000 times, everyone will get very close to 78,500 heads. The relative deviation from the mean shrinks as n increases.
2.3 Application to Parallel Fixation
Suppose n beneficial mutations are segregating simultaneously in a population, each at frequency p. The number of beneficial alleles carried by any individual follows a binomial distribution with mean np and standard deviation √(np(1-p)).
At p = 0.5 (the midpoint of fixation) with n = 157,000:
• Mean beneficial alleles per individual: 78,500
• Standard deviation: 198.1
• Coefficient of variation: 0.25%
The coefficient of variation—standard deviation divided by mean—measures relative dispersion. At 0.25%, the distribution is extremely tight. Virtually everyone in the population carries between 78,000 and 79,000 beneficial alleles.
3. Quantifying the Constraint
3.1 Fitness Differential in a Finite Population
In a population of N = 10,000, using order statistics for the normal approximation:
• Best individual: ~79,237 beneficial alleles
• Worst individual: ~77,763 beneficial alleles
• Difference: 1,474 alleles
If each beneficial allele contributes a selection coefficient of s = 0.01, the fitness differential between the best and worst individuals is:
Fitness ratio = (1.01)¹⁴⁷⁴ ≈ 14.7×
We note that the assumption of multiplicative fitness is conservative with respect to our conclusions. Diminishing returns epistasis—where the fitness benefit of each additional beneficial allele decreases as more are acquired—would compress the fitness distribution further, strengthening the Bernoulli Barrier. Synergistic epistasis (where benefits compound) might in principle alleviate the constraint, but such epistasis is not observed at the genomic scale relevant to this analysis (Wei and Zhang 2019).
3.2 Required Fitness Differential
For n = 157,000 mutations to fix in parallel, selection must discriminate between individuals carrying all beneficial alleles and those carrying none:
Required ratio = 157,000 × 0.01 = 1,570×
3.3 The Shortfall
Shortfall = 1,570 / 14.7 ≈ 107×
Even comparing the most extreme individuals in a population of 10,000—the literal best versus the literal worst—the available fitness differential falls short by more than two orders of magnitude.
Now, that’s as far as the models will take you. But, if you’ve done the work on ancient effective populations like I have, then you know that Nₑ for the relevant period of proto-human development is not 10,000, it is around 2,000. And reducing Nₑ from 10,000 to 2,000 makes the Bernoulli Barrier more severe, not less. The smaller population has less extreme individuals so the fitness differential between best and worst shrinks from ~15× to ~5×. The shortfall increases from 107× to 334×.
Parallel fixation does NOTHING to make up for the observed DNA fixation gap that rules out even the most remote possibility of evolution by natural selection.
There was, of course, no reply to being shown a very small fraction of the math and science presented in the book, that represents the THIRD proof that parallel fixation cannot possibly rescue the case for natural selection.
This is why I don’t bother providing substantive answers to Gamma critics beyond “shut up and read the book”. They not only don’t know what they don’t know, but they don’t accept that what they don’t know exists. Notice how the Gamma never, ever, responds to the direct and substantive refutation of his statements; he doesn’t go and confirm that the Moran models and Haldane models confirm that he is wrong, then explain why the Wright-Fisher and Kimura are superior to them, nor does he back down once the obvious difference between bacteria and humans are pointed out to him, he just sticks to his obviously erroneous case.
And once he throws the math into the very AI systems he denigrates and sees that the math he can’t follow is substantiated, rather than wave the white flag and admit that his criticism of a book he hasn’t read is wrong, he’ll just go radio dark, before popping up again one day to take a shot when he thinks it is safe.
That’s what Gammas do. And that’s why wasting your time on them is pointless, except as a clear demonstration of that fact to others.
Sacredcowkilla is mad that someone completely annihilated his sacred cow.
The Well-Ackshually
The Tantrum
The Parting Shot
The Ad Hominem
The Encore
The Crass, Obscenity-Laden Insult
The Re-Flounce
The Run-and-Hide
Totally textbook gamma argumentation, and I think he hit all of them. He's probably in Reset-to-Factory-Defaults mode now, and will work really hard to tell himself that he won and that the argument never happened anyway.