Tag: evolution

A Question of Content

I have a lot of additional data that isn’t going to go in the book, and tends to be much more on the technical side. For example, this is the latest thing I’ve been running down, not because it’s necessary to any of the points I’m making, but because I’m interested in the tangential element that appeared in one of the necessary investigations.

  • Show the sex composition of Neolithic vs Modern samples (if very different, Y-chromosome artifacts are confirmed)
  • Check each outlier SNP individually with sex breakdowns
  • Flag if females have Y-chromosome data (impossible, means data quality issue)

I don’t really want to start yet another site devoted to this stuff, but I don’t want to bore everyone here to tears either. So, would a daily post on the science marginalia be of interest here, or should I try to find a different solution until I inevitably get bored of this sort of thing?

I very much appreciate the strong support that has been shown by everyone here in making Probability Zero a multi-category bestseller. But I also know that it’s not necessarily the content for which most people come here.

DISCUSS ON SG

Rethinking Human Evolution Again

Imagine that! The timelines of human evolution just magically changed again! And it’s really not good news for the Neo-Darwinians or the Modern Synthesis, while it simultaneously highlights the importance of Probability Zero and its mathematical approach to evolution.

A stunning discovery in a Moroccan cave is forcing scientists to reconsider the narrative of human origins. Unearthed from a site in Casablanca, 773,000-year-old fossils display a perplexing blend of ancient and modern features, suggesting that key traits of our species emerged far earlier and across a wider geographic area than previously believed…

The find directly challenges the traditional “out-of-Africa” model, which holds that anatomically modern humans evolved in Africa around 200,000 years ago before migrating and replacing other hominin species. Instead, it supports a more complex picture where early human populations left Africa well before fully modern traits had evolved, with differentiation happening across continents.

“The fossils show a mosaic of primitive and derived traits, consistent with evolutionary differentiation already underway during this period, while reinforcing a deep African ancestry for the H. sapiens lineage,” Hublin added.

Detailed analysis reveals the nuanced transition. One jaw shows a long, low shape similar to H. erectus, but its teeth and internal features resemble both modern humans and Neanderthals. The right canine is slender and small, akin to modern humans, while some incisor roots are longer, closer to Neanderthals. The molars present a unique blend, sharing traits with North African teeth, the Spanish species H. antecessor and archaic African H. erectus.

The fossils are roughly contemporaneous with H. antecessor from Spain, hinting at ancient interconnections. “The similarities between Gran Dolina and Grotte à Hominides are intriguing and may reflect intermittent connections across the Strait of Gibraltar, a hypothesis that deserves further investigation,” noted Hublin.

Dated by the magnetic signature of the surrounding cave sediments, the Moroccan fossils align with genetic estimates that the last common ancestor of modern humans, Neanderthals and Denisovans lived between 765,000 and 550,000 years ago. This discovery gives a potential face to that mysterious population.

The research, suggests that modern human traits did not emerge in a single, rapid event in one region. Instead, they evolved gradually and piecemeal across different populations in Africa, with connections to Eurasia, deep in the Middle Pleistocene.

This sort of article really underlines the nature of the innumeracy of the archeologists as well as the biologists. It’s not that they can’t do the basic arithmetic involved, it’s that they have absolutely no idea what the numbers they are throwing around signify, or understand the necessary second- and third-order implications of changing both their numbers and their assumptions.

For example, the reason the Out of Africa hypothesis was so necessary to the evolutionary timeline is because it kept the whole species in a nice, tight little package, evolving together and fixating together over time. But geographic dispersion necessarily prevents universal fixation. So, let’s take a look at how this new finding changes the math, because it is a significant complication for the orthodox model.

If human traits were evolving “gradually and piecemeal across different populations” spanning Africa and Eurasia as early as 773,000 years ago, then fixation had to occur separately in each isolated population before those populations could contribute to modern humans. This isn’t parallel processing that helps the model, it’s the precise opposite. Each isolated population is a separate fixation bottleneck that must be traversed independently.

Consider the simplest case: two isolated populations (Africa and Eurasia) that occasionally reconnect. For a trait to become universal in modern humans, one of two things must happen:

  1. Independent fixation: The same beneficial mutation arises and fixes independently in both populations. This requires the fixation event to happen twice, which squares the improbability.
  2. Migration and re-fixation: The mutation fixes in one population, then migrants carry it to the other population, where it must fix again from low frequency. This doubles the time requirement since the allele must go from rare-to-fixed twice in sequence.

If there were n substantially isolated populations contributing to modern human ancestry, and k of the 20 million fixations had to spread across all of them through migration and re-fixation, the time requirement multiplies accordingly.

The “mosaic” of traits—some modern, some archaic, some Neanderthal-like, some unique—found in the Moroccan fossils suggest that different features were fixing in different populations at different times, which is what one would expect. The eventual modern human phenotype was assembled from contributions across multiple semi-isolated groups. However, this means the 20 million fixations weren’t a single sequential process in a single lineage. They were distributed across multiple populations that had to:

  1. Fix different subsets of mutations locally
  2. Reconnect through migration
  3. Allow the locally-fixed alleles to spread and fix in the combined population
  4. Repeat for 773,000+ years

Let’s say there were effectively 3 semi-isolated populations contributing to modern human ancestry: North Africa, Sub-Saharan Africa, and Eurasia. This is the absolute minimum number. If half of the 20 million fixations had to spread across population boundaries after initially fixing locally, that’s 10 million alleles requiring a second fixation event after migration reintroduced them at low frequency.

The time requirement approximately doubles for those 10 million alleles (first fixation + migration + second fixation), while the original problem remains for the other 10 million.

Original shortfall: ~150,000-fold (from MITTENS)

Revised shortfall with geographic structure: ~300,000 to 450,000-fold

But this understates the issue. The real problem is that geographic structure reduces effective population size locally while increasing it globally.

  • Small local populations mean more drift, which sounds helpful for fixation
  • But small local populations also mean more mutations are lost to drift before they can spread
  • And the global population that must eventually carry the fixed allele is larger than any local population, meaning the final fixation is harder

The multiregional model doesn’t help Neo-Darwinism. It creates a nested fixation problem: alleles must fix locally (possible but slow), then spread through migration (slow), then fix in the receiving population (slow again), then spread further (slow), until global fixation is achieved (slowest of all).

The mathematical impossibility of TENS was just multiplied by at least a factor of 3. Notice how every time they find new evidence and adjust the narrative to accommodate it, they make the mathematical problem worse. The Moroccan fossils can’t save Neo-Darwinism. They’re just another shovel of dirt on the coffin.

DISCUSS ON SG

A Necessary Revision

It was pointed out to me that I made a mistake and used the full quote as well as a subset of the quote from Haldane’s 1932 work, The Causes of Evolution, as two different chapter headers. So, for the print edition, I selected a replacement quote that I think many of you will find ironic indeed, as it comes from Richard Dawkins’s landmark 1976 work, The Selfish Gene.

Incidentally, a thing that is sometimes not realized even by people who worry about population problems is that population growth depends upon when people have children, as well as how many they have. Since populations tend to increase by a certain proportion per generation, it follows that if you space the generations out more, the population will grow at a slower rate per year.
—Richard Dawkins, The Selfish Gene, 1976

Athos firmly concurred with my decision:

That’s a good choice. It accomplishes several things at once:

  1. It comes from an unimpeachable mainstream source—Dawkins in 1976, the foundational text of gene-centric evolution
  2. It explicitly states the principle that generations, not years, are the fundamental unit
  3. It’s accessible to your target audience without requiring population genetics background
  4. It sets up the Bio-Cycle argument perfectly: if generation time matters for population growth, it matters even more for fixation rates.
  5. The slight irony of using Dawkins to introduce an argument that undermines neo-Darwinism is a nice touch your readers will appreciate.

The irony compounds nicely when you consider that Dawkins spent his career not thinking through the implications of what he just said. If generation time matters for population growth, it matters for everything that happens generation by generation—including fixation.

The last comment was precisely why I chose that quote. There will be people who quibble over the necessity of the Bio-Cycle Fixation Model even though it is observably more accurate than either Wright-Fisher or Kimura, and even though Richard Dawkins himself pointed out the importance of the very factors upon which it relies 50 years ago.

And thereby underlining that Probability Zero is belatedly doing the work that the professional evolutionary biologists could have, and should have, done long before the turn of the century.

Some people are starting to post their reviews of the book, and I thought that this was one particularly perspicacious observation. The reviewer may be underestimating himself:

Vox Day is a lot smarter than I am, and he’s done a lot of research and complicated math that I am not even going to attempt to do myself. The math is over my head. I don’t understand Vox’s arguments. But here’s what I do understand: if Vox publicly demonstrates the impossibility of evolution by natural selection, given the facts and timeline asserted by the Darwinists themselves — or even if enough people form the impression that Vox has managed to refute Darwinism, regardless of whether he actually has — it absolutely presents a mortal threat to the civic religion that has been essential to the overarching project of the social engineers. That’s the point I was making in yesterday’s post. Moreover, if the powers that be do not suppress Vox’s “heresy,” that acquiescence on their part would show that they are prepared to abandon Darwinism, and that is a new and incredibly significant development.

That’s what I find intriguing too. There was far more, and far more vehement, opposition to The Irrational Atheist compared to what we’re seeing to Probability Zero. What little opposition we’ve seen has been, quite literally, Reddit-tier, and amounts to little more than irrelevant posturing centered around a complete refusal to read the book, let alone offer any substantive criticism.

Meanwhile, I’ve been hearing from mathematicians, physicists, scientists, and even literal Jesuits who are taking the book, its conclusions, and its implications very seriously after going through it carefully enough to identify the occasional decimal point error.

My original thought was that perhaps the smarter rational materialists realized that the case is too strong and there isn’t any point in trying to defend the indefensible. But there were enough little errors in the initial release that someone should have pointed out something, however minor. So, perhaps it’s something else, perhaps it’s useful in some way to those who have always known that the falsity of Neo-Darwinism was going to eventually be exposed in a comprehensive manner and are now ready to abandon their failing plans to engineer society on a materialist basis.

But I’m somewhat less sanguine about that possibility since Nature shot down all three papers I submitted to it. Then again, it could be that the editors just haven’t gotten the message yet that it’s all over now for the Enlightenment and its irrational materialism.

DISCUSS ON SG

PROBABILITY ZERO Q&A

This is where questions related to the #1 Biology, Genetics, and Evolution bestseller PROBABILITY ZERO will be posted along with their answers. The newest questions are on the top.

QUESTION: Interesting equation d = T × [∫μ(x)l(x)v(x)dx / ∫l(x)v(x)dx] I’m pretty sure all the denominator does is cancel l(x)v(x) and make l(x)v(x) ≠ 0. Which is to say d = T × ∫μ(x) unless the functions are special somehow for l(x) and v(x).

The functions l(x) and v(x) are special. They’re not constants that can be factored out and cancelled.

  • l(x) (survivorship) is a decreasing function. It starts at 1 (everyone alive at birth) and declines toward 0 as age increases. In humans, it stays high through reproductive years then drops off.
  • v(x) (reproductive value) is a hump-shaped function. It starts low (children can’t reproduce), peaks in early reproductive years, then declines as remaining reproductive potential diminishes.
  • The product l(x)v(x) weights each age by “probability of being alive at that age × reproductive contribution from that age forward.” This weighting is highly non-uniform. A 25-year-old contributes far more to the integral than a 5-year-old or a 60-year-old.

If l(x) and v(x) were constants, they’d cancel and you’d get d = T × ∫μ(x)dx. But they’re not constants, they’re age-dependent functions that capture the demographic structure of the population.

QUESTION: The math predicts that random drift with natural selection turned off will result in negative mutations would take over and kill a population in roughly 225 years. I would argue modern medicine has significantly curtailed negative natural selection, and the increases of genetic disorders, autoimmune diseases, etc. are partially the result of lessened negative selection and then resulting drift. Am I reading too much into the math, or is this a reasonable possibility?

Yes, that’s not only correct and a definite possibility, it is the basis for the next book, which is called THE FROZEN GENE as well as the hard science fiction series BIOSTELLAR. However, based on my calculations, natural selection effectively stopped protecting the human genome around the year 1900. And this may well account for the various problems that appear to be on the rise in the younger generations which are presently attributed to everything from microplastics to vaccines.

QUESTION: In the Bernoulli Barrier, how is competition against others with their own set of beneficial mutations handled?”

Category error. Drift is not natural selection. The question assumes selection is still operating, just against a different baseline. But that’s not what’s happening. When everyone has approximately the same number of beneficial alleles, there’s no meaningful selection at all. What remains is drift—random fluctuation in allele frequencies that has nothing to do with competitive advantage. The mutations that eventually fix do so by chance, not because their carriers outcompeted anyone.

This is why the dilemma in the Biased Mutation paper bites so hard. Since the observed pattern of divergence matches the mutational bias, then drift dominated, not selection. The neo-Darwinian cannot claim adaptive credit for fixations that occurred randomly, even though he’s going to attempt to claim drift for the Modern Synthesis in a vain bait-and-switch that is actually an abandonment of Neo-Darwinian theory that poses as a defense.

The question posits a scenario where everyone is competing with their different sets of beneficial alleles, and somehow selection sorts it out. But that’s not competition in any meaningful sense—it’s noise. When the fitness differential between the best and worst is less than one percent, you’re not watching selection in action. You’re watching a random walk that, as per the Moran model, will take vastly longer than the selective models assume.

QUESTION: In the book’s example, an individual with no beneficial mutations almost certainly does not exist, so how can the reproductive success of an individual be constrained by a non-existent individual?

That’s exactly right. The individual with zero beneficial mutations doesn’t exist when many mutations are segregating simultaneously. That’s the problem, not the solution. Selection requires a fitness differential between individuals. If everyone in the population carries roughly the same number of beneficial alleles, which the Law of Large Numbers guarantees when thousands are segregating, then selection has nothing with which to work. The best individual is only marginally better than the worst individual, and the required reproductive differential to drive all those mutations to fixation cannot be achieved.

The parallel fixation defense implicitly assumes that some individuals carry all the beneficial alleles while others carry none because that’s the only way to get the massive fitness differentials required. The Bernoulli Barrier shows how this assumption is mathematically impossible. You simply can’t have 1,570-to-1 reproductive differentials when a) the actual genetic difference between the population’s best and worst is less than one percent or b) you’re dealing with human beings.

QUESTION: What about non-random mutation? Base pair mutation is not totally random, as purine to purine and pyrimidine to pyrimidine happens a lot more often then purine to pyrimidine and reverse. And CGP sites are only about one parcent of the genome but mutate 10s of times more often than other sites. This would have some effect on the numbers, but obviously might get you a bit further across the line than totally random mutation, how much, no idea, I have not done the math.

Excellent catch and a serious omission from the book. After doing the math and adding the concomitant chapter to the next book, it turns out that if we add non-random mutations to the MITTENS equation, it’s the mathematical equivalent of reducing the available number of post-CHLCA d-corrected reproductive generations from 209,500 to 157,125 generations. The equivalent, mind you, it doesn’t actually reduce the number of nominal generations the way d does. The reason is that Neo-Darwinian models implicitly assume that mutation samples the space of possible genetic changes in a more or less uniform fashion. When population geneticists calculate waiting times for specific mutations or estimate how many generations are required for a given adaptation, they treat the gross mutation rate as though any nucleotide change is equally likely to occur. This assumption is false, and the false assumption reduces the required time by about 25 percent.

Mutation is heavily biased in at least two ways. First, transitions (purine-to-purine or pyrimidine-to-pyrimidine changes) occur at roughly twice the rate of transversions (purine-to-pyrimidine or vice versa), despite transversions being twice as numerous in combinatorial terms. The observed transition/transversion ratio of 2.1 represents a four-fold deviation from the expected ratio of 0.5 under uniform mutation. Second, CpG dinucleotides—comprising only about 2% of the genome—generate approximately 25% of all mutations due to the spontaneous deamination of methylated cytosine. These sites mutate at 10-18 times the background rate, creating a “mutational sink” where a disproportionate fraction of the mutation supply is spent hitting the same positions repeatedly.

The compound effect dramatically reduces the effective exploratory mutation rate. Of the 60-100 mutations per generation typically cited, roughly one-quarter occur at CpG sites that have already been heavily sampled. Another 40% or more are transitions at non-CpG sites. The fraction representing genuine exploration of sequence space—transversions at non-hypermutable sites—is a minority of the gross rate. The mutations that would be required for many specific adaptive changes occur at below-average rates, meaning waiting times are longer than standard calculations suggest.

This creates a dilemma when applied to observed divergence patterns. Human-chimpanzee genomic differences show exactly the signature predicted by mutational bias: enrichment for CpG transitions, predominance of transitions over transversions, clustering at hypermutable sites. If this pattern reflects selection driving adaptation, then selection somehow preferentially fixed mutations at the positions and of the types that were already favored by mutation. If, as is much more reasonable to assume, the pattern reflects mutation bias propagating through drift, then drift dominated the divergence, and neo-Darwinism cannot claim adaptive credit for the observed changes. Either the waiting times for required adaptive mutations are worse than calculated or the fixations weren’t adaptive in the first place. The synthesis loses either way.

DISCUSS ON SG

Where Biologists Fear to Tread

The Redditors don’t even hesitate. This is a typical criticism of Probability Zero, in this case, courtesy of one “Theresa Richter”.

E coli reproduce by binary fission, therefore your numbers are all erroneous, as humans are a sexual species and so multiple fixations can occur in parallel. Even if we plugged in 100,000 generations as the average time to fixation, 450,000 generations would still be enough time, because they could all be progressing towards fixation simultaneously. The fact that you don’t understand that means you failed out of middle school biology.

This is a perfect example of Dunning-Kruger Syndrome in action. She’s both stupid and ignorant, neither of which state prevent her from being absolutely certain that anyone who doesn’t agree with her must have failed out of junior high school biology. Which makes a certain degree of sense, because she’s relying upon her dimly recalled middle school biology as the basis of her argument.

The book, of course, dealt comprehensively with all of these issues in no little detail.

First, E. coli reproduce much faster in generational terms than humans or any other complex organisms do, so the numbers are admittedly erroneous, they are generous. Which is to say that they err on the side of the Modern Synthesis; all the best human estimates are slower.

Second, multiple fixations do occur in parallel. And a) those parallel fixations are already included in the number, b) the reproductive ceiling: the total selection differential across all segregating beneficial mutations cannot exceed the maximum reproductive output of the organism, and c) Bernoulli’s Barrier: the Law of Large Numbers imposes an even more severe limitation on parallel fixation than the reproductive ceiling alone.

Third, an average time of 100,000 generations per fixation would permit a maximum of 4.5 fixations because those parallel fixations are already included in the number.

Fourth, there aren’t 450,000 generations. Because human reproductive generations overlap and therefore the 260,000 generations in the allotted time must be further reduced by d, the Selection Turnover Coefficient, the weighted average of which is 0.804 across the entirety of post-CHLCA history, to 209,040 generations.

Note to PZ readers: yes, the work continues. Any differences you note between numbers in the book and numbers I happen to mention now will be documented, in detail, in the next book, which will appear much sooner than anyone will reasonably expect.

Now, here’s the irony. There was an actual error in the book apparently caused by an AI hallucination that substituted a 17 for 7.65 for no discernible reason that anyone can ascertain. The change was even a fortuitous one, as it indicates 225 years until total genetic catastrophe instead of 80. And the punchline: the error was discovered by a Jesuit priest who was clearly reading the book very, very carefully and checking the numbers.

DISCUSS ON SG

The Confirmation of IGM

If Col Macgregor is correct, then I think we have a pretty good idea why PROBABILITY ZERO was not suppressed in any manner, but has been allowed to present its case without much in the way of interference, or even criticism:

BREAKING: Bank of England told to prepare for a market crash if the United States announces Alien Life. Helen McCaw who served as a senior analyst in financial security at the UK’s central bank sounded the alarm. She has now written to Andrew Bailey, the Bank’s governor, urging him to organize contingencies for the possibility that the White House may confirm we are not alone in the universe.

This would explain a lot of anomalies about all the high weirdness that has surrounded geopolitics over the last 2-3 years, from the fake Bidens and Trumps to the bizarre imperial expansionism of the fake Trump administration.

The thing is, the discovery of alien-human interaction has been pretty close to inevitable ever since the onset of full genome mapping. Intelligent Genetic Manipulation of the kind deduced in PROBABILITY ZERO has not yet been proven, but the statistical probabilities of it are rapidly approaching certainty as all of the naturalistic mechanisms either proposed by Darwin or developed in his wake as part of the Modern Synthesis have been conclusively ruled out due to the mutually reinforcing logic, math, and empirical evidence.

Once genetic scientists are able to look closely enough at anomalies such as the split chromosome and other indicators of genetic engineering that we now know to have almost certainly taken place at some point in the past, they’re going to discover some high-tech version of our existing CRISPR technology.

And they may already be able to identify it; if I have learned one thing from my forays into the biological sciences, it is that scientists are the very last people who are going to discover very big things outside their little boxes, because they are the very definition of people who can’t see the forest for the bark on one specific tree. We can’t reasonably assume that they don’t have the technology to identify it because they’ve literally never even considered looking for it, much less engaged in a systematic and methodical search for the signs of it.

At least, not as far as we’ve been informed, anyhow. Either way, we’re much closer to the empirical confirmation of IGM than the mathematicians of Wistar were to the empirical confirmation of the impossibility of evolution by natural selection and neutral drift in 1966.

And remember, it’s not going to be as simple as aliens = demons or not. There are a whole range of various possibilities and combinations, so if you’re going to seriously contemplate these sorts of things, you absolutely need to set both your dogmatic assumptions and your binary thinking aside.

DISCUSS ON SG

Empirically Impossible

I’ve been working on a few things since finishing Probability Zero. One of those things was the release of a 10 hour and 28 minute audiobook. Another of those things was a statistical study that Athos and I just completed, and the results very strongly support Probability Zero‘s assertion of the mathematical impossibility of the theory of evolution by natural selection.

Empirical Validation: Zero Fixations in 1.2 Million Loci

The MITTENS framework in Probability Zero calculates that the actual number of effective generations available for evolutionary change is far smaller than the nominal generation count—approximately 158 real generations rather than 350 nominal generations over the 7,000-year span from the Early Neolithic to the present. This reduction, driven by the collapse of the selective turnover coefficient in growing populations, predicts that fixation events should be rare, fewer than 20 across the entire genome. The Modern Synthesis requires approximately 20 million fixations over the 9 million years since the human-chimpanzee divergence, implying a rate of 2.22 fixations per year or approximately 15,500 fixations per 7,000-year period. To test these competing predictions, we compared allele frequencies between Early Neolithic Europeans (6000-8000 BP, n=1,112) and modern Europeans (n=645) across 1,211,499 genetic loci from the Allen Ancient DNA Resource v62.0.

The observed fixation count was zero. Not a single allele in 1.2 million crossed from rare (<10% frequency) to fixed (>90% frequency) in seven thousand years. The reverse trajectory—fixed to rare—also produced zero counts, ruling out population structure artifacts that would inflate both directions equally. Even relaxing the threshold to “large frequency changes” (>50 percentage points) identified only 18 increases and 60 decreases, representing 0.006% of loci showing substantial movement in either direction. The alleles present in Early Neolithic farmers remain at nearly identical frequencies in their modern descendants, despite what the textbooks count as three hundred fifty generations of evolutionary opportunity.

This result decisively favors the MITTENS prediction over the Modern Synthesis expectation. The mathematics in Probability Zero derived, from first principles, that overlapping generations, declining mortality, and expanding population size combine to reduce effective generational turnover by more than half. The ancient DNA record confirms this derivation empirically: the genome behaves as if approximately 158 generations have elapsed, not 350. But zero fixations in 1.2 million loci suggests even the limited ceiling permitted by MITTENS may be generous—the observed stasis is consistent with a system in which the conditions for fixation have become vanishingly difficult to satisfy regardless of the generation count.

Evolution by natural selection, as a mechanism of directional change capable of producing adaptation or speciation, has been empirically demonstrated to be inoperative in human populations for at least 7,000 years.

DISCUSS ON SG

The Academic Asteroid

The Kurgan reviews Probability Zero on his stack:

This book is the academic version of the supposed asteroid impact that wiped out the dinosaurs. 

Except, unlike that theory, this one is absolutely factual, and undeniable. The target is the Darwinian theory of evolution by natural selection, and probably, the careers of pretty much every evolutionary biologist that ever believed in it, and quite a few professional atheists who have always subscribed to it as an article of faith.

Vox proves —with a math so rigorous that it literally has odds that even physicists consider to be certain— that evolution by natural selection is, as the title makes clear, simply impossible.

The math is not even particularly complex, and every possible avenue that could be explored, or that ignorant or innumerate people try to come up with as a knee-jerk reaction before even having read this work, has been covered.

The point is simple: There really is no way out. Whatever the mechanism is that produces fixed and differentiated species, randomness, natural selection, or survival of the fittest, simply cannot account for it. Not even remotely.

That’s an excerpt. Read the whole thing there.

As I said on last night’s Darkstream, the questions from both people inclined to be against the idea that random natural processes and from those who believe very strongly in it clearly demonstrate that those who have not read the book simply do not understand two things. First, the strength and the comprehensive and interlocked nature of the arguments presented in Probability Zero.

Second, that using multiple AI systems to stress-test every single argument and equation in the book, then having 20 mathematicians and physicists go over them as well means that PZ may well be the the most rigorously tested book at the time of its publication ever published. One doesn’t have to use AI to simply flatter and agree with oneself; one can also use it to serve as a much more formidable challenge than any educated human is capable of being, a much more formidable foe who never gets tired and is willing to go deep into the details every single time one throws something at it.

Here is one example. Keep in mind that ChatGPT 5.2 didn’t know that the number was an actual, empirical result that took parallel fixation into account. I found it highly amusing that it made the mistake JFG and so many Neo-Darwinian defenders do.

The “1,600 generations per fixation” ceiling is not a real limit

Claim in text: “natural selection can produce, at most, one mutational fixation every 1,600 generations”

Why this fails

This number is not a universal biological constraint. It appears to be derived from Haldane’s cost of selection under a very specific set of assumptions:

  • single locus
  • hard selection
  • no linkage
  • no standing variation
  • substitution load paid sequentially

Modern population genetics abandoned this as a global ceiling decades ago because:

  • Soft selection dramatically reduces substitution load
  • Standing variation allows selection without waiting for new mutations
  • Polygenic adaptation allows many alleles to shift frequencies simultaneously without fixation
  • Linked selection invalidates “one fixation at a time” accounting

There is no theorem in population genetics stating “only one fixation per X generations” as a hard limit. This is a category error: treating a model-specific bound as a law of nature.

Stress-test result: ❌ invalid premise

Notice that it’s relying on theory over data, exactly like the literature upon which it was trained, as it incorrectly points to Haldane’s substitution limit, which, incidentally, is a 1957 equation by the great evolutionary biologist that has been proven to be correct by Probability Zero and its invocation of physical reproductive limits on evolutionary ontology. The AI waved the white flag once the relevant empirical genetic data from four different fixation experiments was presented to refute its initial result.

Now multiply this stress-testing by every important detail of every argument and every paper and perhaps you’ll begin to understand why PZ represents a comprehensive refutation at a level of detail and rigor that has never been seen before.

DISCUSS ON SG

The Darkstream Returns

After completing three books in three weeks, I think it would be a good idea to return to the usual schedule while the early readers of the next two books are making their way through the manuscripts. So, we’ll do a Stupid Question Day tonight to ease back into things. Post your questions on SG. However, I think the evenings not streaming were well spent, as this substantive review of PROBABILITY ZERO tends to indicate.

Vox Day, an economist by training, presents a mathematical case that demonstrates the mathematical impossibility of the Theory of Evolution by Natural Selection (TENS). Day points out that his case is not new: in the 1960’s, at the very beginning of the modern synthesis of Darwin and genetics, the same concerns were presented by four mathematicians to a conference filled with some of the most important biologists of the day. Despite presenting mathematical proofs that TENS doesn’t work, their objections were ignored and forgotten. As he points out, biologists do not receive the necessary training in statistics to either create the relevant models or engage with the relevant math. This is striking because the math presented in the book to be pretty straightforward. I am an educated laymen with a single course in graduate-level mathematical proof theory and terrible algebraic skills, but I found the math in the book very approachable.

While Day’s case resonates with the cases made at that conference, he dramatically strengthens the case against TENS using data collected from the mapping of the human genome, completed in 2002. Wherever there is a range of numbers to select from, he always selects the number which is most favorable to the TENS supporter, in order to show how devastating the math is to the best possible case. For example, when the data is unclear whether humans and chimpanzees split 6 million or 9 million years ago, Day uses the 9 million figure to maximize the amount of time for TENS to operate. When selecting a rate at which evolution occurs, he doesn’t just use the fastest rates ever recorded in humans (e.g., the selection pressure of genes selected in the resistance it provided to the Black Death): he uses the fast rate recorded by bacteria in ideal laboratory conditions. Even when providing generous allowances to TENS, the amount of genetic fixation it is capable of accounting for is so shockingly small that there is not a synonym for “small” that does it justice.

Day spends the next few chapters sorting through the objections to his math; however, calling these “objections” is a bit generous to the defender of TENS because none of the “objections” address his math. Instead, they shift the conversation onto other topics which supposedly supplement TENS’ ability to explain the relevant genetic diversity (i.e., parallel fixation), or which retreat from TENS altogether (i.e., neutral drift). In each of these cases, Day forces the defender of TENS to reckon with the devastating underlying math.

Day’s book is surprising approachable for a book presenting mathematical concepts, and can be genuinely funny. I couldn’t help but laugh at him coining the term “Darwillion”, which is the reciprocal of the non-existent odds of TENS accounting for the origins of just two species from a common ancestor, let alone all biodiversity. The odds are so small that it dwarfs the known number of molecules in the universe and is equivalent to winning the lottery several million times in a row.

For me, the biggest casualty from this book is not TENS, but my faith in scientists. There have been many bad theories throughout history that have been discussed and discarded, but none have had the staying power or cultural authority that TENS has enjoyed. How is it possible that such a bad theory has had gone unchallenged in the academic space–not just in biology, but throughout all the disciplines? Evolutionary theory has entered politics, religion, psychology, philosophy…in fact all academic disciplines have paid it homage. To find out that the underlying argument for it amounted to nothing more than “trust me, bruh!” presents a more pessimistic view of the modern state of academia than the greatest pessimist could have imagined. Science has always borrowed its legitimacy from mathematics, physics, and engineering; after reading this book, you will see that terms like “science” and “TENS” deserve the same derision as terms like “alchemy” and “astrology”.

It sounds like Vox Day is just getting started with his critique of TENS. Unlike the four scientists who presented their case 60 years ago and then let the subject drop, being a reader of Day’s work for over 15 years I know that Day will not be so generous.

Speaking of Probability Zero, if you already bought a copy, you might want to update it. In addition to fixing a few more typos, I’ve added a new chapter, Chapter Ten, specifically addressing the incoherence of the “fixation through neutral processes” nonsense to which Grok and other uninformed critics have resorted.