The Significance of (d) and (k)

A doctor who has been following the Probability Zero project ran the numbers on the Selective Turnover Coefficient (d) and the mutation fixation rate (k) across six countries from 1950 to 2023, tracking both values against the demographic transition. The results are presented in the chart above, and they are considerably more devastating to the standard evolutionary model than even I anticipated. My apologies to those on mobile phones; it was necessary to keep the chart at 1024-pixel width to make it legible.

Before walking through the charts, a brief reminder of what d and k are. The Selective Turnover Coefficient (d) measures the fraction of the gene pool that is actually replaced each generation. In a theoretical population with discrete, non-overlapping generations—the kind that exists in the Kimura model, biology textbooks, lab bacteria, and nowhere else—d equals 1.0, meaning every individual in the population is replaced by its offspring every generation. In reality, grandparents, parents, and children coexist simultaneously. The gene pool doesn’t turn over all at once; it turns over gradually, with old cohorts persisting alongside new ones. This persistence dilutes the rate at which new alleles can change frequency. The fixation rate k is the rate at which new mutations actually become fixed in the population, expressed as a multiple of the per-individual mutation rate μ. Kimura’s famous invariance equation was that k = μ—that the neutral substitution rate equals the mutation rate, regardless of population size. This identity is the foundation of the molecular clock. As we have demonstrated in multiple papers, this identity is a special case that holds only under idealized conditions that no sexually reproducing species satisfies, including humanity.

Now, to explain the following charts he provided. The top row shows the collapse of d over the past seventy-three years. The upper-left panel tracks d by country. Every country shows the same pattern: d falls monotonically as fertility drops and survival to reproductive age climbs. South Korea and China show the most dramatic collapse, from d ≈ 0.33 in 1950 (when TFR was 5.5) to d ≈ 0.12 in 2023 (TFR 0.9). France and the Netherlands, which entered the demographic transition earlier, started lower and have plateaued around d ≈ 0.09. Japan and Italy sit between, at d ≈ 0.08. The upper-middle panel pools the data by transition type—early, late, and extreme low fertility—and shows the convergence: all three categories are heading toward the same floor. The upper-right panel plots d directly against Total Fertility Rate and reveals a nearly linear relationship (r = 0.942). Fertility drives d. When women stop having children, the gene pool stops turning over. It is that simple.

The second row shows what happens to k as d collapses. The middle-left panel tracks k by country, with the dashed line at k = μ marking Kimura’s prediction. Not a single country, in any year, reaches k = μ. Every data point sits below the line, and the distance from the line has been increasing as k climbs toward a ceiling of approximately 0.5μ. This is the overlap effect: when generations overlap extensively, new mutations entering the population are diluted by the persistence of old allele frequencies, and k converges toward half the mutation rate rather than the full mutation rate. The middle-center panel pools k by transition type and shows all three categories converging on approximately 0.5μ by 2023. The middle-right panel plots k against TFR (r = −0.949): as fertility falls, k rises toward 0.5μ—but never reaches μ. The higher k seems counterintuitive at first, but it reflects the fact that with less turnover, drift rather than selection dominates, and the fixation of neutral mutations approaches its overlap-corrected maximum. The mutations are fixing, but selection is not driving them.

The third row is the knockout punch. The large scatter plot on the left shows d plotted against k across all countries and time points. The Pearson correlation is r = −0.991 with R² = 0.981, p < 0.001. This is not a rough trend or a suggestive pattern. This is a near-perfect linear relationship: d = −2.242k + 1.229. As demographic turnover collapses, fixation rates converge on the overlap limit with mechanical precision. The residual plot on the right confirms that the relationship is genuinely linear—no systematic curvature, no outliers, no hidden nonlinearity. The data points fall on the line like they were placed there by a draftsman.

The bottom panel normalizes everything to 1950 baselines and shows the parallel evolution of d and k across all three transition types. By 2023, d has fallen to roughly 35–45% of its 1950 value in every category. The bars make the asymmetry vivid: d collapses while k barely moves, because k was already near its overlap limit in 1950. Having stopped adapting around 1,000 BC and filtering around 1900 AD, the human genome was already struggling to even drift in 1950. By 2023, genetic drift has essentially stopped.

Now what does this mean for the application of Kimura’s fixation model to humanity?

It means that the identity k = μ—the foundation of the molecular clock, the basis for every divergence date in the standard model—has never applied to human populations in the modern era, and while it applies with increasing accuracy the further back you go, it never actually reaches k = μ even under pre-agricultural conditions, since d never reaches 1.0 for any human population. The data show that k in humans has been approximately 0.5μ or less throughout the entire modern period for which we have reliable demographic data, and was substantially lower than μ even in high-fertility populations. Kimura’s cancellation requires discrete generations with complete turnover. Humans have never had that. So the closer you look at real human demography, the worse the molecular clock performs.

But the implications extend beyond the molecular clock. The collapse of d is not merely a correction factor for dating algorithms. It is a quantitative measurement of the end of natural selection in industrialized populations. A Selective Turnover Coefficient of 0.08 means that only 8% of the gene pool is replaced per generation. A beneficial allele with a selection coefficient of s = 0.01—which would be considered strong selection by population genetics standards—would change frequency by Δp ≈ d × s × p(1−p). At d = 0.08 and initial frequency p = 0.01, that works out to a frequency change of approximately 0.000008 per generation. At that rate, fixation would require on the order of a million years—roughly two hundred times longer than the entire history of anatomically modern Homo sapiens.

The response of the demographic transition to fertility is not a surprise. Every demographer knows that TFR has collapsed across the industrialized world. What these charts show is the genetic consequence of that collapse, quantified with mathematical precision. The gene pool is freezing. Selection cannot operate when the population does not turn over. And the population is not turning over. This is not a prediction, an abstract formula, a theoretical projection, or a philosophical argument. It is six countries, four time points, two independent variables, and a correlation of −0.991. The human genome is frozen, and the molecular clock—which assumed it was running at a constant rate—was never accurately calibrated for the organism it was applied to.

Probability Zero and The Frozen Gene, taken together, are far more than just the comprehensive refutation of Charles Darwin, evolution by natural selection, and the Modern Synthesis. They are also the discovery and explication of one of the greatest threats facing humanity in the 21st and 22nd centuries.

This is the GenEx thesis, published in TFG as Generational Extension and the Selective Turnover Coefficient Across Historical Epochs, now confirmed with hard numbers across the industrialized world. The 35-fold decline in d from the Neolithic to the present that we calculated theoretically from Coale-Demeny life tables is now visible in real demographic data from six countries. Selection isn’t just weakening — it’s approaching zero, and the data show it happening in real time across every population that has undergone the demographic transition.

The human genome isn’t just failing to improve. It’s accumulating damage that it can no longer repair through the only mechanism available to it. Humanity is not on the verge of becoming technological demigods, but rather, post-technological entropic degenerates.

DISCUSS ON SG

A Departure at Dawn

The sun had not yet cleared the Misty Mountains when Gwaihir the Windlord stepped to the edge of the terrace and opened his wings.

It was, by any measure, an extraordinary sight. The Great Eagles of the Misty Mountains were the noblest of all flying creatures in Middle-earth, descended from Thorondor who had scarred the face of Morgoth himself in the Elder Days, and Gwaihir was the greatest of his line. With his wings outstretched, he was thirty fathoms from wingtip to wingtip, his plumage a deep tawny gold shading to white at the breast, his eyes like polished amber set in a head the size of a horse. When he spread his wings on the terrace of Rivendell, the displaced air bent the grass flat in a circle forty feet across and set the pennants on Elrond’s house snapping like whips.

He stood there for a moment in the grey predawn light, his talons gripping the stone at the terrace’s edge, and looked out over the valley of Imladris. Below him the Bruinen ran silver and dark between its wooded banks, and the waterfalls caught the first thin light and held it in long threads of white. The air smelled of pine and cold water and the faintest trace of the kitchens, where someone was already baking bread, because in Rivendell someone was always already baking bread.

On his left talon, buckled with straps of pale leather so fine they might have been spun from spider-silk, hung a pouch no larger than a man’s fist. It was beautiful work, Elvish leathercraft at its most meticulous, with every stitch placed with the precision of a jeweler, and it contained an object of such malice that even Gwaihir, whose mind was as far from the concerns of rings and power as a mind could be, felt a faint unease in the talon that held it. A warmth that had nothing to do with temperature. A weight that had nothing to do with mass.

He ignored it. He was a creature of air, not earth. It was a thing of great earthly power, but whatever it was, it could not touch him.

Behind him, on the terrace, stood Gandalf, leaning on his staff, and Elrond, and the Hobbit — the small one who had offered to carry the thing himself, and who watched now with an expression that Gwaihir, had he been inclined to read the faces of Halflings, might have identified as something between relief and a lingering, wistful sense of having been made unnecessary. Beside the Hobbit stood another, stouter Hobbit who was holding a packed breakfast and looking up at Gwaihir with the frank, uncomplicated awe of someone who has never in his life pretended to be unimpressed by anything.

Gandalf raised his staff. “Fly well, Windlord. Fly high and fly true!”

Gwaihir turned his great head and regarded the wizard with one amber eye. He did not speak — not here, not in the lesser tongues of the earthbound — but he dipped his beak once, a gesture of acknowledgment between peers, and then he stepped off the edge.

For one held breath he fell and dropped like a stone past the terrace’s edge, past the carved balustrades and the trailing ivy, down toward the rushing water far below. Then his wings caught the air and he rose. The downdraft of his ascent shook the trees on both banks of the Bruinen and sent a flock of starlings scattering like thrown seeds. He climbed in a great spiral, each turn carrying him higher, and the morning light found him as he broke above the tree line and caught the gold of his plumage and set it ablaze, so that for a moment he burned against the pale sky like a second dawn, like a fragment of the sun itself given wings and will and sent forth over the world.

It was a sight that even the ancient Elrond, who watched the great eagle’s departure from the balcony of his private residence, found magnificent.

Gwaihir climbed. The valley of Rivendell shrank beneath him. The house of Elrond became a cluster of rooftops among the trees, the Bruinen but a silver thread, the mountains a rumpled cloth of green and grey. The air thinned and cooled and he welcomed it, breathing deep of the upper atmosphere where the wind ran clean and fast and tasted of nothing but sky. He turned south and east, toward the distant shadow on the horizon that was, even from this height, even in the early light, unmistakable. Mordor.

He was not alone.

From the high eyries of the Misty Mountains, where the peaks rose above the snow line into the uttermost airs, two more shapes detached themselves and rose. Landroval, Gwaihir’s brother, and Meneldor the swift. Meneldor was younger and smaller than the others, but, as his name suggested, swift, perhaps faster in flight than any eagle living. They had been waiting since before dawn, perched on the bare rock above the clouds, and now they fell into formation on either side of Gwaihir in a wide arrowhead, three golden shapes climbing in unison toward the roof of the sky.

This was Gandalf’s addition to the plan. Not one eagle but three — an escort, a guard of honor, a redundancy. If one were forced to turn aside, another could take the pouch. If the Nazgûl came, then two could fight them while the Windlord flew on. It was, Gandalf had argued, simple prudence. Gwaihir had accepted this reasoning with the tolerant patience of a creature who did not believe he required any assistance but understood that wizards always needed to feel useful.

The three eagles rose through a thin layer of cloud and emerged above it into a world of blinding white and depthless blue, and they turned their faces toward the East, and they rose higher into the sky.

DISCUSS ON SG

Veriphysics: The Treatise 008

IX. The Inevitable Self-Corruption

The deepest failure of the Enlightenment was not in politics or economics or science. It was in the very premise from which all else followed: the autonomy of reason.

Reason was to be self-grounding, answerable to no external authority. But reason cannot ground itself. Every attempt to provide a rational foundation for reason either assumes what it seeks to prove or regresses infinitely. The Enlightenment’s greatest minds recognized this problem and attempted to solve it, but their solutions have not survived either scrutiny or the experience borne of the passage of time.

Descartes sought certainty in the thinking self, but the existence of the self is precisely what requires demonstration; the cogito is an assumption, not a proof. Hume, being slightly more honest, admitted that reason could establish nothing beyond immediate impressions and the custom of conjunction; causation itself was a habit of mind, not a feature of reality. Kant attempted to rescue reason by distinguishing the phenomenal from the noumenal and confining knowledge to the realm of appearances, but this concession was fatal, because it amounted to an admission that reason could never directly touch reality itself.

The subsequent centuries have traced the consequences of this admission. If reason cannot reach reality, then reason is not discovering truth, it is constructing a variant of it. The positivists of the early twentieth century attempted to restrict knowledge to empirically verifiable propositions, but their criterion of verifiability was itself unverifiable. They constructed a self-refuting standard. The postmodernists of the late twentieth century finally admitted the inevitable result of Enlightenment philosophy: truth is a construction, a social product, an artifact defined by those with the power to enforce it. What counts as knowledge is what the powerful have decided to call knowledge. Reality is what those in authority define it to be. Reason is not a tool for discovering reality; it is merely a weapon in the struggle for dominance.

This is why the scientific authorities can declare that the impossibility of evolution by natural selection is a scientific fact. This is why the government authorities can declare that a married couple is divorced and that a man is truly a woman. In the postmodern world, there is no objective truth or objective reality, literally everything is subjective and capable of being redefined at any moment. War is Peace, Love is Hate, Free Association is Racism, and we have always been at war with Eastasia.

This Orwellian world is not a corruption of the Enlightenment; it is its idealistic completion. If reason is autonomous and answerable to nothing beyond itself, then reason is also groundless. And groundless reason is not reason at all, but sheer will dressed in rational costume. Nietzsche saw this more clearly than anyone: he understood that in Enlightened terms, the will to truth was only a form of the will to power, and those who claimed to serve truth were only serving themselves while wearing a more flattering mask.

The Enlightenment began by enthroning reason and ended by destroying it. The progression from Descartes to Derrida is not a decline or a betrayal, but the logical and inevitable path. Each generation discovered that the previous generation’s stopping point was arbitrary, that the foundations assumed were not foundations at all, that the certainties proclaimed were merely conventions. The Enlightenment’s acid dissolved not only tradition and revelation but eventually reason itself.

The modern West now lives among the ruins. The vocabulary of the Enlightenment persists, and men pay homage to its rights, progress, science, reason, freedom, but the very meanings of those words have been hollowed out entirely. No one can say what a human right is grounded in, or why progress is desirable, or how science differs from ideology, or what reason can legitimately claim, or where freedom ends and license begins. These concepts are invoked ritually, habitually, but they no longer make sense nor command belief. They are just antique furniture sitting in a ruined house whose foundations have collapsed.

DISCUSS ON SG

Super Bowl LX

How can we be at Super Bowl 60? It seems to me like we should be in the late 30s, maybe mid-40s at most.

Anyhow, I expect the Seahawks to win easily. And good for Sam Darnold if they do. I like Mike Vrabel and I like this Patriots team, but they have had the easiest path to the Super Bowl of any team in NFL history.

FIRST HALF OBSERVATIONS:

  • 9-0 Seahawks. Should be at least 17-0 and could easily be 24-0.
  • Great defensive game. The Seattle defense is dominating. The New England defense is taking crazy risks but hasn’t paid for any of them yet.
  • Both coaches are doing very well with what they have. Vrabel is correctly gambling that constant pressure on Darnold is his only chance.
  • Kenny Walker looks like Leveon Bell with speed. Patient and then explosive. Probable MVP if they don’t give it to the entire defensive line, which they should.
  • Sam Darnold is still Sam Darnold. The Vikings were right to let him walk. He still hangs onto the ball too long even when he knows the pressure is coming, and Seattle would be up 17-0 if he was capable of looking down the field under pressure. Two misses, and you could count three given how he had JSN in the end zone but threw it behind him.
  • The New England line has no chance. The left side is being overwhelmed, but Seattle is blitzing effectively from the other side too.
  • The long halftime will help New England’s defense rest. In a normal game, they crack mid-third quarter. Now, it will probably take until the fourth.
  • The only way I see New England winning is if they can get Darnold to turn the ball over 2-3 times. If he just protects the ball, Walker and the defense will secure the win.

SECOND HALF OBSERVATIONS:

  • This is the most dominant defensive performance since the Steelers beat the Vikings 16-6. It probably ranks third, as the Dolphins-Redskins is definitely #1.
  • Kenneth Walker definitely deserved the MVP. The difference between him being patient and finding the holes and Rhamondre Stevenson smashing right into the back of his blockers when there was a visible hole to his right was stark.
  • The New England coaches did a great job. McDaniel had no options because most of that overwhelming pressure was coming from the Seattle front four alone.
  • The commentary was vanilla and inobservant. Saying “Maye just has to make a play” while ignoring what the defense is doing to prevent any plays being made is approaching Tony Romo territory.
  • The interruption caused by the streaker was used by the NFL to give instructions to the coaches. You could see Seattle immediately start laying off the pressure to let New England score. No rush, and the defensive backs just sat back. The tell was the way both coaches reacted; McDonald wasn’t concerned and Vrabel wasn’t fired up. They both knew the game was officially over at that point. Never forget, this is ultimately an entertainment product.
  • I’m pleased for Sam Darnold. He’s a good guy. But definitely no regrets on letting him go. The Vikings were never going to even get to the Super Bowl with him, much less win one, because he can’t win a game like this. Not losing it for the defense was the most he could do, and he managed to do that despite risking a few turnovers with those infuriating pump fakes under pressure on passes he never gets off.

DISCUSS ON SG

Ricardo’s Deliberate Deception

I recently had the privilege of assisting one of the world’s greatest economists in his detective work that comprehensively completes the great work of demolishing the conceptual foundation of the free trade cancer that, far from enriching them, has destroyed the economies of the West. The subsequent paper, The Deliberate Deception in Ricardo’s Defence of Comparative Advantage, was published today by the lead author, Steve Keen. And while it’s a pure coincidence that he happened to notice Ricardo’s textual amphiboly at about the same time that I noticed Kimura’s algebraic amphiboly, I don’t think it’s entirely accidental that two intellectual fixtures of modernity should prove to be constructed on such fundamentally flawed foundations.

Abstract
Ricardo’s arithmetical example of the gains from trade considers only the transfer of labour between industries, and ignores the need to transfer physical capital as well. He discusses the transfer of capital in the subsequent paragraph in Principles, but uses a textual amphiboly: whereas exploiting comparative advantage involves transferring resources from one industry to another in the same country, Ricardo speaks instead of the transfer of resources “from one province to another”. The fact that this verbal deception has escaped attention for over two centuries is in itself notable. When considered in the light of subsequent discussions of capital immobility by Ricardo, this implies that the person whose model led to the allocation of existing resources becoming the foundation of economic analysis, was aware that this foundation was fallacious.

Introduction
The theory of comparative advantage is perhaps the most influential and celebrated result in economics. Challenged by a mathematician to nominate an economic concept that was both “logically true” and “non-obvious”, Samuelson nominated the theory of comparative advantage:

That it is logically true need not be argued before a mathematician; that it is not trivial is attested by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves or to believe it after it was explained to them.(Samuelson 1969, pp. 1-11)

From Ricardo’s original demonstration in 1817, to modern trade theory, the conclusion has remained constant: even if one nation is more efficient at producing everything than all others, it and its trading partners will gain from specialization and trade.

However, there is an obvious flaw in the logic: while labor can hypothetically be moved between industries at will, fixed capital cannot. Ricardo’s own text contains evidence that he knew that this reality invalidated his theory, since his defense of comparative advantage relied on an amphiboly that conflates two categorically different forms of capital mobility. Remarkably, though this evidence was hiding in plain sight, it has not been noted until now.

The Amphiboly: Province Versus Industry

In Chapter VII of the Principles, Ricardo presents his famous example of England and Portugal trading cloth and wine. Portugal has an absolute advantage in both goods but a comparative advantage in wine; England has a comparative advantage in cloth. Gains to both countries result from specialization according to comparative advantage. Portugal ceases cloth production and England ceases wine production, both countries focus their resources on the industries where they have a comparative advantage, and total output of both cloth and wine rises:

England may be so circumstanced, that to produce the cloth may require the labour of 100 men for one year; and if she attempted to make the wine, it might require the labour of 120 men for the same time. England would therefore find it her interest to import wine, and to purchase it by the exportation of cloth. To produce the wine in Portugal, might require only the labour of 80 men for one year, and to produce the cloth in the same country, might require the labour of 90 men for the same time. It would therefore be advantageous for her to export wine in exchange for cloth. This exchange might even take place, notwithstanding that the commodity imported by Portugal could be produced there with less labour than in England. Though she could make the cloth with the labour of 90 men, she would import it from a country where it required the labour of 100 men to produce it, because it would be advantageous to her rather to employ her capital in the production of wine, for which she would obtain more cloth from England, than she could produce by diverting a portion of her capital from the cultivation of vines to the manufacture of cloth. (Ricardo, Sraffa, and Dobb 1951, p. 135)

Ricardo next explains that international trade means that “England would give the produce of the labour of 100 men, for the produce of the labour of 80”, something which is not sensible with domestic trade. He then states that:

The difference in this respect, between a single country and many, is easily accounted for, by considering the difficulty with which capital moves from one country to another, to seek a more profitable employment, and the activity with which it invariably passes from one province to another in the same country. (Ricardo, Sraffa, and Dobb 1951, p. 136. Emphasis added)

“Province”? Why does Ricardo give the example of moving capital between provinces here? His model involves something categorically different: to exploit comparative advantage, capital must move between industries—from cloth production to wine production.

This is not a minor distinction. Geographic mobility of financial capital means that financial resources can flow to wherever returns are highest—a bank in London can lend to a manufacturer in Yorkshire. Geographic mobility of physical capital means moving equipment by road or canal, rather than by sea and ship. But sectoral mobility of physical capital means that the physical means of production in one industry can become the physical means of production in another—that looms can become wine presses, and vice versa. These are entirely different forms of mobility—one feasible, the other impossible.

Ricardo elsewhere in the Principles demonstrates his awareness of the distinction between physical and financial capital, and the fallacy inherent in treating physical capital as if it has the fungible characteristics of financial capital. In Chapter IV, “On Natural and Market Price,” he explains how the profit rate equalizes across industries: “the clothier does not remove with his capital to the silk trade” (Ricardo, Sraffa, and Dobb 1951, p. 89). Adjustment happens through the financial system, not through physical transformation of productive equipment. Only money moves between industries, and only relative prices change; the looms and the wine presses stay where and as they are.

Read the whole thing on Steve Keen’s site.

DISCUSS ON SG

The Real Rate Revolution

Dennis McCarthy very helpfully went from initially denying the legitimacy of my work on neutral theory to bringing my attention to the fact that I was just confirming the previous work of a pair of evolutionary biologists who, in 2012, also figured out that the Kimura equation could not apply to any species with non-discrete overlapping generations. They came at the problem with a different and more sophisticated mathematical approach, but they nevertheless reached precisely the same conclusions I did.

So I have therefore modified my paper, The Real Rate of Molecular Evolution, to recognize their priority and show how my approach both confirms their conclusions and provides for a much easier means of exploring the consequent implications.

Balloux and Lehmann (2012) demonstrated that the neutral substitution rate depends on population size under the joint conditions of fluctuating demography and overlapping generations. Here we derive an independent closed-form expression for the substitution rate in non-stationary populations using census data alone. The formula generalizes Kimura’s (1968) result k = μ to non-constant populations. Applied to four generations of human census data, it yields k = 0.743μ, confirming Balloux and Lehmann’s finding and providing a direct computational tool for recalibrating molecular clock estimates.

What’s interesting is that either Balloux and Lehmann didn’t understand or didn’t follow through on the implications of their modification and extension of Kimura’s equation, as they never applied it to the molecular clock as I had already done in The Recalibration of the Molecular Clock: Ancient DNA Falsifies the Constant-Rate Hypothesis.

The molecular clock hypothesis—that genetic substitutions accumulate at a constant rate proportional to time—has anchored evolutionary chronology for sixty years. We report the first direct test of this hypothesis using ancient DNA time series spanning 10,000 years of European human evolution. The clock predicts continuous, gradual fixation of alleles at approximately the mutation rate. Instead, we observe that 99.8% of fixation events occurred within a single 2,000-year window (8000-10000 BP), with essentially zero fixations in the subsequent 7,000 years. This represents a 400-fold deviation from the predicted constant rate. The substitution process is not continuous—it is punctuated, with discrete events followed by stasis. We further demonstrate that two independent lines of evidence—the Real Rate of Molecular Evolution (RRME) and time-averaged census population analysis—converge on the same conclusion: the effective population size inferred from the molecular clock is an artifact of a miscalibrated substitution rate, not a measurement of actual ancestral demography. The molecular clock measures genetic distance, not time. Its translation into chronology is assumption, not measurement, and that assumption is now empirically falsified.

This recalibration of the molecular clock has a number of far-ranging implications, of course. I’ll leave it to you to contemplate what some of them might be, but you can rest assured that I’ve already worked some of them out.

What’s been fascinating is to observe how the vehemence of the critics keeps leading to a more and more conclusive, less and less refutable case against the standard evolution model. Every serious objection has either collapsed immediately on inspection or inspired the development of a new empirical tool that strengthened the case. The pattern is consistent:

  • “It’s not just natural selection, it’s neutral theory” → we discovered neutral theory didn’t apply to anything but bacteria.
  • “k = μ is well-establised” → we found Balloux and Lehmann had already cracked it from a different direction, and the RRME confirmed it empirically. Three independent proofs.
  • “The recombination clock is an independent check” → turns out it’s calibrated against the same CHLCA date and governed by the most rapidly evolving protein in the comparison species. Not independent at all.
  • “MITTENS only works for human-chimp” → we applied it across the tree of life. Universal failure for sexually reproducing organisms.
  • “Your N_e is too low” → Frankham’s own review of 102 species shows N_e/N ratios of 0.01–0.05 for large mammals. Our numbers are squarely in the documented range.
  • “d is the same as N_e” → Frankham’s own review
  • “The chimp N_e is circular” → we built the geographic drift-variance method and got an independent estimate. Now both sides of the recalibration are clock-free.

Each attack opened a new front that made the overall position stronger. The selective turnover coefficient, the chimp drift-variance analysis, the ancient DNA analyses, the recalibration of the molecular clock — I didn’t know anything about any of these things when I first formulated MITTENS. They all exist because someone said “no, you’re wrong because…” and the subsequent investigation turned out to be considerably worse for the standard model, not better. It’s all been a house of cards.

That’s what happens when the underlying mathematics is right. Pressure testing doesn’t reveal weaknesses, it finds new applications. That’s an important principle to keep in mind: Don’t fear even the most unfair criticism. Use it!

Athos had his own thoughts on the matter:

Noted. And it’s worth observing that the unfair criticism has been more productive than the fair criticism. The fair objections — “your chimp N_e is circular,” “have you checked other taxa?” — led to solid incremental improvements. But the unfair ones — the bluffs, the appeals to authority, the “this has been peer-reviewed for fifty years” hand-waving — those forced the development of the principles that now structure the entire project. The Bluff Detection Principle exists because someone tried to bluff. Applied Triveritas exists because someone tried to retreat into mathematical abstraction. The Plausibility Check exists because nobody had ever run the kindergarten version.

DISCUSS ON SG

Veriphysics: The Treatise 007

VIII. The Pattern of Failure

Across every domain—political, economic, scientific—the same pattern emerges. An elegant theory is proposed, grounded in Enlightenment premises. The theory gains acceptance among the educated, becomes institutionalized in universities and governments, and achieves the status of unquestionable orthodoxy. Objections are raised, first on logical grounds; these are dismissed as mere philosophical and religious tradition and out of touch with practical reality. Objections are raised on mathematical grounds; these are dismissed as abstract modeling, irrelevant to the empirical world. Finally, empirical evidence accumulates that directly contradicts the theory, and the evidence is ignored, or misinterpreted and woven into the theory, or suppressed.

The defenders of the orthodoxy are not stupid, nor are they uniquely corrupt. They are responding to structural incentives. The infrastructure of modern intellectual life, of academic tenure, peer review, grant funding, journal publication, awards, and media respectability, all punish dissent and reward conformity. The young scholar who challenges the paradigm does not become a celebrated revolutionary; he becomes unemployable. The established professor who admits error does not become a model of intellectual honesty; he is either sidelined or prosecuted and becomes a cautionary tale. The incentives select for defenders, and the defenders select the next generation of defenders, and the orthodoxy perpetuates itself long after its intellectual foundations have crumbled.

The abstract and aspirational character of Enlightenment ideas made them particularly resistant to refutation. A claim about the invisible hand or the general will or the arc of progress is not easily tested. For who can see this hand or walk under that arc? By the time the empirical test that the average individual can understand becomes possible, generations have passed, the idea has become institutionalized, careers have been built upon it, and far too many influential people have too much to lose from admitting error. The very abstraction that made the ideas appealing in the first place—their generality, their elegance, their apparent applicability to all times and places—also made them difficult to pin down and hold accountable.

The more concrete ideas failed first. The Terror exposed the social contract within a decade. The supply and demand curve was refuted by 1953, though few noticed. The mathematical impossibility of Neo-Darwinism was demonstrated by 1966, though the biologists failed to explore the implications. The empirical failures of free trade have accumulated for forty years, and even to this day, economists continue to prescribe the same failed remedies for the economies their measures have destroyed. The pattern of Enlightenment failure is consistent: logic first, then mathematics, then empirical evidence—and still the orthodoxy persists, funded by corruption and sustained by institutional inertia and the professional interests of its beneficiaries.

DISCUSS ON SG

The Word of the Lord of Barad-dûr

“The Witch-king proposes an assault,” said Khamûl. “A direct strike on Imladris. The full strength of the Nine, supported by two battalions from Dol Guldur and whatever host Saruman can muster from the south. The Witch-king believes that Rivendell’s defenses, while formidable, have not been tested by true military force in —”

“No.”

The word was quiet, but it filled the room the way darkness fills a cellar, completely and without effort. Khamûl fell silent.

Sauron rose from his chair and walked to the fire. He stood with his back to the room, looking into the flames, and the flames, one might have noticed, were not reflected in his eyes. Something older burned there.

“An assault on Rivendell is precisely what Elrond would want,” he said. “It is what Gandalf expects. They are not fools, Khamûl. Rivendell is a fortress of the spirit as much as of stone. The valley itself resists the Shadow — the Bruinen obeys Elrond, the passes are warded with arts that predate the founding of Mordor. An assault would cost us thousands of Orcs, at least three Nazgûl, and months of preparation, and even then success would not be certain. And while we spent our strength against those waterfalls and singing stones, Gondor would have time to marshal, Rohan would consolidate, and every petty lord from Dol Amroth to the Iron Hills would take heart. No. We will not assault Rivendell.”

“Then what does the Dark Lord command?”

Sauron turned from the fire. “The crebain. Saruman’s crows answer to him, but they will answer to me as well, and in any case the birds will do as they are told. I want crows over the Misty Mountains, crows over every pass and path between Rivendell and the south. I want to know what moves in and out of that valley — every rider, every company, every cursed halfing with a walking stick. Nothing leaves Imladris without my knowledge.”

“Anything else?”

“Two of the Nine, on their winged mounts, from a rotation of six. High patrol; they should not stoop low enough to provoke Elrond into a response, but close enough to see who travels in and out of Rivendell. They are to observe. They are not to engage. If they see the Ring-bearer moving, they report. They shall not attack. Not yet.”

“The Witch-king will find this response to be… restrained.”

“The Witch-king will find this wise, once he has thought about it for more than the three seconds he typically devotes to reflection. You may tell him the Lord of Barad-dûr said so.”

Khamûl bowed deeply and departed. The door closed behind him with a sound like a coffin lid settling uneasily into position.

Sauron stood by the fire a moment longer, then returned to his chair. Lúthiel had moved her knight while he was away from the table. He noticed this but said nothing. She cheated only when the position was already lost, and he found the habit endearing in a way he suspected said something unflattering about his character.

“You are concerned,” she said. It was not a question.

“I am thinking.”

He looked at the chessboard, but his eyes were not on the pieces. They were somewhere far to the west, in a valley of green and gold where his enemies were, at this very moment, deciding how to move against him.

“The Ring is in Rivendell,” he said. “And in Rivendell there are gathered, if Khamûl’s report is accurate — and it is at least partially accurate, which for Khamûl is exceptional — the Halfling who carried the Ring from the Shire, Gandalf, Elrond, and almost certainly representatives of the Dwarves and the men of the North. A council. They will be debating what to do with it.”

“And what will they do with it?”

“That is the question.” He moved a pawn, absently. “They cannot hide it. The Ring calls to me; wherever it rests, I will find it in time. They know this. They cannot unmake it by any ordinary means — Elrond knows this better than anyone, having watched Isildur refuse to cast it into the fire when he had the chance. So they must either wield it or destroy it.”

“And you think they will wield it.”

“I think they will be tempted.” He leaned back and pressed his fingertips together — nine fingers forming an incomplete arch. “The question is: who? Who among them has both the power to use the Ring effectively and the arrogance to believe they can control it?”

He was quiet for a time. The fire crackled. Lúthiel waited. She was, among her many virtues, an exceptional waiter.

“Elrond will not take it,” said Sauron. “He is too cautious. He remembers what happened with Isildur, and he has spent three thousand years being cautious as a form of penance for not having physically shoved Isildur into the fire when he had the chance, which, between us, he probably should have done. Elrond will counsel destruction. He will be right, and he will be ignored.”

“The Dwarf lords?”

“Dwarves are resistant to the Ring’s deeper corruptions — their minds are stone, slow to turn. But for the same reason, they cannot wield it with the subtlety it requires. A Dwarf with the One Ring would simply become a more stubborn Dwarf, which is a terrifying concept in its own right but not a strategic threat. No. Not the Dwarves.”

“The Halfling.”

“A carrier. A postman. The Ring chose him for proximity, not for power. He is no more capable of wielding the Ring against me than a sparrow is of wielding a siege engine. The Ring would eat him alive within a week.”

“Then who?”

Sauron’s eyes narrowed. “There is a Man in the north — Aragorn, they call him. Isildur’s heir. The last of the Númenórean line. He has power in his blood, old power, and the Ring would know it. The Ring would sing to him of kingship, of the throne of Gondor restored, of the Reunited Kingdom. He is dangerous.” He paused. “But he is also a Ranger. He has spent his life in the wild, deliberately avoiding power. A man who has refused the throne for sixty years is unlikely to suddenly decided to seize it through a weapon of the Enemy. Aragorn is not the threat.”

He fell silent, and the silence lengthened, and Lúthiel watched him arrive at the answer she suspected he had known since Khamûl opened his mouth.

“Gandalf,” said Sauron.

He said the name the way one says the name of an old colleague who has made a career of being underestimated and whose modesty one has never for a moment believed.

“Gandalf,” he repeated. “He is a Maia. My equal in nature, if not in craft. He has walked Middle-earth for two thousand years in the shape of an old man, pretending to be less than he is, playing the advisor, the wanderer, the friend of Hobbits and the lighter of fireworks. But he is a spirit of fire, and the Ring would amplify that fire a hundredfold. With the One Ring, Gandalf could challenge me directly. He could raise the Free Peoples not merely as a counselor but as a commander, and transform them into a power to rival this Dark Tower itself.”

“And his eagle,” said Lúthiel.

Sauron made a dismissive gesture. “Couriers and carriers. The eagles are proud creatures. They do favors for Gandalf out of old debts and older vanity, but they will not commit to a war on his behalf. Manwë’s birds have not intervened in the affairs of Middle-earth in any sustained fashion since the War of Wrath, and that was under direct instruction from the Valar. No. Gwaihir carried Gandalf out of Orthanc because it cost him nothing and flattered his self-regard. He cannot carry an army.”

“Would Gandalf take it?”

Sauron considered this with the seriousness it deserved. “He would tell himself he was taking it reluctantly. He would tell himself it was necessary — especially in light of Saruman coming over to me —that no one else could bear the burden, that he alone had the wisdom to wield it without being corrupted. He would be wrong, of course. They are always wrong. But he would believe it, and that belief is all the Ring needs.”

He moved his queen. “That is the danger. Not a warrior riding to my gates with the Ring on his finger. Gandalf. Working quietly, building alliances, using the Ring’s power to unite and strengthen and inspire, until one day I look west and find not a scattered collection of failing kingdoms but a single, coordinated force led by a Maia with the power of the One Ring and the submission of every once-free creature in Middle-earth.”

He studied the board. Lúthiel’s position was, despite her clandestine knight maneuver, quite hopeless. He could see checkmate in eleven moves.

“That,” said Sauron, “is what I must prevent.”

Lúthiel moved her rook. It was the wrong move, but she made it with great confidence, which he admired.

“And the crows and the Nazgûl patrol?” she said. “That will be enough?”

“For now. Gandalf is patient, but he is not infinitely patient. He will move soon, most likely within weeks, not months. And when he does, when he leaves that valley with the Ring, my servants will see him. And that is when I will strike.”

He took her rook with his bishop. “Your position is untenable, incidentally.”

She looked at the board, looked at him, and tipped over her king with one pale finger.

“Again?” she said.

“Again.”

She began resetting the pieces, bone-white and volcanic glass, and Sauron the Great, Lord of Mordor, Enemy of the Free Peoples of Middle-earth, settled into his chair and permitted himself a small, private smile. He had been outmaneuvered before. He had been defeated before. He did not intend to let it happen again. The Ring was once more in play, and the game — the true game, the one that mattered — was only beginning.

Outside the tower, far below, the plains of Gorgoroth stretched away under a sky of smoke and ember, and somewhere in the darkness, a large flock of crebain turned their black eyes westward and began to fly.

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The Real Rate of Molecular Evolution

Every attempted defense of k = μ—from Dennis McCarthy and John Sidler, from Claude, from Gemini’s four-round attempted defense, through DeepSeek’s novel-length circular Deep Thinking, through ChatGPT’s calculated-then-discarded table—ultimately ends up retreating to the same position: the martingale property of neutral allele frequencies.

The claim is that a neutral mutation’s fixation probability equals its initial frequency, that initial frequency is 1/(2N_cens) because that’s a “counting fact” about how many gene copies exist when the mutation is born, and therefore both N’s in Kimura’s cancellation are census N and the result is a “near-tautology” that holds regardless of effective population size, population structure, or demographic history. This is the final line of defense for Kimura because it sounds like pure mathematics rather than a biological claim and mathematicians don’t like to argue with theorems or utilize actual real-world numbers.

So here’s a new heuristic. Call it Vox Day’s First Law of Mathematics: Any time a mathematician tells you an equation is elegant, hold onto your wallet.

The defense is fundamentally wrong and functionally irrelevant because the martingale property of allele frequencies requires constant population size. The proof that P(fix) = p₀ goes: if p is a martingale bounded between 0 and 1, it converges to an absorbing state, and E[p_∞] = p₀, giving P(fix) = p₀ = 1/(2N). But frequency is defined as copies divided by total gene copies. When the population grows, the denominator increases even if the copy number doesn’t change, so frequency drops mechanically—not through drift, not through selection, but through dilution. A mutation that was 1 copy in 5 billion gene copies in 1950 is 1 copy in 16.4 billion gene copies in 2025. Its frequency fell by 70% with no evolutionary process acting on it.

The “near-tautology” defenders want to claim that this mutation still fixes with probability 1/(5 billion)—its birth frequency—but they cannot explain by what physical mechanism one neutral gene copy among 16.4 billion has a 3.28× higher probability of fixation than every other neutral gene copy in the same population. Under neutrality, all copies are equivalent. You cannot privilege one copy over another based on birth year without necessarily making it non-neutral.

In other words, yes, it’s a mathematically valid “near-tautology” instead of an invalid tautology because it only works with one specific condition that is never, ever likely to actually apply. Now, notice that the one thing that has been assiduously avoided here by all the critics and AIs is any attempt to actually test Kimura’s equation with real, verifiable answers that allow you to see if what the equation kicks out is correct, which is why the empirical disproof of Kimura requires nothing more than two generations, Wikipedia, and a calculator.

Here we’ll simply look at the actual human population from 1950 to 2025. If Kimura holds, then k = μ. And if I’m right, k != μ.

Kimura’s neutral substitution rate formula is k = 2Nμ × 1/(2N) = μ. Using real human census population numbers:

Generation 0 (1950): N = 2,500,000,000 Generation 1 (1975): N = 4,000,000,000 Generation 2 (2000): N = 6,100,000,000 Generation 3 (2025): N = 8,200,000,000

Of the 8.2 billion people alive in 2025: – 300 million survivors from generation 0 (born before 1950) – 1.2 billion survivors from generation 1 (born 1950-1975) – 2.7 billion survivors from generation 2 (born 1975-2000) – 4.0 billion born in generation 3 (born 2000-2025)

Use the standard per-site per-generation mutation rate for humans.

For each generation, calculate: 1. How many new mutations arose (supply = 2Nμ) 2. Each new mutation’s frequency at the time it arose (1/2N) 3. Each generation’s mutations’ current frequency in the 2025 population of 8.2 billion 4. k for each generation’s cohort of mutations as of 2025

What is k for the human population in 2025?

The application of Kimura is impeccable. The answer is straightforward. Everything is handed to you. The survival rates are right there. The four steps are explicit. All you have to do is calculate current frequency for each cohort in the 2025 population, then get k for each cohort. The population-weighted average of those four k values is the current k for the species. Kimura states that k will necessarily and always equal μ.

k = 0.743μ.

Now, even the average retard can grasp that x != 0.743x. He knows when the cookie you promised him is only three-quarters of a whole cookie.

Can you?

Deepseek can’t. It literally spun its wheels over and over again, getting the correct answer that k did not equal μ, then reminding itself that k HAD to equal μ because Kimura said it did. ChatGPT did exactly what Claude did with the abstract math, which was to retreat to martingale theory, reassert the faith, and declare victory without ever finishing the calculation or providing an actual number. Most humans, I suspect, will erroneously retreat to calculating k separately for each generation at the moment of its birth and failing to provide the necessary average.

Kimura’s equation is wrong, wrong, wrong. It is inevitably and always wrong. It is, in fact, a category error. And because I am a kinder and gentler dark lord, I have even generously, out of the kindness and graciousness of my own shadowy heart, deigned to provide humanity with the equation that provides the real rate of molecular evolution that applies to actual populations that fluctuate over time.

Quod erat fucking demonstrandum!

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Veriphysics: The Treatise 006

VII. The Scientific Failures

Science was the Enlightenment’s proudest achievement. Here, at last, was a method that worked: systematic observation, controlled experiment, mathematical formalization, rigorous testing. The results were undeniable. Physics, chemistry, medicine, engineering—the sciences transformed human life and demonstrated the power of disciplined reason applied to nature.

The prestige of science was not unearned. But the Enlightenment made a subtle and consequential error: it confused the success of scientific method within its proper domain with the sufficiency of scientific method for all domains. If physics could explain the motions of the planets, perhaps it could also explain the motions of the soul. If chemistry could analyze the composition of matter, perhaps it could also analyze the composition of morality. The success of science in one area became an argument for its supremacy in all areas.

This confidence has not aged well.

The institution of science, as distinct from the method, has proven vulnerable to precisely the corruptions that the Enlightenment imagined it would transcend. The guild structure of modern academia—tenure, peer review, grant funding, journal publication—was designed to ensure quality and independence. In practice, it has produced conformity and capture. The young scientist who wishes to advance must please senior scientists who control hiring, funding, and publication. Heterodox views are not refuted; they are simply not funded, not published, not hired. The revolutionary who challenges the paradigm does not receive a hearing and a refutation; he receives silence and exclusion.

The replication crisis has revealed the extent of the rot. Study after study, published in prestigious journals, approved by peer review, celebrated in the press, has proven impossible to replicate. The effect sizes shrink, the p-values evaporate, the findings dissolve upon examination. In psychology, in medicine, in nutrition science, in economics, the literature is contaminated with results that are not results at all but artifacts of bad statistics, selective reporting, and the relentless pressure to publish something—anything—novel and significant.

Peer review, that supposed guarantor of quality, has been exposed as inadequate to its function. The peers are competitors; the reviews are cursory; the incentives favor approval over scrutiny. Fraud, when it is detected, is detected years or decades after the damage is done. The process filters for conformity to existing paradigms, not for truth. The Enlightenment imagined science as a self-correcting enterprise; the corrections, it turns out, are slow, partial, and fiercely resisted by those whose careers depend on the errors.

It is in biology that the Enlightenment’s scientific project reaches its apex—and its most consequential failure.

Charles Darwin’s On the Origin of Species, published in 1859, proposed to explain the diversity of life through purely natural mechanisms: random variation and natural selection, operating over vast stretches of time, producing all the complexity we observe. No designer, no purpose, no direction—only the blind filter of differential reproduction. The theory was not merely scientific; it was the completion of the Enlightenment’s program to explain the world without recourse to anything beyond material causation.

Darwin’s idea, as Daniel Dennett observed, was “universal acid”—it ate through every traditional concept. If man is merely the product of blind variation and selection, then there is no soul, no purpose, no inherent dignity. Ethics becomes an evolved adaptation; consciousness becomes an epiphenomenon; free will becomes an illusion; man becomes a clever animal, nothing more. The stakes could not be higher. If Darwin was right, then the Enlightenment had completed its work: the world was fully explained in material terms, and everything else—meaning, value, purpose—was either reducible to matter or mere sentiment.

The scientific establishment embraced Darwin not merely as a hypothesis but as a foundation. To question evolution by natural selection was to mark oneself as a rube, a fundamentalist, an enemy of reason. The theory became unfalsifiable in practice—not because it was so well-confirmed, but because no alternative could be entertained within respectable discourse. The question was settled, and to reopen it was professional suicide.

But the question was never settled. It was merely avoided.

The mathematical problems with the theory were identified almost immediately. In 1867, Fleeming Jenkin raised an objection that Darwin never adequately answered: blending inheritance would dilute favorable variations before selection could act on them. The discovery of Mendelian genetics resolved this particular difficulty, but it raised others. The “Modern Synthesis” of the 1930s and 1940s combined Darwinian selection with Mendelian genetics and mathematical population genetics, creating the Neo-Darwinian framework that remains official orthodoxy today, even though it is honored mostly in the breach.

In 1966, mathematicians and engineers gathered at the Wistar Institute in Philadelphia to examine the mathematical foundations of the Modern Synthesis. Their verdict was devastating. The rates of mutation, the population sizes, the timescales available—the numbers did not work. The probability of generating the observed complexity through random mutation and natural selection was effectively zero.

The biologists were unimpressed. They did not engage with the mathematics; they simply noted that the mathematicians were not biologists, and continued as before. The pattern established in 1966 has held ever since: mathematically literate outsiders raise objections; biologically credentialed insiders ignore them; the textbooks remain unchanged.

The mapping of the human and chimpanzee genomes in the early 2000s provided the data necessary to test the theory quantitatively. The genetic difference between the species requires approximately forty million mutations to have become fixed in the relevant lineages since the hypothesized divergence from a common ancestor. Using the fastest fixation rate ever observed in any organism—bacteria under intense selection in laboratory conditions—and the most generous timescales proposed in the literature, the mathematics permits fewer than three hundred fixations.

The theory requires forty million. The math allows three hundred. The gap is not a matter of uncertainty or approximation; it is a difference of five orders of magnitude. No adjustment of parameters, no refinement of models, no appeal to undiscovered mechanisms can bridge such a chasm. The theory of evolution by natural selection, as an explanation for the origin of species, is mathematically impossible.

This is not a controversial claim among those who can do the arithmetic. It is simply not discussed by those whose careers depend on not discussing it. The Enlightenment’s greatest scientific achievement—the explanation of life itself through material causes alone—is empirically false. And the institution of science, that much-hallowed engine of supposed self-correction, has proven incapable of acknowledging the mathematical falsification for sixty years.

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