On November 4, 1960, the journal Science published a paper with one of the least ambiguous titles in the history of academic publishing. It was called “Doomsday: Friday, 13 November, A.D. 2026.”
That date is now 80 days away. It is, as advertised, a Friday. It is also, as advertised, the 13th.
The paper has been quietly circulating for 66 years, resurfacing every time somebody notices the calendar. It is not a prophecy, it was never presented as one, and the people who wrote it did not think the world would end. But the math in it is real, it was better than anyone expected for about 30 years, and the reason it eventually failed is genuinely more interesting than the doomsday framing.
The short version
- Who: Heinz von Foerster, a physicist and cybernetics pioneer, with coauthors Patricia Mora and Lawrence Amiot
- What they did: fitted every available world population estimate from year 1 to 1958 to a single growth equation
- What they found: the best fit was not exponential. It was hyperbolic, meaning the growth rate itself was accelerating.
- The consequence: a hyperbolic curve does not rise forever. It hits infinity at a finite moment, and for this data set that moment was November 13, 2026.
- The joke: von Foerster was born on November 13, 1911. He picked the day out of his own birth certificate.
- What happened next: global population growth peaked around 1962 and has been falling ever since. The hyperbolic era ended almost immediately after the paper ran.
- Where we are now: about 8.3 billion people, growing at roughly 0.83% a year, with the UN projecting a peak near 10.3 billion in the 2080s and a decline after that
What the equation actually says
Most growth you encounter is exponential. A population doubles every so many years, the curve gets steep, and it looks alarming on a chart, but the doubling time never changes. Exponential growth is predictable precisely because its rate is constant.
Von Foerster and his coauthors found something different in the historical record. The doubling time was itself shrinking. It took roughly 1,600 years to go from 250 million to 500 million. It took about 200 years to go from 500 million to a billion. It took 123 years to reach two billion, then 33 to reach three. Each doubling arrived faster than the last.
The equation they fitted takes the form N equals C divided by the quantity t-zero minus t, where t-zero is a critical year. The structure of that expression is the whole story. As the calendar creeps toward t-zero, the denominator shrinks toward zero, and the population the formula predicts climbs without limit. In the fitted data, t-zero came out at late 1826 plus two centuries, or in plain terms, the back end of 2026.
Mathematicians call that a singularity. It is not a claim that anything physically becomes infinite. It is the point where the equation stops describing anything at all, the way dividing by zero on a calculator does not produce a very large number so much as an error message. Von Foerster’s own framing was that any population growing at an accelerating rate is headed for trouble, and the singularity was the most vivid way to say so.
Why humans grew this way in the first place
Standard biology says a population runs into carrying capacity. Food runs out, space runs out, disease finds the crowd, and the curve flattens. Every other species on earth obeys this.
Von Foerster’s argument was that humans partially escape it, and the escape hatch is technology. More people means more ideas. More ideas means better farming, better sanitation, better medicine, better logistics. Those improvements raise the ceiling, which supports more people, who generate more ideas. The feedback loop is not between people and food. It is between people and their own inventions.
That framing has aged remarkably well, even though the prediction attached to it did not. It is the same structural argument that now shows up in every serious discussion of compounding technological progress, including the ones about whether AI systems that improve other AI systems produce a curve nobody can extrapolate. Von Foerster was making a singularity argument decades before the word acquired its current baggage.
The curve broke almost immediately
Here is the twist that makes the paper worth revisiting rather than mocking. The model was not obviously wrong for a long time. It tracked reality closely through the 1970s and only started visibly separating in the 1990s.
That is the defining property of hyperbolic growth, and it is why the paper is a better teaching tool than a punchline. A curve heading for a singularity looks perfectly reasonable right up until it does not. By the time the divergence is obvious on a chart, the model is only a few years from breaking entirely.
| Year | Model prediction | What actually happened | Gap |
|---|---|---|---|
| 1960 | 3.0 billion | 3.0 billion | Fitted to the data |
| 1980 | 4.3 billion | 4.4 billion | Within 3% |
| 2000 | 7.5 billion | 6.1 billion | Overshoot begins |
| 2020 | About 29 billion | 7.8 billion | Nearly 4x too high |
| Nov 2026 | Infinite | About 8.3 billion | The equation ends here |
The mechanism that broke it is not mysterious. Global population growth peaked at slightly over 2% a year in the early 1960s, essentially the moment the ink dried, and it has declined every decade since. It now sits around 0.83%. Falling fertility, rising education, urbanization, later marriage and accessible family planning all pushed in the same direction, and none of them were in the historical record von Foerster was fitting.
In other words, humanity did not hit a wall. It changed its mind. The one variable a curve fitted to two thousand years of data could not anticipate was people deciding, in large numbers and within a single generation, to have fewer children.
About that date
Heinz von Foerster was born on November 13, 1911. The equation gave a year. It did not give a day, and no fit to century scale population estimates could ever resolve one. He chose his own birthday, which in 2026 would have been his 115th. Researchers who knew him have described the specificity as a deliberate wink, a way of signaling that anybody taking the calendar entry literally had missed the argument. The Complexity Science Hub in Vienna is marking the occasion with a conference on that exact day, on the sense and nonsense of end of the world predictions.
The other doomsday equation, and why it disagrees by 9,000 years
Von Foerster is not the only person to have run humanity’s expiry date through a formula. Astrophysicist Brandon Carter proposed what is now called the Doomsday Argument, sometimes the Carter Catastrophe, and it works from an entirely different direction.
Carter’s reasoning is probabilistic rather than demographic. If you assume you are a randomly selected human from the full set of humans who will ever live, then you are unlikely to be unusually early in that sequence. Run the statistics on the roughly 100 billion people born so far and you get a rough bound on how many more are likely to follow. At 95% confidence, that lands somewhere around the year 11,146.
| Prediction | Method | Date | Status |
|---|---|---|---|
| von Foerster | Curve fitted to 2,000 years of population estimates | Nov 13, 2026 | Falsified by 1970s data |
| Carter | Statistical inference from your own birth rank | Around 11,146 | Unfalsifiable in practice, heavily disputed |
| UN projections | Cohort component demographic modeling | Peak in the 2080s | Revised downward repeatedly |
Two mathematical arguments about the end of humanity, separated by more than nine millennia. That spread is the actual lesson. When two rigorous methods disagree by three orders of magnitude, the honest conclusion is that neither is measuring what its title claims to measure.
What the paper got right
Strip away the date and von Foerster’s core observation holds up better than most 1960 forecasting does. He identified that human population growth had escaped the constraints that govern every other species, that the escape was powered by a feedback loop between population size and technological capability, and that any such loop implies a limit somewhere, even if you cannot name the year.
That framework is now used well outside demography. A 2025 arXiv paper applied the same hyperbolic analysis to both population and carbon dioxide emissions, finding that both left their hyperbolic regimes at roughly the same moment. The question of when a compounding curve stops compounding is currently one of the most consequential open questions in energy planning, which is why arguments about whether a single data center should get its own gas fired power plant have become proxy fights about growth limits. The same instinct shows up in climate forecasting, where models built on historical patterns are being asked to predict conditions the historical record does not contain, which is exactly the situation forecasters found themselves in when this year’s El Nino signal came in stronger than anything on record.
There is even a nice symmetry in the fact that the same journals now publish work on machines doing the math themselves, which is how you end up with an AI system clearing decades old mathematical problems for a couple of thousand dollars in compute. Von Foerster’s feedback loop, more or less on schedule, just running through silicon.
So what happens on November 13
A Friday happens. Some of the internet will post about it. A conference in Vienna will discuss why people keep doing this. And the population counter will tick up by roughly 200,000, as it does on every other day, because the curve that was supposed to reach infinity flattened out sixty years ago and nobody made a headline out of it.
The real content of the paper was never the date. It was a warning about what happens when you extrapolate a curve past the point where the conditions producing it still hold. That warning has outlived its own deadline, and it applies to almost every confident projection currently being made about the next twenty years.
