Through the looking glass: The world's population is expected to reach roughly 8.3 billion by the middle of next month, far short of the mathematically infinite population predicted by a 1960 forecast. The failed prediction has relevance for debates over artificial intelligence. It shows how a model can track an accelerating trend for years without establishing that the trend will continue indefinitely. Forecasts of runaway technological progress face the same question: How long will the conditions behind today's growth persist?

Heinz von Foerster and his colleagues reached their prediction using a hyperbolic growth model. Unlike exponential growth, where a population increases at a constant percentage rate, hyperbolic growth assumes the rate itself rises as the population grows.

That feedback produces increasingly rapid expansion. Eventually, the model reaches a singularity, at which point the calculated population diverges to infinity in finite time. The researchers placed that point in November 2026.

Their arithmetic was not the problem. The population changes the model captured did not continue.

The forecast drew on global population estimates from approximately 1 CE through 1958. The researchers published it in Science under the title "Doomsday: Friday, 13 November, A.D. 2026." They also chose the date because it was von Foerster's birthday.

Population figures gave the model some credibility. Humanity reached about 1 billion people around 1800. That number doubled by 1925, then doubled again to 4 billion by 1975. It took less than another 50 years to reach 8 billion.

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