Yesterday was doomsday, at least according to a paper in one of the world’s most famous science journals. In 1960, Science published a study by Heinz von Foerster and two colleagues under a title that sounds like a pulp novel: “Doomsday: Friday, 13 November, A.D. 2026.”
That Friday came and went. The roughly 8.3 billion people alive this year are still here. So what exactly did the math predict, and why did it miss?
The formula that ran out of road
Von Foerster, an Austrian-born physicist at the University of Illinois, wrote the paper with P. M. Mora and L. W. Amiot. They took the best estimates of world population for roughly the previous two thousand years, available as of 1958, and looked for the curve that fit them best.
The answer was not ordinary exponential growth, where population doubles at a steady pace. The fit was close to hyperbolic, where the doubling time itself keeps shrinking. Their equation put the population at 179 billion divided by (2026.9 minus the year), with that bracket raised to the power 0.99.
Look at what happens as the year creeps toward 2026.9. The bottom of the fraction shrinks toward zero, so the answer races toward infinity. The decimal 2026.9 lands on November 13, 2026, which is why the paper named that date. Past that point the formula stops making physical sense; a 2014 analysis by Rein Taagepera noted that it projected “to infinite population in 2026—and to an imaginary one thereafter.”
Running the numbers ourselves
Plug years into the 1960 formula and the curve looks sensible for a long time, then breaks:
- 1960: about 2.8 billion people, close to reality at the time.
- 2000: about 6.9 billion, a little ahead of the real figure of just over 6 billion.
- 2020: about 26 billion.
- January 2026: about 199 billion.
- Mid-2026: about 443 billion.
In the real world, humanity passed 8 billion in November 2022, according to United Nations estimates. The formula was off by a factor of more than three by 2020 and by more than 20 at the start of this year.
It was better than it looks
For a joke-sounding prediction, the equation held up for a surprisingly long time. A simplified version proposed in 1975 predicted about 5.99 billion people for the start of 1997. The actual figure was about 5.92 billion, a miss of roughly 1%.
The reason it eventually broke is that growth slowed. The fastest rates, above 1.8% a year, came between 1955 and 1975, peaking at 2.1% in the late 1960s, just after the paper appeared. By 2015 to 2020 the rate had dropped to about 1.1%. A hyperbolic curve needs growth to keep speeding up forever, and it did not.
A birthday doomsday
One detail makes the date stranger. Von Foerster was born in Vienna on November 13, 1911. The day his equation hit its singularity was his 115th birthday. He died in California in 2002, aged 90, better known for founding second-order cybernetics than for ending the world.
Whether the paper was a warning or partly a provocation has been argued for decades. Its point was that growth on that path could not last, and the slowdown since the 1960s bears that out.
If you liked this, read why the Friday the 13th superstition only took shape in the 1800s, or how the War of the Worlds radio panic was smaller than legend says. More odd history lives in our Offbeat section.
The UN projects the world population will reach between 9 and 10 billion by 2050, no singularity required.
Further reading
- Wikipedia: Heinz von Foerster
- Wikipedia: World population
- Science (1960): Doomsday: Friday, 13 November, A.D. 2026
Image: 組曲師, CC BY 4.0 via Wikimedia Commons
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