[Epistemic status: Very speculative, especially Parts 3 and 4. Like many good things, this post is based on a conversation with Paul Christiano; most of the good ideas are his, any errors are mine.]

I.

In the 1950s, an Austrian scientist discovered a series of equations that he claimed could model history. They matched past data with startling accuracy. But when extended into the future, they predicted the world would end on November 13, 2026.

This sounds like the plot of a sci-fi book. But it’s also the story of Heinz von Foerster, a mid-century physicist, cybernetician, cognitive scientist, and philosopher.

His problems started when he became interested in human population dynamics.

(the rest of this section is loosely adapted from his Science paper “Doomsday: Friday, 13 November, A.D. 2026”)

Assume a perfect paradisiacal Garden of Eden with infinite resources. Start with two people – Adam and Eve – and assume the population doubles every generation. In the second generation there are 4 people; in the third, 8. This is that old riddle about the grains of rice on the chessboard again. By the 64th generation (ie after about 1500 years) there will be 18,446,744,073,709,551,616 people – ie about about a billion times the number of people who have ever lived in all the eons of human history. So one of our assumptions must be wrong. Probably it’s the one about the perfect paradise with unlimited resources.

Okay, new plan. Assume a world with a limited food supply / limited carrying capacity. If you want, imagine it as an island where everyone eats coconuts. But there are only enough coconuts to support 100 people. If the population reproduces beyond 100 people, some of them will starve, until they’re back at 100 people. In the second generation, there are 100 people. In the third generation, still 100 people. And so on to infinity. Here the population never grows at all. But that doesn’t match real life either.