本文探讨了奥地利科学家海因茨·冯·弗斯特在20世纪50年代提出的一个人口增长模型，该模型预测世界将在2026年11月13日终结。文章从一个理想的伊甸园假设开始，然后引入有限资源的现实情况，分析了人口增长与资源限制之间的关系，并最终探讨了该模型的局限性以及对现实世界的启示。

👨‍🏫 该模型从一个理想化的伊甸园开始，假设资源无限，人口每代翻倍。然而，这种指数增长会导致在有限的时间内人口数量远远超过地球的承载能力，这显然不符合现实。

🌏 为了更贴近现实，模型引入了有限资源的假设，例如一个只有100个椰子可以维持的岛屿。在这种情况下，人口增长将受到资源的限制，最终稳定在100人。但是，这与现实世界中人口不断增长的趋势并不相符。

⚠️ 该模型的局限性在于它忽略了人类社会的复杂性，包括科技进步、资源管理、社会组织等因素。现实世界中的资源限制并非一成不变，人类可以通过科技进步和资源管理来缓解人口增长带来的压力。

💡 该模型虽然存在缺陷，但它也为我们提供了一些思考：人口增长与资源限制之间的关系，以及科技进步在应对人口增长挑战中的重要作用。

🤔 该模型提醒我们，人类活动对地球资源的依赖，以及在人口增长和资源管理之间寻求平衡的重要性。

[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.