Just read this and thought it was worth sharing. Von Foerster's hyperbolic model fit population data for decades, then broke. The math was right but the assumptions weren't. Article argues AI scaling forecasts could make the exact same mistake: a model can fit the data perfectly and still fail. Curious what you think.

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.

Critics nevertheless questioned its physical plausibility and criticized its failure to explicitly account for economic and technological adaptation. A close fit to population figures could not establish that people would keep reproducing under the same conditions.

The model was relatively simple and transparent. But that simplicity also left out changes that would eventually undermine its prediction.