Inevitable Uncertainty in Probabilistic World Models

An interesting thought experiment is circulating on LessWrong: even if you knew absolutely everything about a physical system, a probabilistic model describing it would still contain mathematical uncertainty. According to LessWrong's Gretta Duleba, here's why. Say you measure every fish in a pond exactly. A Bayesian model fitted to those weights still holds uncertainty in its parameters—the mean and variance never zero out. Or: you know every particle's velocity in a gas perfectly. A model estimating temperature from that data retains uncertainty. The resolution? The uncertainty isn't in the world; it's in how the model abstracts it. And crucially, that's not a bug. Probabilistic models trade small residual fuzziness for the compression and efficiency needed to make sense of complex systems.

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