Inevitable Uncertainty in Probabilistic World Models

"Even if you know everything about a system, there will still be uncertainty left." In her article, Gretta Duleba explores this counterintuitive claim by John Wentworth using two concrete examples. First, imagine a fish pond: after weighing every single fish and updating your Bayesian model, you know all weights exactly—yet your probabilistic model still shows a posterior spread. The uncertainty is in the model, not the world. Second, consider an ideal gas: even if you know every particle's velocity, your probabilistic model of temperature (via the Boltzmann distribution) retains a small but nonzero uncertainty. Duleba recounts her struggle to grasp why total energy isn't the same as temperature, ultimately realizing that the model itself—not the world—keeps uncertainty alive.