An awareness of irreducible uncertainty is the core of probabilistic thinking, but it’s a tricky thing to measure. To do that, we took advantage of a distinction that philosophers have proposed between “epistemic” and “aleatory” uncertainty. Epistemic uncertainty is something you don’t know but is, at least in theory, knowable. If you wanted to predict the workings of a mystery machine, skilled engineers could, in theory, pry it open and figure it out. Mastering mechanisms is a prototypical clocklike forecasting challenge. Aleatory uncertainty is something you not only don’t know; it is
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