When scientists report measurement uncertainties, what do they mean, and how trustworthy are they? Researchers in fields from Medicine to Physics do a pretty good job of estimating the chance of small errors, but the chance of big disagreements is orders of magnitude greater than naively expected. Unknown problems and mistakes appear to have power-law distributions consistent with how complex systems fail and how unknown errors are constrained. Electrons are a lot simpler than people, so if physicists struggle, we should not be surprised that political polls and Big Data often get it wrong.

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