In physics, math, and computer science, the state of a system is an encapsulation of all the information you’d ever need to predict what it will do, or at least its probabilities to do one thing versus another, in response to any possible prodding of it. In a sense, then, the state is a system’s “hidden reality,” which determines its behavior beneath surface appearances. But in another sense, there’s nothing hidden about a state—for any part of the state that never mattered for observations could be sliced off with Occam’s Razor, to yield a simpler and better description.

When put that way, the notion of “state” seems obvious. So then why did Einstein, Turing, and others struggle for years with the notion, along the way to some of humankind’s hardest-won intellectual triumphs?

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