Computationalism (the idea that everything in existence is fully characterized by states and transition functions) is
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I'm not sure you'd need to know that, but you'd find that to make accurate predictions of consistent events in the universe requires divergent computational effort on a Turing machine. You could probably probe it experimentally with asymmetric problems that are easy to confirm.
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For a concrete example, a halting oracle could search an unstructured space of size N in log(N) operations. So e.g. crack an encryption key in time linear in it's length.
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