Bounds on the rates of growth and convergence of all physical processes

Toby Ord

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arXiv · 2410.10928

Bounds on the rates of growth and convergence of all physical processes

Toby Ord

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Abstract

The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild assumption leads to generous yet binding limits on how quickly or slowly any directly measurable physical phenomenon can grow or converge -- limits that are intimately connected to Rado's Busy Beaver function. I conjecture that these limits are novel physical laws governing which rates of growth and convergence are possible in our universe.

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Toby Ord. 2024-10-14. Bounds on the rates of growth and convergence of all physical processes. https://arxiv.org/abs/2410.10928

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