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saturn comments on Efficient Induction - Less Wrong Discussion
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It seems like you and some others in this thread are assuming that real numbers describe some actual behavior of the universe, but that's begging the question. If the universe is computable, it implies that all quantities are discrete.
Well, if it turns out the universe is continuous, then when we conjecture it to be computable, we typically mean the same thing we mean when we say pi is computable: there exists a fixed length program that could compute it to any desired degree of precision (assuming initial conditions specified to sufficient precision).
Continuous quantities are the simplest explanation for the evidence we have - there are some hints that it could be otherwise, but they're only hints.