evand comments on Causal Universes - Less Wrong
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Well, for starters, an AI living in a universe where infinitely many computations can be performed in finite time can verify the responses a Turing oracle gives it. So it can determine that it lives in a universe with Turing oracles (in fact it can itself be a Turing oracle), which is not what an AI living in this universe would determine (as far as I know).
I don't think that's different, unless it can also make infinitely many queries of the Turing oracle in finite time. Or make one query of a program of infinite length. In any case, I think it needs to perform infinite communication with the oracle.
I'll grant that it seems likely that a universe with infinite computation capability will also have infinite communication capability using the same primitives, but I don't think it's a logical requirement.
Yes, let's replace "computations" with "actions," I guess.