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Right, but if the role of the mapping is just to make the status of the simulation make sense to you, (after all, that's the only thing you would be able to observe it doing), then the inhabitant wouldn't care if the mapping was ever computed. So, it's fine if the mappings would be ridiculously impossible to compute. (Extra note: it is extremely hard to simulate the chaotic motion of nearly every physical system. Does that mean they are doing lots of hard computation? If so, does that make them "more likely" to be interpretable as simulating universes?)

It's not that "the mapping" makes "the simulation" make sense. You have moved most of "the simulation" into "the mapping". So if you don't do the mapping, the simulation mostly does not happen, so there is nothing to make sense of.

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