A Mathematical Foundation for The Simulation Principle

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Quote:. . . we and our entire Universe might be a simulation in a computer in our very Universe. [...] It might be that we comprise a portion of the Universe external to the simulation computer, i.e. our state in toto at time t is specified by wt, and our dynamics is exactly given by g, and therefore we and our dynamics would also be exactly given by the dynamics of n. In other words, we would be both in the Universe external to the computer, and in the simulation being run on the computer. And importantly, there would be no possible experimental test we could perform that could distinguish ‘which of those two entities we are’. Our existence would be duplicated; we would be a duality, in all respects.

In that particular scenario, we are not the ones running the simulating computer. However, if we ever in the future gain the capability of building and running simulation computers, then by the self-simulation lemma, at that time we might even be simulations in a computer that we ourselves run! In such a situation, since the part of our Universe containing us, W, is being reproduced in exact detail inside the computer that is simulating the dynamics of W, the version of us inside the computer is itself running a computer, that in turn is simulating us running a computer in exact detail.

In other words, we the humans running that physical computer inside of W, might ‘be’ either those people running that physical computer—or we might be the people inside the physical computer who are evolving as the simulation runs, and who are indistinguishable from the ‘other’ humans who are running that physical computer. By the RPCT, there is no conceivable physical test, no observable value, that could tell us which of those two dynamic processes ‘is’ us. So in a non-Leibnizian, empirically meaningful sense of the term, we could ‘be’ either one of those two evolving objects. We could even both, and would never know.

One of the simulations would have fewer resources available for fully replicating the other (have to relay more fake appearances to internal observers). And that would be the difference between the two that made one causally subordinate to the other. Even if both are relying heavily on props and perceptual deceptions, one will be dependent a lot more on those short-cuts.
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