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The fact that our Universe (together with the entire Level III multiverse) may be simulatable by a quite short computer program calls into question whether i makes any ontological difference whether simulations are "run" or not. If, as I have argued, the computer need only describe and not compute the history, then the complete description would probably fit on a single memory stick, and no CPU power would be required. It would appear absurd that the existence of this memory stick would have any impact whatsoever on whether the multiverse it describes exists "for real." Even if the existence of the memory stick mattered, some elements of this multiverse will contain an identical memory stick that would "recursively" support its own physical existence. This wouldn't involve any Catch-22, chicken-or-the-egg problem regarding whether the stick or the multiverse was created first, since the multiverse elements are four-dimensional spacetimes, whereas "creation" is of course only a meaningful notion within a spacetime.
So are we simulated? According to the MUH, our physical reality is a mathematical structure, and as such, it exists regardless of whether someone here or elsewhere in the Level IV multiverse writes a computer program to simulate/describe it. The only remaining question is then whether a computer simulation could make our mathematical structure in any meaningful sense exist even more than it already did. If we solve the measure problem, perhaps we'll realize that simulating it would increase its measure slightly, by some fraction of the measure of the mathematical structure within which it's simulated. My guess is that this would be a tiny effect at best, so if asked, "Are we simulated?," I'd bet my money on "No!
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Max Tegmark (Our Mathematical Universe: My Quest for the Ultimate Nature of Reality)