I greatly enjoyed Tegmark's "Is 'the theory of everything' merely the ultimate ensemble theory?", and there are parts of it that I agree with wholeheartedly (for instance, his arguments against the idea that the AUH is "wasteful"). However, whenever he talks about the testability of the AUH, his views seem unjustifiably physics-centric to me.

For instance, he seems impressed by the fact that versions of our physics with more than 3 dimensions are insufficiently stable to support atoms (and presumably, therefore, self-aware substructures), and those with less than 3 dimensions are insufficiently complex to support SASs. These are interesting facts, but I fail to see their importance when you consider the entire ensemble of possible mathematical structures. For instance, consider the infinitely many cellular automata that exist in the Mathiverse. We know of very simple 1D, 2D, and 3D cellular automata that are computation universal, and therefore (I believe) capable of containing SASs. Undoubtedly there an infinite number of 4D cellular automata that are computation universal and contain SASs that perceive their surroundings as 4D. Ditto for CA with dimensions higher than 4.

Perhaps it's true that within the ensemble of all quantum-physical universes in Mathspace, only those with 3+1 dimensionality contain SASs. But what possible reason do we have for believing that these SASs (or the observer-moments of those SASs) have a greater measure than those in the ensemble of all cellular automata?

-- Kory

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