Human potentials, on the other hand, are strong in areas long important for survival, but weak in things far removed. “Computers are universal machines, their potential extends uniformly over a boundless expanse of tasks. Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Figure 12.2 illustrates this four-level multiverse hierarchy, one of the core ideas of this book.” Whereas all the parallel universes at Levels I, II and III obey the same fundamental mathematical equations (describing quantum mechanics, inflation, etc.), Level IV parallel universes dance to the tunes of different equations, corresponding to different mathematical structures. The first three levels correspond to noncommunicating parallel universes within the same mathematical structure: Level I simply means distant regions from which light hasn't yet had time to reach us, Level II covers regions that are forever unreachable because of the cosmological inflation of intervening space, and Level III, Everett's "Many Worlds," involves noncommunicating parts of the Hilbert space of quantum mechanics. “In other words, the idea is the there's a fourth level of parallel universes that's vastly larger than the three we've encountered so far, corresponding to different mathematical structures.
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