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MixedNuts comments on Mixed Reference: The Great Reductionist Project - Less Wrong
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I don't get it. Okay, obviously our universe is a mathematical structure, that's why physics works. "All math is real" is seductive, but "All computable math is real, but there are no oracles" is just weird; why would you expect that without experimental evidence of Church-Turing?
The idea that since there are twice as many infinite strings containing "1010" than "10100", the former must exist twice as much as the latter nicely explains why our universe is so simple. But I'm not at all convinced that universes like ours with stable observers are simpler than pseudorandom generators that pop out Boltzmann brains.
That all math is "real" in some sense you observe directly any time you do any. The insight is not that math is MORE real than previously thought, but just that there isn't some additional find of realness. Sort of, this is an oversimplification.
Also check out: http://lesswrong.com/lw/1zt/the_mathematical_universe_the_map_that_is_the/
That post is a confused jumble of multiple misinterpretations of the word "exist".
If all levels of the Turing hierarchy are about as real, it's extremely unlikely our universe is at level zero. Yet Church-Turing looks pretty solid.
Combine this with the simulation hypothesis; a universe can only simulate less computationally expensive universes. (Of course this is handwavy and barely an argument, but it's possible something stronger could be constructed along these lines. I do think that much more work needs to be done here.)