Is there a good name for a mathematical theorem being true "only because of an astronomically large computation"? I kind of want to say "approximately independent", since the limit as the computation goes to infinity would be actually independent.
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...That didn't come out well. I mean that I don't know of a proof that there exist briefly statable mathematical facts with vast but finite proofs, whose proof doesn't compress in the face of axioms bearing the power of huge ordinals (or large cardinals or Busy Beaver numbers).
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Yeah, it's easy to construct short statements that have short proofs only assuming large cardinals, say, and astronomical proofs otherwise. But I'm comfortable with those being inside the definition, excluded only as necessary by saying "natural" or some such.
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Motivation: I made a bet on Facebook yesterday that 6/7 of the Millennium problems would be solved by 2040. Someone asked why I didn't say 7, and the answer I wanted to give was "hedging against one being independent or approximately independent".
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And therefore out of reach even for a superintelligence.
End of conversation
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