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Dagon comments on New Pascal's Mugging idea for potential solution - Less Wrong Discussion
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Comments (18)
It also depends on the implied probability curve of other things you might specify and the precision you intend to convey. There's no way to distinguish between integers up to and including that one in 30 bits.
Oh, and that's only a counting of identical/fungible things. Specifying the contents of that many variants is HUGE.