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kokotajlod comments on New Pascal's Mugging idea for potential solution - Less Wrong Discussion
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Yes, but I don't think that's relevant. Any use of complexity depends on the language you specify it in. If you object to what I've said here on those grounds, you have to throw out Solomonoff, Kolmogorov, etc.
More specifically, it seems that your c must include information about how to interpret the X bits. Right? So it seems slightly wrong to say "R is the largest number that can be specified in X bits of information" as long as c stays fixed. c might grow as the specification scheme changes.
Alternatively, you might just be wrong in thinking that 30 bits are enough to specify 3^^^^3. If c indicates that the number of additional universes is specified by a standard binary-encoded number, 30 bits only gets you about a billion.
It only takes less than 30 bits if your language supports the ^^^^ notation and that's not standard notation.
True. So maybe this only works in the long run, once we have more than 30 bits to work with.