[FOM] Status of Quantum Computing - Omega Wellfoundedness
Miguel A. Lerma
mlerma at math.northwestern.edu
Mon Oct 21 14:54:08 EDT 2002
> But if we substitute "has an even Goedel number" for "halts", representing
> "end" by bit 0 and interpret the beginning (rest) of the program as being its
> Goedel number in unary notation, then from the above procedure we conclude
> that the probability of a random positive integer being even is 1/4 + 1/16 +
> 1/64 . . . = 1/3. If the Goedel numbers include zero, then the probability
> of a random nonnegative integer being even is 1/2 + 1/8 + 1/32 . . . = 2/3.
>
> Charlie Volkstorf
> Cambridge, MA
Right, with that particular choice of representing programs and
of marking their end, the probability of a program with even
Goedel number is 2/3 - and the probability of odd Goedel number
will be 1/3. Other representations will give different probability
distributions and also different values for Chaitin Omega number.
Miguel A. Lerma
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