[FOM] Status of Quantum Computing - Omega Wellfoundedness

[Miguel A. Lerma]

 > 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