Re: probabilities measures computable universes

2004-01-24 Thread Wei Dai
On Fri, Jan 23, 2004 at 09:04:20PM -0800, Hal Finney wrote: Do you think it would come out differently with a universal distribution? There are an infinite number of universal distributions. Some of them assign greater probability to even integers, some of them assign greater probability to

RE: probabilities measures computable universes

2004-01-24 Thread Ben Goertzel
: Friday, January 23, 2004 9:23 AM To: [EMAIL PROTECTED] Subject: Re: probabilities measures computable universes Are probabilities always and necessarily positive-definite? I'm asking this because there is a thread, started by Dirac and Feynman, saying the only difference between

probabilities measures computable universes

2004-01-23 Thread Juergen Schmidhuber
I browsed through recent postings and hope this delayed but self-contained message can clarify a few things about probabilities and measures and predictability etc. What is the probability of an integer being, say, a square? This question does not make sense without a prior probability

Re: probabilities measures computable universes

2004-01-23 Thread scerir
Are probabilities always and necessarily positive-definite? I'm asking this because there is a thread, started by Dirac and Feynman, saying the only difference between the classical and quantum cases is that in the former we assume the probabilities are positive-definite. Thus, speaking of

Re: probabilities measures computable universes

2004-01-23 Thread Hal Finney
Juergen Schmidhuber writes: What is the probability of an integer being, say, a square? This question does not make sense without a prior probability distribution on the integers. This prior cannot be uniform. Try to find one! Under _any_ distribution some integers must be more likely than