Re: Does provability matter?
Thanks for clarifying the provability issue. I think I understand and agree with you. On Tue, Nov 13, 2001 at 12:05:22PM +0100, Juergen Schmidhuber wrote: What about exploitation? Once you suspect you found the PRG you can use it to predict the future. Unfortunately the prediction will take enormous time to stabilize, and you never can be sure it's finished. So it's not very practical. By exploiting the fact that we're in an oracle universe I didn't mean using TMs to predict the oracle outputs. That is certainly impractical. There are a couple of things you could do though. One is to use some oracle outputs to predict other oracle outputs when the relationship between them is computable. The other, much more important, is to quickly solve arbitrarily hard computational problem using the oracles. I prefer the additional resource assumptions reflected by the Speed Prior. They make the oracle universes very unlikely, and yield computable predictions. Why do you prefer the Speed Prior? Under the Speed Prior, oracle universes are not just very unlikely, they have probability 0, right? Suppose one day we actually find an oracle for the halting problem, or even just find out that there is more computing power in our universe than is needed to explain our intelligence. Would you then (1) give up the Speed Prior and adopt a more dominant prior, or (2) would you say that you've encountered an extremely unlikely event (i.e. more likely you're hallucinating)? If you answer (1) then why not adopt the more dominant prior now?
RE: The infinite list of random numbers
Yes, but think how many Tom Clancy books it would write in the mean-time. Also, think of all the mystery books with the last page re-arranged to be the first, or all those many ones with typos. -Original Message- From: Norman Samish [mailto:[EMAIL PROTECTED]] Sent: 11 November 2001 05:32 To: [EMAIL PROTECTED] Subject: The infinite list of random numbers Thanks to all who replied. Thanks to your instruction, it now is clear to me that, in an infinite series of random characters, every conceivable sequence MUST occur. These sequences must, of course, obey the requirement that all random characters in an infinite sequence must appear an equal number of times. This requirement rules out sequences of only one character. Therefore, in infinite time, the long-lived monkey at the durable typewriter HAS to eventually write the works of Shakespeare, as well as anything else conceivable. More generally, everything that can happen MUST happen, not only once but an infinite number of times. Norm Samish
