Jim Bromer wrote: > The definition of "all possible programs," like the definition of "all > possible >mathematical functions," is not a proper mathematical problem that can be >comprehended in an analytical way.
Finding just the shortest program is close enough because it dominates the probability. Or which step in the proof of theorem 1.7.2 in http://www.vetta.org/documents/disSol.pdf do you disagree with? You have been saying that you think Solomonoff induction is wrong, but offering no argument except your own intuition. So why should we care? -- Matt Mahoney, matmaho...@yahoo.com ________________________________ From: Jim Bromer <jimbro...@gmail.com> To: agi <agi@v2.listbox.com> Sent: Sun, July 18, 2010 9:09:36 PM Subject: Re: [agi] Comments On My Skepticism of Solomonoff Induction Abram, I was going to drop the discussion, but then I thought I figured out why you kept trying to paper over the difference. Of course, our personal disagreement is trivial; it isn't that important. But the problem with Solomonoff Induction is that not only is the output hopelessly tangled and seriously infinite, but the input is as well. The definition of "all possible programs," like the definition of "all possible mathematical functions," is not a proper mathematical problem that can be comprehended in an analytical way. I think that is the part you haven't totally figured out yet (if you will excuse the pun). "Total program space," does not represent a comprehensible computational concept. When you try find a way to work out feasible computable examples it is not enough to limit the output string space, you HAVE to limit the program space in the same way. That second limitation makes the entire concept of "total program space," much too weak for our purposes. You seem to know this at an intuitive operational level, but it seems to me that you haven't truly grasped the implications. I say that Solomonoff Induction is computational but I have to use a trick to justify that remark. I think the trick may be acceptable, but I am not sure. But the possibility that the concept of "all possible programs," might be computational doesn't mean that that it is a sound mathematical concept. This underlies the reason that I intuitively came to the conclusion that Solomonoff Induction was transfinite. However, I wasn't able to prove it because the hypothetical concept of "all possible program space," is so pretentious that it does not lend itself to mathematical analysis. I just wanted to point this detail out because your implied view that you agreed with me but "total program space" was "mathematically well-defined" did not make any sense. Jim Bromer agi | Archives | Modify Your Subscription ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
