Jim, I'm still not sure what your point even is, which is probably why my responses seem so strange to you. It still seems to me as if you are jumping back and forth between different positions, like I said at the start of this discussion.
You didn't answer why you think program space does not represent a comprehensible concept. (I will drop the "full" if it helps...) My only conclusion can be that you are (at least implicitly) rejecting some classical mathematical principles and using your own very different notion of which proofs are valid, which concepts are well-defined, et cetera. (Or perhaps you just don't have a background in the formal theory of computation?) Also, not sure what difference you mean to say I'm papering over. Perhaps it *is* best that we drop it, since neither one of us is getting through to the other; but, I am genuinely trying to figure out what you are saying... --Abram On Sun, Jul 18, 2010 at 9:09 PM, Jim Bromer <jimbro...@gmail.com> wrote: > 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 <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Abram Demski http://lo-tho.blogspot.com/ http://groups.google.com/group/one-logic ------------------------------------------- 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
