Matt, I never said that I did not accept the application of the method of probability, it is just that is has to be applied using logic. Solomonoff Induction does not meet this standard. From this conclusion, and from other sources of information, including the acknowledgement of incomputability and the lack of acceptance in the general mathematical community I feel comfortable with rejecting the theory of Kolomogrov Complexity as well.
What I said was: My conclusion suggests, that the use of Solmonoff Induction as an ideal for compression or something like MDL... What you said was: It is sufficient to find the shortest program consistent with past results, not all programs. The difference is no more than the language-dependent constant... This is an equivocation based on the line you were responding to. You are presenting a related comment as if it were a valid response to what I actually said. That is one reason why I am starting to ignore you. Jim Bromer On Wed, Jul 21, 2010 at 1:15 PM, Matt Mahoney <[email protected]> wrote: > Jim Bromer wrote: > > The question was asked whether, given infinite resources could Solmonoff > Induction work. I made the assumption that it was computable and found that > it wouldn't work. > > On what infinitely powerful computer did you do your experiment? > > > My conclusion suggests, that the use of Solmonoff Induction as an ideal > for compression or something like MDL is not only unsubstantiated but based > on a massive inability to comprehend the idea of a program that runs every > possible program. > > It is sufficient to find the shortest program consistent with past results, > not all programs. The difference is no more than the language-dependent > constant. Legg proved this in the paper that Ben and I both pointed you to. > Do you dispute his proof? I guess you don't, because you didn't respond the > last 3 times this was pointed out to you. > > > I am comfortable with the conclusion that the claim that Solomonoff > Induction is an "ideal" for compression or induction or anything else is > pretty shallow and not based on careful consideration. > > I am comfortable with the conclusion that the world is flat because I have > a gut feeling about it and I ignore overwhelming evidence to the contrary. > > > There is a chance that I am wrong > > So why don't you drop it? > > > -- Matt Mahoney, [email protected] > > > ------------------------------ > *From:* Jim Bromer <[email protected]> > *To:* agi <[email protected]> > *Sent:* Tue, July 20, 2010 3:10:40 PM > > *Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction > > The question was asked whether, given infinite resources could Solmonoff > Induction work. I made the assumption that it was computable and found that > it wouldn't work. It is not computable, even with infinite resources, for > the kind of thing that was claimed it would do. (I believe that with a > governance program it might actually be programmable) but it could not be > used to "predict" (or compute the probability of) a subsequent string > given some prefix string. Not only is the method impractical it is > theoretically inane. My conclusion suggests, that the use of Solmonoff > Induction as an ideal for compression or something like MDL is not only > unsubstantiated but based on a massive inability to comprehend the idea of a > program that runs every possible program. > > I am comfortable with the conclusion that the claim that Solomonoff > Induction is an "ideal" for compression or induction or anything else is > pretty shallow and not based on careful consideration. > > There is a chance that I am wrong, but I am confident that there is nothing > in the definition of Solmonoff Induction that could be used to prove it. > 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/> > *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/> > ------------------------------------------- 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
