Jim, I am unable to find the actual objection to Solomonoff in what you wrote (save for that it's "wrong as in really wrong").
It's true that a lot of programs won't produce any output. That just means they won't alter the prediction. It's also true that a lot of programs will produce random-looking or boring-looking output. This just means that Solomonoff will have some expectation of those things. To use your example, given 000, the chances that the next digit will be 0 will be fairly high thanks to boring programs which just output lots of zeros. (Not sure why you mention the idea that it might be .5? This sounds like "no induction" rather than "dim induction"...) --Abram On Wed, Jul 7, 2010 at 10:10 AM, Jim Bromer <jimbro...@gmail.com> wrote: > Suppose you have sets of "programs" that produce two strings. One set of > outputs is 000000 and the other is 111111. Now suppose you used these sets > of programs to chart the probabilities of the output of the strings. If the > two strings were each output by the same number of programs then you'd have > a .5 probability that either string would be output. That's ok. But, a > more interesting question is, given that the first digits are 000, what are > the chances that the next digit will be 1? Dim Induction will report .5, > which of course is nonsense and a whole less useful than making a rough > guess. > > But, of course, Solomonoff Induction purports to be able, if it was > feasible, to compute the possibilities for all possible programs. Ok, but > now, try thinking about this a little bit. If you have ever tried writing > random program instructions what do you usually get? Well, I'll take a > hazard and guess (a lot better than the bogus method of confusing shallow > probability with "prediction" in my example) and say that you will get a lot > of programs that crash. Well, most of my experiments with that have ended > up with programs that go into an infinite loop or which crash. Now on a > universal Turing machine, the results would probably look a little > different. Some strings will output nothing and go into an infinite loop. > Some programs will output something and then either stop outputting anything > or start outputting an infinite loop of the same substring. Other programs > will go on to infinity producing something that looks like random strings. > But the idea that all possible programs would produce well distributed > strings is complete hogwash. Since Solomonoff Induction does not define > what kind of programs should be used, the assumption that the distribution > would produce useful data is absurd. In particular, the use of the method > to determine the probability based given an initial string (as in what > follows given the first digits are 000) is wrong as in really wrong. The > idea that this crude probability can be used as "prediction" is > unsophisticated. > > Of course you could develop an infinite set of Solomonoff Induction values > for each possible given initial sequence of digits. Hey when you're working > with infeasible functions why not dream anything? > > I might be wrong of course. Maybe there is something you guys > haven't been able to get across to me. Even if you can think for yourself > you can still make mistakes. So if anyone has actually tried writing a > program to output all possible programs (up to some feasible point) on a > Turing Machine simulator, let me know how it went. > > 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
