I made a remark about confusing a domain with the values that was wrong. What I should have said is that you cannot just treat a domain of functions or of programs as if they were a domain of numbers or values and expect them to act in ways that are familiar from a study of numbers.
Of course you can use any of the members of a domain of numbers or numerical variables in evaluation methods, but when you try that with a domain of functions, programs or algorithms, you have to expect that you may get some odd results. I believe that since programs can be represented by strings, the Solomonoff Induction of programs can be seen to be computable because you can just iterate through every possible program string. I believe that the same thing could be said of all possible Universal Turing Machines. If these two statements are true, then I believe that the program is both computable and will create the situation of Cantor's diagonal argument. I believe that the construction of the infinite sequences of Cantor's argument can be constructed through an infinite computable program, and since the program can also act on the infinite memory that Solomonoff Induction needs, Cantor's diagonal sequence can also be constructed by a program. Since Solomonoff Induction is defined so that it will use every possible program, this situation cannot be avoided. Thus, Solomonoff Induction would be both computable and it would produce "uncountable" infinities of strings. When combined with the problem of ordering the resulting strings in order to show how the functions might approach stable limits for each probability, since you cannot a priori determine the ordering of the programs that you would need for the computation of these stable limiting probabilities you would be confronted with the higher order infinity of all possible combinations of orderings of the trans infinite strings that the program would hypothetically produce. Therefore, Solomonoff Induction is either incomputable or else it cannot be proven to be capable of avoiding the production of trans infinite strings whose ordering is so confused that they would be totally useless for any kind of "prediction of a string based on a given prefix," as is claimed. The system is not any kind of "ideal" but rather *a confused theoretical notion. * I might be wrong. Or I might be right. Jim Bromer ------------------------------------------- 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
