As far as I can tell right now, my theories that Solomonoff Induction is trans-infinite were wrong. Now that I realize that the mathematics do not support these conjectures, I have to acknowledge that I would not be able to prove or even offer a sketch of a proof of my theories. Although I did not use rigourous mathematics while I have tried to make an assessment of the Solomonoff method, the first principle of rigourous mathematics is to acknowledge that the mathematics does not support your supposition when they don't.
Solomonoff Induction isn't a mathematical theory because the desired results are not computable. As I mentioned before, there are a great many functions that are not computable but which are useful and important because they tend toward a limit which can be seen in with a reasonable number of calculations using the methods available. Pi is one such function. (I am presuming that pi would require an infinite expansion which seems right.) I have explained, and I think it is a correct explanation, that there is no way that you could make an apriori computation of all possible combinations taken from infinite values. So you could not even come up with a theoretical construct that could take account of that level of complexity. It is true that you could come up with a theoretical computational method that could take account of any finite number of values, and that is what we are talking about when we talk about the infinite, but in this context it only points to a theoretical paradox. Your theoretical solution could not take the final step of computing a probability for a string until it had run through the infinite combinations and this is impossible. The same problem does not occur for pi because the function that produces it tends toward a limit. The reason I thought Solomonoff Induction was trans-infinite was because I thought it used the Bayesian notion to compute the probability using all possible programs that produced a particular substring following a given prefix. Now I understand that the desired function is the computation of only the probability of a particular string (not all possible substrings that are identical to the string) following a given prefix. I want to study the method a little further during the next few weeks, but I just wanted to make it clear that, as far as now understand the program, that I do not think that it is trans-infinite. 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
