--- Jim Bromer <[EMAIL PROTECTED]> wrote: > Matt Mahoney said, > "A formal explanation of a program P would be a equivalent program Q, > such > that P(x) = Q(x) for all x. Although it is not possible to prove > equivalence in general, it is sometimes possible to prove nonequivalence > by finding x such that P(x) != Q(x), i.e. Q fails to predict what P will > output given x." > > But I have a few problems with this although his one example was ok. > One, there are explanations of ideas that cannot be expressed using the > kind of formality he was talking about. Secondly, there are ideas that > are inadequate when expressed only using the methods of formality he > mentioned, Third, an explanation needs to be used relative to some > other purpose. For example, making a prediction of how long something > will fall to the ground is a start, but if a person understands Newton's > law of gravity, he will be able to utilize it in other gravities as > well. And he may be able to relate it to real world situations where > precise measurements are not available. And he might apply his > knowledge of Newton's laws to see the dimensional similarities (of > length, mass, force and so on) between different kinds of physical > formulas.
Remember that the goal is to test for "understanding" in intelligent agents that are not necessarily human. What does it mean for a machine to understand something? What does it mean to understand a string of bits? I propose prediction as a general test of understanding. For example, do you understand the sequence 0101010101010101 ? If I asked you to predict the next bit and you did so correctly, then I would say you understand it. If I want to test your understanding of X, I can describe X, give you part of the description, and test if you can predict the rest. If I want to test if you understand a picture, I can cover part of it and ask you to predict what might be there. Understanding = compression. If you can take a string and find a shorter description (a program) that generates the string, then use that program to predict subsequent symbols correctly, then I would say you understand the string (or its origin). This is what Hutter's universal intelligent agent does. The significance of AIXI is not a solution to AI (AIXI is not computable), but that it defines a mathematical framework for intelligence. -- Matt Mahoney, [EMAIL PROTECTED] ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=101455710-f059c4 Powered by Listbox: http://www.listbox.com
