Matt Mahoney said, "Prediction can be used as a test of understanding lots of things. For example, if I wanted to test whether you understand Newton's law of gravity, I would ask you to predict how long it will take an object of a certain mass to fall from a certain height."
That is ok, but you would need to show that the prediction was accomplished using Newton's law of gravity. This is what Matt was getting at when he 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. Jim Bromer ----- Original Message ---- From: Matt Mahoney <[EMAIL PROTECTED]> To: [email protected] Sent: Saturday, May 10, 2008 8:25:51 PM Subject: [agi] Defining "understanding" (was Re: Newcomb's Paradox) --- Stan Nilsen <[EMAIL PROTECTED]> wrote: > I'm not understanding why an *explanation* would be ambiguous? If I > have a process / function that consistently transforms x into y, then > doesn't the process serve as a non-ambiguous explanation of how y came > into being? (presuming this is the thing to be explained.) 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. Prediction can be used as a test of understanding lots of things. For example, if I wanted to test whether you understand Newton's law of gravity, I would ask you to predict how long it will take an object of a certain mass to fall from a certain height. If I wanted to test whether you understand French, I could give you a few lines of text in French and ask you to predict what the next word will be. -- 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/?&; Powered by Listbox: http://www.listbox.com ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ ------------------------------------------- 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
