James Rogers wrote: > On 11/2/02 9:29 AM, "Ben Goertzel" <[EMAIL PROTECTED]> wrote: > > I think there *is* a "general problem of intelligence", and it's an > > unsolvable problem unless one has infinite computational resources. > > > I don't follow this. What does infinite computational resources > have to do > with it?
OK, let me try to explain... First of all, to mathematically formalize the AGI problem, one needs to formally define "intelligence." There are many ways to do this. But, for many purposes, any definition of intelligence that has the general form "Intelligence is the maximization of a certain quantity, by a system interacting with a dynamic environment" can be handled in roughly the same way. It doesn't always matter exactly what the quantity being maximized is (whether it's "complexity of goals achieved" , for instance, or something else). My own definition of intelligence as "the ability to achieve complex goals in complex environments" -- which I've also formalized mathematically -- fits in here. Let's use the term "behavior-based maximization criterion" to characterize the class of definitions of intelligence indicated in the previous paragraph. So, sppose one has some particular behavior-based maximization criterion in mind. Then Marcus Hutter's work on the AIXI system, descrigives a software program that will be able to achieve intelligence according to the given criterion. Now, there's a catch: this program may require infinite memory and an infinitely fast processor to do what it does. But he also gives a variant of AIXI which avoids this catch, by restricting attention to programs of bounded length L. Loosely speaking, the AIXItl variant will provably be as intelligent as any other computer program of length <= L, satisfying the maximization criterion, within a constant multiplicative factor and a constant additive factor. Hutter's work draws on a long tradition of research into statistical learning theory and algorithmic information theory, mostly notably Solomonoff's early work on induction and Levin's work on computational measure theory. At the present time, though, this work is more exciting theoretically than pragmatically. The "constant factor" in his theorem may be very large, so that in practice, AIXItl is not really going to be a good way to create an AGI software program. In essence, what AIXItl is doing is searching the space of all programs of length L, evaluating each one, and finally choosing the best one and running it. The "constant factors" involved deal with the overhead of trying every other possible program before hitting on the best one! A simple AI system behaving somewhat similar to AIXItl could be built by creating a program with three parts: . The data store . The main program . The metaprogram The operation of the metaprogram would be, loosely, as follows: . At time t, place within the data store a record containing: the complete internal state of the system, and the complete sensory input of the system. . Search the space of all programs P of size |P|< L to find the one that, based on the data in the data store, has the highest expected value for the given maximization criterion . Install P as the main program Conceptually, the main value of this approach for AGI is that it solidly establishes the following contention: **If you accept any definition of intelligence of the general form "maximization of a certain function of system behavior." Then, the problem of creating AGI is basically a problem of dealing with the issues of space and time efficiency** As with any mathematics-based conclusion, the conclusion only follows if one accepts the definitions. If someone's conception of intelligence fundamentally can't be cast into the form of a behavior-based maximization criterion, then these ideas aren't relevant for AGI as that person conceives it. However, we believe that the behavior-based maximization criterion approach to defining intelligence is a good one, and hence we believe that Hutter's work is highly significant. The limitations of these results should be understood, along with their power. For instance, consider Penrose's contention that non-Turing quantum gravity computing (as allowed by an as-yet unknown noncomputable theory of quantum gravity) is necessary for true general intelligence. This idea is not refuted by Hutter's results, because it's possible that . AGI is in principle possible on ordinary Turing hardware . AGI is only pragmatically possible, given the space and time constraints imposed on computers by the physical universe, given quantum gravity powered computer hardware I very strongly doubt this is the case, and Penrose has not given any convincing evidence for such a proposition, but our point is merely that in spite of recent advances in AGI theory such as Hutter's work, we have no way of ruling such a possibility out mathematically. My own AGI work -- like yours, and that of other serious AGI designers/builders on this list -- deals with ways of achieving reasonable degrees of intelligence given reasonable amounts of space and time resources. > > With finite computational resources there are always going to be some > > complex goals that one can achieve better than others.... > > > This is the "jack of all trades, ace of none" problem. But a properly > designed generally intelligent system should be adaptive enough > that it can > become highly tuned to solving specific classes of problems if > that is what > it is faced with on a regular basis. Just like people. Yes. But given ANY finite system S, the class of all problems that S can solve, is a zero percentage of the total class of all possible problems that are mathematically formulable. And given any finite system S whose information capacity is significantly less than that of the universe, the class of all problems that S can solve is a VERY SMALL percentage of the total class of all possible problems within the universe... The adaptiveness you're talking about can increase the size of the class of problems S can solve, but can't solve the fundamental limitations implied by algorithmic information theory, i.e. that "You can't solve a twenty-pound problem with a ten-pound AGI program." [I'm paraphrasing Chaitin's rendition of Godel's Theorem as "You can't prove a twenty-pound theorem with a ten-pound formal system"] > > Hutter and Schmidhuber's mathematical approach to general intelligence > > basically verifies this idea, in a more formal & theoretical way... > > > I continue to like and follow their work, with some reservations. My > reservations mostly are of the nature that some implicit assumptions are > made without qualification that I can state for a fact should be > substantially different from the essential implied qualification. > Its great > stuff, just subtly misleading in certain respects in that it causes you to > ignore things that should be looked at more critically. > > Unfortunately, I'm not at liberty to talk about this (or a number of other > things for that matter) in detail or I would. I apologize if I > can't fully > explain some of the assertions I might make. Arrgh. :-/ Well, I think their work is of limited practical value for the reasons I mention above, but, you're obviously hinting at something else. But since you won't tell us, it's not a very interesting topic of conversation huh ;) ben ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/