Ben, I read your paper and have the following observations...
>From 1968-1970, I was the in-house numerical analysis and computer consultant at the University of Washington departments of Physics and Astronomy. At that time, Ira Karp, then the physics grad student who had been a grad student longer than any other in the history of the Physics department, was working on simulating the Schrodinger equation - the very equation that some today think is uncomputable. We had to devise methods to get past the numerical challenges, such as computing some of the terms 3 different ways and taking the median value, to deal with some horrendous numerical problems. Ira got his PhD, and in so doing, pretty much settled the debate as to whether such phenomena are "computable" using conventional computers. Rest assured, they ARE computable. Given the poor employment situation for physics PhDs, Ira went on to get another PhD in Computer Science. Ira now lives in the San Jose area. I'm sure that he could write a MUCH better article about this. On a side note, there is the "clean" math that people learn on their way to a math PhD, and then there is the "dirty" math that governs physical systems. Dirty math is fraught with all sorts of multi-valued functions, fundamental uncertainties, etc. To work in the world of "dirty" math, you must escape the notation and figure out what the equation is all about, and find some way of representing THAT, which may well not involve simple numbers on the real-number line, or even on the complex number plane. With this as background, as I see it, hypercomputation is just another attempt to evade dealing with some hard mathematical problems. My recent postings about changing representations to make unsupervised learning work orders of magnitude faster and better is just one illustration of the sorts of new approaches that are probably needed to "break through" present barriers. Hypercomputation is worse than a cop-out, because it distracts people from tackling the hard problems. In short, I see the present conception of hypercomputation mostly as a tool for the mathematically challenged to show that it isn't THEIR fault that they haven't solved the hard problems, when yes, it IS their fault. All that having been said, sometimes it IS worthwhile stating things in terms that aren't directly computable, e.g. complex differential equations. Escaping the need for direct computability often leads to seeing things at a higher level, which of course is where a numerical analysis person steps in once something has been stated in an obscure form, to somehow coerce the thing into a computable form. Just because something can be shown to be "hard" or "not generally solvable" is no reason to give up until you can somehow prove that it is absolutely impossible. Indeed, sometimes on the way to such proofs, the "chinks" are found to solve them. Even where it IS impossible, an adequate approximation can usually be found. In summary, there ARE problems that could be classified as needing hypercomputation, but hypercomputation itself is not as stated in your paper. Everything that can be computed can be computed by conventional computers of sufficient capability, as nothing in physics has yet been shown to be uncomputable. Steve Richfield =================== On 12/29/08, Ben Goertzel <[email protected]> wrote: > > Hi, > > I expanded a previous blog entry of mine on hypercomputation and AGI into a > conference paper on the topic ... here is a rough draft, on which I'd > appreciate commentary from anyone who's knowledgeable on the subject: > > http://goertzel.org/papers/CognitiveInformaticsHypercomputationPaper.pdf > > This is a theoretical rather than practical paper, although it does attempt > to explore some of the practical implications as well -- e.g., in the > hypothesis that intelligence does require hypercomputation, how might one go > about creating AGI? I come to a somewhat surprising conclusion, which is > that -- even if intelligence fundamentally requires hypercomputation -- it > could still be possible to create an AI via making Turing computer programs > ... it just wouldn't be possible to do this in a manner guided entirely by > science; one would need to use some other sort of guidance too, such as > chance, imitation or intuition... > > -- Ben G > > > -- > Ben Goertzel, PhD > CEO, Novamente LLC and Biomind LLC > Director of Research, SIAI > [email protected] > > "I intend to live forever, or die trying." > -- Groucho Marx > > ------------------------------ > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com/> > ------------------------------------------- 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=123753653-47f84b Powered by Listbox: http://www.listbox.com
