Well, some of the papers in the references of my paper give formal mathematical definitions of hypercomputation, though my paper is brief and conceptual and not of that nature. So although the generic concept may be muddled, there are certainly some fully precise variants of it.
This paper surveys various formally defined varieties of hypercomputing, though I haven't read it closely.. http://www.amirrorclear.net/academic/papers/many-forms.pdf Anyway the argument in my paper is pretty strong and applies to any variant with power beyond that of ordinary Turing machines, it would seem... -- ben g On Mon, Dec 29, 2008 at 4:18 PM, J. Andrew Rogers < [email protected]> wrote: > > On Dec 29, 2008, at 10:45 AM, Ben Goertzel wrote: > >> 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... >> > > > As more of a meta-comment, the whole notion of "hypercomputation" seems to > be muddled, insofar as super-recursive algorithms may be a limited example > of it. > > I was doing a lot of work with inductive Turing machines several years ago, > and most of the differences seemed to be definitional e.g. what constitutes > an algorithm or answer. For most practical purposes, the price of > implementing them in conventional discrete space is the introduction of some > (usually acceptable) error. But if they approximate to the point of > functional convergence on a normal Turing machine... As best I have been > able to tell, and I have not really been paying attention because the > arguments seem to mostly be people talking past each other, is that ITMs > raise some interesting philosophical questions regarding hypercomputation. > > > We cannot implement a *strict* hypercomputer, but to what extent does it > "count" if we can asymptotically converge on the functional consequences of > a hypercomputer using a normal computer? It suspect it will be hard to > evict the belief in Penrosian magic from the error bars in any case. > > Cheers, > > J. Andrew Rogers > > > > ------------------------------------------- > 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/?&; > Powered by Listbox: http://www.listbox.com > -- 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 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
