Ben, Very interesting, but it leaves (me) with two questions unanswered:
1. What (if anything) is super-Turing about ARNNs that isn't super-Turing about (bidirectional) analog computation in general? You can build an ARNN with an analog computer, but are not (necessarily) able to do general purpose analog computation with an ARNN. 2. Is there any reason not to be throwing terms like super-Turing around? Aside from many issues I liken to how many angels can stand on the head of a pin, as I see it the REAL issue is efficiency of computation. Even some simple transcendental functions are in a way super-Turing, because most of them can NOT be perfectly computed. The transcendental functions found in every computer's library are approximations, that for some arguments may be very slow, and they are often wrong in several of the low-order bits. I have worked on several projects where I had to write better (and slower) transcendental functions to get programs to work right. At CDC I worked next to a couple of career programmers whose ONLY job it was to constantly work to improve their transcendental functions!!! However, there is a fundamental difference in capability and computability between unidirectional (Turing) functions, and bidirectional (super-Turing) equations, as I have discussed in other postings. In addition to my own opinions, many philosophies and basic physics state that all forces are balanced by equal and opposite forces - not only in physical systems, but in life and general, e.g. karma, yin v. yang, etc. To see your future problems, you have only to look for the forces that will resist the forces that you exert. In my own mind, everything is balanced, and even when it seems to be unbalanced, it is actually balanced when seen as part of a larger picture. Analog computation lives in this balanced world, while this balanced world remains foreign and is only borderline computable by Turing machines. It isn't that some systems require super-Turing computation, it is that Turing machines are severely impaired for computing in the real world. Note that I think may be possible to have the best of both worlds and more, by switching from computing continuous numerical values to computing with equations. An accumulator or memory cell would hold one side of an equation, with the other side always being presumed to be zero, so that everything represented would be zero. Then, for example, you could compute a formula for anything by taking an equation that includes it, and subtracting out its term, or taking more complex action when it appears in several places. Real world equations would often/typically yield multi-valued and/or range solutions. However, several of them as simultaneous equations would yield the entire list of computable possibilities given all known constraints. This could go WAY beyond the present concepts of super-Turing, because you don't just get "a" solution, you can get ALL of the solutions in a single shot, and time need no longer take time to represent!!! There appear to be ways around obvious problems, e.g. equations that grow in complexity without limit, by simply discarding the smallest of the terms when you get more equation than you can handle. Strings would be an obvious but inefficient way to implement this. My point is that I believe that we compute by keeping all things in balance, and there are several radically different ways of doing such things. Common concepts like the retrograde flow of information are actually mechanisms of balance. However, trying to do this on a Turing machine (that isn't programmed to compute with equations or ???) seems horrifically complex, cumbersome, inefficient, and it isn't at all easy to see how to use them in the real world, or we would have had intelligent computers a long time ago. Steve ============= On Tue, Jul 10, 2012 at 7:33 PM, Ben Goertzel <[email protected]> wrote: > > Ben or Sergio: Could one of you send me an off-forum message explaining >> this? >> >> > http://en.wikipedia.org/wiki/Hypercomputation > > Hava Siegelmann's papers on hyper-computation in analog neural nets are > classic... some titles are in the paper section here > > http://en.wikipedia.org/wiki/Hava_Siegelmann > > and the links are here > > http://binds.cs.umass.edu/publications.html > > While I suspect hypercomputation is unnecessary for AGI, it's interesting > and worth knowing about..... And her points about the hypercomputation > power of theoretical analog neural nets seem consilient with the ideas of > some on this list, including you... > > Selmer Bringsjord (at RPI) has written a lot about hypercomputation and AI > as well... > > ben > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/10443978-6f4c28ac> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Full employment can be had with the stoke of a pen. Simply institute a six hour workday. That will easily create enough new jobs to bring back full employment. ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
