OK Ben and Sergio, back to reality. The simplest hyper-Turing task I know of is simple electric circuit simulation. With herculean methods it is now possible for supercomputers to simulate rather simple electric circuits. However, you get more accurate results by simply building those same circuits with $10 worth of small parts. Now, simulation is usually used when there is something impractical about simply building a prototype, e.g. involving massive and expensive components like substation transformers, is running at such high speed that it needs to be made into a silicon chip just to test, involves super-high impedance so that test equipment can't be used, utilizes components that don't yet exist, etc., etc.
Note that I was involved in developing the first program to solve the Schrodinger equation, working with Dr. Ira Karp at the University of Washington Physics Department. Yes, like in electric circuit simulation, it IS possible for Turing computers to eventually simulate hyper-Turing phenomena, but the simulation is imperfect and ever SO slow. Steve =============== On Tue, Jul 10, 2012 at 7:06 AM, Ben Goertzel <[email protected]> wrote: > > This is ground that has been well-trodden in the recent literature on > hypercomputation. > > Mathematically, yes, analog computers (and analog neural nets) can in > principle do hyper-Turing computation > > Quantum physics appears to rule out this kind of analog computing existing > in reality, but general relativity would permit it... and as you know these > theories have not yet been unified. String theory and loop quantum gravity > would also, according to my best understanding, not permit it... > > Since the totality of scientific data consists of a large finite set of > finite-precision numbers, there is no possible way for science (as > presently conceived) to validate or refute the hypothesis that hyper-Turing > computers (of the analog or other variety) exist physically. In this > sense, the hypothesis of trans-Turing computing in the brain or any other > physical system is non-scientific. > > -- Ben G > > > On Tue, Jul 10, 2012 at 8:57 PM, Sergio Pissanetzky < > [email protected]> wrote: > >> Ben, **** >> >> ** ** >> >> You asked recently for comments on analog computation (I forgot what >> thread that was, so I started a new one). My comment is on the need for a >> comparison between Turing computation and analog computation. Of course, AC >> can do all that TC can do, but can it do more? I believe it can. TC is >> particularly weak in everything related to binding, associations, and the >> resulting structures (BAS). Anywhere that BAS are needed, humans are called >> for help. Have you noticed? It never fails. I have compiled a list of >> problems that are "easy for humans but very difficult for computers to >> solve", the GUAPS, great unsolved automation problems of software >> engineering. They all critically depend on BAS. They include OO analysis >> and design, object recognition, self-programming, and many others. Turing >> himself was concerned about this limitation, and he wrote extensively about >> it in the context of morphogenesis but never solved the problem. **** >> >> ** ** >> >> The GUAPs, of course, include the invariant structures that our brains >> make (I know a chair is a chair even if it is upside down => invariance >> under transformations).**** >> >> ** ** >> >> It seems to me that AC can do more than TC. Because physical systems do >> self-organize and make structures. Physics even has theorems about this. If >> so, AGI would be squarely outside the domain of TC, and strictly within >> that part of the domain of AC that is not TC.**** >> >> ** ** >> >> Sergio**** >> >> ** ** >> >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/18883996-f0d58d57>| >> Modify <https://www.listbox.com/member/?&;> Your Subscription**** >> >> <http://www.listbox.com>**** >> >> ** ** >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/212726-11ac2389> | >> Modify<https://www.listbox.com/member/?&;>Your Subscription >> <http://www.listbox.com> >> > > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "My humanity is a constant self-overcoming" -- Friedrich Nietzsche > > *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
