Peter, About physics and computation --
The following is my understanding. To prove these statements rigorously would take some work.. According to the Standard Model (accounting for all known forces besides gravity), any physical system could be simulated by some (potentially massively parallel) femto-computer, without dramatic inefficiency Any physical system not relying on degenerate matter (i.e. keeping its nuclear particles inside atoms) can be simulated by some (potentially massively parallel) quantum computer without dramatic inefficiency Any physical system not depending on macroscopic quantum coherence, can be simulated by some (potentially massively parallel) classical digital computer (say, a big Connection Machine), without dramatic inefficiency All this is based on the Standard Model without including gravity. There is no consistent, acknowledged unified theory of the Standard Model and gravitational (General Relativity) theory. According to string theory or loop quantum gravity theory, two of the leading contenders for a unified theory, it is my impression that any physical system could be simulated by some appropriately defined massively parallel string or loop computer, without dramatic inefficiency. But this is less clear to me since the math of these theories is rather incompletely understood. If one takes General Relativity Theory or classical mechanics, and imposes some minimum size (to crudely emulate quantum limits), then one finds that any physical system with "moving parts" above that size can be simulated by some (potentially massively parallel) classical digital computer, without dramatic inefficiency. If one takes General Relativity or classical mechanics at face value and allows them to deal with infinite-precision real-number variables, then one finds that they can lead to hypercomputational dynamical systems that can't be simulated on any digital computer. Some of these hypothetical hypercomputational systems may be set up as n-body problems. However, please note that the total corpus of existing (or possible) scientific data is a big set of finite bits. So, it's a bit odd to place faith in a theory stating the universe depends on infinite-precision numbers, based on a collection of finite-set data points. Note that all of the above comments are about massively parallel digital computers. Obviously simulating massively parallel systems on computers with a small number of processors is going to be inefficient. -- Ben G On Thu, Jun 28, 2012 at 10:05 AM, Peter Voss <[email protected]> wrote: > This issues has bothered me for a long time, and I’d like to explore it a > bit:**** > > ** ** > > While digital computers obviously can be set up to solve equations, there > still seems to be a significant difference in efficiency of simulating/ > calculating versus physical analog ‘doing’/ execution – like for example in > solving an n-body problem. Real systems system just produce the result by > interaction of all the forces (electro/ mechanical), while computers have > to approximate/ iterate. **** > > ** ** > > Key question: Are there AGI common problems where digital/simulated > approaches need hyper-exponential amounts of computing power compared to > physical systems? Is this kind of equation-solving core to AGI? I don’t > think so, but…**** > > ** ** > > Other may be able to formulate this better. **** > > ** ** > > What has bothered me is the glib assertion that a digital computer an > calculate to any arbitrary level of precision (true)… but does the cost > become unworkable in practice, even with Moore’s law.**** > > ** ** > > Peter**** > > ** ** > > *From:* Steve Richfield [mailto:[email protected]] > *Sent:* Thursday, June 28, 2012 6:39 AM > *To:* AGI > *Subject:* Re: [agi] Happy 100th Birthday Alan Turing - No, computers > will never think, but machines will!**** > > ** ** > > Hey everyone, > > Remember my discussions about how computers fundamentally compute > functions, while biological neurons appear to fundamentally solve equations > - a MUCH higher level thing to do. It appears possible to design something > resembling a computer to do this, but NOT to simulate this sort of > functionality in any sort of practical way because of the astronomical > inefficiency of solving huge systems of simultaneous NON-linear equations > using conventional computational methods. > > No, I don't think that we need any sort of silicon wetware, but we DO > appear to need a radically more advanced sort of "computer", but probably > NOT anything that Turing has ever thought of - in short, NOT a "Turing > machine". > > Besides, you'll never get 2-D silicon to work like 3-D wetware. > > Steve > ================**** > *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 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
