Peter, One (questionable, of course!) approach to this is to extrapolate from narrow AI. From the existing AI research, I think it is reasonable to say that a core concept of AI is the approximate solution of exp-time problems in polynomial time, especially linear time. (Real-time on-line algorithms will have to be either linear, or very close, especially those which work on "big data" problems.) The essential problems of AI tend to have exponential blowups, such as finding good plans, probabilistic reasoning from a model, searching for a possible model, etc.
Now, you're talking about super-exponential... and some combinatorial problems of this sort are super-exponential... but, I get the impression that you intend something "even harder" than combinatorial-type problems, namely, analog problems. There are few examples of this in the existing AI literature. There are plenty of cases where continuous values are handled, but (my impression is) these do not tend to present the kind of serious difficulty that you mention. The closest thing to a "3-body problem" type difficulty which we face on a regular basis is weather forecasting. The chaotic nature of the system (in the chaos-theory sense) prevents us from making a highly accurate forecast over long periods of time. However, this could in no way be solved by switching to analog computers: the bottleneck is not the error that comes from approximating floating-point operations, but rather, the error that comes from an incomplete and uncertain model of the global atmosphere. (Steve, can you give any reason to think otherwise? In what practical situations does it help to have an analog computer?) Best, Abram On Thu, Jun 28, 2012 at 7:05 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/303/7190161-766c6f07> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Abram Demski http://lo-tho.blogspot.com/ ------------------------------------------- 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
