On 11/03/2008, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > > An attractor is a set of states that are repeated given enough time. If > > > agents are killed and not replaced, you can't return to the current > state. > > > > False. There are certainly attractors that disappear, first > > seen by Ruelle, Takens, 1971 its called a "blue sky catastrophe" > > > > http://www.scholarpedia.org/article/Blue-sky_catastrophe > > > Relatedly, you should look at Mikhail Zak's work on "terminal attractors", > which occurred in the context of neural nets as I recall > > These are attractors which a system zooms into for a while, then after a > period > of staying in them, it zooms out of them....
That is how one would describe the classic and well-studied "homoclinic orbit" -- zoom in for a while then zoom out. > They occur when the differential > equation generating the dynamical system displaying the attractor involves > functions with points of nondifferentiability. homoclinic orbits don't need non-differentibility; just saddle points, where the stable and unstable mainfolds join at right angles. Even with differentiable systems there's a dozen types of attractors, bifurcations (attractors which split in two) and the like; only one is the "attracting fixed point" that seems to be what the original poster was thinking of when he posted. > Of course, you may be specifically NOT looking for this kind of attractor, > in your Friendly AI theory ;-) Remember that attractors are the language of low-dimensional chaos, where there's only 3 or 4 variables. In neural nets, you have hundreds or more (gasp!) neurons, and so you are well out of the area where low-dimensional chaos theory applies, and in a whole new regime (turbulence, in physics), which is pretty much not understood at all in any branch of science. Of course, we just paint artistic impressions on this list, so this is hardly science... --linas ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=95818715-a78a9b Powered by Listbox: http://www.listbox.com
