Path: utzoo!attcan!uunet!zephyr.ens.tek.com!uw-beaver!mit-eddie!wuarchive!usc!apple!bbn.com!archive.bbn.com!aboulang From: aboulang@bbn.com (Albert Boulanger) Newsgroups: comp.ai.philosophy Subject: Re: emergent properties Message-ID: Date: 27 Oct 90 16:11:46 GMT References: <1990Sep29.213139.2876@watdragon.waterloo.edu> <3499@media-lab.MEDIA.MIT.EDU> Sender: news@bbn.com Reply-To: aboulanger@bbn.com Organization: BBN, Cambridge MA Lines: 49 In-reply-to: minsky@media-lab.MEDIA.MIT.EDU's message of 29 Sep 90 23:12:37 GMT In article <3499@media-lab.MEDIA.MIT.EDU> minsky@media-lab.MEDIA.MIT.EDU (Marvin Minsky) writes: In quantum electrodynamics as well, I have the impression that, again, there are no mysterious emergents, in the sense that the two-at-a-time exchange-interactions account for everything. However, each exchange implies a new particle, and you have to include the two-at-a-time interactions of all of these, hence the annoying infinite series. Also, now things are a little different, for many-particle problems, because the equations can no longer be solved within a manifold of fixed dimension, because they require , not in a low-order vector space they require the dimensionality of at least the configuration-space. Despite all that complexity, however, one still feels that the predictions come directly, albeit in a complicated manner, from one's understanding of the elemetary particules and their local interactions. No mysterious emergents. I guess you are right, but the 1/r^7 Casmir potential always seemed bizarre to me ;-). (This is a force between two plates that are explained by the vacuum fluctuations. A recent result is that light will travel faster between two such closely spaced plates.) You know, QM does not support chaos (it tries real hard as witnessed by studies in quantum chaos, but does not quite hack it). QED is an uninteresting domain to look for emergent properties because of the essential point below: Ahem, now to the real point. The term 'emergent' is one that has been used in experimental *non-linear* science (the land o' chaos) and the significance of what it implies is reduced if taken out of that context. For instance, the principle of superposition does not work in nonlinear systems in general. This is a very important fact. Simple CA systems (in general they have nonlinear local interactions dictated by table lookup), like the life game, Ising systems, and the HPP lattice gas, (where people were initially surprised that spherical waves would emerge from a hexagonal lattice) are nice contexts the examine this issue of emergent properties. Again, 4-wave-mixing in photorefractive crystals (October's Scientific American has an article on photorefractive crystals) and video feedback are example physical nonlinear systems to use as contexts. It is the fact that superposition does not work in nonlinear systems in general that has given birth to *experimental* mathematics. Of course, after the emergence, the reason for the emergence can be obtained, but this is a pretty trivial point if you ask me. Not just a linear superposition, Albert Boulanger aboulanger@bbn.ocm