Path: utzoo!utgpu!watserv1!watmath!att!att!bu.edu!bbn.com!archive.bbn.com!aboulang From: aboulang@bbn.com (Albert Boulanger) Newsgroups: comp.ai.philosophy Subject: Re: Emergent Properties Message-ID: Date: 3 Nov 90 18:37:02 GMT References: <1990Oct12.214636.7945@ncsuvx.ncsu.edu> <30@tdatirv.UUCP> <1990Oct19.201604.7280@ncsuvx.ncsu.edu> <3369@aipna.ed.ac.uk> <1990Oct26.214354.11063@ncsuvx.ncsu.edu> <3383@aipna.ed.ac.uk> <1990Oct31.001104.22908@ncsuvx.ncsu.edu> <1990Oct31.102704.18335@csc Sender: news@bbn.com Reply-To: aboulanger@bbn.com Organization: BBN, Cambridge MA Lines: 57 In-reply-to: csmith@cscs.UUCP's message of 2 Nov 90 10:32:19 GMT In article <1990Nov2.103219.24132@cscs.UUCP> csmith@cscs.UUCP (Craig E. Smith) writes: It seems to me that the idea of emergence (at least in the way I have most commonly seen the term used) is a lot like religion, a convenient way to explain things that are either too complicated, or about which we have too little information to adequately understand. If you think you have a system which is more than the sum of its parts, then probably you are either overlooking some of the parts, or you are arbitrarily defining an axiomatic property which coincides with the properties possessed by the system. I am amazed by the fact that a view like this can be held! It indicates an urgent need to inform on recent (last 20 years, let's say) developments in nonlinear science and mathematics. There are many fine *analytical* folk in this necessarily experimental field, who are uncomfortable as anybody else is about not being able to predict the manifold unexpected behavior of nonlinear systems. There are nonlinear systems where one can make piecewise linear approximations to the system and study them from the "bottom-up", but in general *superposition* does not hold for nonlinear systems. The method is to first observe the emergent behavior *experimentally* - often using the computer as a virtual reality - and build the route to its emergence after the fact. I do not see why this is such a sticky point. I should also mention that generic motifs are to be found in emergent properties across many nonlinear systems, and these will probably become part of a established theory in the decades to come. Nonlinear science and mathematics does not halt because of the lack of such a theory, and the many fine researchers in the field of nonlinear science do not invoke mysticism, but they must observe first, be amazed, and *then* explain. This particular and mandatory process of investigating nonlinear behavior is the setting for the term "emergence". Pure mathematics is not untouced by this either: From "Incompleteness Theorms for Random Reals" G. J. Chaitin Advances in Applied Mathematics, 8. 119-146 (1987) "In conclusion, we have seen that proving whether particular exponential diophantine equations have finitely or infinitely many solutions, is absolutely intractable. Such questions escape the power of mathematical reasoning. This is a region which mathematical truth has no discernible structure or pattern and appears to be completely random. These questions are completely beyond the power of human reasoning. Mathematics can not deal with them. Quantum physics has shown that there is randomness in nature. I believe that we have demonstrated in this paper that randomness is already present in pure mathematics, This does not mean that the universe and mathematics are lawless, it means that the laws of a different kind apply; statistical laws." Experimentally, Albert Boulanger aboulanger@bbn.com