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Mailing List complex-science@necsi.org Message #1152 | |
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| Cris Moore wrote: > > > (1) How many parts should a complex system have? In other words, is there > > any restriction on the size of a complex system? Does the upper limit on > > the size, if any, depend on the strength of the interactions between the > > parts of the complex system? > > three should do it :-) The issue is not chaotic behaviour, but complexity. Two are enough. The minimum requirement is irreducibility - thus combining two components into a system that cannot be described be looking at either of its components in isolation makes a two-component complex system. On the upper end: think of Benard cells: 1000 ml of water contains some 3x10E25 water molecules with some 10E26 interacting hydrogen bonds. Since the hydrogen bond organizes small biomolecular complex machines of some 10E3 bonds and Benard cell 20 orders of magnitude larger, I doubt a good relationship between size and interaction strength can be found. > > > (2) Can complexity ever arise out of purely local interactions? That is to > > say, if a system has no global constraints can it ever be a complex > > system? Is it always possible to implement a given complex system using > > local constraints and nothing else? > > yes, indeed yes, and probably no. Since a Turing machine works from local interactions alone, any computable complex system (i.e. also any computer simulable complex system) can be implemented by local interactions. I cannot think offhand of an interesting non-computable complex system (any suggestions ?) even though for most, obviously, computation is not practical. > > > (2') When is it possible to implement a given complex system using > > local rules if the context is fixed and predetermined, i.e., if there are > > a priori boundary conditions? > > by "implement," do you mean a desired outcome, or the dynamics leading to > it? One very general requirement is, that the system should be exhaustively specified. In the analysis of natural systems, we are usually thrown off by non-additivity, multi-body effects, entropy and other problems that make it difficult to define interaction potentials precisely enough to be of real use. Best wishes, Boris Steipe +---Dr. Boris Steipe------------<steipe at LMB.uni-muenchen.de>---+ | Genzentrum | | Feodor-Lynen Str. 25 Tel +49 (0)89 2180-6987 | | 81377 Muenchen, Germany Fax -6999 | +---<http://www.LMB.uni-muenchen.de/users/steipe/boris.html>---+ |
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