On Thu, Jul 09, 2009 at 10:04:53AM -0700, glen e. p. ropella wrote: > > And neither is position or momentum because they both have to be defined > _relative_ to something, trivially to an arbitrary vector space origin, > non-trivially to other particles.
The origin of phase space is arbitrary, but the model is invariant to translations, so this this is irrelevant. The properties x_i and p_i are properties of the individual particles. The dynamics includes a term F_{ij} which is defined relative to pairs of particles, but force is not an emergent property of pairs of particles. If force were not included in the model description, the model would behave completely differently. The definition of resultant emergence (the very weakest notion of emergence) is such that the system cannot behave any differently whether the emergent property is recognised or not (since the underlying syntactic description of the model is complete). > Unless you're treating the particle > as a system, itself. And then position and momentum are emergent > properties of the sub-particle components. So, either way, they are a > result of the systems organization and the interaction of their components. There are no sub-particles in Newtonian mechanics. They're point particles. > > Emergence is a trivial (but not entirely useless) word except in the > sense of emergency: "A serious situation or occurrence that happens > unexpectedly and demands immediate action", which boils down to "poorly > understood" or, at least, unpredictable. > If you are using the word emergence in this way, then you are using a completely different (and quite probably meaningless, but that's another story) meaning for the word than how I use it or Mark Bedau or most of the rest of the complex systems community for that matter. Its not fair play to use a word in a completely different way, then to go complaining that the concept is incoherent. That proves nothing, other than the incoherence of your particular definition! You're better off attacking other people's definitions, its more productive. > -- > glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpco...@hpcoders.com.au Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org