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
>
>
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