[From Bruce Gregory (961024.1115)]
From Rick Marken (961023.1320)
Have you seen Bill Powers' "Gatherings" program in action? I think it's
available on Dag's PCT Demos disk. Anyway, in one scenario (called "guru" I
think) a bunch of dots (representing individuals) converge toward and
eventually encircle a stationary dot -- the "guru". I am thinking that a plot
of the dynamical pattern of movements of these dots resembles an "attractor".
I presume that are a set of dynamical equations -- the attractor "theory" or
equations -- which (with the appropriate parameter settings) can generate an
approximation to the dynamical behavior of the set of dots. These equations
do not (to my mind) provide an explanation of the behavior of the dots; they
simply describe the behavior of the dots.
Indeed. But this is not what Martin is talking about. Martin,
like Kent, is talking about the behavior of control systems.
Both are using the same "dynamical equations." Bill's "guru"
exists as an "attractor" in real space (or at least in a
two-dimensional representation of real space). Martin is
talking about behavior in a more abstract phase space. The
paths of the individuals in this phase space look different
than the paths of the individuals in 3-space. In the phase
space the paths may or may not reveal the presence of an
attractor. This attractor is not a new "force" or principle. It
is simply a way of describing the trajectories in phase space.
You can certainly prefer not to look at what is happening in
phase space. It is not something that I find illuminating
either. Martin is fond of phase space. He finds it
illuminating.
Bruce