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From: weissert@xxxxxxxxxxxxxxx (Thomas Weissert)
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Date: Wed, 22 Jun 1994 11:03:27 -0400 (EDT)
;
; If D&G maintain that all intensities (traits of attraction) are
; speeds, is every state-space mapping of machinic trajectories a phase-
; space after all? (I'm beginning to think i ducked out of this one too
; quickly).
If intensities may be thought of as states (which i see not touble doing),
then the speed and direction in which they are changing is the
conjugate to those states and so, together, this pairing constitutes a
phase. Each intensity and its conjugate is one pair of dimensions
in the phase space of your schizo- dynamcial system, yes. So the
attractor you see emerging for your system undergoes catastrophe after
catastrophe in a long chain of bifurcations. The two-dimensional
space of each conjugate pair shows a trajectory for that intensity, but
this trajectory is but a cross-sectional view of the high-dimensional
attractor. The nice thing about this kind of Poincare perspective is
that any structural similarities between each trajectory refects
something about the whole attractor and therefore represents related,
stable features of the whole.
; Could you expand your definition slightly, and indicate any
; opinions you might have yourself on the subject (i.e. is De Landa
; employing a notion of phase-space that you would consider 'strict'?).
;
done.
-Tomas
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Thomas Weissert, PhD ] He's out there, crossing disciplinary lines
Dynamicalogist ] without restraint, synthesizing dynamical
Saint Joseph's University ] theories into some elusive theory of time.
Philadelphia, PA USA ] His methods are ... unstatic.
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