From: weissert@xxxxxxxxxxxxxxx (Thomas Weissert)
Date: Mon, 11 Jul 1994 11:27:04 -0400 (EDT)
; > If intensities may be thought of as states (which i see not touble >
; > doing),
; I'm not so sure. An intensity is D's work is a kind of amalgam of a
; Spinozan attribute with a Bergsonian intensity. They are to do with
; affects, not total states. Thus, "moving through an intensity" (note that
; intensities are predicated of the plane, not the moving "object") does
; not necessarily map onto "changing state"...
If we can think of an "intensity" as an attribute of the "system" that
changes over some ranges of variation, such that the essence of that
intensity remains intact over some period of evolution and it remains
within the range, then even if it is a speed already, we can still think
of it as a degree of freedom of the system and so it can be one
component of the state of the system: the value of that particular
intensity at any time. But I would like to understand better what
exactly we are talking about for these intensities. Can anyone give me
an example of a simple systems and an intensity of that system?
; > then the speed and direction in which they are changing is the
; > conjugate to those states and so, together, this pairing constitutes a
; > phase.
; Speeds are not the same as rates of change in intensity. Intensities
; *are* becomings, granted, but they are thus *already* speeds... I
; think your application of the word "speed" here means "acceleration",
; which is a different matter.
Even though they are already speeds, they still describe one degree of
freedom of the system, so in that sense, the rates of changes of
intensities are the conjugate.
; > Each intensity and its conjugate is one pair of dimensions
; > in the phase space of your schizo- dynamcial system, yes.
; Point of clarification request: what's the conjugate of an intensity? Do
; D&G ever refer to this? It's not s/thing I've come across
I too would like to know this. In dynamical terms, the conjugate of the
intensity is whatever we call the "momentum" that goes along with
changes in intensity. If an intensity does not vary in some example,
then let us think about what might be conserved in that special case.
To do this I would really like to have one good and "simple" example.
; > 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.
; This all sounds ingenious, but my maths isn't up to it. Also, I'm not
; sure how well it really squares with Deleuze, as my comments point
; out. Can you give me a reference for this stuff? Is it connected with
; the stuff on Boulez in *Thousand Plateaus* about directed spaces
; and fractals? I just wrote a paper on Deleuze and Boulez (also Cage)
; and it would be nice to see how far our readings coincide/diverge.
Dynamics is not something that needs to be square with anyone. It
applies to modelling changes in system. All that need be square is what
we call the variables and the model, what we include in the system, what
are the degrees of freedom, what is the phase (or state) space.
; Richard Cochrane
; email: senrc@xxxxxxxx
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.