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----- Original Message -----
From: "Terry Boyce" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Friday, October 27, 2000 8:22 PM
Subject: Re: Zackmann criticisms of Dusek on Deleuze 1


> Sorry, but I get very annoyed when I receive text in this kind of format!
Maybe it has something interesting to say, but I get blinded by the
disjointedness of the thing and find it impossible to read.
>
>
> >After his free-swinging attack on me, I asked Zackmann to send me more=20
> >detailed criticisms of my defense of Deleuze against Sokal and Bricmont.
He=
> >=20
> >did so.  I asked him to forward it to SCIENCE AS CULTURE and he attempted
to=
> >,=20
> >but it was returned as it was too long (10 pages).  It contains
interesting=20
> >stuff on chaos theory and Bohm and non-standard analysis, among other
things=
> >,=20
> >even if some his criticisms really aren't of what I said, so I though
it=20
> >worth forwardsin
> >
> ><<You asked for it, so here IT is: (I) Val Says: Obviously Deleuze is
no=20
> >mathematical virtuoso, but his treatment of the issues of the calculus is
fa=
> >r=20
> >more detailed, informed and serious than Sokal and  Bricmont let on.
> >
> >DZ: Ah yes, how Zen-like of you -- the old mystical Superstitions
again -no?=
> >=20
> >But on with my  response. Now as to Deleuze whom you keep obtusely
defending=
> >=20
> >when there is marvelous work on the philosophy of science out there to
be=20
> >assimilated, we get from Deleuze (and Guattari) the absolutely and
thoroughl=
> >y=20
> >laughable claim that the  first difference between science and philosophy
is=
> >=20
> >that philosophy deals with concepts [simpliciter??? I do ask.] while
science=
> >=20
> >deals with functions [a manifest _conflation_ of science with
mathematics.=20
> >More Postmodernist rubbish.] Here are how our two Postmodernist
Glitterati=20
> >whom Val Dusek seems hell-bent to defend characterize this truly bizarre
cla=
> >im
> >
> >"[THE] first difference between science and philosophy is their
respective=20
> >attitude toward chaos. Chaos is defined not so much by its disorder as by
th=
> >e=20
> >infinite speed with which every form taking shape in it vanishes."
(from=20
> >"What is Philosophy" by Deluze and Guattari, New York, Columbia
University=20
> >Press, 1994) - as an aside I would like to ask WHY such a prestigious=20
> >university as Columbia would CON-descend to publish such utter drivel?
Guys,=
> >=20
> >I REALLY want an answer to this one!!!
> >
> >DZ:  WRONG: Not only is this NOT a definition of the essence of
mathematical=
> >=20
> >chaos, such an assertion does not even attempt to give us sufficient=20
> >conditions for  the manifestation of chaos in natural and artificial=20
> >phenomena -- in the technical sense of the word used in
mathematics,=3D=20
> >physics, and science generally.  Moreover, very many branches of
mathematics=
> >=20
> >have NOTHING WHATSOEVER to do with fractals, chaos, or nonlinear
dynamics.
> >
> >N.B.!: For all interested parties, and nontechnically put, the
sufficient=20
> >conditions for chaos are as follows: (i) nonlinearity, which can be
the=20
> >result of a large initial displacement away from equilibrium or
feedback=20
> >within the system, (ii) energy dissipation, and (iii) an external
driving=20
> >force.
> >
> >REALITY CHECK:  Back to Rigorous Mathematics
> >
> >To be even more precise, Chaos may be more rigorously defined as follows:
> >
> >Chaos is APERIODIC long-term behavior in a deterministic system that
exhibit=
> >s=20
> >sensitive dependency on initial conditions (assuming continuum
mathematical=20
> >models in this context).
> >
> >(A) "Aperiodic long-term behavior" means that there are trajectories [of
the=
> >=20
> >3 or more systems of ODEs] which do not settle down to fixed points,
periodi=
> >c=20
> >orbits, or quasiperiodic orbits as t-->+Infinity. For pragmatic purposes,
we=
> >=20
> >should require that such trajectories be not too rare. For instance, we
coul=
> >d=20
> >insist that there be an open set of initial conditions leading to
aperiodic=20
> >trajectories, or perhaps that such trajectories should occur with P(E)
=3D 0=
> >,=20
> >given random initial conditions.
> >(B) "Deterministic" means that the system has no random or noisy inputs
or
> >parameters. The irregular behavior arises from the system's intrinsic=20
> >nonlinearity, rather than from simply noisy driving forces.
> >(C) "Sensitive dependence on initial conditions" means that nearby=20
> >trajectories separate exponentially fast: That is, that the system has
a=20
> >positive Liapunov exponent.
> >
> >Clearly what I have been mostly describing above is Chaos which can
only=20
> >occur in systems of 3 or more nonlinear ODEs, while postponing
discussing=20
> >Chaos which can occur in nonlinear PDEs and iterated maps.  Moreover
there i=
> >s=20
> >a myth that Chaos can occur in 2 dimensional Phase Space, but this
contentio=
> >n=20
> >is refuted by The  Poincare=B4 - Bendixson theorem which states that if
a=20
> >trajectory is confined to a closed, bounded region, and there are NO
fixed=20
> >points in the region, then the region must eventually approach a
closed=20
> >orbit. In short, no Chaos in 2 dimensional Phase space under these
condition=
> >s.
> >
> >The Poincare-'Bendixson Theorem
> >
> >Suppose that
> >
> >(1) R is a closed bounded subset of the plane,
> >
> >(2) dX/dT =3D F(X) -- where X is a vector function of a vector variable,
and=
> > so=20
> >is F -- is  a C^(1) vector field on an open set containing R,
> >
> >(3) R does not contain any fixed points and,
> >
> >(4) There exists a trajectory C that is confined in R in the sense that
it=20
> >starts in R and stays in R for all future time.
> >
> >THEN, either C is a closed orbit, or it spirals toward a closed orbit
as=20
> >t--->+Infinity. Consequently, R contains a closed orbit and we have NO
chaos=
> >=20
> >in 2 dimensional phase space under these conditions.>>
> >
> >I thank Zackmann for this concise exposition of chaos and the lack of
chaos=20
> >in 2 dimensions.  However with respect to what I said
> >
> >1.) I granted that stuff Deleuze wrote with Guattari was pretty crazy
and=20
> >concentrated on works he wrote by himself.
> >
> >2.) The chaos Deleuze and Guattari are talking about in the book quoted
abov=
> >e=20
> >is old-fashioned molecular chaos, ie. Brownian motion, not the post-
1970=20
> >modern use of chaos in chaos theory.  As I recall, Gabriel Stolzenberg=20
> >(probably on the STS list) wrote that he pointed this out to Sokal,
who=20
> >granted it, but later wrote in the article in Koertge's "House Built on
Sand=
> >"=20
> >as if the chaos talked of was chaos theory, rather than old-fashioned=20
> >molecular chaos.
> >
> >Val Dusek