All postings to the St. Johns discussion lists must be sent as pure .txt files in order to avoid the problem. Special coding for colors of fonts and the like are inserted when a posting is sent in html or htm format. However the Science as Culture list is housed at St. Johns University - which apparently cannot handle htm/html formatting. To overcome this, the sender must manually check the posting format on the mail client to make sure the posting is being sent in .txt format. Best wishes, Stephen Stephen Miles Sacks, MPA, Ph.D., Editor and Publisher SCIPOLICY-The Journal of Science and Health Policy Box 504, Haverford, PA 19041 Voice and Fax: 610-658-2332 (24 hours) Website: http://www.Scipolicy.net E-mail: [log in to unmask] The premier issue is for Fall 2000 is now in publication. The issue focuses on The Future of Large-Scale Health Systems and includes several articles on health systems and the problems, changes in institutional ethics, and a case study of the University of Pennsylvania Health System. Subscriptions and orders for individual copies can be placed on line at http://www.Scipolicy.net. Proposals and contributed articles are welcome. ----- 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