[lbo-talk] "Theory's Empire," an anti-"Theory" anthology

Les Schaffer schaffer at optonline.net
Wed Jun 4 10:41:53 PDT 2008


</lurking>

Ben Jackson wrote:
> How about the Katherine Hayles quote about Irigaray?
>
> [snip]
>
> I won't assume that this one paragraph is representative of all of
> Theorydom, the way Dawkins does. But seriously, what kind of
> intellectual tradition produces something like this?

well, Hayles words seemed clear enough to me that i looked up her intellectual tradition: she did in fact study Chemistry through a master's degree. and if you check her preface to "Chaos and Order: Complex Dynamics in Literature and Science" you will see she does know a few things about chaos "theory".

the problem with her comments is more clearly revealed in the stuff you or others snipped from the quote; look at it again:

The privileging of solid over fluid mechanics, and indeed the

inability of science to deal with turbulent flow at all, she

attributes to the association of fluidity with femininity. Whereas

men have sex organs that protrude and become rigid, women have

openings that leak menstrual blood and vaginal fluids. Although men,

too, flow on occasion -- when semen is emitted, for example -- this

aspect of their sexuality is not emphasized. It is the rigidity of

the male organ that counts, not its complicity in fluid flow.

{{{These idealizations are reinscribed in mathematics, which

conceives of fluids as laminated planes and other modified solid

forms. In the same way that women are erased within masculinist

theories and language, existing only as not-men, so fluids have been

erased from science, existing only as not-solids.}}} From this

perspective it is no wonder that science has not been able to arrive

at a successful model for turbulence. The problem of turbulent flow

cannot be solved because the conceptions of fluids (and of women)

have been formulated so as necessarily to leave unarticulated

remainders. [Hayles (1992), p. 17]

from: http://www.math.tohoku.ac.jp/~kuroki/Sokal/bricmont/node17.html

The '{{{ ...}}}' are my emphasis.

in a sense, this is an excellent *description* of the problem: much of the early fluid mechanics did focus on static situations (like water behind a dam) or laminar flow problems, where the fluid is kind of sort of like laminated plates sliding over each other.

The approach of chaos theory to the problem of turbulence was to continue this movement from the male to the female (if you like), by taking two additional steps. First was the traditional one -- which goes under the name linear stability analysis -- whereby the "laminated planes" are given some flexibility. specifically, they are allowed to take on a weak, wavy character, and then one checks to see if the waves damp out, remain unchanged, or become unstable and grow to large amplitudes. Then comes the non-linear step, where attempt is made to be self-consistent by adding in higher order correction terms, so that as the unstable modes grow large, they interact with other modes or with itself in such a way as to remain finite in amplitude. As a result, we see chaotic motions in the fluid.

But by the late 80's, someone near the forefront of chaos theory at that time told me that the field had failed to meet one of its objectives, which was to explain fluid turbulence. and the reason is that the weakly non-linear theories had one foot solidly in the male end of the description, which was the laminar flow.

in a sense, chaotic descriptions of fluids are too tied to epicycles. this is not to say that epicyclic descriptions of fluids are powerless: i remember in particular one excellent paper on the mechanics of Saturn's ring system, which can be thought comprised of a granular fluid. in this case the epicyclic description allowed the authors of the paper to examine non-linear problems in a tractable way. yet the non-linear wave description of Saturn's rings does not contain turbulence.

Seen from the perspective of the journey from solids to laminar planes to wavy planes, Hayles statement is at least richly suggestive: perhaps there is a completely different framework for understanding turbulent fluid flow. but stating a description of the problem is not solving that problem. And it is not possible to say that yet another step from non-linear wave interactions to ???? might bring us closer to a theory of turbulence. but we do not know what ???? is either.

for completeness, i should mention another approach to understanding turbulence taking small interacting eddies or whirlpools of fluid as the essential background description. we know that eddies are formed when liquids and gases flow past obstacles, and at sufficiently high flow rates these eddies take on a random character. yet there is still no complete theory of turbulence from the eddy perspective either.

If you compare Hayles statement with Sokal and Bricmont's reviews of same, the latter seem awfully trite. Here is Dawkins:

You do not have to be a physicist to smell out the daffy absurdity

of this kind of argument (the tone of it has become all too

familiar), but it helps to have Sokal and Bricmont on hand to tell

us the real reason why turbulent flow is a hard problem: the

Navier-Stokes equations are difficult to solve.

That the Navier-Stokes equations are "difficult to solve" says absolutely nothing, nor is it richly suggestive as Hayles. And Hayles last sentence, on "unarticulated remainders" does suggest an appreciation for the averaging approach to turbulence:

http://en.wikipedia.org/wiki/Reynolds-averaged_Navier-Stokes_equations

which is often used, for example, in models for weather and climate systems.

an interesting side-note: while googling on Hayles and turbulence i came across two interesting threads.

The first one takes Sokal and Bricmont to task for not acknowledging cellular automata as a new approach to turbulence:

http://www.adequacy.org/stories/2002.5.16.143527.295.html

In this post by "jsm", lavish praise is heaped on Stephen Wolfram for describing his approach to cellular automata as follows:

Cellular automata theory doesn't deal with rigid things which fly

around in continuously differentiable trajectories; it deals with

things which diffuse outward gradually, then experience sudden

unpredictable changes in complexity.

jsm then compares this to Iragaray:

"continuous, compressible, dilatable, viscous, conductible,

diffusable... it enjoys and suffers from a greater sensitivity to

pressures... it changes - in volume or in force... it allows itself

to be easily traversed by flow by virtue of its conductivity to

currents... it mixes with bodies of a like state, sometimes dilutes

itself in them in analmost homogenous manner, which makes the

distinction between the one and the other problematical: and

furthermore that it is already diffuse "in itself ", which

disconcerts any attempt at static identification. "

and yet cellular automata has not, to date, solved the problem of turbulence either. Here is Wolfram himself in "A New Kind of Science":

But in practice over the years since 1985, cellular automaton

methods have grown steadily in popularity, and are now widely used

in physics and engineering. Yet despite all the work that has been

done, the fundamental issues about the origins of turbulence that I

had originally planned to investigate in cellular automaton fluids

have remained largely untouched.

The second thread is here:

http://www.math.columbia.edu/~woit/wordpress/?p=470

which describe one woman mathematician's attempt to prove some results related to the Navier-Stokes Equations (NSE) of traditional fluid mechanics. the paper, originally submitted to arxiv.org, raised a brief burst of hyperbole in Nature

http://www.nature.com/news/2006/061002/full/news061002-14.html (not sure if this is free or not)

but then the paper was withdrawn due to discovery of an error. the only remaining discussion i can find is here:

http://notes.dpdx.net/2006/10/06/penny-smiths-proof-on-the-navier-stokes-equations/

where we learn that Smith allowed a crude form of compressibility to enter into the NSE. traditionally, turbulence in fluids has been studied using the incompressible form of the equations. the idea that weakening the stiff member can be a powerful metaphor shows itself, for example, in the solution to the (rigid-)sphere packing problem. fake compressibility has also been shown to be effective in fluid flow simulations, though not yet for the kind of exact results attempted by Smith. finally, Smith set out to prove existence of solutions to the NSE, which is different from elucidating how the NSE predicts turbulence.

Les

<lurking>



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