Date: Wed, 3 Jul 1996 01:44:51 -0500
From: rahul-AT-peaches.ph.utexas.edu (Rahul Mahajan)
Subject: Economic field theory


There's been some talk in the last few weeks about using "field theory" in
economics, using the concept of value as a field. Since I'm a naturally
irritable guy, this annoyed me.

First, general comments. In physics, a field is merely a function from
spacetime to some mathematical space, which could be real numbers, complex
numbers, vectors, what have you. In other words, it's a quantity which at
each point of spacetime has a given "value" in some space. In and of
itself, this implies astoundingly little, so that saying "value as a field"
is profoundly meaningless as a way to describe an economic theory. To go
even further, how can even making value into a field make any sense? Do you
specify some "economic manifold" on which value is a function? If so, so
what? (The last point wil be echoed many times in the rest of the post)

Specific comments:

Paul C:

>I suggest you have a look at Farjoun and Machover's book The Laws of
>Chaos, published by Verso. They argue that the formulation of value
>theory in marxist debate has been hampered by the adoption of a
>determinist formalisation whereby people attempt to derive prices
>of production from input costs plus a given average rate of profit.
>They argue that the appropriate mathematical formalism to analyse
>something as disordered as a capitalist economy is not this sort
>of determinist model but the statistical mechanics of Boltzmann.

The statistical mechanics of Boltzmann is based on a strictly deterministic
model. It arises from considering the situation of an observer's imperfect
information about a completely deterministic system. In order to formulate
such a model mathematically, you need a deterministic microdynamics, and a
quantity which can characterize the essential "alikeness" of an ensemble of
microscopically different systems, as in physics one does with, say,
temperature (canonical ensemble). Then you need to show that the results
you get are independent of the details of how you pick your ensemble. As
far as I know, no economists have any pretense to the first or third, and
at best vague ideas about the second, so saying that statistical mechanics
is what is needed seems absurd. Paul, if you get time, I'd like some more
information about the considerations in the book you mentioned. I try not
to read books if I'm reasonably sure they'll be idiotic before I start.

>Exchange value as a field? I wonder what you exactly mean.
><<<<<<<<
>
>Paul C:
>The usage derives from Mirowski's book, More Light than Heat, which
>focuses on the borrowing of concepts from physics by economists.
>Refering to Marx, he argues that Marx had two value theories the
>substance of value theory wherebye labour time is defined in terms
>of the past labour embodied in a commodity, and what he
>calls the field theory. In this, value is defined in terms of the
>labour necessary to reproduce the commodity.

What makes this a "field theory" rather than a pink elephant?

>In principle the two measures can diverge, since technical change
>tends to make the second measure smaller than the first.
>
>Mirowski makes an analogy between the substance theory and the first
>conceptualisations of energy in thermodynamics as a conserved substance,
>and says that the field theory of value is analogous with latter treatments
>in physics that focus instead upon the gravitational, electrostatic etc
>fields, with energy then being defined in terms of integrals over
>paths through fields.

I suppose by the last part you're referring to the potential energy of a
particle in a field. The important thing about field theory, though, which
is what makes real, and which specifically makes it a real solution of the
problem of action at a distance rather than a formal one, is the fact that
the fields carry energy themselves, that they are therefore dynamical
quantities. In the absence of field equations, field theory is completely
empty -- this would seem to be the case in any economic theory. Also, I
don't see this analogy at all.

>It should be noted that it is 'value' not exchange value that is being
>spoken of as a field.

Chris B:

>In school it is true, that nowadays computers can
>model the effects of a simple non-linear equation, whereas until
>recently all science was presented in linear form. Trying to
>get a non-linear perspective required dedicated attention to
>the values of dx/dy over and over again with vanishing small results.
>I confess I was one who could never see the magic of differential
>calculus.

This is nonsense. More accurately, the last clause of the first sentence,
insofar as it is meaningful, is untrue, and the second is literal nonsense.
Nonlinear equations have always been part of physics (since Newton). I
can't imagine what you think you could mean by saying that biology or
geology "was presented in linear form" and this is scarcely more meaningful
for physics. There is not such thing as "trying to get a nonlinear
perspective" or "studying nonlinear physics." In fact, some physicist
likened the study of nonlinear physics to the study of nonelephant animals.
We generally get nonlinear equations, which we often linearize because
that's the only way we can solve them analytically (as opposed to
numerically with a computer), but it's always clear that the approximations
we make may not be self-consistent, so we have to be careful. The last
sentence I can hardly disagree with, but I'd like to point out that
"differential calculus" is not supposed to be magical, any more than "See
Dick run" is. It's merely the first step in learning to speak in physics,
and in many other areas as well.

A SHORT SERMON ON CHAOS

Very few people seem to understand properly the import of "chaos theory"
(definitely a bad term). It is not that "everything's chaos" or that
scientists can't really know anything. It is not, as Chris B says so often,
that "nonlinearity has entered science," or, as I'm sure some say, that
science has finally become truly dialectical. It is not the discovery of
sensitive dependence on initial conditions (SDOIC), which has been known
about since the beginning of mathematical physics.

What is it? I would identify two primary discoveries. First is the fact
that very simple systems can be chaotic, in the sense, for example, of
showing SDOIC; you don't need to model the weather, all you need is a
one-term-recursion difference equation. Second is the use of techniques
taken from particle theory and condensed matter theory (renormalization
group analysis, if anyone's interested) to identify certain general
features of a wide variety of systems -- universality. The same discoveries
were made earlier in condensed matter theory with respect to phase
transitions. Anyone who studies the field specifically may be able to add
something to this, but I'm pretty sure there has been nothing else this
big.

Chaos does not herald an epistemological revolution. We always knew that,
since we could never get perfectly accurate information about the initial
state of any system, there would be a duration beyond which we could not
really predict the behavior of the system. You can see references to this
by Poincare, Feynman, and presumably many others long before Mandelbrot
began pimping for himself. If nearby trajectories diverge exponentially
with time rather than linearly, clearly the length of time over which we
can extrapolate is dramatically less, but we always knew this behaviour
could (and sometimes would) come out of the equations of motion.

Let's see if this leads to as much fun here on the "real" mar'xism l'ist as
it does with all the revisionist Menshevik social-democrat petty-bourgeois
intellectuals in the ninth circle of hell (otherwise known as M2 -- brrr!).

Rahul




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