Marxism and Mathematics
John Landon
nemonemini at SPAMyahoo.com
Fri Feb 9 21:58:19 MST 2001
re post from juliahuato at hotmail.com
The questions of equilibrium models versus mathematics
and economics in general make up separate issues. I
was merely pointing to the negative research project
over the equilibrium issues of Walrasian type
mathematical models. The failure of that project, by
and large, in the fifties and sixties has been
insufficiently publicized, and never reached the
textbooks in economics. That is part of my lack of
enthusiasm, which can be misinterpreted. It is hard to
obtain reliable information. I don't study such things
in courses for a certificate. I do it because I want
some hard information, and you learn from experience
that textbooks are giving you a misleading picture.
Beware of them, they will indoctrinate without mercy,
and sacrifice understanding.
We are back to deja vu, it sounds like Marx's Critique
of Political Economy all over again. He was
experiencing Ricardo's thinking, was impressed, but
could see the blending in of ideology with a supposed
new science.
So if bourgeois economists in the know aren't
convinced, I will demur. that's all. I don't want to
get in a 'woe to world' about it. Enough said. There
were some good posts on pen-l just recently on this,
with some references.
The point is that the free market with its equilibrium
assumptions idea so heavily promoted is a theoretical
fancy whenever it is made to seem like a proven
scientific construct, just because of these illusory
models. A book like Mirowski's More Heat Than Light
tries to explore more general limitations of all of
this.
The applicability of mathematics is an outstanding
puzzle. I would not wish to seem dogmatic, but I don't
feel confident looking backwards at two centuries of
'social science', with or without mathematics. It's
not as bad as the fashion models on the platform
walks, but it gets close. The Hegel fad, the Comte
fad, the Freud fad, now the sociobiological fad...
The unreasonable effectiveness of mathematics, in the
famous phrase, in physics is not yet matched by
anything in social science. Mathematical economics is
often held up as an exception, but we can see that it
is not.
None of this is about the many reasonable uses of
mathematics in many instances, not what we are talking
about. But a model that matches the reality of a full
social context is simply not here yet.
One issue is the differential equation. You might look
at Paul Davies' The Fifth Miracle. He talks about the
limitations of such equations. They don't change their
information content, so to speak. Specify the initial
conditions, the solution, and the future of the curve
is fixed, etc... This works with planets and inert
blobs of rock in the asteroid belt, but doesn't seem
to fit the beast. Things that evolve increase their
interiority and their information increases.
Differential equations can only match a limited
version of such things. The relation of life to
information is clear in DNA, these are virtual
computational devices in molecular form, and they
contain a huge amount of information. Where does it
come from?
Davies also goes into a new approach to such things,
algorithmic complexity theory (you said 'invent new
theories', they are appearing post haste)with its
deeper insight into questions of randomness and
complexity. The life sciences need new tools. Another
recent popular work is Randomness by David Beltrami.
Or the Emperor's New Mind by Penrose.
If you look at physics, you see a major math revamping
at each stage, Newton's calculus, then the vector
analysis in electromagnetics, then quantum mechanics.
The subject is reborn for each advance. Everyone else
seems stuck on a first calculus course and a book of
dog and pony tricks from a differential equations
manual. It is all suspiciously underpowered. Who
knows.
We may be talking at cross purposes. The use of
mathematics are always a point of important
exploration, but it is not anti-science to wonder
where it is all going in the social sciences.
John Landon
http://eonix.8m.co
nemonemini at aol.com
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