Marxism and Mathematics

John Landon nemonemini at SPAMyahoo.com
Sun Feb 4 11:06:22 MST 2001


"Could you pass me a full indication of this text?",
from mjlima at uol.com.br

Presumably you mean Philip Mirowski's Against
Mechanism. I will obtain a copy from library tommorrow
and present a summary, it has been a while since I
read it. I am already supposed to be an Indian
bibliography and Jared Diamonds' Guns Germs and Steel,
but this one I will do asap.
This legacy of dissent against the marginalist
revolution is nothing new. Wesley Mitchell (the great
student of economic cycles) wrote a strong attack, as
did Veblen, if I am not mistaken.
Basically the text deals with the rise of marginalism,
so-called, in the last part of the nineteenth century.
This change in the direction of economics departed
from the thinking of Smith and Ricardo and proceeded
in a new direction. The labor theory of value, present
in Smith and Ricardo, and taken over by Marx, was
ditched and the concept of 'utility' takes over.
Mirowski's basic thrust is the way in which economics,
influenced by the world of physics, started using
various models and a lot of calculus that were
imitative without really resolving the issues. You see
a lot of technique, but the concepts are very
artificial, a point open to debate, to be sure. It is
a vast field that noone can quite keep up with, and I
should be wary of categorical rejection, but with some
experience your discover that while technical
expertise is one thing, the ability to model basic
concepts and structures is quite another.The
foundations aren't really there. You simply find
yourself in the middle of a series of assumptions you
are under no real obligation to take as fundamental,
whatever their partial value.
 Newton wasn't just good in math, he understood the
basics. But in that field, once the start is
discovered, you can piggyback on the math. It will
protect you. And it might fool you. You can become
semi-proficient all the way to quantum mechanics and
not understand it properly.
That match of math and subject matter is not true in
the social sciences.

The point about Poincare in Mirowksi was that he
discovered the attempt to ape thermodynamics with its
line integrals (in some of the early models) was
simply preposterous.
Another more accessible work is the recent "Death of
Economics", which makes many of the same points.
Now the great thing is complex systems as its author
indicates. Whatever those are. Time will tell if a new
brand of mathematical economics will basically correct
the problems using the ideas of complex systems. Chaos
theory was supposed to finally do it. But I don't see
it coming over the horizon yet.

Let me obtain Mirowski's book and take it from there.
The best approach is in the study of economic cycles.
You have real data, statistical maps of hard facts,
and you are in the present using data to make choices
about the future. That's basic sanity. A descriptive
subject producing genuine dynamical realities (whose
mechanism is not always clear!) Note that basic sanity
is factored out in a differential equation. You have
to say how a determined system,from starting
conditions will evolve in the future. Beside the math,
you have a real physical entity, gravitation, say,
which supplies the causal entity.
 You can't do all that with economies (although, of
course, you never know,you might get lucky). It's not
physics. You haven't specified the domain, say the
'force'. There is no causal backbone. You can only do
the more limited task of assessing past data to decide
about future choices, which sounds like goobbledygook,
but it is what Alan Greenspan does all the time, and I
think he told his number 2, who was in the news a
while back, who was good at mathematical economics and
raring to go, to forget all of it once at the Fed.
Keep lunatics away from serious money.

Note that this approach satisfies my Kant's Antinomy
criterion, causality is, say, in the past(fixed
cycles, or economic acitivity, as history), and still
influencing the future perhaps, but choice is present
in our decisions about how to influence this. Thus, by
definition, there is a difference. There are two
processes, a causal and a free process. I don't know
if that helps, except to see why just throwing math at
economies won't work.
The bottom line is then our current decisions about
how to act in relation to economies. It sounds simple,
but the decision to produce a science negates common
sense.
Many will disagree with such a negative assessment,
but no dogmatism is necessary. Try it as one
perspective. Simply don't be disappointed when the
great science of economics is found wanting once again
at the end of the day.



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