Marxism and Mathematics
John Landon
nemonemini at SPAMyahoo.com
Sat Feb 3 22:42:31 MST 2001
It is worth reading a work called *Against Mechanism*
by Philip Mirowski on the subject of mathematical
economics in general and the birth of marginalist
economic modeling in particular. The basic mismatch of
mathematics and content, in the imitation of physics
models, is described bluntly. There is an interesting
account of the great mathematician Poincare being
shown one of the early models and complaining about
the confusion of basic assumptions.
The problem is that these models don't really model
the subject they address. An exception are the
descriptive studies of economic cycles which use
different methods.
If you remember a recent post on Kant's Third Antinomy
you can see the reason why there is a problem: to
create the model, it must be deterministic, you would
want to use a differential equation, therefore you
must make a determination of the mechanics of choice,
and an elimination of any free action factor. But the
very act of doing so creates something artificial.
It's hard to believe it is that simple, but it is.
None of the models really work (it is always dangerous
to overgeneralize off course, it's a vast field, but
never be intimidated by pages of arcane symbols), a
point forgotten when mainstream economists pronounce
against the 'labor theory value'. It is worth
remembering that the Hayek people were always too
cagey to take marginalist economics seriously.
Modern social science tends to attract half-educated
math whizzes who target a math chestnut and go off the
deep end. The results never seem to amount to
anything.
Cf. also Robert Kuttner's Everything for Sale, for a
humourous account of the way models and reality are
always colliding.
Read Cohen's How many people can the Earth Support, it
is essentially the same effort to match an equation
with a social science in a simplified example. It has
a good history of demographics. That's the simplest
case, the application of the exponential function to
populations. That one has to work, it does work, yet
it doesn't work, the book shows how hard it is to make
predictions. Another useful work I know of is
Economics and Utopia by Geoffrey Hodgson on the
history of the socialist calculation debate. Marxists
outsmarted themselves by taking marginalism a little
too seriously, no doubt while the Hayekians had a good
laugh.
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