Marxism and Mathematics
John Landon
nemonemini at SPAMyahoo.com
Mon Feb 5 20:32:41 MST 2001
Looking at "Against Mechanism" by Philip Mirowski, I
find about what I said already, that the marginalist
revolution starts at about the time of the
'energetics' advances in physics, and the mathematical
economists appropriate the 'energy' metaphor in an
artificial transposition by 'analogy' to the concept
of utility. If you have studied physics, you might
recall the 'work' line integral and the relation of
conservative forces to exact differentials. Suddenly
we find price x marginal quantities of commodities, p1
x dq1 + p2 x dq2.... and this is to be integrated to
produce 'utility'. The strangeness of this once
pointed out borders on absurdity. Not Poincare as I
said but the mathematician Laurent actually initiated
a correspondence with Walras to see if Walras was
really serious or understood what he was doing. The
use of this analogy simply won't work beyond a
superficial resemblance, due to issues of an
integrating factor,and other questions. Walras
couldn't understand the objection. A second well known
physicist Gibbs also challenged Fisher. Then Laurent
challenged Pareto, trying again. Volterra also intoned
on the question. Then amnesia seems to have set in.
That's a brief summary, a rather shocking apochrypha
behind the coming triumph of mathematical economics.
This isn't too clear, but it is hard, to say the
least, to summarize this in an email. But Mirowski's
book, which is hard to obtain, is succeeded by his
accesible More Heat Than Light, which is much more
thorough and available at amazon.com and is well worth
looking at. Read the reviews there. Using the
Hamiltonian in economics raises all sorts of problems,
ones that are really not obvious to the mathematically
inexperienced, not also crack shots at physics. The
result doesn't make any sense, as far as can be
determined. Mirowski's second book amplifies at length
on these issues and makes a magnificent behind the
scenes intro to all the issues of macroeconomics, and
a lot of physics too. I just got it this morning, so I
barely register its extensive contents.
Mirowski's perspective is that (mathematical)
economics isn't a science, and its presentation as
such is socially strategic for all the obvious
reasons. Vernon Chalmers in his Blowout also suggests
the explosion of mathematical economics is correlated
with the cold war.
Moral: economics isn't a science, then. So don't be
intimidated by books on mathematical economics. The
rigor is not sufficient to establish the claims made.
Mirowski might seem extreme, to some, but I suspect he
is right. You know, Hayek, in spite of many blunders
of his own as Mirowski points out, wrecked his
reputation trying to denounce all this in 1944.
Marxists might take a hint.
All this said, these are Mirowski's perspectives, they
have my ear, but not necessarily my complete
endorsement. I am not prepared to completely reject
all mathematical economics, if only because I am not a
expert in these fields. However, I think he is
correct, in the main.
Again I am not an expert here, precisely the contrary,
but I do know the math, up to a point, and have a
sense of 'smell' (?) which is say, life is short,
these subjects are not so hard, but take time, which
is in short supply. Is it worth mastering these
subjects? My unconscious answer was always, not unless
you have to refute this propaganda! So my instincts
were born out in this case. Study some good physics,
this other stuff is junk.
Same incidentally in population genetics in biology.
The equations there baffle-convince amateurs,and they
work well enough in limited cases like dishes of
bacteria, or the effects of simple selection, but they
are presented as proof of a Darwinian science in toto,
complete with a fundamental theorem of natural
selection with a natural selection as a 'force'. That
is misleading, if not hogwash, and it is not a
newtonian science by any stretch. Blarney. But the
facade goes on and on to the point that whole
generations of students have been trained that way.
Another doubter, George Soros! I glanced at his recent
Open Society, and he has a chapter on economics, which
is worth looking at.
Read the last section of David Berlinski's A Tour of
the Calculus, where he muses on the failures of math
and calculus in biology.
Also look at Michael Perelman's The Natural
Instability of Markets.
John Landon
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