Marxism and Mathematics
S Chatterjee
schatterjee2001 at SPAMyahoo.com
Sat Feb 10 17:41:44 MST 2001
Just some comments on this interesting thread. For
Marx's work in mathematics (i.e., calculus) see "Karl
Marx: Mathematical manuscripts", Trans. P. Baksi,
Viswakos Parisad, Calcutta, 1994.
Many of us have studied calulus. But when a genius
like Marx studies it, there are always some new
insights to be gained. For example, he and Engels say
that dy/dx actually means 0/0 in the limit whereas in
the traditional interpretation, common to this day, it
is interpreted as a tendency towards 0/0 but never
actually equals 0/0. This later is anathema to
mathematicians according to whom it is undefined (try
inputing 0/0 in any math program and see the results).
However, 0/0 is perfectly well defined depending upon
the actual circumstances (i.e., the nature of the
function involved). This I learnt from Marx.
In my work, I have used and still use a lot of math
but since some time I have become wary and conscious
of the use of it, especially blindly. Mathematical
modeling of physical systems is very widespread today
as can be gleaned by opening any scientific journal.
One of the problems arise when the equations
describing a phenomena are taken as God and the
underlying physical reality treated as secondary. The
scientist then lapses into a kind of idealism.
Mathematics works well in describing what is called
inanimate matter but does not work well when living,
conscious beings are involved. For then, as has been
stated here by one of the correspondents, the element
of free will arises.
Inspite of all the work in stochastics and probablity,
there is no way (as far as I know) the problem of free
will can be treated. You may write a differntial
equation (deterministic even if it has so called
random terms in it) to predict my future behavior but
I can always act in a way to negate your prediction,
especially if I learn about your intent.
Here, we encounter the difficult problem of
understanding the nature of living consciousness in
which area some of the best scientific minds are
working in recent times. However, I do not think that
the problem of consciousness can be tackled
satisfactorily by the fragmentary approach of modern
Western science. The problem of consciousness is also
connected to understanding the reasons for the
collapse of the socialist states and also in
developing the new socialist human being.
As to bourgeois mathematical economics, the
foundations are flimsy on which elaborate mathematical
structures have been constructed. Give a little shake,
and they will fall like a house of cards. There
probably are also holes in mathematical logic and
philosophy which is a human creation. I still do not
understand how can a collection of zero dimensional
objects (points) form a one dimensional line - a
philosophical conundrum. How can microscopic random
quantum processes give rise to well ordered and well
behaved macroscopic processes which can be described
quantitatively by well known laws of nature. Here,
David Bohm's work on the implicate order can shed some
light.
Sid
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