From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Tue Mar 15 2005 - 18:07:38 EST
Gerry
Taken literally, the above combined with the excerpt below from a
previous post can be interpreted as making one or both of the following
claims:
i) the mathematical techniques employed alter our view of production;
-------------------------
Yes they certainly do
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ii) our view of production is that it can be represented by (linear and)
matrix algebra.
------------------------
That is the most common formalism used by Marxist economists certainly.
It provides the common basis for most discussions on the theory of
value.
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G
i) seems to me to be arse-backwards: i.e. our view of production
determines (or should determine) what quantitative techniques are
employed to describe that process rather than vice versa.
-----------------------------------
P
I don't think you can isolate things in this way. Once you try to
think about something complex, you have to formalize it mathematically.
You can not have a 'view' of a complex subject matter unless you
have a mathematical model of it.
----------------------------
G
ii) seems to assert that the production process can be described
as a linear process. Yet, shouldn't we view production as
part of a non-linear dynamic process?
-----------------------------
P
It may be that one may want to see it as part of a non-linear process,
but in formulating a theory of something it is helpful to use linear
models so long as they give reasonable results. But of course
Sraffas model is non-linear. A part of the results of Ochoa et all
has been to show that in practice the non-linearities in the Sraffa
model do not seem to be of much practical significance.
----------------------------
G
You also make a history of thought claim that Sraffa and
Leontief "were responsible for the importation of matrix
representations into Marxist economic discourse." Have you
forgotten about von Bortkiewicz?
-----------------------
P
I was under the impression the VB just dealt with simultaneous
equations and small numbers of them at that.
The full matrix formalism arose as a result of the development
of socialism and the problems of socialist planning.
It came from Gosplan, early copies of whose tables became
available to economists at Cambridge - Keynes mentions
having access to them.
The person I should have mentioned was Von Neumann. It
is likely that his facility with the application of matrix
formalisms in his growth model was a combined result of
reflections on what was going on in the USSR along with
his own background in providing a systematic mathematical
basis for Heisenbergs matrix mechanics in his work
on the mathematical basis for quantum mechanics.
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