**From:** Paul Cockshott (*wpc@DCS.GLA.AC.UK*)

**Date:** Tue Mar 15 2005 - 18:07:38 EST

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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 ------------------------ 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. --------------------------------------- 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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