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

**Date:** Tue Sep 21 2004 - 07:13:14 EDT

**Next message:**ajit sinha: "Re: (OPE-L) RE: 'simple commodity production'"**Previous message:**Paul Cockshott: "Re: (OPE-L seminar] Paul Cockshott's "Hibert Space Models Commodity Exchanges""**Maybe in reply to:**Alejandro Valle Baeza: "Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott"**Next in thread:**Alejandro Valle Baeza: "Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott"**Reply:**Alejandro Valle Baeza: "Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott"**Reply:**Alejandro Valle Baeza: "Seminar: Value redundancy and price value deviations"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

________________________________ From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Alejandro Valle Baeza Sent: 21 September 2004 06:46 To: OPE-L@SUS.CSUCHICO.EDU Subject: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott is very interesting, especially for me because value-price correspondence is one of my research fields. Since Shaikh published "The transformation from Marx to Sraffa" (1984) there are several articles discussing value-price closeness. Shaikh used correlation coefficients to support the idea that market prices are close to labor values. Petrovich (1987) criticized such measure because spurious correlation and proposed mean absolute deviation for measuring price value deviations. And recently Steedman (1998) proposed to measure such deviations by the angle between market price and value vectors, as pointed out by Cockshott. Nobody uses Euclidian distance to measure value-price deviation. Nevertheless is not clear to me if according to Paul's paper are all of them wrong? Could Paul explain practical implications of his paper for measuring labor value-price deviations? --------------------------------------------- I think that Steadman's measure is probably wrong, and that mean absolute deviation is a more appropriate measure. --------------------------------------- On the other hand, Paul showed that commodity space is not Euclidian could Paul explain why is a Hilbert space? -------------------------------------- Because a complex valued Hilbert space has the properties that: 1. It allows exchanges to be modelled by Unitary rotation operators. In this space the budget frontier is a circle and exchanges move agents round the circle. 2. It has a dual or projection space represented by the square of the amplitudes in which the budget frontier has the normal form of a straight line which we observe empirically. The complex Hilbert space thus seems an appropriate form of mathematical abstraction to allow us to linearise what goes on in exchange relations. In thinking about this I admit to being heavily influenced by the literature on quantum computations which encourages one to think about using Hilbert space representations of problems. All references are in Paul Cockshott's paper. In solidarity Alejandro Valle Baeza

**Next message:**ajit sinha: "Re: (OPE-L) RE: 'simple commodity production'"**Previous message:**Paul Cockshott: "Re: (OPE-L seminar] Paul Cockshott's "Hibert Space Models Commodity Exchanges""**Maybe in reply to:**Alejandro Valle Baeza: "Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott"**Next in thread:**Alejandro Valle Baeza: "Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott"**Reply:**Alejandro Valle Baeza: "Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott"**Reply:**Alejandro Valle Baeza: "Seminar: Value redundancy and price value deviations"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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