Re: Seminar: HILBERT SPACE MODELS COMMODITY EXCHANGES by Paul Cockshott

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Tue Sep 21 2004 - 07:13:14 EDT


 

________________________________

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? 

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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


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