Re: (OPE-L seminar] Paul Cockshott's "Hibert Space Models Commodity Exchanges"

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Tue Sep 21 2004 - 07:04:55 EDT



From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Gerald A. Levy
Sent: 20 September 2004 14:13
Subject: (OPE-L seminar] Paul Cockshott's "Hibert Space Models Commodity

Hi Paul C.
I expect to be busy later today so I'm going to just jump in and 
ask a couple of questions about your paper while I have a few 
1) You suggest that it is possible to posit an "underlying
linear vector space of which commodity space is a
representation" (p. 3)  and "*unlike commodity space itself*,
this space, is a true vector whose evolution can be modeled
by the application of linear operators" (Ibid, emphasis added,
JL).  This is repeated in the last sentence of the paper where
you write that commodity amplitude space "*unlike 
commodity space*, is a linear vector space within which 
angles of rotation have a clear meaning" (p. 6, emphasis again
added, JL).   I am confused by this.  
a) If commodity "space" is *not*  a linear space, *why* is it 
reasonable to suggest that the "underlying" representation 
can be linear?   
The analogy here is between classical probability
space which is non linear, and the Hilbert space
of quantum amplitudes which is linear.  One observes
phenomena that can not be accounted for classically (Bells Inequality)
but which can be accounted for by positing an 
underlying linear space. There is obviously a lively
debate about the ontological status of this linear space,
but what I was consciously doing was using this model
applied to commodity exchange.
It struck me that there has been a wealth of models applying
linear algebra techniques to examining the magnitude of
values, but so far no attempt to use linear algebra to analyse
the value form. Since the value form is presented in the 
context of the exchange of equivalents, how can we model
this in linear terms - obviously it has to be in terms of 
unitary, and thus value conserving, operators. The 
problem is that one can not apply these directly to exchange
values but one can posit a dual space in which linear unitary
operations are possible.
b) If "commodity space" is non-linear shouldn't methods 
of measurement which take into account this non-linearity be 
I think this is a very valid point. It indicates that if one
is for example looking at the fit between a price predictor
and actual prices it may be better to look at the sum
of absolute deviations rather than the sum of square deviations.
c) are there any tests that you can use which use non-linear
methods which can be applied to the data to confirm or not 
confirm the empirical propositions about the closeness of 
market prices to vertically integrated labour values?
See the above
2) For those who wish to do further research in this area, what
do you identify as the major directions requiring further 
I am interested in the possibility of analysing the 
creation of money in terms of creation and annihilation operators
so that the analysis extends to monetary circulation.
I think one may be able to make analogies between
such operators and the cancellation of debts in 
a system of credit money. 
In solidarity, Jerry

This archive was generated by hypermail 2.1.5 : Wed Sep 22 2004 - 00:00:03 EDT