Ajit Sinha asks what problem I was trying to solve in my
posting on the nature of the value metric.
It is not so much what problem am I trying to solve, but what
problem am I able to discover.
What I am asking is whether there is a theoretical problem here in
the nature of the value metric. The background is that over the
last few years Allin Cottrel and I have been trying to rehabilitate
labour values as a tool for economic planning. In the course of a
conference in Lausanne last year at the Walras institute is became
clear to us that the level of scepticism felt by many left wing
economists to the labour theory of value required us to carry out
a more thorough going defence of that theory.
One step has been to replicate Shaiks results for the US and Italian
economies with the British data on the empirical validity of
labour values. Another thing we have been doing is to look again
at the theoretical arguments for labour values. We looked at whether
labour values correspond to some naturalist fallacy by comparing them
to other possible 'natural' standards of value like energy, and
found that one can not construct a convergent series of production
equations that give non-null energy values. The stuff on the value
metric is concerned with a re-examination of the argument about
the form of value in Capital I.i.
Marx's arguments about the value form are phrased in Hegelian terms,
reflecting his theoretical formation. My theoretical formation is
in contemporary computer science, and certain topics of my research
there are spilling over to the economics. In particular I have ben
working on fractals and fractal image compression and reading a lot
of Barnsley (Fractals Everywhere). This has led to two chains
of thought in the economic area:
1) Concerning the nature of metric spaces and the metric space
of commodity bundles.
2) The realisation that the Sraffian distinction between basic and
non basic sectors is homo-morphic to a possible technique for encoding
the entirety of a visual image in terms of a set of fractal transforms
that take as domain a subset of the image.
(In general the existence of these two areas of similarity indicates
that Barnsleys mathematical apparatus may be a useful conceptual tool
for economic thought.)
But the specific concern with the value metric is to see if that line
of argument can provide a re-inforcement of the arguments Marx put
forward on the value form. For example, whilst it is easy to see that
the fact that exchange value is a relation between commodities means
that there are n-1 relative values for n commodities and that this
is related to the fact that the isovals in an n dimensional commodity bundle
manifold will be n-1 dimensional sub-spaces, it does not by itself
explain why these sub-manifolds are flat rather than being, for example,
hyperspheres or saddle shaped. One hypothesis would be that the flatness
expresses a conservation law - that value in the sense of embodied labour
must be conserved in exchange relations of the form c-m-c.
This interpretation would give a more specific meaning to the phrase
'law of value' which marxists seem to throw about with some abandon.
An alternative interpretation would be that it was some property of
the logic of exchange per-se that gave rise to this flatness, irrespective
of the conditions of, or even the existence of social production.
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Paul Cockshott , WPS, PO Box 1125, Glasgow, G44 5UF
Phone: 041 637 2927 [EMAIL PROTECTED]
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