Thanks to Paul for his careful response to my queries about model
interpretation. However, his attempt to finesse the issue by reference to the
mathematics of chaos seems rather to evade it. My concerns can be expressed as a
series of questions to him:
1. Is it your position that a capitalist economy approximates a chaotic system?
(In the sense in which, for example, the solar system may be said to approximate
a Newtonian particle system.)
2. Are prices, to some degree of approximation, what they are 'presented as' by
F&M- random variables with a sharp-pointed distribution of the kind you
describe?
3. If so, why are the random? Is it because we have not or cannot discover any
structural determinations of them? Or because we can discover so many that
variations approximate random movements.
4. Or are you enough of an instrumentalist to say that it doesn't matter since
the predicted correlation between price and vertically integrated labour times
seems to be empirically supported? Are we not interested in why labour times and
production prices are attractors of prices? How are attractors and attractees
distinguished - is it in the mathematics? or in the data? The term 'attractor'
invites a causal comparison (gravitational or electromagnetic attraction) But we
are not to interpret it like that - is that right? Why can we not instead (as I
think Duncan came close to mooting some time ago) take this correlation as
grounds for doubting the usefulness of trying to separate the labour-time system
from its monetary expression in prices?
5. We know that you and I work with widely varying methodological 'settlements',
and that such settlements are not susceptible to definitive empirical or logical
determination. Nevertheless I would be interested in your reasons for assuming
that a system characterised by Marx as people making history, but not in
conditions of their own choosing is adequately grasped ('represented'?) by the
mathematics of chaos. Perhaps only because of my ignorance, I do not find
implausible the ontological claim of some physicists that physical (sub-atomic
particle) systems are in them selves mathematical. I have not seen an argument
why we should even consider the possibility that variables which are indeed the
outcome of intentional action within social constraints should approximate a
chaotic system. John Hicks, and more recently Frank Kahn both seemed to think
that the non-linear dynamics of economic variables involved a path dependence
pushing us inevitably towards real historical and sociological description. One
advantage of the Marxist tradition is that it offers a much richer
conceptualisation for such a task. Doesn't it?
6. I think that the complexity of capitalist competition, and therefore the
expected weakness and intermittent nature of tendencies dependent upon entry and
exit of firms into markets ( a medium if not a long-term process) does make
demands on an adequate interpretation of single-system, as well as the
two-system 'models'. However, the task of the former is less formidable given
that it deals with the variables upon which capitalists actually make their
calculations, about which they form their expectations, etc.
Michael
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Dr Michael Williams
"Books are Weapons"
Department of Economics Home:
School of Social Sciences 26 Glenwood Avenue
De Montfort University Southampton
Hammerwood Gate SO16 3QA
Kents Hill
Milton Keynes
MK7 6HP
tel:+1908 834876 tel/fax: +1703 768641
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email: mwilliam@dmu.ac.uk 100417.2625@compuserve.com