Julio,
I will post to the list a copy of http://werple.net.au/~andy/txt/complexi.htm by Michael Brand, because I think we owe Michael some comments on his contribution which was posted on the site in April. ...
What is needed is:
(1) An economic theory that does NOT depend on mathematical modelling which will allow us to perceive the trends of the world economy in order to inform political strategy for the overthrow of capitalism. Revolutionaries don't have access to the data and the supercomputers necessary for applying mathematical modelling.
(2) An economic theory (using any available technique) adequate for millions of workers to participate in managing an economy during the transition phase, in which commodity exchange should wither away and capitalism continues to dominate a part of the world.
* I am a bit sceptical about the statements you make about Marx's theory of Capital. It's essential purpose was to throw light on the historical tendencies rather than laws of equilibrium. Now, Marx's value theory does not *exclude* supply-and-demand analysis of course, so short-term dynamics co-exists but it is questionable the extent to which such theory could be attributed to Marx.
* I see the "Notion" of capital as "generalised commodity production", but this is just an *abstract* notion, which is developed in the general theory as you describe, from abstract notion to more and more concrete notion, but that's only words...
* Marx's premises are "real individuals, their activity and the material conditions under which they live..." The premises of classical economics are individual abstract profit-maximisers exchanging abstract product with every other. Again, Marx's theory is not mutually exclusive with classical economics, but includes it, so I agree that a superior mathematical model is a step towards a concrete understanding of capitalism. Our task is to use the conceptual framework provided by Marx and Hegel and the positive results provided by our bourgeois economists to try to give us (1) above.
In the meantime, the technological revolution taking place is transforming the presuppositions in relation to economic planning, workers control and the self-organisation of the working class and the relation between them. And we should start thinking hard about (2) above, because we may not have much time.
* Reading this book, makes me think that there is room for some thinking about the relation between Hegel's logical system and the passage from mathematical model to emergent property. Thanks Julio.
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Some off-the-cuff general reflections about mathematical modelling
* Phenomena come to us in the form of "levels", in which relatively simple phenomena arise at one level on the basis of fully developed complexity at lower levels; mathematical models can "encapsulate" essential relations underlying activity at a given level and through numerical modelling or mathematical analysis reveal the emergent properties; as we have discussed (Julio) in earlier mails, these mathematical models contain all sorts of implicit assumptions of which economists for example are usually blissfully unaware (stationarity implicit in uncorrelated stochastic Fourier analysis, 50-50 a priori likelihood of hypotheses (however absurd) implicit in hypothesis analysis (e.g. quality control) using Bayes Theorem, independence of events and stationarity of conditons implicit in statistics of extremes, and the others pointed out in "Complexity");
* therefore, more often than not, so far as the *real* issues are concerned, such mathematical modelling is simply tautological, proving what was assumed in the premises, even though there may be real value in terms of emergent phenomena along the way.
* it is a hopeless task to think that a mathematical model based on one level of phenomena can adequately model "input" from phenomena at another, or that one can deterministically compute phenomena at one level from those at another. * Every mathematical model has a material theory implicit in it and that should be explicit, not just implicit.
* I suspect that the project of adequately modelling capitalist crises sort of assumes what has to be proved - capitalism would have to abolished before we would have the material conditions to solve the problem.