Dialectics and complexity

P8475423 at vmsuser.acsu.unsw.EDU.AU P8475423 at vmsuser.acsu.unsw.EDU.AU
Sat Aug 26 18:16:28 MDT 1995

Jerry says that he wants:
|to understand more about what you mean concerning the chaotic
|character of capitalism... the "anarchy of capitalist production"
|refers to the unplanned character of capitalism and is not the
|same thing as chaos... So how is capitalism inherently chaotic and
|what does it imply? Does it imply, for instance, that capitalism is
|aperiodic? That idea seems to fly in the face of capitalist economic
|history and business cycle behavior. We need a theory that not only
|explains how crises occur but also how they are overcome. How can a
|chaotic model produce such a result?

Hey, this is going to be a lengthy thread! (though hopefully a
short post). A few points:

* Aperiodicity does not mean non-cyclical: it means cycles
which do not have a regular period. Cycles composed of sums of
sine and cosines do have a regularity, for example (the basis
of Fourier analysis, so heavily applied in electronics).

* Chaotic systems generate aperiodic cycles: you cannot decompose
a long set of complex cycles into a set of identical shorter
cycles overlaid on each other. This is of course quite consistent
with history and business cycle behaviour, since though we can
say that it was approximately 20 years between depressions in
the 19th century, it could have been as short as 15 years or as
long as 30; and so on.

* The basic proposition is that any (continuous time) system
which has more than 2 variables, and where there is at least one
nonlinear relationship (for example, capitalists investing more
as the rate of profit rises) will be a chaotic system, to some
degree. But as you add extra levels of complexity (by which I
mean more variables) you don't necessarily get more chaotic
(by which I mean more random) behaviour. Extra variables can
well involve "homeostatic feedback" which can very effectively
stabilise a system (our own bodies are superb examples of
complex systems with multiple feedbacks which thus maintain
such body signals as temperature within narrow limits).

* These homeostatic feedbacks are part of how crises can be
overcome (as well as caused). Marx gave plenty of insights that
can be seen in this light, as in for example the quote I
posted from Ch. 25 a few days ago.

* Capitalism itself is clearly replete with nonlinear relationships:
capitalists to investment, as I commented above; compound interest
on debt; workers, wage demands and unemployment; technological
development and asset values. There are so many that, as Allin or
Paul commented, statistical work to unravel any chaotic components
from stochastic ones is pretty useless. But modelling sufficient
of them in sufficient detail may well generate a dynamic mathematical
model of capitalism which behaves much like the real thing.

* Of course, in selecting what to model, a theoretical guide is
indispensable, so it still comes back to the validity of the
theoretical guide. Which is why so much (neoclassical) work on
chaos has been bumpf.

Steve K

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