Chaos theory versus complexity theory
glevy at acnet.pratt.edu
glevy at acnet.pratt.edu
Sun Aug 27 03:54:17 MDT 1995
Chris B. -- in a very informative post -- writes:
> 5. Let us now in the traditional marxist manner, proceed from appallingly
> abstract discussions to try to apply things to reality in a way that
> has a glimmer of familiarity. Let us take our own dear example of an
> economy. Complexity theory would start off saying there are 6 billion
> people in the world, half of whom can trade their labour power as a
> commodity for commodities in return. ie 3 billion widgets who can interact.
> Will they interact absolutely smoothly and evenly or will patterns
> creating inequalities build up? Inequalities might indeed build up.
We don't need complexity theory to be able to say that there will not be
"absolutely smooth" interaction and "inequalities might indeed build up."
Why is a deterministic model needed to come to such a conclusion? Sounds
like math overkill to me.
> Chaos theory would say 3 billion is merely one number, a constant for
> the purposes of our simple deterministic equation -
> - and would ask what is the positive or the
> negative feedback in the equation we want to iterate. One application
> is to say that while increasing technology means endless pressure on
> use values to increase, there is a ceiling on exchange value, rather like
> the limits on the size of the lake in which the fish breed. The total
> amount of exchange value on the planet is limited to the population selling
> their labour power. Hence the population equation of chaos theory might
> model to some extent the fluctuations in the capitalist business cycle.
The sizes of the population and the wage-earning population are only two
variables that must be specified. What other variables must be specified
as well? I am skeptical of economic models fashioned after
fish-in-the-lake models. It is easier to specify and estimate the variables
for the fish than for capitalist reality. In a recent post, Steve pointed
out that one model (Goodwin? ...Minsky?) treated technology "as a given."
Now, if one is to make sense out of business cycle behavior, how can one
simply take technology as a given? Don't we have to first understand
technological change as a process before we can understand capitalist
dynamics? I still don't understand how the use of chaos theory can
produce more meaningful results than can more "traditional" methods of
abstraction and dialectics. What is the advantage that this math gives us?
Steve -- beware the white whale! Ahab, as I can recall, was a little too
overconfident concerning his ability to slay Moby. Could the struggle
between the Pequot's crew and the great white one be expressed using a
deterministic chaotic model?
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