Chaos theory versus complexity theory

glevy at acnet.pratt.edu glevy at acnet.pratt.edu
Sun Aug 27 07:38:05 MDT 1995


Ahab (aka P8475423) wrote:

> The predator-prey model is not the same as the population equation. To explain
> the latter to any non-afficionados still reading, the population equation
> encapsulates two details about population growth:
>
> * that if resources were unconstrained a population can expand exponentially
>
> * that the resources are ultimately limited, so that in a given environment,
> there will be a maximum carrying capacity.

Expressed as above, the predator-prey model seems to have a
neo-Malthusian component. How does technological change affect resources
and population? Although Steve cited Ch. 25 of _Capital_
recently, this seems a far cry from the idea of a relative surplus
population brought on by the consequences of increased centralization and
concentration of capital and increased relative surplus value through
technological innovation. In large part, the purpose of that chapter was to
develop a contra-Malthus explanation for population changes under
capitalist production.

> The idea is pretty simple to express in verbal terms: if you have a rapid
> growth rate and you're very near the carrying capacity, you'll overshoot
> it with the next round of births, and the excess population will lead to
> starvation-caused deaths, reducing you below the capacity; and then next
> time you overshoot it again.

The above also sounds very neo-Malthusian to me.  Beyond that, does it
express a relation that corresponds to the reality of population growth
changes under capitalism? I don't think so, although, I believe that more
theoretical work needs to be done to more specifically connect changes in
the rate of the accumulation of capital to changes in population.

I don't even know that the fish and sharks model is a very good
predictor of changing fish and shark populations. The ecosystem is too
complex for such a simple relation.

>
> Strange attractors in nonlinear models result when there are two
> or more unstable equilibria, and their regions of attaction and
> repulsion overlap. Imagine drawing a box in the sand, and then
> making two "Mexican sombrero" patterns in the sand, so that the
> rims of the sombreros just overlap. The you hit the sand with a
> small, "nice" French atomic bomb, turning the sand into glass
> without disturbing the sombreros ( -:)). Now roll a ball within
> the box. The ball will have to fall into the rims of the
> sombreros, but the path it takes depends on where you pushed it
> from, and how hard you pushed it. At one level, it might
> spin around one sombrero once, then move to the other.
> A slight difference, and it might spin around one sombrero 5
> times, then shoot across.
>
> That ain't strictly chaos, but I hope it's a useful mental
> picture of the process.
>
> What does this have to do with capitalism? Lots, if the
> underlying processes are nonlinear, which I assert they
> are. This kind of picture could help explain why, for example,
> we might move from 20 years of high growth and low inflation,
> suddenly to low growth and high inflation, and then suddenly
> again, to low growth and low inflation...
>
Well ... the Mexican sombrero and French nuclear bomb analogy doesn't
seem to conform to any nonlinear relations that I know about concerning
capitalist dynamics. Again, Steve repeats that understanding nonlinear
relationships has a lot to do with understanding capitalism. I certainly
agree. Can a predator-prey model help us understand those nonlinear
relations? I'm still waiting for an example of how it can be used to
further our understanding of capitalist accumulation and crises. As for
the last part concerning growth and inflation, Steve seems to be
suggesting that this type of model can be used for understanding the
breakdown of the so-called Phillips Curve relationship (i.e. the PC
states that the  rate of inflation and the rate of unemployment are
inversely related) that can be observed empirically. An interesting line
of inquiry, I will admit. How will technological change, the role of
financial institutions, and the role of the state be incorporated into
such a model?

Jerry


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