Re: Chaos theory versus complexity theory

[P8475423@xxxxxxxxxxxxxxxxxxxxxxxx]

Jerry, while I liked your Ahab/whale predator-prey analogy (and no,
I don't think you could capture their interaction in a deterministic
nonlinear equation -:) ), I'm going to have to ask you to read a
bit more carefully! When you excerpted me as follows:

> 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.

You then commented:

Expressed as above, the *predator-prey* model seems to have a
neo-Malthusian component.

I've highlighted the fact that I was explaining the "population equation",
while you thought I was describing predator-prey.

As for your comments on the Marx's anti-Malthusian explanations for the
mechanism keeping workers wages' at or near subsistence, while I agree
in part, Ch 25 's purpose "was to develop a contra-Malthus explanation
for population changes under capitalist production", the population
equation (more accurately known as the logistic equation) was I think a
development in biology mainly used to explain the growth of cell populations
in cultures.

The essence of Malthus was not the concept of population growth,
but the presumption that any increase in the standard of living of the
working class would result in an increased birth rate, hence returning the
working class to subsistence once more. That Malthusian mechanism has been
well enough refuted by history, as rising living standards have gone hand
in hand with declining birth rates.

Please also remember that economists in general (and Marxist economists
in general) are small-fry when it comes to the development of mathematical
tools of analysis. The logistic equation analysis, as I said, was a
development of biology, and applied to the circumstances of the experiments
it was used to explain--the growth of cells in a culture--it gave a
very good explanation.

If anyone wanted to apply it to the far more complex issue of population
growth under capitalism, then a lot more causal factors would need to
be brought in.

I think I diagnose a bit of math-phobia here -:). I can understand why--
on the one hand, a lot of nonsense has been developed on mathematical
foundations (in economics), and on the other hand, to those who either
haven't learnt it, or have been taught it badly, it is a rather
daunting discipline. But don't try to demolish it with a straw-man
picture of its strengths and weaknesses. When you comment:

|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.

You're not saying anything that a competent and honest mathematician
would dispute. Yes, the basic model is not a very good predictor--but
it was good enough to capture the general, cyclical trends that had
baffled observers before that simple equation was worked out. Yes,
the ecosystem is too complex for such a simple relation, but
embellishments of that simple relation capture a surprising amount
of the detail of ecosystem behaviour.

To give you a feeling for how a good applied mathematician approaches
his (technical) art, the following is a quote from "On the
mathematical biology of arms races, wars and revolutions" by JM
Epstein, in _1992 Lectures in Complex System_, L Nadel &
DL Stein (eds.) [from the Santa Fe Institute]:

"I find the following fact intriguing: The Richardson and
Lancaster mdoels of human conflict are, mathematically,
specialisations of the Lotka-Volterra ecosystem equations."

"Before proceeding, I must make one point unmistakably clear.
I do not claim that any of these models is really 'right' in
a physicist's sense. They are illuminating abstractions. I
think it was Picasso who said, 'art is a lie that enables
us to see the truth'. So it is with these simple models. They
continue to form the conceptual foundations of their
respective fields. They are universally taught; mature
practitioners, knowing full-well the models' approximate
nature, nonetheless entrust to them the formation of the
student's most basic intuitions. And this because, like
idealizations in other sciences--idealizations that are
ultimately 'wrong'--they efficiently capture qualitative
behaviours of overarching interest. That these ecosystem
and, say, arms race equations should look at all alike is
quite interesting. That, on closer inspection, they are
virtually identical is, to me, really quite interesting.
Let me go a bit further..."

Which indeed he does. To anyone who has a curiousity about
mathematical modelling, I highly recommend this very
readable (with or without mathematical ability) chapter
and its successor.

Next:

|I'm still waiting for an example of how it can be used to
|further our understanding of capitalist accumulation and crises.

Check out my paper in the JPKE; it's a very simple model, but
I think it captures the essence of a financial crisis.

And on 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.

Yes indeedy; but I haven't done the work on this yet (or more
honestly, I've had a couple of tries and not got very far; currently
I'm trying a "bottoms up" tack on this issue, and I'll return to
the "tops down" approach once I've got some way down the track). But
basically, I think that the "shifts" in the Phillips curve relation
that so bedevilled "Keynesian" economics can be explained by a model
of nonlinear interactions with prices, as an extension of the
non-price model I've done in the JPKE. Will report on this if I
pull it off, of course.

|How will technological change, the role of financial institutions,
|and the role of the state be incorporated into such a model?

Much the same stylised way as they are in the model in the JPKE:
the former as an unconstrained source of loan capital, the latter
as a counter-cyclical force.

Cheers,
Steve K


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