Re: Chaos theory versus complexity theory

[glevy@xxxxxxxxxxxxxxx]

Concerning the excerpt from Steve's post on the population equation, I
should have, as Steve points out, read that section more carefully.
Sorry, Ahab.

> 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.

I thought that Malthus's essential argument (and the one that is
continued in somewhat modified forms today by neo-Malthusians like ZPG),
is that the food supply would grow arithmatically over time and
population would grow exponentially. The result: famine, death, wars and
other "good" things that would "help" check the growth of population in
the short-to-medium term but couldn't overcome the population growth
crisis. This argument is not only refuted by history but also fails to
comprehend the cyclical growth of population and the role of technical
change in increasing the productivity of labor in agriculture.

> I think I diagnose a bit of math-phobia here -:).

I'm not really math-phobic (is that a real word?). Yet, even Steve must
admit that most mathematical models in economics have not helped us to
understand capitalism any better. When I was a student, I read a lot of
stuff on growth theory, a field of economics that can be rather
mathematically-inclined. Going back to simple one-sector models like the
Harrod-Domar model and the VonNeumann model and continuing to ever more
sophisticated multi-sectoral models, how has that literature helped us to
advance our understanding of the dynamic processes of capitalist
accumulation and crises? Moreover, while Steve quotes a scientist (I do
*not* consider economics a science), economists from all schools of
thought who employ mathematical models are generally not as careful about
stating the assumptions of their models and the limitations of their
mathematical techniques. For instance, it is now known that all
one-sector growth models have a analogous problem to the "knife-edge"
problem in Harrod. The math itself was OK in Harrod but the form of math
chosen prevented the model from making meaningful statements about
capitalism. So, the question isn't only whether math helps us to
understand particular topics in political economy, but is also trying to
identify the limitations of particular mathematical techniques for
understanding specific questions. The question that I asked before that
Steve did not answer is whether the non-linear relationships that occur
under capitalism can be grasped by chaos theory. Turning the question
around somewhat: what non-linear relationships related to capitalism can be
expressed using chaos theory and which non-linear relations
can not? And: why? Doesn't one first have to have a clear understanding
of the limitations of the mathematical technique and also ask whether a
particular technique is relevant for addressing a particular topic?
Simply saying that one is examining a non-linear relation does not, by
itself, mean that any type of non-linear mathematical technique can grasp
the relation in its essentials. Expressing the question somewhat
differently again: do the mathematical properties of a model correspond
to actual dynamics under capitalism? If not, don't we have to look
somewhere else?
>
> You're not saying anything that a competent and honest mathematician
> would dispute.

Mathematical economists, though, are frequently not very competent and
honest. As a Post_Keynesian, Steve should remember the very insightful
and blistering critiques by Joan Robinson concerning mathematical
economics. Joan would probably agree with me when I say that economists
from all schools of thought need to give a more careful consideration of
the methodology of their math models. So, in the spirit of Joan Robinson,
let me ask: what can we say about the methodology of chaos theory and its
relevance for understanding capitalist dynamics?
>
> Check out my paper in the JPKE; it's a very simple model, but
> I think it captures the essence of a financial crisis.
>
I'll do that. As for the topic of growth, inflation and the Phillips
Curve, I'm a little leery of the "stylized facts" approach. The
literature that I referred to before on growth theory also often used
"stylized facts" in a less than satisfactory manner, in my view.
Sometimes one can style the facts to show what you want to show rather
than to advance knowledge.

Jerry


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