personal [mail on] chaos (fwd)
glevy at acnet.pratt.edu
glevy at acnet.pratt.edu
Mon Aug 28 17:12:48 MDT 1995
Lisa sent me the following message and said, as you will see, that I
could forward it to the list with my reply. -- Jerry
---------- Forwarded message ----------
Date: Mon, 28 Aug 1995 16:27:21 -0600
From: Lisa Rogers <EQDOMAIN.EQWQ.LROGERS at email.state.ut.us>
To: glevy at acnet.pratt.edu
Subject: personal [mail on] chaos
Dear Jerry, from the language in your post, I suspect that you [and
maybe Chris B too] are not operating on the same definition of chaos
as the rest of us yet. I find it rather tricky, I think it's a bit
of a misnomer. The mathematical terms which create chaos are
non-linear equations. The number of variables determines the number
of dimensions required to define phase-space. These are somewhat
separable.
What chaos math does is to produce previously unexpected,
random-looking patterns from simple math. Or, in the other
direction, to find that behind an apparently "chaotic" mass of
unpatterned data, there is actually one or a few relatively simple
principles which generate patterns that masquerade as irregularity.
Not that this is always possible, but part of the point of the new
[chaos] math. methods is to give us new tools to be able to see if
there is order within the apparent disorder. It is sort of like
discovering the microscope, but its effects may be more subtley
shifty than that.
We don't want to ignore or over-simplify too much, but maybe we might
as well take a look to see if there are some primary relations to get
hold of. A place to start, in digesting the elephant? Models are
always simpler than reality, and should be, I was taught. But the
point is to aid understanding.
I don't think of math-models as an alternative to another kind of
analysis, but perhaps a complement. It seems that you do? Could you
explain a bit more? I mean, if there are very many variables, for
instance, do you think they are better expressed in prose that math?
To me, math is a kind of language, so that some things can be said in
either prose or math, and translated back and forth.
I'm very far from making claims about applying chaos math to
economics and social organization. But certainly for the examples
explained by Gleick, in terms of building on the "standard science"
concepts of modelling, it makes all kinds of sense to me. (Take a
look at Gleick if you can, it reads very quickly.)
Feel free to forward this post to the list with your reply if you
want, your choice.
Lisa
Jerry
It would seem to me that the very process of creating a dynamic
model in mathematical terms tends towards the chaotic because of the
amount of variables that one is allowing for. .... One has to,
therefore, build a theory that creates order from the chaos but
doesn't ignore or oversimplify complex relationships. This suggests
to me that theory-building shouldn't necessarily take the form of
mathematical models where complex and dialectical relations are
involved.
********************************************************************
Dear Lisa:
Some comments:
1) The section of the post that you excerpted was written in the context
of discussing Steve's ideas about the possible uses of chaos theory in
political economy. I do not believe that the issues are the same when
one considers the applicability of chaos theory to modelling in the
natural sciences. I was addressing doubt about the applicability of chaos
theory to economic dynamics under capitalism and how one goes about
developing a theory that explains those dynamics.
2) I *do* believe that math models can be a complement to
theory-building in political economy. The questions that I was asking
concerned which subjects in political economy and which math, if any are
required.
3) Math *is* a kind of language, but it is a rather special kind of
language. Different types of math models have different properties and
logic. It is important to consider this when one decides if math should
be used and which math should be used. The language of math tends to
express relations formally and frequently deals with dialectical
relations in a less than satisfactory (i.e. misleading) way in political
economy.
4) Chaos theory is (as you say)a new tool, like a microscope once was.
Before you use a new tool you should have a very good idea about what it
was designed for, how it was built, and what the limitations are to the
use of that tool. Scientists seem to understand this better than economists.
5) You are right, "the point is to aid understanding." Can chaos theory
help us to understand specific nonlinear relationships related to
capitalism? If so, which ones? ... and why? Also, what type of chaos
model should we use (if we decide to use chaos theory)? All of the above
are questions that I would like to see answered.
6) I think the problem we have he-re ... is a fail-ure to commun-i-cate.
You seem to think that I am anti-math and anti-chaos theory -- I am not.
I am questioning the use of chaos theory in *political economy*. If you
want to use chaos theory to understand lemmings, that's fine by me. I
confess I know very little about lemmings. If you want to use chaos
theory in political economy, then I have the questions that I listed above.
Jerry
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