My view on the "four C's" is laid out in my Journal of
Economic Perspectives, 1999, article, "On the Complexity
of Complex Economic Dynamics," which can be seen
on my website, with a much more thorough discussion in
the book I have already mentioned. Briefly, there were
indeed "intellectual bubbles" regarding cybernetics,
catastrophe theory, chaos theory, and complexity theory,
which rose and then fell. However, this does not mean
that therefore the ideas of the theories were wrong
or misguided. Indeed, I argue that there is a clear
intellectual link between them and that they are all part
of the "broad tent complexity" view that is becoming
increasingly dominant and important, not less so. The
chaoplexologists should accept the designation, just
as impressionist painters accepted that designation
from a critic.
I have recently addressed this business of fads
more directly in my paper, "The Rise and Fall of
Catastrophe Theory Applications in Economics:
Was the Baby Thrown out with the Bathwater?"
to which the quick answer is "yes." It is also on
my website. Critics like Horgan thought that they
were really doing in the later C's by pointing out what
happened to cat theory. But it is back big time.
The collapse of the intellectual bubble overshot in
the other direction and the baby was indeed thrown
out with the bathwater.
As editor of a journal that is a major outlet for
this kind of stuff I see lots of papers using chaos
theory in a more or less "normal science" way,
to use Kuhnian terminology. The term "complex"
is currently being less used, hence maybe was a
fad. However, I see lots of papers, many of them
very interesting and challenging, that use the methods
and techniques of the newer ("small tent") complexity
theory. It is very much alive, but more in its multiple
and distinct versions and parts rather than as some
big whole. The very variety of definitions of complexity
almost guarantees this.
The term "catastrophe theory" has essentially been
purged. The current papers using it speak of Skiba
points or multiple equilibria, with some authors consciously
avoiding the term because they know using it will damage
their prospects of publishing their papers. The term
"cybernetics" has also largely disappeared, although
many of its ideas were folded directly into the modern
"small tent" complexity theory where it essentially survives.
Barkley Rosser
http://cob.jmu.edu/rosserjb
----- Original Message -----
From: "Sabri Oncu" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, June 17, 2003 7:58 PM
Subject: Re: [PEN-L] Complexity
Chris:
> On the basis of one hundred years of western mathematics
> chaos theory has produced something as mystical as the
> Mandelbrot set. It also produces that heart stopping
> moment for all of us, when we learn that the cardiac
> rhythm is not actually mechanically totally regular,
> but is in a pattern which conforms to chaos theory.
Hi Chris,
I happen to believe that mathematics is neither western nor
eastern but a common product of all humanity. A very powerful
tool that we humans have developed and something that I am deeply
in love with.
However, I also happen to believe as Horgan does, whom Barkley
quoted in his article, that the concept of "complexity" more
generally, not just in economics, as just the latest in a string
of fads, "the four C's." Complexity is one of them and chaos is
another. Because it was very fashionable when I was a graduate
student, I read a few books about chaos. Reading a few books on
chaos or any mathematical subject for that matter doesn't mean
much because you don't learn mathematics simply by reading books
and agreeing with their authors, at least, to my experience. You
have to work out the details and try to solve some problems, some
of which, preferably, are problems that you yourself formulated.
As I told Barkley, I don't know anything about complexity and
because of that, "complexity" is a fad is just a belief of mine.
I have no proof of the proposition that "complexity" is a fad, if
it can be proved, in the first place. We will see, or, at least,
I need learn more about it to make my subjective judgment about
"complexity".
However, with what I know about chaos, and it is not much, mind
you, my subjective judgment is that "chaos" is a fad as
"topology" was once to "mathematical analysis" or "game theory"
was to "economics".
I am your average neighborhood mathematician so this is not a big
deal. However, some mathematicians are mistakes of God, as John
Von Neumann was, and I happen to know one such mistake, a
childhood friend of mine. He once said this, in exaggeration,
maybe: all this chaos theory does is proving the "non-existence"
of the solutions of this or that nonlinear dynamical problem.
What kind of mathematics is that? As mathematicians, aren't we
supposed to solve some problems?
Best,
Sabri
