> An economic system is dynamically complex if its deterministic
> endogenous processes do not lead it asymptotically to a fixed
> point, a limit cycle, or an explosion.
This sounds like a classic statement based on well established chaos theory but trying to embrace the concept of complexity.
But being dynamically complex, which chaotic dynamics can produce under certain conditions, is an adjective and is by no means necessarily the same as "complexity theory", although IMHO chaos theory probably also applies in economics.
Both theories explain on the basis of western rationality how under certain conditions, quantitative changes can lead to qualitative change.
These are theoretical approaches which do not historically relate to dialectical materialism, but suggest to my mind one reason why previous generations found it useful to look at phenomena from the competing contrasting viewpoints that are inherent in a dialectical approach, but which are not necessarily in mechanical logical contradiction with one another.
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.
Chaotic dynamical systems can sometimes flip into phenomically chaotic states.
Ironically, complexity theory models how the interaction of numerous smaller units can create a higher level order.
Barkely Rosser is a hero expert on this area in economics, and manages to negotiate the interface between conventional academic scholarship, and progressive interpretation, with subtle good natured humour. (Just to stifle him with praise.) I cannot keep up with the detail of the argument and would not attempt to, but it is clear to me it is making a contribution in an area of economics that conventional economists cannot afford totally to dismiss.
I appreciate the serendipity of this email, which took me back to Barkley's web site, with the aid of a Google search. The URL for the actual article is
http://cob.jmu.edu/rosserjb/GENERIC.CPX.doc
Journal of Economic Perspectives, Fall 1999, vol. 13, no. 4, pp. 169-192
On the Complexities of Complex Economic Dynamics
From this it is possible to see that Barkley is actually citing a particular writer giving a "broad tent" definition, with which he does not necessarily agree.
Just before, he says amiably,
Unsurprisingly, there is no agreed upon definition of such a complex term as "complexity." Indeed, MIT's Seth Lloyd has gathered over 45 such definitions, most of these listed in Horgan (1997, Chapter 8, footnote 11, p. 303), with many of these definitions emphasizing computational or informational measures. This plethora leads Horgan (1995) to complain that "we have gone from complexity to perplexity." Without doubt, this is a serious problem.
