I'm usually very quiet on this group. I almost always follow the discussions and often look up the references, but I must say that you've hit on a topic that has been bothering me for a decade. I did my thesis work applying chaos theory to astrophysical systems (about 15 years ago). It was always critically important that we could define what a chaotic system was, we had statistical tools for showing that a system was probably chaotic according to the scientific definition, and there was a rapidly growing body of mathematical literature (not all of which I could follow) providing a theoretical basis.
Complexity theory troubles me because it is treated like pornography. "I know it when I see it." I remember a brief discussion around the launch of the Journal of Complexity (I think it was that one), where someone asked, "Don't we need a definition of complexity to have a journal of complexity?" They were rebuffed by the editors with the comment that "the submitting authors will create the definition". I am sympathetic to the difficulty in defining complexity, but I have always felt that the lack of a clear definition is the primary thing holding back complexity theory. With chaos theory, if someone publishes a book on "chaos theory in literary review of the renaissance" (don't laugh), we have tools to point out that they are abusing a mathematically grounded scientific term (even if the choice of the word "chaos" is partly responsible for the abuses). In complexity, I lack the tools to go to the author of a book on "complexity theory in business management" and discuss whether it is being used properly or the author is just stealing a term for purposes of marketing. So, this is where I am out of date. At this point, do you all consider chaos theory to be a subset of complexity? (I have my doubts, since three bodies in orbit are chaotic, but are they "complex"?) Owen listed some useful statistics to compute to identify chaos theory, but are any of these or the Reynolds number really viewed as a definition of complexity? (Robert is pursuing this question and I'm glad to read it.) Do you believe that a definition (verbal or mathematical) of complexity now exists which would allow a practitioner to confirm that a system is "complex"? Again, I'm showing how long ago I worked in this area, but complexity always seemed to be defined in terms of "emergence", which also had a troubling definition -- along the lines of "something we didn't expect". Again very bad. I've asked too many questions for this kind of forum, but if a seminal paper has come along in the last decade which resolves all this, I would greatly appreciate a reference. Thanks much, and I'm sorry if I've stepped on any toes. I tend to go stomping about without my glasses rather often. Joe Breeden ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
