Definition of Complexity

Posted by Joseph L. Breeden on Jul 24, 2006; 3:56am
URL: http://friam.383.s1.nabble.com/Definition-of-Complexity-tp522229.html


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So, this is where I am out of date.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