What is Complexity?

Louis J. Gross
Professor of Ecology and Evolutionary Biology and Mathematics
University of Tennessee
gross@tiem.utk.edu

There are numerous attempts to define "complexity" in the modern 
scientific useage of the term. Here's my take on this:

A complex system is one in which a well trained scientist knowledgable 
about the system of concern cannot rapidly intuit how the system will 
behave. By rapidly here, I mean with the aid of simple computational 
tools (pencil and paper, computer, calculator, etc.) in a few minutes. 
My point is that complexity should include systems that may be quite 
easily described, but have underlying complicated responses (e.g. the 
chaotic dynamics models of single or multiple populations, non-degenerate 
limiting distributions arising from some easily described stochastic 
models such as Polya urn schemes) that one cannot intuit easily, as well 
as systems that most of us would agree are complicated due to multiple 
interacting factors (food webs with many components, ecosystems with 
dynamic and spatial responses on multiple scales). Perhaps we need a 
terminology to describe these differences in modes of complexity. I 
think the standard approach of describing complexity as arising
from "middle number systems" is inadequate.

I am not much of a fan of what goes under the rubric of "complexity
theory" these days. By this I mean that to me this is just the latest 
"buzz word" hot topic and will go the way of game theory, catastrophe 
theory, chaos theory, and self-organized criticality to name a few. All 
these were supposedly going to provide "the answers" to major scientific 
questions. They all have contributed of course but never lived up to the 
hype. They merely provide a variety of constructs to allow us to phrase 
our questions in new ways, and tools to potentially allow us to tease 
apart similarities in behavior between systems arising in very different 
scientific fields.