I’ve started this post eight different times, each time I tried a different tact and each time I gave up. Over the past year I’ve gained a real interest in Complexity theory. I’ve read multiple books, papers, blogs… on different aspects of Complexity, Chaos, Emergence and related topics. In fact, in some of these posts I’ve referenced Complex Adaptive Systems (I’m using John Holland’s nomenclature) yet I’ve never adequately defined my terms. So, this week I decided to reread and do some additional reading to actually define my terms since, and I’m ashamed to admit this, I wasn’t completely sure what I mean by complexity. It turns out, from what I can tell, no one else is sure what the definition should be either. So, in the spirit of arrogance that comes so naturally to blogging I’ve decided to lay out some definitions below in the hope that people will want to comment and help me refine them. Actually, even if people don’t comment I’ll probably refine them. Anyway, here goes, my definitions for Complexity, Atomic Part (I might want to change that) Emergence and Complex systems.
Complexity: the the measurement of an ideal observer’s ability to predict the outcome of the interaction of a system’s atomic parts.
Atomic Parts: The arbitrarily chosen component parts that appear irreducible, when compared against each other at some arbitrarily chosen level.
Complex system: A system that can not be reduced to the sum of it’s parts. Effectively it is a system that is greater than the sum of it’s parts or as Stuart Kauffman would say, “a system that gives you something for nothing.”
Emergence: The observed qualities (or perhaps regularities) as perceived by the ideal observer that were unpredictable when said observer was given a complete description of the observed system’s atomic parts.
Caveats:
1) You’ll note in an effort to simplify my understanding of these concepts I’ve (temporarily) discarded the notion that complexity or emergence exist with out an observer. I don’t like making this assumption but I’m having trouble finding any way around it.
2) The use of an “ideal” observer is meant to do away with the argument that the unpredictability of a system is a factor of ignorance on the part of the observer. I know there are mathematical proofs that appear to prove some class of systems as complex given near infinite computational resources but I must admit I don’t have the expertise necessary to evaluate said proofs.
3) When speaking of the arbitrariness of component parts or chosen level, I’m enforcing my belief that there are in fact “levels” of a system that are internally cohesive when judging whether parts of the system are irreducible. Example, if one were to look at a human society one could just as easily argue that humans are the component parts as that human brains (or organs) or atoms are the irreducible component parts. I suspect that a part is irreducible if if possess a high enough (any?) level of complexity but, for purposes of this discussion, it seems it circular to argue this point.
4) Given the above definitions, Complexity can be an emergent property of a system, though I’d argue, that complexity will not necessarily emerge. If complexity doesn’t emerge, I’d call the Birthing System a Final Complex System and the Emergent System would be a Simple System. However, as I write this I wonder if any system is ever final since, depending on where you look, it would seem that it will birth some form of complexity even if not at a different level. Example, the interaction of ants is a complex system, the resultant ant hill is a simple system but future ant hives that come from the original ant system will, of course, be complex systems.
5) I’m still wrestling with whether complexity is a qualitative measurement, a quantitative measurement or both. In other words we can argue some system is more or less complex based on, potentially, how many complex systems it births, how many atomic parts and kinds of interactions said system starts with, how hard it is to predict Emergent phenomena…
So there it is, my first take on this issue. In my next post I’ll give some fuller descriptions of complex systems and why they’re of interest.