Saturday, March 27, 2010

Complexity vs. Chaos

There seems to be different phenomenon between complexity and chaos that I would like to explore in this post. First, I admit to a Brussels-Austin perspective of thermodynamics. The measure of chaos seems to be a distance from thermodynamic equilibrium. In open systems, this is the distance - or degrees - above absolute zero. In closed systems, this is thermodynamic difference (in heat and other kinetic motion) between the system elements.

Compare this to objective complexity, which is simply defined by 3 (or more) degrees of mutual, non-linear coupling between system elements. This three-body problem defines the simplest form of complexity.

We can compare the complexity / chaos system of problems by considering the three-body problem at thermodynamic equilibrium. Nothing is moving, no mutual orbits. The coupling mechanism may be underdetermined (subjective complexity), but may be considered as a thermodynamic perturbation (even though the perturbation has nothing to do with the heat component). As the thermodynamics increases, there emerges motion in the three-body system. The complexity within the system moves from "potential" complexity to "actual" complexity - a form of realization.

Of course there is subjective complexity, referring to the uncertainty, stochastic nature or lack of knowledge in systems - but this happens in simple systems as well as complex systems.

The term complexity is often used indiscriminately to describe both complexity and the coupling between complexity and chaos. If it were up to me, I would create a different word for the complex/chaos coupled system - something like "chomplexity" - but I hate neologisms, so I merely add a footnote to distinguish the two.

It makes sense that the Inuits have many words for snow. We have overloaded our one word, complexity, almost to the breaking point. Maybe it's time to rethink our lexicon.

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