What is complex?

A couple of days ago, I was reading a document regarding a "complex system". The document's author was describing a "complicated system", but hardly complex. It seems to me, the casual term "complex" has become so broad as to become almost meaningless, and this is becoming increasingly unfortunate. Years ago, Dr. Seth Lloyd (no relation) used to collect definitions of the term - interesting, enlightening, but ultimately short of the goal. But S. Lloyds's collection does provide patterns that become interesting.

I suggest we start by some characterizations of patterns of complexity. The first separates "subjective complexity" - aspects of complexity caused by incompleteness, lack of understanding or information, uncertainty and of a probabilistic nature. This "simple" aspect of complexity is the focus of most books on complexity. Compare those aspects to "objective complexity" - aspects that emerge from 3 or more, mutual, non-linear couplings (sometimes referred to as non-linear recurrence). Careful study shows that subjective and objective aspects are themselves coupled into what becomes a foundation for potentially complex systems. Yet this is incomplete, as well.

A major contribution came from Steven Strogatz in his book "Non-linear Dynamics and Chaos, with Applicatons to Physics, Biology, Chemistry and Engineering" (Perseus, 1994). The problem was the word "chaos", which Strogatz attributed to 3 or more, mutually-coupled, non-linear systems. Strogatz's chaotic systems are only complex and chaotic at some energetic or thermodynamic non-equilibrium.

Chaos becomes associated with the exchange of entropy, information, or energy at some "distance from equilibrium"(1) that acts upon the potential complex system. Contextually, chaos has some relationship with stability, in that systems at or near informational, entropic, and energetic equilibrium are not ultimately complex, regardless of how complicated (how many parts exist). For example, we may speak of a potential instability, that is currently at equilibrium (balancing an egg on end).

When we couple the subjective incompleteness, with the energy, entropy, and informational dynamics of 3 or more, mutually coupled, non-linear objective systems , the potential complex systems becomes a realized complex system - or simply a "complex system". The 3 coupling of these aspects implies that complex systems are potentially meta-complex.


(1) See the Brussels-Austin Group and pioneering work by Ilya Prigogine.