Friday, 20 September 2013

Complexity: The Fifth Dimension

When complexity is defined as a function of structure, entropy and granularity, examining its dynamics reveals its fantastic depth and phenomenal properties. The process of complexity computation materializes in a particular mapping of a state vector onto a scalar. What is surprising is how a simple process can enshroud such an astonishingly rich spectrum of features and characteristics. Complexity does not possess the properties of an energy and yet it expresses the "life potential" of a system in terms of the modes of behaviour it can deploy. In a sense, complexity, the way we measure it, reflects the amount of fitness of an autonomous dynamical system that operates in a given Fitness Landscape. This statement by no means implies that higher complexity leads to higher fitness. In fact, our research shows the existence of an upper bound on the complexity a given system may attain. We call this limit critical complexity. We know that in proximity of this limit, the system in question becomes delicate and fragile and operation close to this limit is dangerous. There surely exists a "good value" of complexity - which corresponds to a fraction, ß, of the upper limit - that maximizes fitness:

Cmax fitness = ß Ccritical

We don't know what the value of ß is for a given system and we are not sure on how it may be computed. However, we think that the fittest systems are able to operate around a good value of ß. Fit systems can potentially deploy a sufficient  variety of modes of behaviour so as to respond better to a non-stationary environment (ecosystem). The dimension of the modal space of a system ultimately equates to its degree of adaptability. Close to critical complexity the number of modes, as we observe, increases rapidly but, at the same time, the probability of spontaneous (and unwanted) mode transitions also increases quickly. This means the system can suddenly undertake unexpected and potentially self-compromising actions (just like adolescent humans).