Sunday, November 1, 2009

Dr. Stogatz, Meet Dr. Lawvere

There are interesting ways of categorically mapping the structure, behavior and evolution (morphisms) of dynamical systems ala Steven Strogatz in "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering", by Perseus Publishing. This has been detailed by Category Theory (CT - Eilenberg, Mac Lane, Lawvere, among many more) and the use of functors - a programmatic analog affecting state evolutions.

Rather than the set-theoretic approach, with it's limitations of First Order Logic, CT provides a more accurate logical / analytical framework in which to understand complex, dynamical systems, and categorize (or classify) their patterns of change.

Curious. This particular technique seems grossly under-utilized in Complex Systems Theory, and in understanding complex, dynamical systems, their processes, growth and evolution. Furthermore, it seems that these known techniques are actually ignored.

If someone has a good explanation for this phenomenon, I'd sure like to hear it - or am I not looking for exemplars in the right places?