There sometimes exists an intuitive or cognitive disconnect between the idea that Earth surface systems (ESS) may exhibit divergent evolution associated with dynamical instability and deterministic chaos; and the fact that ESS sometimes evolve so as to increase their complexity and interconnectedness.  Despite the initial apparent inconsistency, these two phenomena can and do happen simultaneously within the same ESS.

Instability/divergence and evolution of increasing complexity are readily reconciled when you realize that instability and chaos are scale-contingent, so that divergence and pseudo-randomness occur within firm limits. Also, these phenomena in effects expand the options an ESS has for its development, thus creating more room for evolution of complexity.

The ecologist Robert Ulanowicz developed the notion of ascendancy as a measure of the complexity and interconnectedness of a system. Ascendancy is influenced by the quantity of matter and energy throughputs, and the network of mass/energy exhanges between system components. Almost 10 years ago (!) I used the notions of ascendancy and Kolmogorov entropy to show how dynamical instability and chaos can increase ascendancy.

This was one of those things that was successful, but not quite enough to justify a publication. Having come back to it now and again over the past decade, I still cannot convince myself there’s enough there for an article. However, I also think it’s too interesting and too good to bury forever.  Thus, I attach here my formal demonstration that instability can lead to increasing ascendancy. It’s in the form of a manuscript with the “theory” section fully developed, but nothing else.