Paradigm Shift: Complexity, Uncertainty, Entropy

Paradigm shifts tend to be inadvertently dramatic.

Uncertainty is an indirect measure of the sum-over-all combinatorial possibilities of any definable (or intelligible) systems state space. The combinatorial possibilities of any non-trivially sophisticated – i.e. complex – state space are larger than any definition (or empirically-derived knowledge) of that same complex entity.

Complete descriptions are impossible for the same essential reason that mathematical logic was proven incomplete: the system self-description is a member of the set of all entities described (or strictly speaking – describable) by that system and for this reason inexhaustible extensibility (and uncertainty) is endemic and irreducible. All of our attempts to describe the proliferating complexity of this world are bootstrapped into and incorporated by that same recursive complexity, without end.

Beyond the mischievously labyrinthine logic and hyper-inflating combinatorial dimensionality of indefinitely-extensible state-spaces there exists the (corollary) matter of entropy. The extensibility and proliferating complexity of systems that are of most interest are also subject to a distributed property of thermodynamic diffusion. Emergent complexity autonomously harnesses this diffusion through concise self-representational system-encoding and so should we.

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