The First Law of Complexodynamics

Introduction to the Time Conference

The author attended a conference on the nature of time and proposes to answer why complexity increases then decreases, unlike monotonically increasing entropy.

Complexity vs. Entropy

Physical systems exhibit a pattern of increasing then decreasing complexity, contrasting with the monotonic increase of entropy, as illustrated by a coffee cup mixing example.

Defining and Measuring Complexity

The challenge lies in defining complexity formally and proving it peaks at intermediate times, with Kolmogorov complexity and sophistication proposed as potential tools.

Entropy and Kolmogorov Complexity

Entropy can be modeled using Kolmogorov complexity, but its increase is too slow for deterministic systems; this can be resolved using probabilistic systems or resource-bounded Kolmogorov complexity.

Sophistication and Complextropy

Sophistication, a concept related to Kolmogorov complexity, attempts to formalize the intuition that neither simple nor random strings are complex, but it needs refinement for time-dependent systems.

Resource-Bounded Complextropy

A resource-bounded definition of complextropy is proposed, where complexity is measured by the shortest efficient program outputting a sample from a set where the target string is not efficiently compressible, potentially explaining the observed complexity patterns over time.

PS: Neutrinos and XKCD

A postscript unrelated to the main topic references an XKCD strip discussing neutrinos traveling faster than light.