The First Law of Complexodynamics
This post explores the idea that the complexity or
Episodes
Chapters
01Introduction 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.
1:34Explained02Complexity 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.
1:28Explained03Defining 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.
1:28Explained04Entropy 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.
2:17Explained05Sophistication 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.
1:53Explained06Resource-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.
1:56Explained07PS: Neutrinos and XKCD
A postscript unrelated to the main topic references an XKCD strip discussing neutrinos traveling faster than light.
1:24Explained