Information, Entropy, and the Persistence of Form

Claude Shannon's foundational insight was that the information content of a message is a function of its improbability: I(x) = -log₂P(x). A highly probable event, when it occurs, resolves little uncertainty and therefore carries little information. A rare event resolves a great deal. This is not merely a mathematical convenience — it reflects something deep about the relationship between Possibility spaces and meaning. The more states a system could occupy, the more informative it is to learn which state it actually occupies.

This framework converges with Boltzmann's thermodynamic entropy, which also measures the number of microstates compatible with a given macrostate. High entropy corresponds to a large Possibility space — many equivalent configurations — and therefore low informational distinctiveness. Low entropy corresponds to a constrained, improbable configuration, and therefore high information content. Shannon entropy and Boltzmann Entropy are not merely analogous; they are structurally isomorphic, unified by the same underlying logic of possibility and constraint.

The implications extend to questions of identity and persistence. David Krakauer at the Santa Fe Institute has developed the concept of the 'Informational Individual': an entity that maintains a stable Figure-Ground Distinction from its environment across time. Such an entity is not merely physically bounded but informationally coherent — its internal states are not simply reflections of environmental fluctuation but preserve a distinctive causal signature. entropy, on this reading, is the adversary of individuation. To persist as a recognisable entity is to continuously resist the dissolution of informational structure into background noise.