This question is prompted by the books review in the September 2020 Physics Today of The Evolution of Knowledge: Rethinking Science for the Anthropocene, by Jürgen Renn.
I suspect that there is such an equation. It is related to thermodynamics and statistical mechanics, and might be characterized, partly, as network entropy.
Two articles that relate to the question are:
Article Lexical growth, entropy and the benefits of networking
Article A theory of intelligence: networked problem solving in anima...
and also there is a book, the ideas in which preceded the two articles, above:
The Intelligence of Language.
The question is related somewhat distantly to an idea of Isaac Asimov in his science fiction, The Foundation Trilogy, psychohistory.
Read Friston's free energy articles. That's the equation, which is simply a way to write the second law of thermodynamics in terms of information theory.
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