The word probability didn’t take on a likelihood-related meaning until maybe the 18th century. The original meaning was synonymous with “worthy of approval”.

Also interesting: Ian Hacking suggests that the creation of probability & chance concepts was intimately tied to equiprobable outcomes, like rolling fair dice. Since fair dice are harder to make than unfair dice, the games through most of history were played with raw dice, such as animal bones.

That jives with my own experience of the linguistics of randomness. It’s easier to talk about “completely random” things — draws from the uniform distribution — than to call other probability distributions random. Unpredictable-outcomes-with-tendencies-or-bias (the other random variables) somehow don’t feel quite “random”.

(Then again, people use the word “random” to mean “crazy” or “arbitrary” as well as “uniformly random”.)

Similarly, I think, our shared intuition of the “expectation” concept is intimately involved with gambling and fairness notions. So maybe it’s no surprise that the St Petersburg paradox, early mathematical correspondences on probability, and L. J. Savage’s Dutch books philosophical formulation of probability rely on rational bettor gedankenexperiments.

That games of chance provide the Bayesian foundation for quantum communication is creepy. Or maybe the quantum communication theories provide a mirror at our own ways of thinking (as social animals) as we try to describe physical phenomena.

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