hyperthesis

If mathematics comprises algebra and analysis, it's curious that Spivak's Calculus begins with an axiomatization of algebra.

It's not complete - addition and multiplication are not defined, nor even "number". Instead, it's properties of commutativity, associativity, distributivity, identities and inverses, and it's astonishing how far that takes us.

I really enjoyed this approach, but it has omissions: details like equality transitivity (things equal to something are equal to each other), and there's deliberate gaps (like using 0.a=0 twice in a proof before being proven, while claiming a comsequence).

I'd like full rigour, a treatment I could code, without need of mathematical maturity to paper-over abbreviations.

This is a big ask: I also want this detail without tedium; to retain the joie de vivre of Spivak, without gaps. The fun of building, like a construction set or building blocks.

Any recommendations? (perhaps I'll have to write it myself)

We run simulations of others all the time, trying to predict what they do. One theory is that this was a driver of the evolution of intelligence - which also enabled us to simulate ourselves, giving us self-awareness.

For people will know well, we often have a definite idea of how they would react in situation - so that even when they have passed on, they still live, in some sense, within us. Perhaps in quite a real sense, they do, via the model/simulation we have of them.

Authors explicitly simulate characters, and some authors report their characters making their own decisions, and leading a life of their own, frustrating the author's plans for them.

So... a "partial Turing Test" would be for a computer to predict what a given person will do; and compare this with what another human, who knows them equally well, predicts they will do. The more accurate prediction of how that given person does respond, has a better model/simulation of that person.