Sorry if this is a stupid question *, but is there any not complicated literature about how mass point geometry is related to, or used to teach more efficiently, or something else, probability theory? I used to fantasize about going through a middle-highschool-level book on MPG with my middle-highschool pupils (with added benefits of reinforcing Newtonian mechanics), and to get them into Bayes law (probability masses as masses and odds as lengths:), but... It was hard to imagine, say, triangles formed by probabilities.
I Googled it up, didn't find "exactly the thing" and moved on.
Huh, MPG seems like an interesting trick.
The obvious way to pursue an analogy is that masses are probabilities, but that seems to not work - the distances have no meaning, and there's no advantage over adding and subtracting probabilities of disjoint events.
So what if we make the distances probabilities. Now we can have P(A) be some distance AA', and P(A|B) be AB... No, no good... or if we make the probability the position of a point on the middle, is there anything interesting we can do with the weights of P(A) and P(B) to make P(AB)... So if you fix one ...
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