[ajkjk]

glad you liked it

I wonder if we should really just call them... vectors? Like the thing that torsors do, being defined only relative to a choice of origin in some space / group, is exactly what displacement vectors do. So really they are just generalizations of the concept of a vector. (In this scheme I would be careful to _not_ refer to points as vectors, so as to reserve the term for things that act like, well, torsors. I happen to think that much pedagogical harm has been done by not distinguishing the two concepts, points and displacements, early on.)

[xelxebar]

> I wonder if we should really just call them... vectors?

Maybe. I think the term is just unfamiliar. The word "vector" is equally unhelpful when you first encounter it, but the concept has enough mindshare that we just acclimate.

Apparently, "vector" in the mathematical sense was coined by Hamilton in the mid 1800s, so around the same time as "torsor". It means something like "courier" which is sensible in Euclidean space but kind of divorced from the algebraic definition. You can still see the "carry along" roots if you squint, but I think the same is mostly true of "torsor", too.

In other words, instead of renaming things, maybe we should just evangelize more? Maybe the quintessential example should be radial directions just to hint at the historical terminology use?

[ajkjk]

Meh. I'm fine with trying to rename things if it feels justified. And the more obscure the thing, the easier it is to rename in principle. Maybe the better name will help it be less obscure. But of course whether it works is proportional to how good of an argument there is for doing it, as it should be.