I do know about torsors actually but I didn't think to link it from there. I guess I don't find the term very useful; it feels like things are still hard to think about even after you know it's a torsor!---but also, I think I need to get more familiar with the concept, because the other commenter on here who described my basis-logarithm as a "GL(V)-torsor" really said it much more succinctly than what I was hacking out manually.
Regardless of the terminology, I thought it was interesting because I have never seen the logarithm thought about in that way.
Thanks for the article. I do think your more elementary approach is good pedagogy since the subject is so broadly familiar already. I just like torsors, since they elegantly encode the "arbitrary choice" needed to deal with lots of objects.
Thanks for the writeup!
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.)