Unfortunately, in mathematics there already is a long tradition of reusing common words to designate concepts that have no relationship whatsoever with the original meanings of those words. This obfuscates the content of many mathematical books or research papers, because even when they state trivial facts the statements are opaque for those unfamiliar with the specific jargon used in that niche branch of mathematics.
The hypothesis seems to be that the idea of affine spaces came out of that theory, for whatever reason, which was subsequently generalized to principle bundles and finally into what we have now. The point is that, at every step along the way, we want to connect the incrementally new ideas to existing ones, and creating a hard break with new, idiosyncratic terminology is itself obfuscatory.
My beef is more with use of the heavily-overloaded words "regular" and "normal" in math, which just seems like lazy naming:
> In the normal extension K/Q, every normal subgroup of the regular representation acts on a normal scheme that is regular in codimension one, whose normal bundle — orthonormal to the regular surface at each regular value — carries a normal operator whose spectrum follows a normal distribution over a space that is at once regular and normal, all indexed by a regular cardinal.
That's like 8 different meanings of normal and 6 different meanings of regular. lol
"a person who makes calculations, especially with a calculating machine."
Google ngram view:
https://books.google.com/ngrams/graph?content=computer&year_...
https://golem.ph.utexas.edu/category/2013/06/torsors_and_enr...
Consider in particular that use of ‘distance’
>I think you can look at adjoint profunctors from the unit category and show that they consist of giving a consistent ‘distance’ to every object, which in a torsor will be represented.
Regardless of the terminology, I thought it was interesting because I have never seen the logarithm thought about in that way.
Thanks for the writeup!
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.)