alt Hacker NewsUsing the term "torsor" for that mathematical concept has been a very bad choice, both because the concept does not have any obvious relationship with the meaning of the word and because the word "torsor" had already been used for a very long time in classical mechanics for a very different concept, i.e. for the quantity that must be null for a rigid body to stay in equilibrium (i.e. the pair of a resultant force and a resultant torque).
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.
Replies
Yeah, see this thread --- I assume these guys haven't heard of the other meaning neither
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.
Words happen more than they are chosen, cf. "computer". The term "torsor" in this sense likely comes from the French "torseur" [0], which was used to describe rigid-body motions via a fundamental screw-like action.
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
[0]:https://fr.wikipedia.org/wiki/Torseur