holonomy
Etymology
From holo- + -nomy.
holonomy means given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P. Lexicurio rates it Sui generis — a strength score of 90 out of 100.
Why this word is great
HOLONOMY — [Noun] In differential geometry, the measure of how a geometric object, such as a vector, rotates when parallel transported around a closed loop on a manifold. From the combining form holo- (from Greek holos, meaning "whole" or "entire") and -nomy (from Greek -nomia, from nomos, meaning "law" or "management"), thus signifying "entire law" or "law of the whole." Unlike curvature, the local whisper of a space’s infinitesimal bend, or monodromy, which charts the branching fate of an analytic function around a singularity, holonomy is the global, accumulated memory of a journey completed. It is the stubborn tilt of a compass arrow after circumnavigating a mountain, the silent scribble of a Foucault pendulum proving the Earth’s spin, or the ghostly phase shift of a quantum particle completing its loop—the quiet proof that to travel far and return is never to arrive exactly where you began.
noun
- Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.