Terence Tao on Nostr: So, somewhat in desperation, I lay on the floor, closed my eyes and tried to imagine ...
So, somewhat in desperation, I lay on the floor, closed my eyes and tried to imagine _being_ the plane being rotated. I imagined the base point being moved in the x-direction, and rolled accordingly; then in the y-direction. With this, I was able to figure out that if I could find a rotation matrix depending on both time and space whose derivatives behaved in a certain way, then I could find my good change of variables and solve the problem. (In retrospect, I was trying to flatten a connection by choosing an appropriate gauge.)
Miraculously, the algberaic form of the equation was such that a natural choice of gauge that did nearly flatten everything was evident. (Again, in retrospect: the connection attached to this problem happened to have a small curvature.) After some frenzied calculations with pen and paper, I was able to get a plan to solve my problem, and then write the paper. (Which actually ended up earning me a Bocher prize.)
I was visiting my aunt in Australia at the time, and she managed to walk in on me while I was rolling around on the floor with my eyes closed. In the grand scheme of things, not the most embarrassing situation to be in, but I am not sure how satisfied she was by the explanation that I was "thinking about math". In a strange way, though, my profession can occasionally benefit from our reputation for eccentricity; she did not ask any further questions. (3/3)
Miraculously, the algberaic form of the equation was such that a natural choice of gauge that did nearly flatten everything was evident. (Again, in retrospect: the connection attached to this problem happened to have a small curvature.) After some frenzied calculations with pen and paper, I was able to get a plan to solve my problem, and then write the paper. (Which actually ended up earning me a Bocher prize.)
I was visiting my aunt in Australia at the time, and she managed to walk in on me while I was rolling around on the floor with my eyes closed. In the grand scheme of things, not the most embarrassing situation to be in, but I am not sure how satisfied she was by the explanation that I was "thinking about math". In a strange way, though, my profession can occasionally benefit from our reputation for eccentricity; she did not ask any further questions. (3/3)