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stoutfellowThe ongoing discontent in the department has left me feeling somewhat depressed, if only intermittently. But when I think about the last couple of weeks as a whole, they've actually been pretty uplifting.
1) There was a discussion a while back on the American Dialect Society mailing list, concerning the behavior of the word "tolerate" - not, precisely, its meaning, but some of its overtones. I posted a possible explanation, and received a "What he said" comment from a linguistics professor at Yale. Seeing that I'm not, in actual fact, a linguist, that felt pretty good.
2) In the last lecture of my History of Math class, I gave an overview of one of the newer branches of mathematics, something called "category theory". Evidently I caught the fancy of one of the students; he wants to learn more, and he's found some online lecture notes that will help him in this. I've also recommended a book on the subject to him. This is the kind of thing that teachers live for.
3) The study of geodesics on deltahedra seems, at least temporarily, mined out to me - I don't see any likelihood of further progress using our current techniques. So, I've turned my attention to another family of polyhedra, which I call "capped cubes". I've been thinking about them, from time to time, for a couple of years now, not making any real progress but learning enough to see that there are a lot of interesting things going on. On Sunday, I suddenly saw how to apply some of the techniques we developed for deltahedra, and I've got a nice new little theorem. (Basically, it puts a bound on the size of simple closed geodesics; the next step is to run a complete check on all the candidates below that size. I'm working out the necessary algorithms now.)
Of course, there are lots of other good things going on as well, but I specifically needed things that make me feel better about myself, and they've been there. I just had to remind myself of them.
1) There was a discussion a while back on the American Dialect Society mailing list, concerning the behavior of the word "tolerate" - not, precisely, its meaning, but some of its overtones. I posted a possible explanation, and received a "What he said" comment from a linguistics professor at Yale. Seeing that I'm not, in actual fact, a linguist, that felt pretty good.
2) In the last lecture of my History of Math class, I gave an overview of one of the newer branches of mathematics, something called "category theory". Evidently I caught the fancy of one of the students; he wants to learn more, and he's found some online lecture notes that will help him in this. I've also recommended a book on the subject to him. This is the kind of thing that teachers live for.
3) The study of geodesics on deltahedra seems, at least temporarily, mined out to me - I don't see any likelihood of further progress using our current techniques. So, I've turned my attention to another family of polyhedra, which I call "capped cubes". I've been thinking about them, from time to time, for a couple of years now, not making any real progress but learning enough to see that there are a lot of interesting things going on. On Sunday, I suddenly saw how to apply some of the techniques we developed for deltahedra, and I've got a nice new little theorem. (Basically, it puts a bound on the size of simple closed geodesics; the next step is to run a complete check on all the candidates below that size. I'm working out the necessary algorithms now.)
Of course, there are lots of other good things going on as well, but I specifically needed things that make me feel better about myself, and they've been there. I just had to remind myself of them.
