There are so many ways to do wordplay on "limits" that I don't even try. One of the first things I made sure I knew when I began my math and physics studies was that any piece of wordplay, on any word at all connected with math or physics, has already been done a million times. Therefore I have no need to do it again. But my title this time is also a piece of wordplay. The title comes from "Esthetique du Mal," a long, rambling, overfull poem about the the philosophy of existence by my favorite modern poet Wallace Stevens. We last saw Wallace doing calculus in rural Pennsylvania by graphing haystacks. Here he tries to figure out why poetry can't describe real existence. The "Mal" is a sense of "evil" that Stevens associates with beauty, but I haven't figured out why yet. I'd rather do "Math" than "Mal."

One of my goals in studying mathematics is to learn to appreciate what mathematicians call "elegance," or in general the aesthetics of mathematics. I have only had a glimpse or two of it, and I know it is a sense acquired over many years. My "Friendly Mathematicians" have not been able to explain it to me, so I'll have to discover it myself. I think I'm on the right track though. It's not only the beautiful shapes made by the graphs of functions, though that is part of it. It's in the concept of limits, where in a kind of kinetic gesture, the trail of a function's results drifts closer and closer to the limit while never quite getting there. Or in a stronger statement, the limit soars off into positive infinity or descends into black negative infinity. I think limits are elegant.

There's plenty of inelegant math too. I dare not be impolite by calling some math "inelegant" when mathematicians, unbeknownst to me, consider it lovely. But in finding limits mathematically rather than visually with a graph, the book leads me through some algebraic polynomial-pushing which seems sort of contrived. I'm too much of a beginner to make this comment. It will be revealed to me later why this is being done. Learn first, ask questions later. In my case, questions are expensive, because it means contacting the Friendly Mathematician or Physicist and reserving time with him.

I am doing limit problems now. There are a lot of them and I intend to do them all, in the way the book has taught me. In this I am indulging in rote learning, whether it is good or not, because I'm not sure where this is leading me. But I will do them with the methods the book has taught me, until they are familiar to me. Each problem contributes, atom by atom, to my sense of mathematical beauty.

Posted at 3:04 am | link