There hasn't been a lot of action at the Electron for the last week or so, due to unrelated concerns. But I have been paying attention to the math and have had quite enough of trigonometry again, so I am back to reviewing derivatives before I move into the derivatives of trigonometric functions. How to find the derivative of a ratio of polynomials? How to find the derivative of a quadratic function, playing with exponents for fun and profit. Is this fun and profit? I regret that I do not appreciate trigonometry. If I were a "true" mathematician I would find trigonometric identity problems, and all proofs, fascinating.

If I had loads of time, I'd sit and work through trigonometry again and again until I could do it as easily as I read the newspaper in a coffee house. If I really put my efforts into it, I could learn to do trigonometric identity problems easily. I'd cover many sheets of paper with scribbles. But I do not have the time, nor do I have the, uh, preference for it. Spending that kind of time making sure my math is perfect, against increasing resistance, seems a bit perverse to me, a form of masochism, or rather, "math-o-chism."

And yet I know people who will not give up until they have mastered some sort of highly abstract craft, whatever it might be. I know a pianist who insisted that one could learn keyboard technique by obsessively playing scales and arpeggios until he could play them quickly and mistake-free in all keys. And then after that were pre-written, repetitive exercises for the piano by that scourge of old-style piano players, "Hanon," and after that at least some sublime music in the preludes and fugues of Bach. This doesn't necessarily have anything to do with mathematics, but is enacted with a kind of obsessiveness that can often be a trait in mathematicians, musicians, or anyone else who does creative activity.

I can get caught up in that, and it is a trap, because then I won't learn anything new. I remember three years ago how I tried to work through logarithms using the now-archaic method of interpolating readings from logarithmic tables. For what purpose? A calculator would do the same thing in a fraction of a second. I wanted to do the craft perfectly, and I found, to my frustration, that the more I tried, the less accurate and efficient I got. I could do it again with trigonometric identities, but where would I go with calculus? Since none of my mathematical studies has any practical value, why would I try to attain perfection trying to master irrelevant processes? If I find I need to do more with trigonometry, it is always waiting, flattened in its two dimensions between the pages of my books.

Posted at 2:41 am | link