Of all the mathematics I have yet done on my now seven-year journey, I have been least fond of trigonometry. And the part of trigonometry that I've disliked the most has been trigonometric identities. These are those arcane laws or perhaps descriptions of how one trigonometric feature is the same as two others in relationship. Or they describe the relationships between sines and cosines which are added or subtracted. There seems to be no end to them. I remember when I tried to work with them three years ago. The memory numbs the mind. I am sure that somewhere out there are math geeks who just LOVE trigonometric identities. But I'm not sure I want to have any contact with these people.

The Identities are placed in light blue boxes in the text, so that we students will notice them. The mild light blue does not convey the metallic, riveted quality of the math. Underneath these revealed windows are the proofs, which we are supposed to work through. That's right, it just isn't math without a proof. Show us the proof! In math, unlike in real life, there actually IS a proof, at least at this level. The atheist says, Show me the proof of heaven! Show me the proof of God. Is religion the same as math and science? Must there be proof? Is citing the Bible or the Koran a proof? Certainly not to the scientist!

Heaven, for a mathematician, is where all the proofs come out correctly. It is the domain of right answers, for all the legitimate functions that exist in the universe. There in mild blue mathematical heaven, where the light of those identity windows suffuses the bright sky, mathematicians inhabit the crystalline structures built from what were only concepts down below on old Earth. In heaven, calculus angels draw diagrams in shining sand.

And what of Hell? The mathematics of monotheism demand a reciprocal, no? Hell is where all the answers are wrong, but no one can find a way to disprove them. Hell is endlessly multiplying garish purple, green, and red fractals of complication with no way out of the labyrinth. Hell is a vast noisy neon-lit techno club where you are forced to take math exams while you are stoned. Some people probably would like this Hell.

How can I make myself want to study trigonometric identities again? By daring myself, as in "I DARE you to work through that proof that's in the book?" By shaming myself, as in "You managed to finally get to calculus but you can't go on because you can't hack high school math?" Should I perhaps cajole myself into doing the work, because I will get to learn new things if I manage to remember the old things? Or should I appeal to my peculiar pride and remind myself of the singular path that I have traveled now for almost seven years, as I have watched all my fellow aspirants drop their programs and disappear? I'm not going to get to math heaven, and I'm not going to get to physics heaven, which are attained only by the canons at the Accelerator Cathedrals, or the Academically Tenured. Why on earth should I study trigonometric identities again? Because somewhere, somehow, I will demonstrate the proof.

Posted at 2:32 am | link