We've all heard of the phenomenon called deja vu, where something we experience seems to be familiar, even though we know we have never seen it before. Esotericists like to think of this as evidence of reincarnation or at least some form of time-warping perception, but there are numerous neuroscientific theories for why this happens. The opposite of deja vu also happens, called jamais vu, where you are in familiar territory or see something you know well, but have the feeling that you have never seen it before. I have recently had it driving through the town at twilight on a clear June evening, where the deep green leaves cover the street signs and I feel as though I am anywhere in America, in some Ray Bradbury dreamworld lit by fireflies, where ghosts sit talking comfortably with the living on the quiet porches.

When I once again open my calculus book to trigonometry review after the flurry of distractions from the art show and maternal visit, is it deja vu or jamais vu I experience when looking at the mechanical orbits of the Unit Circle? During my bout with trigonometry back in 2004, I was concerned almost entirely with angles in degrees, not radians. Now, for calculus, I must learn them in radians. I lull myself to sleep by recounting to myself the formulas for how to transform measurements in degrees to radians (multiply by pi/180) or radians to degrees (multiply by 180/pi). I have to keep reminding myself that Pi is not just a Greek letter but a specific number, even though it spins its digits off into a random-like infinity. You'd think I'd be used to Pi the number by now, but I'm not, probably because I was a Greek scholar and think of Pi as a letter, for instance the first letter of "Pyracantha." (Pi, Upsilon, Rho, Alpha, …)

I've seen radians before. I know that they are expressed in some fraction or multiplication of Pi. It's an interesting idea, to wrap the radius around the circumference like a thread. I wouldn't have thought of it. I am told that in calculus trigonometry, you have to use radians rather than degrees, and the reason was explained to me by a patient Friendly Mathematician at the recent Baltimore convention. But the convention was a bustling, noisy place, and I confess that I have entirely forgotten the explanation. As with a lot of my math, I have to take it for granted and memorize it, whether I falsely feel that I have seen it before or whether I have forgotten something that once was familiar.

Posted at 4:24 am | link