By repeating a simple, rhythmic motion a student can access levels of concentration and perception not otherwise available to him.
by Bill Mehlman
There's a famous scene in the movie The Karate Kid in which Mr. Miyagi begins teaching Daniel karate by having him wash and wax all of his cars. "Wax on, wax off, wax on, wax off," is the mantra to this exercise, which can be viewed on several levels.
The obvious purpose of this silliness is to teach Daniel dedication to the art of karate while building up his strength. Beyond that, he is learning some fundamental hand movements, rhythmic clockwise and counterclockwise circles, which apparently underlie karate blocking techniques. The subtext of the scene, for our present purposes, is that the washing and waxing provide a physical counterpart to an abstraction.
By repeating a simple, rhythmic motion the student gains access to levels of concentration and perception not otherwise available to him. I've done some simple martial arts, and I would agree that mental conditioning counts as much as physical development. In fact, I base my advocacy of martial arts as a defense against ADHD largely upon this perception.
Pure abstraction has always presented problems for me, and I'm sure that my oblique, metaphoric approach to the world derives from this difficulty. If I can put my hands on it, literally or figuratively, I can usually understand it. Arithmetic wasn't hard, and algebra made sense, and geometry was intuitive. I hit trig, on the other hand, like the Titanic.
Sines, co-secants, tangents? I could go through the motions. But what in the name of Euler did the damn things mean? And why did they keep showing up in non-trig courses? Co-sines in my chemistry course? Come on.
Years later, I finally began to accept the idea that the trig functions were just... there. Even if I can't touch them, or see them except as a ratio. We've made peace. Or maybe it's just an armed truce. And I'm probably not designing any bridges in the future.