Wednesday, March 14, 2007

The Wittgenstein Within

When you toss a golf ball straight up into the air, and you say to the class, "Today I thought we could talk about the acceleration of the golf ball when it's at the peak of the trajectory," it's like the moment when a psychoanalyst says, "Today I thought we could talk about your mother." The key thing is to maintain a pleasant neutral expression no matter what you hear next.

Many years ago while living in Oxford, I went to see an art film about Ludwig Wittgenstein (let's call him "W" for short). One memorable scene takes place during the years when W was still living in Vienna; it gives a hilarious impression of what a terrible teacher he was supposed to be. As I recall the scene, W is tutoring a youngster in math. We see the child sitting at a desk, W standing by her side, and a blackboard behind both of them, its surface virtually painted white with chalked expressions from the propositional calculus. The student is all of twelve years old, and looks terrified. W says to her: "So. What is" (gesturing vaguely at the board behind him) "this." The child puts her head down and gives no answer. After a second or two of this, W loses control completely, yelling at her and yanking her earlobe painfully. There's a quick cutaway before we see the melee go any further....

I don't support that kind of student-teacher interaction, but I have to admit that there are times in office hours when I do feel a little like this guy. I can feel my patience beginning to wear thin like Ken Doral's hair, and I can actually almost hear his voice in my head saying "Obviously energy is the strategy to use here because THAT'S what this CHAPTER is about!"

In general, it is the subtlety of Newton's Laws that impresses me. But then again, sometimes I catch myself thinking that the laws are so simple! Why can't people just get it? I wish I could remember more clearly what I myself was like at the end of my first college physics course. Maybe if I could see how limited my own understanding was, it would help me to make sure that I never end up yanking somebody's earlobe.

(Side question: Are any experiments such as diSessa's classic study being done longitudinally, so that we can see retrospectively what future Ph.D.s' freshman understanding of mechanics was really like?)

Stuart Crampton, the Barclay Jermain Professor of Natural Philosophy at Williams College, taught me mechanics in the spring semester of 1988, when I was eighteen years old. I had arrived at Williams to find myself far behind many of my classmates in terms of preparation, and I was finding Physics 104 so difficult and so intimidating that before the first midterm I went to Stuart's office and asked him if getting a C in his class would mean that I couldn't be a physicist someday. To Stuart's great credit, he was very kind to me while also giving me a straight answer to the question I'd put to him.

That midterm proved to be one of the memorable turning points in my life. I still remember two of the problems with complete clarity. One of these was to compute the rate of energy dissipation in a ball bearing dropped through a cylinder of oil. Another was to imagine trying to stop an oncoming tank by throwing thousands of mudballs at it. (The mudballs stick to the tank.) At first I was completely nonplussed by the tank problem, but suddenly I realized that this was essentially a rocket in reverse: whereas the rocket dispels exhaust and consequently speeds up, the tank gains mud and consequently slows down. So I wrote down the rocket equation, fiddled with a couple things in it, and answered the question.

The test came back with an A, or maybe even an A+. Coming from the place I'd come from, I saw this grade and the first thing I thought was that I could make it here, that I'd found a subject and a society to which I belonged.

But no one sails through physics. I remember in that same class struggling mightily with the problem of "popping a wheelie" on a motorcycle. The point of the problem was to understand why the rider must continually speed up in order to maintain the bike in a wheelie position. (Ever notice how brief these "wheelie" events are? It's because you can only keep speeding up for so long before you decide you're going fast enough!)

In fact, I still have a hard time thinking about this problem unless I move to an accelerating reference frame - which is a move that I enjoy trying to avoid. So I have work to do. I'll take another crack at it sometime soon. It'll help me remember that we all struggle.

1 comment:

Anonymous said...

The guy sitting next to the "host" in that video clip looked just like Gary Snyder.