In response to my recent column about Foucault's pendulum, a physicist friend pointed out that my explanation contained an error. To assuage my feelings, he added that my explanation was similar to that given in most museums and that it required graduate work in physics to explain the shortcoming.
That episode has led me to physics books to try to develop the background necessary to understand not only the pendulum but also the spinning motions of tops and gyroscopes. My exploration is leading me further and further back to the elements of physics. Although my self-education is far from finished -- and, in fact, will never be in any sense complete -- I am enjoying the research and will share with you here a recent experience.
A major resource I have been studying is "The Feynman Lectures on Physics," which records the author's Cal Tech course given in the early 1960s. Richard Feynman was not only a world-class physicist who was awarded the 1965 Nobel Prize, but a great entertainer. Because of these two qualities, he was a superb lecturer. I never met him, but I have watched films of his teaching. He was a dead-ringer for Art Carney in both appearance and actions. Of course both are lost to us for Feynman died in 1988, Carney just last year.
I offer here two examples of Feynman's skill as a teacher.
The first is his tale about Isaac Newton's confirmation of the universality of gravity. He tells us: "The problem (for Newton) was whether the pull of the earth on its people was the "same' as its pull on the moon. If an object on the earth falls 16 feet in the first second after it is released, how far does the moon fall in the same time? We might say that the moon does not fall at all. But if there were no force on the moon, it would go off in a straight line, whereas it goes in a circle instead, so it really falls in from where it would have been if there were no force at all. We can calculate how far the moon moves in its orbit in one second, and can then calculate how far it falls in one second. This distance turns out to be 1/2 0 of an inch in a second."
Feynman then shows that calculations by Newton's inverse square law make this measure fit just right with the 16 feet per second that things fall on the earth. He then continues, "Wishing to put this theory of gravitation to a test, Newton made his calculations very carefully and found a discrepancy so large that he regarded his theory as contradicted by facts, and did not publish his results. Six years later a new measurement showed that the astronomers had been using an incorrect distance to the moon. When Newton heard of this, he made the calculation again, with the corrected figures, and obtained beautiful agreement."
The second appears in Feynman's discussion of velocity: "In order to get to the subtleties in a clearer fashion," he said, "we remind you of a joke which you surely must have heard. At the point where a lady in a car is caught by a cop, the cop comes up to her and says, "Lady, you were going 60 miles an hour!' She says, "That's impossible, sir, I was traveling only seven minutes. It is ridiculous -- how can I go 60 miles an hour when I wasn't going an hour?'
How would you answer her if you were the cop? Of course, if you were really the cop, then no subtleties are involved; it is very simple: you say, "Tell that to the judge!' But let us suppose that we do not have that escape and we make a more honest, intellectual attack on the problem, and try to explain to this lady what we mean by the idea that she was going 60 miles an hour. Just what do we mean? We say, "What we mean, lady, is this: If you kept on going the same way as you are going now, in the next hour you would go 60 miles.' She could say, "Well, my foot was off the accelerator and the car was slowing down, so if I kept on going that way it would not go 60 miles.' The lady can also argue this way: "If I kept on going the way I'm going for one more hour, I would run into that wall at the end of the street!' It is not so easy to say what we mean."
The study of physics is a serious undertaking, but Feynman worked hard to make its deep concepts entertaining. He was truly a master teacher.