The Pendulum

July 7th, 2005

In the summer of my 16th year I became a physicist. I didn’t realize what I was doing, but I set out to understand the mysteries of motion. Since I am no Isaac Newton, I didn’t quite get as far as he did, but I did have some fun along the way. Where Newton had his apocryphal apple, I had my pendulum. I got a 1.5 kg fishing weight -- a lead sphere about 5 cm in diameter. I hung it from a fine wire which I attached to the bottom of the roof overhang at the highest point on the side of the house. This gave me a little spot on the side of the house in which to play with my pendulum, which was about 3 or 4 meters long. I watched it for hours, trying to understand its motion. Since I had just finished my sophomore year in high school, I wasn’t exactly equipped to figure it all out by myself, but then, I’ve always had a preference for wrestling with the truth fighting and kicking, rather than having it served up dead and limp in a classroom.

I had been particularly interested in the elliptical motion of a pendulum swinging around, and one day I came up with a novel way of considering the problem. I sat on the ground and set the pendulum swinging in an elliptical orbit such that the weight went swooping a few inches in front of my nose on each pass. I then blindered my vision with my hands so that I could concentrate on just the velocity of the weight as it swept by me. From above, it looked like so:

On the third pass I noticed that the weight seemed to be closer to my nose than previously. That made no sense at all, but I resolved to check it, and so on the fourth pass I noted carefully its distance from my nose. Sure enough, it was closer -- how could that be? My mind grappled with the problem as the weight continued on in its orbit. It was tracing an elliptical orbit; the only way that it could be getting closer to me would be if its ellipse was fattening -- that seemed impossible, because that would require the pendulum to gain energy from nowhere.

Having rejected that possibility, I cast about for other explanations. Then the answer came to me: the ellipse was precessing, like so:

This was fascinating! The next thing to do was to predict its behavior to see if my hypothesis was correct. So I projected the precession to get a mental image like this:

Yipes! It was going to hit me in the side of the head! I instantly swept my right hand just in time to catch the oncoming sphere. I caught my breath -- another fraction of a second, and I would have taken a severe blow to my left temple. But then the fear evaporated into a smile. I had seen it coming in my mind’s eye. If I could develop that sense, what other things could I see in advance? It was a heady discovery for a 16 year old, and I ever after I have retained my confidence in seeing with my mind rather than just my senses.