WHO CARES ABOUT FIREFLIES?: STEVEN STROGATZ (p2)

The story of how I got interested in cycles goes back to an epiphany in high school. I was taking a standard freshman science course, Science I, and the first day we were asked to measure the length of the hall. We were told to get down on our hands and knees, put down rulers, and figure out how long the corridor was. I remember thinking to myself, "If this is what science is, it's pretty pointless," and came away with the feeling that science was boring and dusty.

Fortunately I took to the second experiment a little better. The teacher, Mr. diCurcio, said, "I want you to figure out a rule about this pendulum." He handed each of us a little toy pendulum with a retractable bob. You could make it a little bit longer or shorter in clicks, in discrete steps. We were each handed a stopwatch and told to let the pendulum swing ten times, and then click, measure how long it takes for ten swings, and then click again, repeating the measurement after making the pendulum a little bit longer. The point was to see how the length of the pendulum determines how long it takes to make ten swings. The experiment was supposed to teach us about graph paper, and how to make a relationship between one variable and another, but as I was dutifully plotting the length of time the pendulum took to swing ten times versus its length, it occurred to me after about the fourth or fifth dot that a pattern was starting to emerge. These dots were falling on a particular curve that I recognized because I'd seen it in my algebra class—it was a parabola, the same shape that water makes coming out of a fountain.

I remember having an enveloping sensation of fear; it was not a happy feeling, but an awestruck feeling. It was as if this pendulum knew algebra. What was the connection between the parabolas in algebra class and the motion of this pendulum? There it was on the graph paper. It was a moment that struck me, and was my first sense that the phrase, "law of nature," meant something. I suddenly knew what people were talking about when they said that there could be order in the universe and that, more to the point, you couldn't see it unless you knew math. It was an epiphany that I've never really recovered from.

A later experiment in the same class dealt with the phenomenon called resonance. The experiment was to fill a long tube with water up to a certain height, and the rest would contain air. Then you struck a tuning fork above the open end. The tuning fork vibrates at a known frequency—440 cycles per second, the A above Middle C—and the experiment was to raise or lower the water column until it reached the point where a tremendous booming sound would come out. The small sound of the tuning fork would be greatly amplified when the water column was just the right height, indicating that you had achieved resonance. The theory was that the conditions for resonance occur when you have a quarter wavelength of a sound wave in the open end of the tube, and the point was that by knowing the frequency of the sound wave and measuring the length of the air, you could, sitting there in your high school, derive the speed of sound. I remember at the time not really understanding the experiment so well, but Mr. diCurcio scolded me, and said, "Steve, this is an important experiment because this is not just about the speed of sound. You have to realize that resonance is what holds atoms together." Again that gave me that chilling feeling, since I thought I was just measuring the speed of sound or playing with water in a column, but from diCurcio's point of view this humble water column was a window into the structure of matter. Seeing that resonance could apply to something as ineffable as atomic structure—what makes this table in front of me solid—I was just struck with the unity of nature again, and the idea that these principles were so transcendent that they could apply to everything from sound waves to atoms.

The unity of nature shouldn't be exaggerated, since this is certainly not to claim that everything is the same, but there are certain threads that reappear. Resonance is an idea that we can use to understand vibrations of bridges and to think about atomic structure and sound waves, and the same mathematics applies over and over again in different versions.