Given the general coolness of simple robots like thermostats, steam engine governors and telephone ringers, I already had the idea as a child that there is something wonderful about things that operate by going in cycles.
Then when I was thirteen I discovered that there really isn’t any such thing as a “sine wave” or a “cosine wave”. Every time you see something that looks like it is going back and forth to make a wave — like a pendulum, or a water ripple, or a guitar string — what’s really happening is that something is going in a circle. The reason it doesn’t look like a circle is that one of the two dimensions of the circle is hidden from you.
For example, the left to right movement of a pendulum is one dimension of a circle. The other dimension of this circle is the momentum of the swinging pendulum. Think about it — when the bob of the pendulum is in the center, it is moving the fastest, and when it is all the way to one side, it isn’t moving at all. Just like sines and cosines. In other words, the bob is really moving in a kind of circle.
Once I realized this, I saw that all sorts of things work this way — light, sound, tides, people’s changing moods — anything that has a repeating rhythm to it.
And movement in a circle just means always being pulled toward a point. It’s like when you twirl a rock around on a string. The string is always pulling the rock toward a point (in this case, your hand holding the string), so the rock goes in a circle.
For the pendulum or the guitar string or the ocean wave, that point is always there, constantly pulling something toward it. You can’t always see the hand that holds the string, but it is always there.