When I was in high school, my trigonometry teacher drew a right triangle inside a unit circle and defined the sine and cosine functions as the ratios of the lengths of the opposite and adjacent sides of the triangle to the hypotenuse, vertical and horizontal values divided by 1.

As the radius vector spun around, he plotted the sine and cosine values on a Cartesian coordinate system where the x axis represented the angle of the vector and the y was the value of the function. The sine and cosine curves, identical but 90 degrees out of phase, marched off to the right, in an endless progression into infinity.

In a terrifying flash of insight, I realized triangles had been playing these games with each other long before there were human minds to contemplate them, indeed, even before there was a universe at all, and that this simple mathematical trick could be used to model any oscillating system: springs, guitar strings, waves, alternating current, sound. This was the meaning of the display on an oscilloscope. All these “real” things, matter and energy, space and time, could be represented precisely in a human mind by a process of pure thought, and it was based on a concept that didn’t seem to need human minds at all–it was simply a property of triangles.

I still haven’t come to grips with just what it all means.