Pythagoras, the guy who invented the hypotenuse, led a cult of brilliant but sometimes confused mathematicians. They believed that harmonics held the key to understanding how things functioned. At the heart of their work was the study of ratios, of dividing things into their basic components in search of the harmony of the universe.
According to the myth, Pythagoras was stuck on a theory, and he went for a walk to clear his head. He passed a blacksmith’s shop and heard five workers inside, all using hammers to bend iron. As their hammers struck in unison, the clang organized into a beautiful sound, with all the hammers singing out in harmony at once.
He walked into the blacksmith’s shop and, with a bluster that would have been fun to watch, took all five hammers away with him. He wanted to study what made their harmony so beautiful… it might unlock the secret he was seeking.
Over the following weeks, Pythagoras weighed and measured each hammer. He wanted to understand why they didn’t sound identical and, more important, why they sounded so good when they all clanged in unison.
His work helped us discover a physical connection between math and the world.
It turns out that the ratios in the weights of the first four hammers led to their ringing in harmony—each had a weight that was a multiple of the other. More fascinating to me, though, was that the fifth hammer didn’t follow any of the rules. The fifth hammer was spurious, data that didn’t fit, something to be ignored.
Like many researchers throughout time, he threw out the fifth hammer (and the pesky mismatch) and published his work only about the first four. But it turns out that the misfit, the fifth hammer was the secret to the entire sound. It worked precisely because it wasn’t perfect, precisely because it added grit and resonance to a system that would have been flaccid without it.