By Cris Moore, Professor, Santa Fe Institute
Note: This column is part of a series written by researchers at the Santa Fe Institute and published in The Santa Fe New Mexican. Read this article in the New Mexican.
You love math. You really do. I’m not talking about the kind of math that makes cell phones work or the kind that bankers use. I’m talking about math in its purest, most natural form — the kind that moves the planets in their orbits, gives flowers their shape, and makes a chorus sound like angels.
Maybe you’re thinking: “No, I don’t love math. I hated math in school and I still do.” Not so. You only think you hate math because of the way it was taught to you.
Most people are taught in school that mathematics is a mechanical process: plug the numbers in, turn the crank, follow the rules. If you get the right answer, you get a gold star. If it’s wrong, you get a big red X.
But this isn’t what math is about, any more than English (or Spanish) is about spelling and grammar. Language is about beautiful poetry and great stories, not about dry rules and memorization. If we taught English the way we teach math, no child would be allowed to read a poem until they could spell it and diagram its sentences. No wonder so many people are turned off. (Sadly, our focus on standardized tests is only making this worse.)
Despite the damage done in school, your natural love of math is still there, deep down. It reveals itself in the way your brain grabs on to music, to art, to the natural world — to anything with beauty and structure hidden in it.
Math and music are both about patterns. When we hear a rhythm or a melody, we tap our feet and sing along. We like it when the music does what we expect it to. But we also like it when it surprises us, with a key change or a new variation on a theme. A good composer or songwriter includes just enough surprises to keep us on our toes, until at the end of the song when the pattern falls into place.
When scientists and mathematicians look for patterns in the world, we’re doing the same thing you do when you listen to music — or even better, when you create your own! We try different patterns on, see if they lead somewhere, see if they sound right (or fit the data), and keep playing with them until they make sense. And then we try to understand why that pattern is there.
Next time you see a pine cone or a sunflower, look at the spirals. Some go clockwise, some go counterclockwise. If you count them, you almost always get the same pairs of numbers — 5 and 8, or 8 and 13, or (in a big sunflower) 13 and 21. These are pairs of Fibonacci numbers, where each one is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21...
Why do plants grow that way?
How do leopards get spots, and zebras get stripes? Does their DNA have a map of spots and stripes in it somewhere? Or do their cells color their fur using mathematical rules? Do zebras use the same math as tigers?
And back to music: why does making a pipe or a string half as long make it sound an octave higher? What frequencies of sound are hidden in a C major chord? Why do some combinations of notes, like a C and an F#, sound so weird?
On Saturday night, Nov. 2, in a special concert at the Lensic with The Santa Fe Symphony, I explored the patterns hidden in music. The Symphony and I took the audience on a journey, from the rhythms of molecules to the harmonies of the planets, from the dissonance of the “devil’s interval” to the Halleluiah Chorus, from bone flutes that are 40,000 years old to the soundtrack of Harry Potter.
We explored how great composers use mathematical concepts that go all the way back to Pythagoras in ancient Greece. We talked about how Johann Sebastian Bach used symmetries and fractals in his fugues — music that looks the same if you flip it over, or if you zoom in or out.
Symphony Director Gregory Heltman and I developed the program to show how mathematics can help us understand why we love the music we love, and how to create new music that no one has ever heard before. And many of the same patterns hidden in music are hidden in the world around us, and they can help us understand the universe we live in.