by Andy Boyd
Today, minimal. The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them.
I recently read an obituary of Dennis Lee Johnson, a musician turned mathematician, and it brought back memories.
Many years ago I wasn't sure if I wanted to pursue a career in music or math, so I chose to attend Oberlin College which was home to both a college and music conservatory. I soon realized just how difficult it would be to make a living as a musician and pursued math. But not before I'd taken numerous courses in music composition.
Oberlin College - Bosworth Hall Photo Credit: Wikimedia
It was the late seventies and all types of experimentalist music were in vogue. I learned how German composers created music from computer generated sine waves while French composers fashioned music by tape recording everyday sounds. I attended a concert where a performer plucked the amplified spines of a cactus. I personally composed a piece that consisted of a famous Shakespearian passage read in a phony British accent over the sound of percolating coffee. It was surprisingly well received. However, when I posted a flyer in the electronic music studio seeking a keyboardist, I returned to find a note scribbled on it declaring that keyboards were a form of musical oppression. All in all it was, shall we say, an interesting experience.
Einstein on the Beach Photo Credit: Wikimedia
Along the way I developed a taste for certain minimalist compositions. Minimalist music needn't be spare - a note here, a note there - though it can be. Some minimalist music is richly textured as, for example, parts of Phillip Glass's work The Photographer.
[excerpt from The Photographer by Phillip Glass]
Minimalist music, to the extent that it can be defined, is minimal in that it typically builds upon a minimal number of elements. A good analogy is that of Lego building blocks. Suppose we agreed to start with a huge bag of Legos but made up of just four shapes and four colors. Even constraining ourselves in this way, we can build elaborate structures. Some beautiful. Some dazzling. We're limited only by our reliance on the four shapes and colors in our bag.
Philip Glass Photo Credit: Wikimedia
And that's how math works as well. Mathematicians start with just a handful of simple operations - like addition and multiplication - then build their own elaborate structures. Higher math is no different than basic arithmetic. It's just more abstract.
As I read about the life of Dennis Johnson, I couldn't help but smile. Johnson, it seems, was involved in the early minimalist music movement. I'd share some of his recently rediscovered composition November, but it moves so slowly it doesn't lend itself to short clips. Nor can I explain his most celebrated mathematical result, the Johnson homomorphism. But I can say that Johnson wasn't merely a musician turned mathematician. He was, throughout his career, a minimalist.
[excerpt from Glassworks by Phillip Glass]
I'm Andy Boyd at the University of Houston, where we're interested in the way inventive minds work.
Thanks to Carol Lienhard for bringing the New York Times obituary of Dennis Lee Johnson to my attention.
Allan Kozinn. "Dennis Johnson, 80, Creator of a Rediscovered Minimalist Score, Dies." New York Times, January 9, 2019. See also: https://www.nytimes.com/2019/01/09/obituaries/dennis-johnson-dead.html. Accessed January 15, 2019.
Minimal Music. From the Wikipedia website: https://en.wikipedia.org/wiki/Minimal_music. Accessed January 15, 2019.