January 7, 2019 | By Kimberly Uslin

Peter Pesic is Tutor Emeritus, Musician-in-Residence, and Director of the Science Institute at St. John’s College in Santa Fe. He recently participated in a roundtable discussion on “The Beauty and Unity of Mathematics” at the Helix Center in New York, followed by a speech at the “Polyphonic Minds and Cubist Jazz” event at Cornelia Street Cafe. Here, he discusses the enduring power of polyphony and the connection between music, mathematics, and the physical world. (For more from Mr. Pesic on polyphony, check out these recent articles in the Economist and The New York Times.)

How was the roundtable discussion on “The Beauty and Unity of Mathematics?” What surprised or intrigued you about it?
It was very enjoyable and interesting, a real conversation in the St. John’s style—friendly and open, a broad discussion about what mathematics means and its significance for human experience. The participants were the distinguished mathematicians Barry Mazur, Michael Harris, and Avner Ash, as well as the philosopher Garry Hagman and myself; the audience seemed very engaged and asked many interesting questions.

I was surprised by the degree to which the process of mathematical invention does not merely deal with mathematical objects, triangles, or equations. It has to do also with going from one state of mind, a state of being confused or perplexed, to another in which things become clearer. Mathematics particularly illuminates how that change occurs because in every other subject—like political discussions, for example—people have prior opinions that may reflect their personal experience or social environment, but mathematics has to do with even more basic preconceptions about space or quantity. Thus, the process of thinking in mathematics highlights the simplest—and deepest ways—ideas can change.

How does this relate to the St. John’s education?
What we do at St. John’s has a lot to do with changing minds, for which mathematics has been a prime example since the Greeks. From the New York discussion and the response of the audience, I saw how great is the general interest in the problem of how people change their opinions. There are many people who wish to have the kind of thoughtful, nonconfrontational discussions that would allow them to reconsider and even change their thinking. This larger interest seems to me to underline the importance of what we do here at St. John’s.

Tell me about the other event, “Polyphonic Minds and Cubist Jazz.”
In connection with my latest book, Polyphonic Minds: Music of the Hemispheres, David Sulzer, a neuroscientist at Columbia University, kindly invited me to participate in “Entertaining Science,” a science cabaret held at the Cornelia Street Cafe in Greenwich Village, pairing scientists with artists. I spoke about polyphony and its relationship to the mind, which grew very much out of my experience in the St. John’s music tutorial over many years—particularly such questions as "What does it mean when people start to sing in many voices as opposed to one? What’s the relationship of that to the human mind and society?"

The venue was a small, lively jazz club, packed with people—a pretty large fraction of which were neuroscientists, I was told, drawn by the evening’s connection between neuroscience and music. The superb jazz ensemble that played gave living proof that this music is brought to life by improvisation. The human mind, too, is brought to life by a kind of improvisation between the neurons—there not being any controlling center or boss neuron in the brain that tells all the others what to do. All these neurons form a cooperative (and improvisatory) society that may be more like a kind of jazz, I think, than anything else.

Are you working on a new book at the moment?
I am. My last two books have concerned the ways music has influenced science. The first considered music’s effect on mathematics and physical science, the second its connections with neuroscience and the human sciences more broadly. This new one, which I think is going to be called Sounding Bodies, is about the ways in which music influenced the development of medicine and biological sciences. Since antiquity, these studies had a different relation to music and mathematics than did the physical sciences. I’m in the midst of it now and learning a lot. While I was in New York, I met with neuroscientists to learn more and get help with the various examples I’m considering in this new book.

What draws you to the connections between music, mathematics, and the sciences?
I’ve been fascinated by music, physics, and mathematics all my life. They’ve been interests of mine since childhood. For the longest time, I was pursuing them quite separately. I knew there was some kind of relation, but it has taken me a very long time—like 50 years—to figure out what I think it was. People tend to assume that somehow science influences music, but I think the influence may rather go in the opposite direction: Music comes first and influences science. That’s the general insight I’m trying to scrutinize.

How would you describe that influence?
It takes a different form in each field. Perhaps the clearest and most direct is in the physical sciences. Music first showed that there was a connection between number and the physical world. After the discovery that numbers seem to govern the recurrent positions of the heavenly bodies, the Pythagoreans connected consonant musical intervals to simple whole number ratios (of string lengths, for instance). This was the first earthly observation that number somehow corresponded to what we can hear and feel. These were also the first experiments, in the sense that word came to be used in later science.

On the other hand, Aristotle thought there were no numbers in the physical world: you don’t look at rocks and trees and sense any connection with numbers, which seem to be abstract or separated from the things in this world. The world of growth and change seems far from the immutable constancy of numbers. I think music first showed how numbers could underly the vivid changes in what we feel and are. In the realm of medicine, sound was the way in which the mysterious interior of the body was first probed past what could be seen on the surface.