Math, Music, and the Moral Imagination

Math Music and the Moral Imagination.

What continues to draw me back into math and music is this notion of transcendent beauty. It is a siren song that has at time tempted me out of some days and months, and perhaps some dollars and cents. For much of my life, the tune of the siren sufficed. Math and Music both require a fair amount of cloistering and in many ways this can be time spent in the theoretical. But, I’m an introvert and this orientation toward life satisfied me.

There are many interesting ideas in this field. Some recast common practice music theory using mathematical physics and abstract algebra. Others look at subtle proportions in classical scores. A few use theorems and formulae as compositional elements. None of it hit on what draws me into the math and music in the first place. So when I began writing and speaking on the topic, I came up with a Math and Music “word cloud” that included curiosity, imagination, and creativity, with beauty, guiding the whole inquiry. My discussion of the topic at the National Museum of Mathematics resonated with people in such a way that I was able to give a TEDx talk on math and music. I struggled, however, to figure out what could be produced from this notion. Was there actually a tangible or useful result, or was the idea just cool enough that people would invite me to talk about it? The question vexed me, because I had a nagging feeling that the part of beauty that was truly siren-like, in that it was leading me to some metaphorical death, was its stark contrast to the dire state of the world. That beauty somehow functioned as an unhealthy escape from reality.

Still, I stuck with the topic, continuing to study, solve, and create. These are wonderful hobbies to have during COVID, by the way. I made a policy not to read short form pieces to encourage focus and step out of the fast paced news cycle, as I set out to brush up on Complex Analysis and Quantum Mechanics, compose some classical work, and develop my skills on piano and bass. Staying in the house, with my reading, writing, rhythm, and ‘rithmetic, unbothered by the outside world, has been a blessing. Time enough at last, as it were, like Burgess Meredith in the Twilight Zone. 

And then one day something happened. Retreating to pencil, paper, laptop, and instrument, (my vision of a perfect day for the past 2 years) became wholly unacceptable. The change came with no clear, actionable demand. There was no specific issue that revealed itself as the locus of urgency; simply, a kind of primordial psychological feeling that something must be done, about everything, and I must be an active part of the doing. And at that moment the scope of my effort changed. The question ceased to become simply about the connection between math, music and the beautiful, but turned to what this connection could bring to bear on the condition of humanity.

This change in worldview occurred about a week before the murder of George Floyd, an event that would force my attention outward. At the time of this writing, The United States is in the throes of a painful transformation, as several concurrent forces put pressure on a leadership and infrastructure that consistently shows itself unprepared and unbothered. In my view of history, the reason is America’s refusal to come to terms with race, not so much because race is at the center of all questions, but that it has been the weapon of choice to divide people, direct resources, and protect some while crushing others, since the 17th century. This is true by the way of both major political parties and many public and private institutions of American life. Robbing the topic of its distorting power would likely prevent us from being systematically derailed, but that requires a sobering look at history, internal work to see the world anew, and a dramatic leap of moral imagination. Taking a larger view, beyond just America’s dysfunction, avoiding climate apocalypse, achieving a resource distribution that preserves dignity, and adopting technology in a way that doesn’t undermine our humanity are major challenges that all require an actionable paradigm.

So I began to think about how math and music show up during upheaval and what role they play making things more functional. During the civil rights movement, music was a focusing element. The song, “We Shall Overcome” originally credited to Lucille Simmons, a Black Woman who helped to lead the Charleston Tobacco Strike of 1946, was tweaked by musicians at the Highlander Folk School in Tennessee and became the anthem of the civil rights movements of the 60s. James Brown saved Boston with a concert on the day after Dr. Martin Luther King Jr. was murdered and several American cities descended into riot. Songs by Bob Marley and Marvin Gaye from the 70s have become anthems of protest and uplift in times since. Having participated and performed in demonstrations organized by Jon Batiste, I can say that live music, and communal singing have an enormous effect on the focus and morale of a group and while I’ve never participated in the kinds of long marches that marked the 60’s, I understand what role music would have had in helping demonstrators to endure in peace and solidarity.

Mathematics’ place in all this seems to be in the numbers. Organizations like the Center For Policing Equity and Campaign Zero are using data driven approaches to make specific policy proposals that their models say will reduce police brutality. Virus models, aided by computer, are used to track and manage the spread of the disease. Social Network theory relies on graph theory analysis to model how information and infection spread; analysis which then takes shape in policy. Journalists have added infection and death rates to their set of headline numbers, which used to focus on economy or presidential approval rating. Numbers are the fuel for decision and debate, and appear, in our culture, to be the instrument of choice for the informed mind.

Zoom out a little and we find that math underlies so much of the modern era, finding expression in technology. Consider that protests and boycotts can be organized and advanced quickly in ones own bedroom by posting, rather than requiring the coordination of the 60s. It’s now possible to completely bypass the publishing apparatus to be heard. We can create, consume, and disseminate information far faster than at any time in known history. Our technological connectedness frames both COVID and the movements of justice we see today.

But, like music, mathematics via technology is amoral. We, as moral agents, must use it to shape the world as a reflection of ourselves. If we are to continue as a civilization, we need a greater ability to imagine more harmonious, sustainable, and beautiful relationships with one’s self, between individuals, and amongst groups. We need to do “inner work” to develop “moral imagination.” These terms are vague but consider some of the following questions to get a sense of what I mean. How can you take a religious or philosophical doctrine and find the best application to current circumstances? How can you consistently honor personal priorities and promises to others? How can you better relate to your family? How can you best lead a team of people? How can you relate to groups of people whose beliefs may be different or even threatening to you? What is your part in keeping the world from ending? These are hard questions and the big ideas in the “solution word cloud” include truth, honor, power, dignity, belonging, integrity, service, Self, and often, God. I posit that the more we take the opportunity to struggle with these concepts, the more we do inner work and grow our moral imagination.

So right now, I’m interested in how the study and practice of mathematics and music offer opportunity to build a relationship with these ideas. For me, I notice some ways that my work as a musician informs my love of mathematics and how studying both subjects has added to my life in novel ways. But, I don’t yet have a fully coherent system or curriculum. So the rest of this piece is a series of observations, (both my own and from the literature) and questions that will hopefully get you to think differently about the role of mathematics and music for inner growth, mental and emotional health, and ability to build a better world.

The most obvious way is to think about how mathematics and music are produced. Making music is a fundamentally communal act that establishes relationships between the members of the band internally, and the audience externally. Within the band the “jamming” dynamic requires trust, safety both in the competence and non-judgment of the band mates. You have to feel safe that the level of love and skill are high enough for you to explore, experiment, and even screw up.

As a performer you are offering a unique environment for others to think and feel in ways that they could not without you. I’ve found that allowing oneself to be vulnerable as a performer, not hiding behind the notes or the “purity” of ideas, or the psychologically superior position of the stage, tends to make performances more captivating for both the band and the audience. I try to conceive of performance as an act of service, then, like a good servant, develop a sense of what my band mates and audience need, and finally offer my art with respect to those needs. This is a subtle technique, all happening in real time, that doesn’t lend itself to words easily. Jazzmeia Horn usually frames this technique a gift of healing and achieves the transcendent effect consistently. It can also be thought of as a movement of the “second self,” described in The Inner Game of Tennis by Tim Gallwey. People tend to use words like “real” or “blown away” “spiritual” after experiencing this from an artist.

The best mathematical presentations I’ve seen have the similar energy. Of course there is the emphasis on the quality and correctness of the content, but great talks deliver a palpable enthusiasm and curiosity. It’s clear that even in some esoteric field, the presenter has a personal relationship with the material and conveys a sense of emotional journey either in the proof itself or in the human process of arriving at a solution. In college, I remember feeling this love and engagement from Joe Harris as he was teaching field extensions. Something about his excitement to pull the curtain back and reveal Galois Theory, this marvelous achievement of human logic, was endearing. I felt warm inside, even though I was confused and having an extremely tough semester overall. The Youtube Presenters, “Black Pen Red Pen”, “Flammable Maths” and “3blue1brown”, convey their own brand of joy and humanity, as does a presentation on the Surreal Numbers by the Late John Conway.

Perhaps surprisingly, mathematics also holds a jam dynamic. In college, I saw many a sunrise with my problem set crew, who spent the night up tossing ideas around, trying to land the final details of some complex proof. The environment needed to do this well is characterized by a sense of comfort, play, the silliness that comes with extreme tiredness, and the sense that each person had something to contribute, that everyone had done the reading. Those moments of working toward finishing hard problem sets with friends are some of my favorite memories of being with people. The deadline, the creativity, the common struggle, the competition to contribute…all had a sense of aliveness, purpose, safety, and exploration that I recognize as a musician. Reflecting on these experiences, I begin to consider larger life questions: how can I create greater harmony with collaborators? How can I teach in order to grow a sense of communal self as well as knowledge? How can I serve an audience, even while presenting musical or mathematical esoterica? How can I compete with vigor and grace?

I’ll comment now on the musician’s journey from beginner to master, because it has quite a bit to do with the notions of structure and creativity and how they relate to strength and vulnerability so desired in the jamming dynamic and is akin the Hero’s Journey described by Joseph Campbell in the Hero with 1000 faces. A musician has an enormous amount of skills to learn to become competent. The work includes learning harmony and rhythm, mastering the instrument, and transcribing older musicians’ work. And through this difficulty, the practitioner learns humility and respect. Considering one’s own place in the world of music, and then considering the vastness and interrelatedness of that landscape, the dragons that came before, and the giants that reign now, a good musician will become humble to it all. This humility, and the sacrifice to the craft that comes with it, make the musician strong enough to earn the trust of both self and colleagues. With this trust, a musician will enter into novel circumstances which will force their creativity into action producing their own, personal magic, a style, distinguishing features that drawn not from theory, but from experience. And the cycle begins again as the musician becomes humble sacrifices to master the inspiration that comes from life itself. As strength grows via structure, so do vulnerability, honesty, and inspiration grow through creativity. These concepts support and chase and flow into each other like yin and yang. Without enough skill, creativity is impossible to support, but one’s own creative sense can dictate what skills to develop.

It’s interesting to think about how this notion could apply to learning and growing within math. Consider that mastering the algebra, the elementary functions, and calculus in math, might be analogous to learning harmony, repertoire, and important solos in jazz. But as we develop, we find novel applications of these rules, maybe by solving unusual problems. We ask interesting questions where rules become loose and there is more freedom to explore. We may prove novel theorems or old theorems in a personalized way way. With time, perhaps we can come up with completely new, more general ways of looking at old ideas. Mastering structure to attain the freedom to discover higher structure, which allows greater freedom…and so forth. If we were all good Daoists, then the suggestion of practicing anything in a way that harmonizes yin and yang would convince us that there is moral and even spiritual content to mathematics. But, I’ll personalize it a little for anyone who hasn’t brushed up on their Yellow Emperor lately. In my mathematical journey, which has been informal since my undergraduate days, I researched ideas I wanted to learn and solved problems that interested me. With the help of great mentors, I can now follow along in advanced talks and papers, and, in some cases, teach the basics of topics I never learned in school. The idea of chasing one’s interest, walking off the beaten path, and applying self discipline to find a creative voice are usually ideas reserved for artists and not really spoken of in the same way in math. I would contend that they are still there, for they are a natural bi-product of the journey to mastery.

The life lesson is that creativity inspires discipline, which in turn inspires greater creativity, which in turn demands more discipline etc. This has given me a personal framework for growth in any endeavor, but it gives me empathy for others as well. I have a way of relating to anyone who is working toward something. This relatedness allows me to honor their perspective. Thusly the inner work of mastering a craft can give rise to a deeper relationship to other humans. Humility toward the ancestors (of your craft or otherwise), creative passion, and freedom of being are often markers of a spiritually healthy person or a functioning community. For me math and music can be teachers of this orientation toward life.

I’d like to finish where I started: transcendent beauty. That which is beautiful or sublime pushes us out the mundane into a world marked by vividness, clarity, and wonder not easily found in every day life. Having this experience is important to ones moral imagination because it lets us know that such a texture of life is possible. And if we assert, as axiom, that we can achieve such grace by conducting ourselves and relating to one another in the proper way, then beauty in math and music offer us a reference point; an aroma of the soul’s home to which we are drawn, and it is our inner work which enlarges the space for this feeling in us. It is the reason I am drawn to these topics in the first place, and ultimately the aspects of beauty, such as elegance, clarity, balance, timelessness, proportion, allure, harmony, and truth deeply inform our internal growth and our moral consciousness

One could argue that for most of us, it is easier to receive music as beautiful than it is math. As it turns out, the “beauty area” of mathematicians brains, lit up upon seeing beautiful math so there is some neuropsychology to back the claim. And for those who see, the subject is itself a construct of grace. But, rather than rest there, I return to my earlier claim that math and music offer an opportunity for such an opening into transcendence, not that they guarantee it. We may choose to look at math and music from this perspective. I believe that, teaching and discussing these topics in such a light will add a certain richness to life, as it has mine. And given that the world is in so much upheaval, orienting our perspective to build a deeper love, appreciation, and understanding for ourselves, one another, and our collective work feels like an idea worth investigating. I don’t know that it will produce novel mathematics or music, but I suspect that it will produce novel mathematicians and musicians.