By Maria Popova (brainpickings.org)

“All truth is comprised in music and mathematics,” Margaret Fuller wrote as she was spearheading the Transcendentalist movement and laying the groundwork for what would later be called feminism.

A century and a half after Fuller, theoretical physicist, cosmologist, and jazz saxophonist Stephon Alexanderexamines this dual seedbed of truth in The Jazz of Physics (public library) — part memoir of his improbable path to science and music, part captivating primer on modern physics, part manifesto for the power of cross-disciplinary thinking and improvisation in unlocking new chambers of possibility for the human mind’s intercourse with the universe and the nature of reality.

Stephon Alexander

Drawing on the legacy of Kepler, who composed the world’s first work of science fiction — a clever allegory advancing the then-controversial Copernican model of the universe through a conceptually ingenious analogy — Alexander writes:

Contrary to the logical structure innate in physical law, in our attempts to reveal new vistas in our understanding, we often must embrace an irrational, illogical process, sometimes fraught with mistakes and improvisational thinking. Although it is important for both jazz musicians and physicists to strive for technical and theoretical mastery in their respective disciplines, innovation demands that they go beyond the skill sets they have mastered. Key to innovation in theoretical physics is the power of analogical reasoning.

But while Alexander does draw heavily on analogies throughout the book, the parallels and equivalences between music and physics are often far more literal. “It is less about music being scientific and more about the universe being musical,” he writes, reminding us that stars, galaxies, and planets arose from sound waves in the plasma of the infant universe as spacetime vibrated like an instrument to produce the waves that leavened these essential cosmic structures.

Born in Trinidad, Alexander fell in love with science shortly after his family moved to the United States. Visiting the American Museum of Natural History with his third-grade class, he was mesmerized by a set of papers behind a thick pane of glass, inscribed with symbols that seemed otherworldly to his eight-year-old consciousness. Next to them was a portrait of their author — a wild-haired, mischievous-eyed oddball. This was his first encounter with Einstein, who would go on to be a lifelong hero as Alexander devoted himself to decoding the secrets of the universe.

Page proof corrections of Einstein’s paper Propagation of Sound in Partly Dissociated Gases, in Einstein’s hand. (Einstein papers, Instituut-Lorentz)

A few years later, as a teenager in the Bronx, he had a parallel experience of encountering a new, almost mystical language and recognizing it as an encoding of elemental truth. Through the gateway of hip hop and its wide-ranging influences spanning Caribbean and Latin music, Alexander discovered the saxophone and became besotted with the free jazz of Ornette Coleman. His parents eventually bought him a vintage alto saxophone at a garage sale, and so began his second great love affair with the universe. At the intersection of these two loves, Alexander found his calling. Within a decade, he was working on some of the most complex problems in modern physics by day, performing with some of the most legendary jazz musicians by night, and cross-pollinating the legacies of his great heroes: Einstein, Pythagoras, John Coltrane. He recounts a definig moment:

About a decade ago, I sat alone in a dim café on the main drag of Amherst, Massachusetts, preparing for a physics faculty job presentation when an urge hit me. I found a pay phone with a local phone book and mustered up the courage to call Yusef Lateef, a legendary jazz musician, who had recently retired from the music department of the University of Massachusetts, Amherst. I had something I had to tell him.

Like an addict after a fix, my fingers raced through the pages anxiously seeking the number. I found it. The brisk wind of a New England autumn hit my face as I called him. At the risk of rudely imposing, I let the phone ring for quite a while.

“Hello?” a male voice finally answered.

“Hi, is Professor Lateef available?” I asked.

“Professor Lateef is not here,” said the voice, flatly.

“Could I leave him a message about the diagram that John Coltrane gave him as a birthday gift in ’61? I think I figured out what it means.”

There was a long pause. “Professor Lateef is here.”

We spoke for nearly two hours about the diagram that appeared in his acclaimed book Repository of Scales and Melodic Patterns, which is a compilation of a myriad of scales from Europe, Asia, Africa, and all over the world. I expressed how I thought the diagram was related to another and seemingly unrelated field of study — quantum gravity — a grand theory intended to unify quantum mechanics with Einstein’s theory of general relativity. What I had realized, I told Lateef, was that the same geometric principle that motivated Einstein’s theory was reflected in Coltrane’s diagram.

Part of Einstein’s genius, Alexander points out, was his willingness to leap beyond the limits of his particular mathematical problem and into a field of possibilities, which he explored through improvisational experimentation — gedankenexperiments, or thought experiments. Einstein himself, who believed his best ideas came to him during his violin breaks, called his ideation process “combinatory play” — a wilderness of associations reaching across boundaries of various theories and fields of thought, not as deliberate problem-solving but as unforced mental meanderings.

Art by Vladimir Radunsky from On a Beam of Light: A Story of Albert Einstein by Jennifer Berne.

Alexander, too, had a pivotal breakthrough in his scientific work during one such unexpected cross-pollination of ideas across disciplines, which steered the direction of his research in a way he could not have necessarily thought his way to directly and deliberately. During his time at as a postdoctoral student at London’s Imperial College, he met — at a “quantum gravity cocktail hour,” as one does — a serious-looking man with a gold tooth, dressed in black, who engaged in intense conversations about spacetime and relativity and the mathematics of waves. Alexander took him for a Russian physicist. He turned out to be the pioneering musician Brian Eno. The two soon became friends and Alexander came to see Eno as a singular species of “sound cosmologist.” He recounts the moment that catalyzed his breakthrough:

One of the most memorable and influential moments in my physics research occurred one morning when I walked into Brian’s studio. Normally, Brian was working on the details of a new tune — getting his bass sorted out just right for a track, getting a line just slightly behind the beat. He was a pioneer of ambient music and a prolific installation artist.

Eno described his work in the liner notes for his record, Ambient 1: Music for Airports: “Ambient music must be able to accommodate many levels of listening attention without enforcing one in particular; it must be as ignorable as it is interesting.” What he sought was a music of tone and atmosphere, rather than music that demanded active listening. But creating an easylistening track is anything but easy, so he often had his head immersed in meticulous sound analysis.

That particular morning, Brian was manipulating waveforms on his computer with an intimacy that made it feel as if he were speaking Wavalian, some native tongue of sound waves. What struck me was that Brian was playing with, arguably, the most fundamental concept in the universe — the physics of vibration. To quantum physicists, particles are described by the physics of vibration. And to quantum cosmologists, vibrations of fundamental entities such as strings could possibly be the key to the physics of the entire universe. The quantum scales those strings play are, unfortunately, terribly intangible, both mentally and physically, but there it was in front of me — sound — a tangible manifestation of vibration.

“Behavior of Waves” by Berenice Abbott, 1962, from her series Documenting Science.

This unexpected contact with sound made tangible shone a sidewise gleam on a question Alexander had been puzzling over ever since graduate school, when he had asked his mentor — the famed cosmologist Robert Brandenberger — what the most important question in cosmology was. Rather than an expected answer, like what may have caused the Big Bang, Brandenberger surprised the young man with his response: “How did the large-scale structure in the universe emerge and evolve?” Suddenly, in watching Eno manipulate waveforms, Alexander had a revelation. He explains:

Sound is a vibration that pushes a medium, such as air or something solid, to create traveling waves of pressure. Different sounds create different vibrations, which in turn create different pressure waves. We can draw pictures of these waves, called waveforms. A key point in the physics of vibrations is that every wave has a measurable wavelength and height. With respect to sound, the wavelength dictates the pitch, high or low, and the height, or amplitude, describes the volume.

If something is measurable, such as the length and height of waves, then you can give it a number. If you can put a number to something, then you can add more than one of them together, just by adding numbers together. And that’s what Brian was doing — adding up waveforms to get new ones. He was mixing simpler waveforms to make intricate sounds.

To physicists, this notion of adding up waves is known as the Fourier transform. It’s an intuitive idea, clearly demonstrated by dropping stones in a pond. If you drop a stone in a pond, a circular wave of a definite frequency radiates from the point of contact. If you drop another stone nearby, a second circular wave radiates outward, and the waves from the two stones start to interfere with each other, creating a more complicated wave pattern. What is incredible about the Fourier idea is that any waveform can be constructed by adding waves of the simplest form together. These simple “pure waves” are ones that regularly repeat themselves.

[…]

I was enthralled by the idea of decoding what I saw as the Rosetta stone of vibration — there was the known language of how waves create sound and music, which Eno was clearly skilled with, and then there was the unclear vibrational message of the quantum behavior in the early universe and how it has created large-scale structures. Waves and vibration make up the common thread, but the challenge was to link them in order to draw a clearer picture of how structure is formed and, ultimately, us.

In the remainder of The Jazz of Physics, Alexander explores how these questions reverberate through the consciousness of our species, from Pythagoras to string theory and beyond, into the future of probing the unfathomed depths of reality. Couple it with Nick Cave on music, transcendence, and artificial intelligence, then revisit the fascinating story of the century-long quest to hear the sound of spacetime.