The link between music and mathematics that so fascinated the ancient Greeks gets a new appraisal in Stephon Alexander’s The Jazz of Physics. The Pythagoreans and Plato suspected that the creation of matter and the structure of the universe were based upon sound, harmony, and geometric patterns, and the conceptual analogies between physics and music have been developing ever since.

Alexander points out that both jazz musicianship and problem-solving in theoretical physics depend upon conceptual tools and practices worked out by past masters. 21st-century jazz musicians still count on ideas that originated with Louis Armstrong, Duke Ellington, Charlie Parker and others. In the 17th century, Johannes Kepler extended the Greeks’ geometrical-musical reasoning to develop his three laws of planetary motion, and even transcribed Pythagoras’ celestial music into a workable score. (In 2011, Willie Ruff and John Rogers released a CD of Kepler’s score called The Harmony of the World: A Realization for the Ear of Johannes Kepler’s Astronomical Data from Harmonices Mundi 1619— “an auditory representation of the harmonies the planets make as they go around the sun in elliptical orbits, blending to create a unified rhythm corresponding to the periodic orbits of the planets.”)

The correspondence between musical and mathematical notions recurs through physicists’ work on special relativity, quantum mechanics, supergravity, and more, as Alexander shows. His own work on the origins and structure of the universe drew inspiration from the ‘spontaneous’ improvisations of Lennie Tristano and Warne Marsh, but as Alexander points out, what seems spontaneous in jazz improvisation requires a deep understanding of music theory and harmony, years of practice, memorization and making mistakes—an approach familiar to the practicing physicist.

The device that symbolizes for Alexander the ultimate correspondence between music and physics is the hand-drawn circular chart of musical scales that John Coltrane gave to Yusef Lateef in 1957. The ‘mandala,’ as Alexander calls it, is a geometric structure that identifies patterns between some of the key scales and harmonic devices that Coltrane used in his repertoire. Coltrane reportedly told David Amram that he was inspired by Albert Einstein to find a simple idea for his music; the mandala suggests that that idea was symmetry. As Alexander explains, Coltrane played symmetric scales to create tension or a sense of ambivalence, and used symmetric chords with multiple tonal centers. The consonant or dissonant relationship between notes played simultaneously opened new harmonic possibilities. Alexander also sees an analogy between jazz improvisation and Richard Feynman’s description of quantum mechanics: just as all potential paths are open to a particle moving between two points, so does a musician subconsciously consider all notes in a scale before deciding which note to play. “The ability to improvise is to find the hidden patterns and regularities underlying harmonic forms and to use those insights to generate new kinds of melodic sequences.” The physicist in search of answers is also an improvisor.

Alexander also claims as an influence Ornette Coleman. Instead of moving through scales and chords, Ornette played with sound, giving melody, harmony and rhythm equal place in his improvisations. Ornette’s polytonal motifs are like the lattice of vortices formed by magnetic fields in the quantum realm, says Alexander, and Quantum Field Theory can be understood in terms of the elements of modern jazz: broken symmetries, inherent uncertainties (improvisation), the idea that each outcome is the sum of all possible outcomes.

Alexander takes the link between math and music back to the origins of the universe, then, and discovers Coltrane particles and Coleman fields in the music of the cosmos. His solution to the Fine-Tuning Problem posits vibrational patterns in the early universe generating a complex structure with an improvisational nature. In the best jazz improvisation, the vibration and resonance of notes and tones, like the vibration and resonance of quantum fields, tend to harmonize into a self-tuning structure. A harmonic or cyclical universe, undergoing an infinite succession of expansions and contractions, arrives at the optimum cosmological constants (a pure tone) by continually improvising new values during the ‘bounce’ between a contraction and expansion.

…the unfolding of the structures in the universe has a musical character. The dance among harmony, symmetry, instability, and the gaps of improvisation—all cooperate to sustain cosmic structure. It is as if the unfolding cosmos transpires like a John Coltrane solo.

It would be fun to know what Plato thinks of John Coltrane and Ornette Coleman, or quantum mechanics for that matter. We’ve come a long way since the Greeks, but they were on to something, and they raised all the good questions first. What Alexander gives us in The Jazz of Physics is another way to think about and hear the work of musical geniuses, whether or not we can make heads or tails of the physics. When he says that the solos on Coltrane’s Interstellar Space ‘expand and free themselves from the gravitational pull of the rhythm section,’ I think I know what he means.

I very much enjoyed this book, although I think I enjoyed it more as an autobiography then as a work of popular science. As a non-physicist with a science background, I still found myself struggling to follow in some of the more complex physics sections. In the end, I just let those parts wash over me, and I could enjoy the rest. ( )

This was a book that I was looking forward to reading. Two words caught my fancy: Physics and Jazz.
Alexander is an accomplished physicist and a working musician. He was fascinated by both parts of his life when he was a child and managed to be able to do quite well in both spheres as an adult. He was able to convey his own natural attraction and obsession to both physics and jazz in a very natural and passionate way. He does an excellent job in eliciting in me a corresponding response in me that was as natural and passionate as his.
His intent is to present the advanced physics that he is working on as an academic as being analogous to the jazz improvisations that he is working on as a gigging jazz musician. Unfortunately, he was much less successful.
My own expertise in both physics and jazz are skin deep at best. Physics being more naturally aligned with my engineering training, while jazz is limited by scant my musical background. So it would seem to be natural that his explanations of the physics would be easier for me to comprehend, it wasn’t. In fact the musical analogies that he explained made much more sense that his explanations of physics. As I slogged through the explanations, I wondered about the more general audience, whether they were having as difficult of a time as I was.
The center motif that he presented at the beginning of the book involved John Coltrane’s mandala in which Coltrane was trying to create a connection with his own very original musical expressions with the evolution of modern physics during that time. Coltrane worshiped Einstein and his ideas, for example. According to Alexander, Coltrane’s last three albums were his own experimentation with the mathematical ideas that Einstein had speculated upon.
Taking inspiration from arguably the most prominent minds of their era, in completely disparate areas of achievement, Alexander decided to work on both simultaneously. Of course, this was not a conscious choice, he had been foundering in his physics career since physics had become a calculators domain with the mathematics heavy emphasis on the superstring theory.
Indeed, Alexander employed the method of no method, or the idea of wu-wei to use jazz as a means of training his mind in a way that perhaps the jazz could elicit some original ideas in his physics. By the accounts in the book, he was indeed successful in doing good physics while also playing some good jazz. What he failed to do in the book however, was cogently leading us through his maze of twin spheres of influence and the complexity contained therein with each one. While he did a very admirable job trying to explain himself, I suspect that the culprit is more the complexity of the subjects rather than his familiarity with both subjects. Indeed, the book would be 100 times longer if he had indeed taken care to explain the minutiae of the two subjects. His hope of using analogy rather than detailed explanations to convey his message was somewhat successful but also somewhat a failure. But no matter, because the book did a great job of creating an ethos of what he was trying to convey, and there was a denouement of sorts toward the end. I will never listen to Coltrane again, and I will now understand a little bit better what all the fuss about modern physics is in regard, so I can say that I learned something new. ( )

This is a book I'll read again one, Stephon Alexander does a great job explaining physics, jazz and cosmology in a way I could (mostly) understand. ( )