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The Jazz of Physics
The Secret Link Between Music and the Structure of the Universe
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More than fifty years ago, John Coltrane drew the twelve musical notes in a circle and connected them by straight lines, forming a five-pointed star. Inspired by Einstein, Coltrane put physics and geometry at the core of his music.
Physicist and jazz musician Stephon Alexander follows suit, using jazz to answer physics' most vexing questions about the past and future of the universe. Following the great minds that first drew the links between music and physics-a list including Pythagoras, Kepler, Newton, Einstein, and Rakim — The Jazz of Physics reveals that the ancient poetic idea of the "Music of the Spheres," taken seriously, clarifies confounding issues in physics.
The Jazz of Physics will fascinate and inspire anyone interested in the mysteries of our universe, music, and life itself.
Music is the pleasure the human mind experiences from counting without being aware that it is counting.
On a sunny summer day, Ruby Farley—Mum to her grandchildren—sat sternly in her rocking chair, a flowery Caribbean head tie wrapped around her head. Children were playing Wiffle ball outside her Bronx brownstone. With her melodious Trinidadian accent, Mum cried, “Ah don’t care if yuh have to sit down and practice on de piano for hours, yuh not leaving until yuh learn dat song!” Her eight-year-old grandson found it hard to place his fingers correctly on the keys. He was on the verge of tears because the only music he could hear were the joyful sounds of his friends playing outside. Suddenly, Mum’s grimace softened. She smiled and sang to herself, “Ah can see it now, my grandson’s name in lights on Broadway.” Mum had saved her money working as a nurse’s aide in the Bronx for thirty years in hopes of getting me there, but I never became that concert pianist.
Ruby Farley, my father’s mother, grew up in Trinidad in the forties, when Trinidad was a British colony, and moved to New York City in the sixties. There was a dynamic exchange of music between the Caribbean and New York at the time, and Mum carried more music with her than just her Trinidadian accent. When she would return to New York from Trinidad, she would bring records of calypso greats, like the Mighty Sparrow and Lord Kitchener, and it was through those albums that I was exposed to the merging of soul music with calypso indigenous to Trinidad. This “soul of calypso,” or soca music, was a fusion of the East Indian and African cultures. The music was developed in the late sixties and reached its modern form, which included influences of soul, disco, and funk music, in the seventies, when Trinidadian artists were recording in New York City.
To Mum, and many Afro-Caribbeans of her generation, being a musician was one of the few professions that afforded economic and social mobility. Mum’s grand plans for me to study classical music and become a concert pianist began even before my parents and siblings left Trinidad to stay with Mum for a few years when I was eight. It was her way of handing me a ticket to the economic freedom that she and my parents had never tasted. My piano teacher Mrs. Di Dario, an Italian woman in her seventies, was a strict taskmaster. For an average eight-year-old, five years of learning études and memorizing scales with her was arduous, but it was the implicit pressure of the need to succeed that made it oppressive. Still, while I didn’t enjoy the tedium of practicing under Mum’s expectant eye, the classical composers, whose music I was learning to play, hooked my adolescent curiosity. They were able to put the scales together to make music! The idea that so many songs could come from only twelve keys fascinated and absorbed me. As I practiced, I became distracted by thoughts that were shaping into profound questions. How did people come to invent this thing called music? Why was it that when I played a major scale, I felt happy? C, E, and G, all notes in the key of C major, were happy notes. These are the first three notes in the first line of Elvis Presley’s song “I Can’t Help Falling in Love”—“Wise (C) men (G) say (E).” But when my finger climbed down from that white E key to the black E-flat key, that happy sound became sad. Why?
I was more interested in how music worked than learning to play others’ compositions. This intrigue stayed with me throughout my youth and adulthood, but it couldn’t focus my attention on regular practice. Eventually, my melodious Trinidadian grandmother realized that her money wasn’t enough to nurture talent and so put up the white flag, and the piano lessons ended.
At that time I was attending Public School 16 and was in Mrs. Handler’s third-grade class. My handwriting was bad, and my shy and inquisitive nature was interpreted as “slow.” I had a near miss being put in a class for the mentally challenged because teachers doubted what my parents didn’t. But I was spared, and one day found myself on a life-changing field trip. Back in those days, there were programs for public school classes to go to Broadway plays and museums for free. Mrs. Handler’s class got to go see the dinosaurs at the Museum of Natural History. We students walked in a line holding hands through the grand corridors of stuffed creatures, seemingly ready to pounce, sleep, feast, or cry out.
Approaching the main hall, I noticed a smaller corridor to the left. At the back of the line, like a curious cat, both determined and naïve enough to potentially sacrifice one of its nine lives, I took the liberty of sneaking off to see what was there. I found myself alone staring at some papers protected by a thick glass pane. The writing on them was hieroglyphic and clearly handwritten. To my eight-year-old eyes, it didn’t look like it was from this planet. Then I saw the picture of the person behind these puzzles. His wiry hair formed an uncombed white-gray halo. His intensely focused gaze was calm but touched with mischief. I pictured him hunched over a desk, scribbling in code, perhaps humming to himself in satisfaction or grunting in frustration. It was the first time I had seen Albert Einstein and his equations describing his theory of relativity. The magic began.
I didn’t know that those enchanting scribbles described time and space as a single, changeable entity. But I did feel that those moments of contemplation stretched into what felt timeless. My eyes darted back and forth between Einstein’s image and the symbols he had written. I sensed I was like him, and not just because my curly Afro resembled his wild locks, but because I saw a loner who liked to play with symbols and ideas the way I liked to play with musical notes on paper to make my own songs and try to answer my own questions. I wanted to know more. I wanted to figure out what he wrote. Something in me felt that, whatever Einstein was, I wanted to become like him. In those moments, I realized that there was something beyond my reality in Mrs. Handler’s third-grade class, beyond the Bronx, maybe beyond this world, and that it had to do with those enigmatic symbols written down long ago by Albert Einstein, now preserved behind glass.
Fast-forward four years. In the early eighties in the Bronx, most teenagers, including me, were consumed with hip-hop, a music that reflected our experiences and backgrounds. It blended the funk of James Brown and Parliament with the extemporaneous lyrical forms of Caribbean and Latin music. A handful of my neighborhood friends would go on to become successful hip-hop producers and artists. My friend Randy, who later became Vinny Idol, was the most memorable. Randy was a tall, handsome twelve-year-old music fanatic of Jamaican ancestry who lived in a building on my newspaper delivery route. We bonded over our shared love for and understanding of music. I would frequently stop at Randy’s apartment, and he would play me soul music from his record collection. He would often jam on his electric bass to the records. That, I liked. There it was again—that fascination in me to use notes to create, not just reproduce. Improvisation. This was my first true taste of it.
I had a room in the attic of our home that became my “mad scientist” lab—my workshop for experimentation. It was filled with disassembled radios, failed electronic toy projects, and a Marvel comic-book collection. Most every night, before going to sleep, I would play the radio stations that were popular with seventh-graders—98.7 Kiss FM or 107.5 WBLS—but one night, I decided to look for a new station. As I turned the tuning knob, half-hoping to find a new beat to share with my friends, my ears autofocussed onto a sound that, at first, I mistook for the white noise one hears between stations. It wasn’t. After a few seconds, I recognized it as a saxophone. The music initially seemed chaotic and random, but it filled me with a mysterious energy that kept my attention locked on the station. I was spellbound by this sound, and I listened until the song’s completion. The disk jockey came on and said, “You were just hearing the free jazz music of Ornette Coleman.” There it was again. Improvisation.
My father was a big fan of the saxophone and noticed my growing interest in it. He and my mother got me a used vintage alto sax that they purchased at a garage sale from the wife of New York Mets baseball player Tim Teufel. My parents paid fifty dollars for the sax, and despite the few dings and the worn-out lacquer, it played well. I later joined the band at my middle school, John Philip Sousa Junior High School, which Mr. Paul Piteo, a professional jazz trumpeter, led. He showed me how to get notes out of the sax and to make my own reeds. “Finally,” I thought to myself, “I don’t have to practice.” Armed with tools of musical independence, I could play free jazz, like my friend Randy, like Ornette Coleman. I could just improvise. This was fun. This was music to me. Nothing like practicing the piano.
Looking back today, I had no idea how wrong I was. I had fun mimicking and jamming to the popular songs on my portable radio, but there’s no free lunch in free jazz. In traditional jazz, there are well-defined melodic themes and harmonic movements throughout a song. During my early days as a student of jazz, I used to think that playing free jazz meant that anyone can pick up an instrument with no training or practice and improvise meaningfully. As I matured musically and came to understand the rules of harmony and the basic forms in the standard jazz tradition (which I will later discuss), I discovered that free jazz does have its own internal structure and is an extension of the standard jazz tradition. A free jazz musician has very little structure to depend on and is challenged to improvise something that moves the audience. But what is this thing we call music?
Music is deeply human.1 Everyone has different tastes and preferences in music. I have some friends who only listen to electronic music; others think that jazz is the only thing worth listening to. I also know people who believe the only “real” music is classical. There is a growing community of individuals that enjoy noise music. Given the difficulty in finding a definition of music that works for everyone, I am going to restrict our discussion of music to the classical Western tradition. I do this because much of the music discussed in this book is based on the classical Western twelve-tone system. In general, a piece of music can be represented as a complex sound waveform that evolves in time. Contained within this waveform are perceived elements such as tone, meter, rhythm, pitch, melody, and harmony.2
Defining the various elements of Western music is a subtle matter. For the sake of brevity, I will provide a simplified description. Imagine hearing a song that begins with just a piano; that discrete sound is an example of tone or note. A tone can be perceived to have a definite frequency (or pitch) that belongs to a specific musical scale with a finite set of frequencies. A melody is a succession of tones that is usually the main theme in a musical piece. We all have a favorite melody—mine is “My Favorite Things.” Dancers pay special attention to meter, which is the recurring coherent pattern of accents that provide the pulse or beat and is important in developing the song’s rhythm. Beats in a meter are grouped in bars. For example, the meter in the waltz will have beats in groups of three for each bar, while a techno beat will have four recurring beats. Harmony involves the consonant or dissonant relationship between notes played simultaneously, and these chords create a movement between musical tension and release.
Music is a physical event, and like most nontrivial physical systems, it has structure or, as musicians call it, form. Just as the skeleton determines the shape of an animal, the musical form provides the scaffold for melody, rhythm, and harmony to unfold in a coherent manner. In many cases, at the beginning of a composition, a motif or theme is initiated. We see this in a lot of classical and baroque music. One of the most famous motifs is the first four notes in Beethoven’s Fifth Symphony: ta ta ta taaaa. This motif can be tied together into a phrase, which is the musical equivalent of a sentence, a grouping of notes with a coherent musical sense.
Phrases can fit into a given chord, or key. In many popular forms of music, the chords will change and eventually return back to the home chord. Many songs begin with a home key and take a journey deviating away from that key with a return to the home key, usually designated by the Roman numeral I. A typical chord movement in most Western music is the II-V-I progression. In the key of C, this corresponds to D-G-C. One of my favorite II-V-I songs is Cole Porter’s “Night and Day,” made popular by Frank Sinatra. Another common music form is the blues, which uses twelve bars that move from I–IV with a few repetitions and an eventual return to I. Listen to any B.B. King song and you can hear how this progression functions.
These forms create a progression: tensions and resolutions are created, tapping into human feeling and the aspect of storytelling. Our description of music started with a single note, then chords, phrases, rhythms, and forms—a complex structure that started with a wave and its characteristic wavelength and frequency. All of this opens the doors to human emotion and creativity—using notes to express the personal and connect the self to nature. It emerges almost as if by magic. Indeed, music is deeply human.
Although most popular songs from rock, pop, and jazz are based on straightforward forms like that in Figure 1.1, modern composers, such as György Ligetti, based some of their compositional structures on more intricate self-similar forms like fractals. In these forms, the smaller piece mirrors the form of the larger structure. Many structures in nature, such as snowflakes, leaves, and coastlines, have fractal properties.3 Research has found a fractal structure in some of Bach’s compositions.4 Fractal structures in music occurs when shorter musical lines are mirrored in longer musical passages.
For me, playing my sax was like playing basketball. I did it for fun. It was a hobby, a passion of the times. But lurking somewhere in the depths of myself was that tickle to know more, not just about how to create music but also about its greater origins, its link to our emotions, how to get that something called “music” from “notes.” What were “notes” anyway? What I hadn’t realized yet is that science would help give me those answers. Science would become my true passion.
John Philip Sousa Junior High was situated in the Edenwald Projects, off Baychester Avenue. A few years before I matriculated to Sousa, it was rated as one of the most crime-ridden and dangerous middle schools in the country. That was until Dr. Hill Brindle came on board. Brindle, as we called him, was a towering militant and possessed an articulate baritone voice. His fatherly presence evoked a mixture of admiration, respect, and fear in both the students of the school and the thugs that lurked in the neighborhood. Sousa was a public school, but Brindle ran it like a military private school. As a student at West Point military academy, Brindle had been an Olympic hopeful for the 400-meter dash. But while training on the track one day, Brindle was shot in his thigh by an unknown gunman, destroying his Olympic dreams. His energies needed a new focus, so maybe that was the reason why he later joined Dr. Martin Luther King’s civil rights movement and ended up devoting himself to the education of inner-city students. Every morning at Sousa, Brindle and his deans would be at the school’s two entrances to check that every individual came in with his or her notebook and textbooks. And every Wednesday, Brindle himself delivered a gospel-like speech to the entire school, all students expected in semiformal attire.
During one significant and fortuitous Wednesday morning assembly, Brindle, composed as ever, informed us that we had a special guest, and then exited the stage. I was in eighth grade, and I have never forgotten that day. An older man in an orange jumpsuit with a boom box on his shoulder appeared from behind the stage’s curtains. A well-known hip-hop beat was thumping out of the radio. Some students started laughing as if the man were a clown; others were confused. But most enthusiastically bobbed their heads to the music. The guy certainly got our attention. Then he shut off the music and introduced himself. He was Fredrick Gregory, an African American astronaut. Gregory, speaking with his native Washington, DC, accent, asked, “How many y’all liked that beat? Wasn’t it cool?” The students cheered, smiles on their faces. “Yeah . . . that beat was cool!” he said. The assembly had become a party. Then the astronaut asked, “But do you know how this radio was able to make this music?” He continued, “It’s powerful to own a radio and hear this music, but true power is in the ability to make one of these radios. Knowing how this radio works helped me to become an astronaut. I studied science. I went to college and I got an engineering degree.” It was a powerful message. He had come to the school, to us, and to make it clear why science was important. And he was like us, culturally, socially, economically, geographically. He put it simply. “I’m from the same background as y’all, and if I could do it, so can you!” Science. It wasn’t the first time I had thought about studying science. But this was different.
However, I didn’t begin my journey in science to become a physicist, describing the physics of music or unraveling Einstein’s equations; I wanted to become a roboticist. Next to my radio, my secondhand sax, and all my cluttered bedroom experiments sat my stack of Marvel comics. Tony Stark, the comic-book superhero who built his own Iron Man suit, was a huge inspiration. After that school assembly, although I kept playing my sax in the middle-school jazz band, my main fascination became science.
One day shortly before graduation, Mr. Piteo pulled me aside and said, “Son, you are one of the two most talented music students I ever had. The other guy is the director of the Apollo Theater band. I can get you into the High School of Performing Arts. No problem.” Being able to attend the top music high school in New York City was a tremendous opportunity and would have made Mum proud. But I never told her about it because I had other ideas. I was on the science path and chose to attend DeWitt Clinton High School.
My first day at DeWitt Clinton, which had around six thousand students, threw me. I was sitting in my English class, discussing Hamlet, when the class was disturbed by the sounds of young men rhyming with each other. Outside the classroom windows, a sea of Latino students were playing handball, break dancing, and engaging in “free-style battle rap.” This was an improvisational form of rhyming with rhythmic complexity, and battle rappers would compete with each other while being judged by enthusiastic onlookers. Miss Bambrick, our jolly Irish Shakespearian teacher, interrupted our lesson with an enthusiastic “Now that’s mastery of the English language!”
Life took a turn. I would cut the classes I found boring and take the bus to the basketball courts. It was on the courts that we would both play pickup ball, taking breaks to rap and break-dance on flattened refrigerator cardboard boxes. On the bus, I was joined by others from my high school, who were also cutting class. I would overhear the discussions of some guys who called themselves Five Percenters. They’d debate about humanoid-like aliens that came from space to interact with “the original Asiatic black man.” No joke. I overheard tidbits of other sci-fitopics and realized they really believed them! My high school was one of the meccas of the Five Percenter Nation, and no one messed with them. Those guys were far from feeble and seldom smiled. I thought of the Five Percenters as another gang, but I turned out to be wrong about that. They were highly disciplined and committed to their spiritual and independent intellectual studies, and we had something in common—and it wasn’t just that we were cutting class and toying with “science.” A common practice for Five Percenters was “dropping knowledge,” which is similar to an intellectual debate, sometimes in the form of battle rapping. We both wanted an escape from the dismal prospect the future held for us. I sought my escape through comic books, video games, and my newfound love for science. These guys adopted a worldview from their leader Clarence 13X, a former student of Malcolm X, who, after attaining spiritual enlightenment, spread the following gospel throughout the streets of New York City:
• 85 percent of the masses blindly follow religion.
• 10 percent of the masses are deliberately misleading the masses.
• 5 percent are enlightened and realize that they are “gods” of their own destiny.
• Mathematics is the language of reality, and in order to master nature, a Five Percenter must understand the mathematical patterns underlying nature: they called this supreme mathematics.
The Five Percenters were the 5 percent. So when the “gods” saw me repeatedly on the bus by myself, quietly playing with equations I was learning from my mathematics teacher, Mr. Daniel Feder, they would try to engage me in their debates about alien life-forms that had communicated with the original Asiatic black man. Eventually, they invited me to join them. Granted, I was fascinated with their speculations, but I refrained and proceeded with my precalculus homework. Although I never joined the Five Percenters, they admired and protected me from the thugs that often preyed on the weak or nerdy. And I admired them, because MC Rakim, a devout Five Percenter, had just released a debut album, Eric B is President, that had taken New York City and the world by storm. Rakim was, and still is, my favorite MC, and unlike today’s hip-hop, his lyrics promoted self-knowledge and he approached his improvisational delivery like a scientist. Rakim has gone down in history as the greatest battle rapper because of his ingenious improvisational capabilities and the unique polyrhthmic cadence of his rap delivery. I sometimes like to think that the great mathematician Leibniz prophesied Rakim with his quote “music is the pleasure the human mind experiences from counting without being aware that it is counting.” Rakim equates his rhymes to “dropping science.” His hit song, “My Melody,” went something like:
That’s what I’m sayin’, I drop science like a scientist.
My melody’s a code, the very next episode.
Has the mic often distortin’, ready to explode.
I keep the mic at Fahrenheit; freeze MCs to make ’em colder.
The Listener’s system is kickin’ like solar . . .
I had my first physics class a year later when I was a sophomore. I was anxious. I wasn’t alone. All the nerds who sat in the front of the room were also scared. A thin bespectacled man with a wild head of hair walked into the room and wrote a simple equation on the blackboard. Three characters and an equal sign: F = ma. Force equals mass times acceleration. An object will accelerate when an external force is applied to it. The more mass an object has the harder it is to accelerate with the same external force. We had never seen such an equation. Mr. Kaplan walked into the middle of the room, sat on an empty desk, and took a tennis ball out of his pocket. He threw the ball up in the air and caught it. He saw everyone was so attentive that he didn’t have to do it again and, after a moment, asked, “What’s the velocity of the ball when it returned back to my hand?” The class sat silent. No one knew what to say. And in that minute or two, magic began to happen. I pictured that tennis ball going up, coming to rest in the air above our heads, and landing again in Kaplan’s hands. Again I saw it happen. And again. I became that ball. My hands trembled, and perhaps, somehow, my eyes deceived me. Kaplan honed in on me.
“What’s your name?” he asked.
“Stephon,” I said.
“So Stephon, what do you think?”
And to my amazement afterward, the words just spilled out: “The ball will have the same velocity as it did when it left your hand.”
Kaplan had a big smile on his face “That’s exactly the answer! This is a sacred principle of nature called the conservation of energy.”
- "I'll forever be grateful to musician/physicist Stephon Alexander.... He'll help you see how our awe-inspiring universe is on a never-ending, cosmological riff."—Felix Contreras, NPR, "Best Books of 2016"
- "Interwoven with solid physics and personal anecdotes, the book does an admirable job of bringing together modern jazz and modern physics."—Physics World, Shortlisted for "Book of the Year (2016)"
- "Marvelous."—New Scientist
- "[Alexander] gives an engaging account of his uncertainties and worries as he made his way in the highly competitive world of theoretical physics, seeking to acquire the 'chops' needed to deal with the formidable mathematics of his day job along with those needed to solo on the sax after dark.... Mr. Alexander's rhapsodic excitement is infectious."—Peter Pesic, Wall Street Journal
- "In the most engaging chapters of this book -- part memoir, part history of science, part physics popularization and part jazz lesson -- Dr. Alexander ventures far out onto the cutting edge of modern cosmology, presenting a compelling case for vibration and resonance being at the heart of the physical structure we find around us, from the smallest particle of matter to the largest clusters of galaxies.... His report on the state of research into the structure and history of the universe -- his own academic field -- makes for compelling reading, as does his life story."—Dan Tepfer, New York Times
- "The book's attempt to bring together modern jazz and modern physics strikes me as admirable.... It is an intriguing comparison, and it certainly seems fresher than drawing analogies between classical music and classical physics.... Time to put on some Coltrane and riff some new research ideas?—Trevor Cox, Physics World
- "Groundbreaking.... [Alexander] illustrates his points with colorful examples, ranging from the Big Bang to the eye of a galactic hurricane."—Down Beat
- On Sale
- Apr 26, 2016
- Page Count
- 272 pages
- Basic Books