The mathematics of music
Full STEAM ahead.
The divide between USyd arts and STEM students is both literal and metaphorical. Engo grill and PNR Hub, the cornerstones of the engineering faculty, lie far away from the light-filled, wooden interiors of Courtyard. The metaphorical divide, however, manifests itself as a subtle, simmering contempt, grounded in stereotypes. Science and engineering students bemoan the relative freedom and relaxation of arts students while dragging their feet to 20+ contact hours a week. Arts students bemoan the starting salaries of chemical engineers.
But this divide is a superficial one. Arts and sciences are just two fields of study, each hoping to accomplish the same simple thing with differing methodologies: to understand the mechanisms of the world. Arts and the humanities do this by interrogating culture, using language. Science does this by modelling the world, using mathematics. Jupiter, then, is a gaseous giant and also a mythological giant. Metaphysics and physics parallel each other in thought, if not in practice. And both reveal facets of the same phenomena.
Richard Feynman, one of the most famous theoretical physicists of the 20th century, once said that “if we look in a glass of wine closely enough we see the entire universe”. He describes the physics it revealed—the fluid mechanics of the liquid, the reflections in the wine. It revealed geology, for glass is from the earth, and its materials can be traced back to their formations in the cores of stars. It revealed chemistry in the fermentation of the wine. Hence all there is to know about the universe is in this humble glass.
It is easy to see STEM, with its mathematical symbolism and inscrutable proofs as cold, technical, and removed from the everyday. But to view it in this way is to ignore the romance of the extra dimension it adds to the everyday, to glasses of wine, to arts and the humanities.
Music, for example, is a human creation that relies heavily on emotion, and subjective preferences concerning sonic aesthetics. And yet underlying music is physics and mathematics. Sound is perceived when vibrations in the air, themselves initiated by a string vibrating from a struck guitar chord or air blown through a series of tubes, propagates to your eardrums as waves, causing them to vibrate similarly. This then sends signals to your brain that allow you to perceive sound. The frequency (rate of vibration) affects pitch and the amplitude (how much it vibrates) affects loudness. Notes all have unique frequencies: an E’s frequency, and therefore pitch, is higher than a C’s. C and E are separated by four semitones and when played together make a major third, a chord known for its ‘happy’ sound. Meanwhile, C and E flat are separated by three semitones, and as a minor third, together make a ‘sad’ sound. This difference of one semitone has implications—physical distinctions in the properties of soundwaves and their relations with each other trigger a subjective, emotional response.
Mathematics is hidden not just in our aesthetic sensibilities, but the very ways in which evolution has progressed. The fibonacci sequence, 1 1 2 3 5 8 13 21…, is formed by simply adding the previous two numbers for the next number in the sequence, a mathematical concept reflected in plant growth, for instance. Flowers often have a number of petals corresponding to numbers on the fibonacci sequence, and this extends to the number of leaves on plants, the number of spirals on the inside of a sunflower, a pineapple, a pinecone. To appreciate the beauty of a flower is to appreciate its mathematical origins, the patterns that shape nature itself.
And yet not only are there mathematical underpinnings to beauty—there are beautiful, romantic implications of mathematics and science itself. Chaos theory explicates the randomness of the world, and how wildly divergent outcomes can arise from one system, giving rise to the idiom of The Butterfly Effect (and its terrible film counterpart). This leads to the second law of thermodynamics: entropy can never decrease, and hence our world must always tend towards disorder. This terrifying certainty, hidden in functions of energy and temperature, offers startling insight into our contemporary political climate. Perhaps a bit less pessimistic is the concept of quantum entanglement: two quantum particles, once entangled, will both exist in a state of superposition until one is disturbed—the other particle, no matter how far, will immediately respond to this disturbance. Quantum entanglement is the only example of faster-than-light information transfer we have witnessed, and hints at some esoteric, romantic reading of intrinsic connection, bridging insurmountable gaps and distances.
Science and mathematics reveal a world that is weird, uncertain, and inextricably tied to the ways in which we live and experience our environment. Learning science does not remove one from the world—it adds to one’s understanding of it. Any perceived coldness or technicality results from forgetting to augment our study of science with the arts, with humanities, with philosophy and politics, literature and language, and music.
That this is lost in the way we think about and approach science is not surprising given its relationship with the development of technology and related industrial pressures. Darwin’s theory of evolution came as a result of imperialist expansion. Nuclear energy was a result of the Manhattan project that saw the destruction of Hiroshima and Nagasaki. Therefore not only should science and philosophy be considered together—they have to be.
The value of STEM and arts cannot be divided by the vocational value they offer late capitalism and its drive for production. The value of either increases when combined with the other. Commercialism has shrouded the beauty, the romance in the mathematics of music, the universe in a glass of wine. Perhaps it is best to follow Feynman’s concluding advice: “let us give one more final pleasure: drink it and forget it all!”