“Mathematics and music! The most glaring possible opposites of human thought! And yet connected, mutually sustained!” Thus enthused German scientist Hermann von Helmholtz in an 1857 essay on harmony in music.
Today, mathematicians, ecologists and physicists search for harmony alongside musicians, if not always explicitly. But the link used to be even stronger.
A typical academic curriculum circa 1600 — and for centuries before — blended music and (what we would call) science to a degree rarely seen in today’s undergraduate syllabi. The four subjects of the ‘quadrivium’ were arithmetic, geometry, astronomy and music.
Today’s scientific training programmes tend to leave music out. They have changed in other ways too, of course, and for the better. Although some universities offer degrees in mathematics and music, or physics and music, modern scientists more often miss the chance to seek musical connections.
“Many people think music is a charming accompaniment to thought,” says musician and scientist Peter Pesic of St John’s College in Santa Fe, New Mexico, in the latest episode of Nature’s sound-science podcast, Audiofile (go.nature.com/xhluk3). “But developments in music,” he notes, “influence other aspects of human thought.”
The podcast — one of a series — contains plenty of musical stories from the history of science. Take the astronomer Johannes Kepler, who was preoccupied with the motions of the planets. He was desperate to find harmony that he felt sure existed in the way the Universe was set up. In 1619, he produced a giant volume called Harmonices Mundi, or The Harmony of the World. In one particularly musical moment, he expresses planetary motions in musical notation — the orbits of Mercury, Venus and their neighbours spun out into crotchets and quavers. You can hear the resulting song on the podcast. Without such explicitly musical thinking, it is possible that Kepler may never have arrived at his third law of planetary motion — the relationship between a planet’s distance from the Sun and the time it takes to orbit.
Then there is the tantalizing suggestion that Galileo Galilei’s musical father might have influenced the way his son thought about science. In the late 1580s, Vincenzo Galilei carried out an experiment on the sounds made by strings held at different tensions. Vincenzo’s home-made experiments could well have instilled in his son the idea of looking at a physical system to produce a hypothesis, rather than retrofitting the one to the other.
Musical analogies continue to help scientists to make sense of tricky concepts. String theorists speak of tiny vibrating strings instead of point-like particles. The comparison with stringed instruments is easy to see; the strings represent elementary particles in the same way that the strings on a guitar make different notes.
Musical inspiration can often remain buried under the surface of scientific work; there might not seem to be an immediate harmony between, say, a genome-wide association study and one of Erik Satie’s études. But if music remains apart from the sciences, there is much we might lose. Anecdotally, neuroscientists talk of musical theory aiding the analysis of brain patterns. And a theory of strings is more intelligible to some than a theory of tiny, massless, vibrating subatomic squiggles.
Looking too hard for harmony might be misleading if the real picture turns out to be more discordant. But, as explained in the podcast by Jim Bennett, emeritus director of the Museum of the History of Science in Oxford, UK, music has already provided a great template for interpreting our surroundings: “The insight, which plausibly came from music, that the world has a mathematical blueprint is fundamental to science.”
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