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The 'music of the spheres' was born from the effort to use numbers to explain the universe:

If you've ever heard the phrase "the music of the spheres," your first thought probably wasn't about mathematics.

But in its historical origin, the music of the spheres actually was all about math. In fact, that phrase represents a watershed in the history of math's relationship with science.

In its earliest forms, as practiced in ancient Egypt and Mesopotamia, math was mainly a practical tool for facilitating human interactions. Math was important for calculating the area of a farmer's field, for keeping track of workers' wages, for specifying the right amount of ingredients when making bread or beer. Nobody used math to investigate the nature of physical reality.

Not until ancient Greek philosophers began to seek scientific explanations for natural phenomena (without recourse to myths) did anybody bother to wonder how math would help. And the first of those Greeks to seriously put math to use for that purpose was the mysterious religious cult leader Pythagoras of Samos.

It was Pythagoras who turned math from a mere tool for practical purposes into the key to unlocking the mysteries of the universe. As the historian Geoffrey Lloyd noted, "The Pythagoreans were ... the first theorists to have attempted deliberately to give the knowledge of nature a quantitative, mathematical foundation."

[...] Pythagoras believed that, at its root, reality was made from numbers. That sounds crazy to modern minds taught that matter is made of atoms and molecules. But in ancient times, nobody really knew anything about what reality is. Every major philosopher had a favorite idea for what sort of substance served as reality's foundation.

[...] Specifically, Pythagoras identified the root of reality in what he called the tetractys, consisting of the first four integers: 1, 2, 3 and 4. Added together, those numbers equal 10. Ten, Pythagoras concluded, is the "perfect" number, the number that holds the key to understanding nature.

And why 1, 2, 3 and 4? Because those numbers were the key to creating harmonious sounds.

[...] The Pythagoreans surmised that the motions of the heavenly bodies generated pleasant music. As Aristotle later explained it, those bodies move rapidly and therefore they must make sound, because anything moving quickly on Earth makes sound (think arrows whizzing through the air). Proper ratios of the planets' speeds (which depended on their distances from the central fire) guaranteed that the sounds would be harmonious. Hence the moving planets created a "harmony of the heavens." Because later Greek writers supposed that each planet is carried on its orbit by a rotating sphere, eventually that harmony became known as "the music of the spheres."

[...] Using math for understanding nature was unknown before Pythagoras. It was his idea. Previously math had been a tool for scribes or surveyors or cooks. "Pythagoras freed mathematics from these practical applications," the Dutch mathematician B.L. van der Waerden wrote in his classic history of ancient math. "The Pythagoreans pursued mathematics as a kind of religious contemplation, as a way to approach the eternal Truth."

As for the music of the spheres, one issue remained. If the heavens made harmonious sounds, why didn't anybody hear them? Aristotle reported that the Pythagoreans "explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence."

Aristotle rejected that explanation, just as he rejected the idea of a "counter-Earth" as well as the whole notion that everything was made from numbers. And yet, the importance of numbers in science, first expressed by Pythagoras, ultimately proved to be much more resilient than most of Aristotle's ideas. As experts on early Greek philosophy André Laks and Glenn Most have written, "Of all the early Greek philosophers," Pythagoras "without a doubt exerted the longest-lasting influence until the beginning of modern times."

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