Figuring

by Maria Popova

Alongside his mathematics, Pythagoras coined the word philosopher to describe himself as a “lover of wisdom” and invented a whole symbolic language of mysticism. His progressive views on social reform led him to flee the tyrannical rule of his native Samos. When he settled in the Greek colony of Croton, he founded a philosophical school whose sect of disciples, known as the Pythagoreans, originated a novel conception of the universe—they placed at its center a ball of fire more than a millennium before Copernicus proffered his heliocentric model. In fact, in his letter to the Pope, Copernicus cited the Pythagoreans as his inspiration for upending the Ptolemaic system. In another highly unusual model for their time, the Pythagoreans admitted women. One of them, Hypatia of Alexandria, became the world’s first known woman astronomer, predating Caroline Herschel by fourteen centuries. A millennium and a half before Kepler’s Harmonices Mundi, Pythagoras discovered the relationship between musical harmony and the mathematical harmony of numbers. In his day, the most widespread musical instrument was the tetracord—the Hellenic four-string lyre. Musicians had no standardized system of tuning their instruments and only an intuitive sense of how to produce harmonious melodies rather than discord, with no understanding of the underlying tonal patterns. According to the fourth-century Syrian scholar Iamblichus, who became Pythagoras’s foremost biographer, Pythagoras took it upon himse...