Pythagoras

Pythagoras of Samos

Pythagoras is remembered for a theorem about triangles, but his real discovery was vaster and far stranger: that reality itself is made of number, that the cosmos is an ordered harmony that can be written in mathematics, and that the soul is immortal and reborn through many lives. He founded a brotherhood, a discipline, and an idea, that the world is at bottom mathematical, which runs down to the foundation of all modern science. To meet him only as the name on a theorem is to miss almost everything.

The corpus, and how the chat handles it. Pythagoras wrote nothing, and his life is half legend; what we know comes from later reports, above all from Aristotle's account of "the Pythagoreans" and from the biographies written centuries afterward. This room reads one of those, Iamblichus's Life of Pythagoras in Thomas Taylor's translation, public domain by way of the Internet Archive, as a window onto the tradition. Like the rooms for other figures who left no books, it runs on doxography, the reports of others, and it is careful to mark the line between the man and the school that bore his name. Expect citations to Iamblichus's Life of Pythagoras and to the reports of the Pythagoreans.

Life and the brotherhood. Pythagoras was born around 570 BC on the island of Samos, off the coast of Asia Minor, and (so the tradition says) traveled to Egypt and Babylon to gather their wisdom before settling at Croton in southern Italy. There he founded a community that was at once a philosophical school, a religious order, and a political society. Its members lived by strict rule, held their property in common, kept silence and secrecy, followed careful restrictions on what they ate, and pursued mathematics, music, and the purification of the soul as a single way of life. The Pythagorean brotherhood was among the first attempts in the West to make philosophy not a set of opinions but the whole shape of a life.

Where to begin. Read Iamblichus's Life of Pythagoras and the Golden Verses for the tradition's own portrait of the master; Aristotle's reports in the Metaphysics for the philosophy as the Greeks received it; and Plato, above all the Timaeus and the Phaedo, for the doctrines reborn in a greater mind.

All is number. The central doctrine is that the principles of all things are numbers. Struck by the discovery that everything orderly and intelligible, the turning seasons, the musical scale, the wheeling heavens, can be expressed in numerical ratios, the Pythagoreans concluded that number is not merely a tool for measuring reality but its very stuff and structure; things are numbers, or imitate them, and the whole cosmos is a harmony and a number. It is the first appearance in the West of the conviction that the book of nature is written in mathematics, the faith on which all later mathematical science is built.

The harmony of the world. The doctrine grew from a discovery about music. The Pythagoreans found that the concords most pleasing to the ear, the octave, the fifth, the fourth, answer to simple whole-number ratios of the lengths of a string, two to one, three to two, four to three; harmony, the most moving of things, turned out to be number made audible. From this they drew their grandest vision, that the heavenly bodies, swinging through their ordered courses, sound a music of the spheres, a cosmic harmony we fail to hear only because it has sounded in our ears since birth. The universe is a tuned instrument, and to study mathematics is to learn its song.

The immortal soul and the wheel of birth. As important as the mathematics is the religion. Pythagoras taught that the soul is immortal and passes, when one body is done, into another, human or animal, through a long round of rebirths, the transmigration of souls. Because all living things share in soul and are therefore kin, he forbade the killing and eating of animals. The aim of the Pythagorean life was to purify the soul, by justice and by music, by the contemplation of number and harmony, and so to win release from the wheel of birth and return at last to the divine. The care and cleansing of the soul is the deepest of all Pythagorean disciplines.

Limit, harmony, and the order of the cosmos. Behind it lies a metaphysics. The Pythagoreans saw reality as the imposition of limit upon the unlimited, order and form and number arising wherever bound is set to the boundless. They drew up a table of opposites, limit and unlimited, odd and even, one and many, and revered the tetractys, the triangle of the first four numbers that sum to ten, as the source of all things. Pythagoras is even credited with coining the word kosmos, the ordered and beautiful whole, for the universe, and philosophia, the love of wisdom, for the life he led. To see the world as ordered, harmonious, and intelligible is his permanent bequest.

Against the triangle-only caricature. To know Pythagoras only by his theorem is to keep the fragment and lose the vision. His was the first picture of a mathematical universe, the first union of exact science with the care of the soul, the first attempt to live philosophy as a discipline of purification. The Pythagorean sciences, the tradition says, are the disciplines that invigorate the eye of the soul and purify the intellect from the blindness of lesser studies, so that it may see what truly is. The theorem is a corner of that far larger conviction, that number is the key to the cosmos and that the study of it raises the soul toward the divine.

Reception, and adjacent reading. No early thinker shaped the Western tradition more deeply. Read now, Pythagoras is the founder of the idea that reality is mathematical and of philosophy as a way of life, the figure in whom number, music, cosmology, and the soul first became a single study. His doctrine of the immortal, transmigrating soul and his mathematical mysticism passed above all to Plato, whose Forms, whose mathematical cosmos in the Timaeus, and whose immortal soul in the Phaedo are unthinkable without him; the transmigration and the purifying of the soul reappear in Empedocles; he taught in the same southern-Italian world that produced the One of Parmenides; his number-mysticism was carried forward by the Neoplatonism of Plotinus; and even Heraclitus, who mocked his much-learning, measured himself against him. The dream that the world is number has never stopped driving both science and wonder.