Early Speculation: The Cult of Pythagoras

Sources

Man and Myth . The life and views of Pythagoras are hard to reconstruct, since the man himself inspired a cult and became quickly shrouded in legends spun by his disciples. According to Empedocles, who was strongly influenced by his thinking, Pythagoras “stretched his mind and easily saw each and every thing in ten or twenty generations.” His followers were concentrated in the southern Italian town of Croton and remained active as a group from approximately the year 530 through the fourth century b.c.e. In general, they tended to divide themselves into mystics on the one hand and mathematicians on the other. The main concern is with the latter group, though both shared the same premise that the essence of all things could be expressed in numbers.

Structure and Form . The chief proof for this claim that reality is numerical was their observation of the simple ratios that underlie harmony in musical scales—that of the octave (1:2), for instance, in which a string divided in half vibrates twice as fast to produce the same note in a higher register. The fact that some phenomena exhibit a numerical orderliness suggested to the Pythagoreans that the universe as a whole might have a quantitative, mathematical basis. At its best, this theory marked an important shift away from how the Milesians approached nature, since their primary aim seems to have been to isolate the physical material of the world. For this reason, the Milesians are generally identified as materialists. For the Pythagoreans, on the other hand, the search for truth pointed not in the direction of matter but instead of structure and form. Numbers and ratios expressed in numbers were the keys to understanding the essence of reality. The influence of this belief on both the direction and also the language of all later Western science is obvious.

Listeners . At its worst, however, the same insights also tended to promote a kind of mystical speculation among the Pythagoreans. For some of them, especially those who belonged to the mystical group called the Akousmatikol (“Listeners”), numbers had the status of quasidivine objects of worship. The Listeners, that is to say, went far beyond strict, mathematical research and sought to discover numbers beneath all aspects of experience. They assigned numerical values not just to objective relations but also to things and

qualities. The number 3, for instance, was identified as male; 2 as female; and 5 as marriage.

The Universe . The Pythagoreans generalized their discovery of ratios in music into a view of the whole universe itself as “a musical scale and a number.” This theory is the source of the famous idea of the “music of the spheres,” according to which the moon, sun, planets, and stars were believed to produce different musical notes as they spin through space. To the mind trained to hear them, these notes all blend together into perfect harmony. Here it is easy to see how the same point of departure could produce both pure mathematics and a kind of mysticism. Contemplation of the music of the spheres is simultaneously a scientific and a spiritual act.

Astronomy and Geometry . Empirical investigation and experimentation among the Pythagoreans were more consistent than in the case of the Milesian phusiologoi. A great deal of Pythagorean attention was in fact directed to astronomy, in attempts to calculate the relative distances and sizes of the heavenly bodies and to provide accounts of both lunar and solar eclipses. The group was especially noted for its research on acoustics, through the measurement of lengths of vibrating strings and columns of air. They have been credited with classifying numbers into odd and even. Geometry, the science of solid numbers, was also a central part of their work. The proof that bears their name—the Pythagorean theorem (the square of the hypotenuse of a right triangle equals the sum of squares of the other two sides [a² + b² = c²])—seems to date from the late fourth century b.c.e. Its truth was in fact an old one, known even to the ancient Babylonians as many as five hundred years earlier; what the Greeks did was to provide a conclusive demonstration.

Impact . The major and abiding contribution of the Pythagorean group is what could be called its arithmetization of the world, its view of reality as somehow numerical. Even if it tended to become entangled in mystical beliefs, their basic insight—that the science of numbers is fundamental to every science of nature—had profound influence. Reality is viewed as orderly, regular, mathematical, and easily accessible to rational minds. Nature indeed is number, at least in the sense that mathematics provides the most objective way of talking about natural events. At the same time, Pythagorean work on geometric problems also helped to further hone a scientific language of theorem, evidence, and proof.

Sources

Walter Burkert, Lore and Science in Ancient Pythagoreanism (Cambridge, Mass.: Harvard University Press, 1972).

Cornelia J. de Vogel, Pythagoras and Early Pythagoreanism: An Interpretation of Neglected Evidence of the Philosopher Pythagoras (Assen, Netherlands: Van Gorcum, 1966).