THE PYTHAGOREANS

Pythagoras, founder of the Pythagorean School, was born at Samos about 570 B.C. His life is surrounded by legend. Many voyages -- one of them to Egypt -- are attributed to him. It is certain that at about the age of forty years he came to Italy in Magna Graecia, and in Croton, the Doric colony, founded a school with scientific, religious, and political leanings.

To this school were admitted youths of both sexes of the high aristocracy who were divided into various sections according to the grade of initiation to learning. The political aims of the school raised up much opposition, and in a popular uprising in 497 the school was given to the flames. Pythagoras seems to have removed himself to Metapontum before this uprising and died there either in the same or the following year. Pythagoras left no writings, and the doctrine which is known under his name must be attributed to him and to his disciples, especially to Philolaus, who lived until the time of Socrates.

The Pythagoreans cultivated the mathematical sciences and the study of mathematics led them to the observation that everything could be represented through a number. The number appears not as an abstraction, but as a real being, the generator of all things: they concluded that the number should be retained as the essence, the principle of reality.

This passing from the abstract order of number to the actual order of being today seems simple-minded and silly. It was not, however, so considered by the Pythagoreans, for they were the first to observe that number applied not only to the motions of the heavens and the succession of time, but also to the harmony of sounds (the height of the sound is in inverse proportion to the length of the string). It was easy for the cultivators of mathematics to bow down before the number and consider it as a divine reality.

Through a long theory on numbers the Pythagoreans attempted to explain the multiple and the notion of becoming. Numbers are divided into even and odd; the even numbers unlimited, the odd ones limited. Since everything is a number, the constitutive elements of things are the evens and the odds, the unlimited and the limited, the worse and the better. This radical opposition would give the explanation of all the world of multiplicity, even its moral aspects: justice is represented by the square (even multiplied by even); love, friendship, because they indicate perfect harmony, were identified with the number eight; health with the number seven.

Even and odd number originated from the "One." It is from the One that all the other numbers, which are the constitutives of multiplicity, proceed. Multiplicity hence is reduced to unity, and it is in unity that all differences and contrasts are annulled, and the harmony of the multiple ends in silence.

The perfect and sacred number for the Pythagoreans is ten, which results from the principal combinations: 1, 2, 3, 4 -- these are identified as the point, line, surface and volume, and when added, they result in the number ten. For the Pythagoreans there are ten heavens. To make up this number, they add to the traditional nine a tenth, which they call "antiterra." The heavens all revolve around one central point which is called "Fire."

For the Pythagoreans the soul is harmony. Descended to earth through some mysterious fault (Orphic-Dionysian doctrine), it passed through various bodies (even those of animals) by successive births (metempsychosis) to reestablish primitive harmony and to return to the place where it lived in happiness.

Pythagoreanism indicates progress over the Ionic School. It is elevated from a natural element found in the Ionic School to a conceptual one, such as number. The Pythagoreans also affirmed the sphericity of the earth and of the other heavenly bodies, and the revolution of the heavenly bodies around a central Fire. The concept of the soul and of its purification induced the Pythagoreans to ascetical practices although, of course, these were not shorn of superstitions.