The Historians' History of the World 04

Here we have the germ of the speculations of Pythagoras, on which, as is well known, the laws of Copernicus and Kepler are founded. The vein of poetry in the Ionian character is manifest not only in this intuitive perception but in the aptness of his imagery, when he calls these spheres “chariot-wheels,” from the rim of which the fiery flames of the sun, moon, etc., start out like felloes. The scientific element in his system is evident in the manner in which he follows out biologically the idea of Thales concerning water. If all things have at one time been water, then organisms cannot originally have been created as land animals. Hence man, who now comes into the world utterly helpless, has been gradually evolved from pisciform creatures—the first germ of Darwinism.

Lastly the pessimistic mysticism which had lately arisen is clearly manifest in him. When he regards the origin of all individual existences as a wrong committed by them in separating themselves from the All-One, we can only understand him by referring to Orphic religious ideas, in which birth is looked upon as a decline and fall from the blissful seats of the gods and earthly life is represented as a vale of misery. Death is consequently the penalty which the individual pays for his presumption, whether the individual be a man or a celestial body. For the earth and all other Cosmoi are doomed to extinction in an “Infinite” which corresponds to the ancient idea of Chaos, and, like that, is not conceived of as a vacuum but as matter in an undefined form. This alternation of creation and annihilation, this perpetual motion, anticipates the eternal flux of Heraclitus of Ephesus, who at the end of the sixth century and the beginning of the fifth, transformed the teaching of Anaximander into keener dialectics.

In comparison with this Ephesian thinker the successors of Anaximander at Miletus and whatsoever following they had down to the end of the fifth century sink into total obscurity. Before turning our attention to Heraclitus, however, we must first consider the man who transplanted the Ionic Historia from Ionia to Italy and there elaborated both the scientific and mystic side of it with marvellous assiduity—that is, Pythagoras.

Pythagoras left Samos about the year 530, and turned his steps towards Croton in lower Italy, where he found virgin soil for his labours. The mathematical foundation upon which the Ionic school is based attains an excessive predominance with Pythagoras. Epoch-making maxims are associated with his name, and probably not without good reason. But the speculative tendency of the Ionic mind prompted him to set up number itself as a principle; the Infinite of Anaximander being conceived of arithmetically as the Uneven, i.e., that which cannot be divided by two. Since the Even and Uneven alone co-exist, the sacred Three is compounded of Unity and Duality, as is also the Four (tetraktys), the root of Being. By simply adding these first four numbers together the Decas (1 + 2 + 3 + 4 = 10) is obtained. The cosmos is made to consist of ten celestial bodies, corresponding to this Decas, by the addition of the heaven of the fixed stars as an outermost crust, and the earth and the “anti-earth” (antichthon) containing the central fire, at the heart of it. The earth and other stars moved round this centre, and here we have the first glimpse of the modern conception which explains the apparent diurnal motion of the heavens by the rotation of the earth. This rudimentary idea, as elaborated by later Pythagoreans, and particularly by Aristarchus of Samos in the Alexandrine period, constitutes the first starting-point we can assign to the Copernican system of the universe.

Pythagoras made the astounding discovery that the harmonic intervals of the seven-stringed lyre can be reduced to simple rational proportions (the octave = 1:2, the fifth 2:3, the fourth 3:4, the whole tone 8:9). He then sought for a like scheme in the harmony of the spheres, and, as the geometric habit of the Greek mind converted these arithmetical relations into lines and planes, the whole process by which the universe came into existence seemed to be a sum in arithmetic.