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.