A further step in the direction of the abstract was taken by Anaximander, the Milesian astronomer, who is reported to have made a sundial, to have calculated the recurrence of the equinoxes and the solstices, and to have projected geographical charts for the first time in Greece. This practical mathematician derived the universe from the unlimited, #to apeiron#, hurling thought thus at a venture, as it were, into the realm of metaphysical conceptions. It would appear from the dim and hazy tradition which we have received about Anaximander, that he instituted a polemic against the so-called physicists, arguing that to the elements of fire or water there can be attributed a beginning and an ending, but that the abstract indefinite, as uncreate and indestructible, takes precedence of all else. His thought, however, though fruitful of future consequences, was in itself barren; nor have we any reason to conclude that by the #apeiron# he meant more than a primordial substance, or _Grund_, without quality and without limitation--a void and hollow form containing in itself potentialities of all things. It is characteristic of this early age of Greek speculation that Simplicius found it necessary to criticise even Anaximander for using poetic phraseology, #poiêtikôterois onomasin#. In his polemic, however, he started one of the great puzzles, the contrast between birth and death, and the difficulty of discovering an element subject to neither, which agitated the schools of Greece throughout their long activity. While the thinkers of Ionia were endeavoring to discover terms of infinite subtlety, through which to symbolize the uniform and unchangeable substance underlying the multiplicity of phenomena, the Pythagoreans in Italy turned their attention to the abstract relations of which numbers are the simplest expression. Numbers, they saw, are both thoughts and also at the same time universally applicable to things of sense. There is nothing tangible which can escape the formulæ of arithmetic. Mistaking a power of the mind for a power inherent in the universe, they imagined that the figures of the multiplication-table were the essential realities of things, the authentic inner essence of the sensible world; and to number they attributed a mystic potency. Speculation was still so immature that they failed to observe the sterility of the conception. This much, however, they effected: by resting upon the essentially mental conception of quantity, and by apprehending the whole universe as number, they took the first important step in the direction of pure metaphysic.