In dealing with speculations so remote, we have to guard against reading modern meanings into writings produced in ages whose limitations of knowledge were serious, and whose temper and standpoint are wholly alien to our own. For example, shrewd as are some of the guesses made by Anaximander, we find him describing the sun as "a ring twenty-eight times the size of the earth, like a cartwheel with the felloe hollow and full of fire, showing the fire at a certain point, as if through the nozzle of a pair of bellows." And if he made some approach to truer ideas of the earth's shape as "convex and round," the world of his day, as in the days of Homer, thought of it as flat and as floating on the all-surrounding water. The Ionian philosophers lacked not insight, but the scientific method of starting with working hypotheses, or of observation before theory, was as yet unborn. In this brief survey of the subject there will be no advantage in detailing the various speculations which followed on the heels of those of Thales and Anaximander, since these varied only in non-essentials; or, like that of Pythagoras and his school, which Zeller regards as the outcome of the teachings of Anaximander, were purely abstract and fanciful. As is well known, the Pythagoreans, whose philosophy was ethical as well as cosmical, held that all things are made of numbers, each of which they believed had its special character and property. A belief in such symbols as entities seems impossible to us, but its existence in early thought is conceivable when, as Aristotle says, they were "not separated from the objects of sense." Even in the present day, among the eccentric people who still believe in the modern sham agnosticism, known as theosophy, and in astrology, we find the delusion that numbers possess inherent magic or mystic virtues. So far as the ancients are concerned, "consider," as Mr. Benn remarks in his Greek Philosophers (vol. i, p. 12), "the lively emotions excited at a time when multiplication and division, squaring and cubing, the rule of three, the construction and equivalence of figures, with all their manifold applications to industry, commerce, fine arts, and tactics, were just as strange and wonderful as electrical phenomena are to us ... and we shall cease to wonder that a mere form of thought, a lifeless abstraction, should once have been regarded as the solution of every problem; the cause of all existence; or that these speculations were more than once revived in after ages."