For instance, in geometry, angles are measured by the number of degrees. Now, as already pointed out, considering all these facts, we might well be justified in concluding that number is a very important aspect of the universe, and is fundamental in it. But the Pythagoreans went much further than this. They drew what seems to us the extraordinary conclusion that the world is _made of_ {36} numbers. At this point, then, we reach the heart of the Pythagorean philosophy. Just as Thales had said that the ultimate reality, the first principle of which things are composed, is water, so now the Pythagoreans teach that the first principle of things is number. Number is the world-ground, the stuff out of which the universe is made. In the detailed application of this principle to the world of things we have a conglomeration of extraordinary fancies and extravagances. In the first place, all numbers arise out of the unit. This is the prime number, every other number being simply so many units. The unit then is the first in the order of things in the universe. Again, numbers are divided into odd and even. The universe, said the Pythagoreans, is composed of pairs of opposites and contradictories, and the fundamental character of these opposites is that they are composed of the odd and even. The odd and even, moreover, they identified with the limited and the unlimited respectively. How this identification was made seems somewhat doubtful. But it is clearly connected with the theory of bipartition. An even number can be divided by two and therefore it does not set a limit to bipartition. Hence it is unlimited. An odd number cannot be divided by two, and therefore it sets a limit to bipartition. The limited and the unlimited become therefore the ultimate principles of the universe. The Limit is identified with the unit, and this again with the central fire of the universe. The Limit is first formed and proceeds to draw more and more of the unlimited towards itself, and to limit it. Becoming limited, it becomes a definite "something," a thing. So the formation of the {37} world of things proceeds. The Pythagoreans drew up a list of ten opposites of which the universe is composed. They are (1) Limited and unlimited, (2) odd and even, (3) one and many, (4) right and left, (5) masculine and feminine, (6) rest and motion, (7) straight and crooked, (8) light and darkness, (9) good and evil, (10) square and oblong.