Since, by his idea of the source of universal order, Pythagoras partly accepted the theocosmic monad as the final and necessary root of all life, and of all that is knowable, he could not fail to see the convertibility of the unit into the Being. But if the unit must always precede the manifold, there is a first unit from which all the others proceed; if this first and eternal unit is at the same time the absolute being, it follows that number and the world have a common origin and a common essence, and that the intrinsic causes and possible combinations of number are virtually accomplished in the development of the world, and these causes and combinations are ideal forms of this development. The monad is developed by these laws through all the generative processes of nature, while at the same time it remains eternal in the system of the universe; so that things not only have their origin and essence, their place and time according to numerical causes, but each is in effect a number as far as its individual properties and the universal process of cosmic life are concerned. The reason of the number must depend upon the substance, by the configurations of which it is defined, divided, added, and multiplied, and to this geometry is added, which measures all things in relation to themselves and others. This eternal cause makes it intelligible that if immaterial principles precede and govern the whole material world, it is also by means of these that the classification of science is in intrinsic agreement with that of nature. Numbers have their value in music, in gymnastics, in medicine, in morals, in politics, in all branches of science. The Pythagorean arithmetic is the bond and universal logic of the knowable. But at the same time Pythagoras and his school peopled the world with demons and genii, which were the causes of disease; they did not abandon the old mythical ideas of the incarnation of spirits and the transmigration of souls--theories and beliefs which recur in nearly all primitive and savage peoples.