The imperceptible which in an experienced universe is implicit in what has emerged out of the eternal substratum, includes necessary relationships, both universal and general. Necessary, that is, in the sense that it was not possible that they did not hold. Thus they were both eternal and divine because only the eternal is outside of time and only the divine is true necessarily without question. Pythagoras, an evangelistic Orphic preacher from the island of Samos called the recognition of these relationships wisdom. It was he who coined the term philosopher, which he called those who love wisdom. Orphism was a mystery religion practiced by many of the Greek peoples in opposition to the state religion. Pythagoras was driven from his home in Samos for political reasons and he made his way to Miletus. Here he fell under the spell of the Milesians and here he began to develop a religion of rationality and numbers.

Consider the Lyre. Unlike modern stringed instruments, the strings were all made of the same material. So, when two strings sound good when plucked together there will always be a mathematical relationship between their lengths. Mathematical relationships and harmony are one and the same, he said. Thus all relationships, he claimed, could be stated in some mathematical form. Therefore numbers are the real substratum. of the universe. The number one, for example, is Anaximenes divine fire, Anaximander's boundless. It alone of all of the numbers is indivisible. Nothing can be without being one. This makes One real. It is separated from what is only apparent, from everything else, the many. From it all other things become.

Experience taught men that the sides of a right triangle always maintained a ratio of 3, 4, 5. Reason led Pythagorus to the generalization for which he has become known. The theorem is real, it does not depend on the existence of ephemeral entities. That the square of the hypotenuse is equal to the sum of the squares of the other two sides does not depend on the existence in nature of right triangles. The ratio 3, 4, 5 does. Just as important, Pythagorus brought to the archaic Greek culture an answer to one of their most important cultural problems, that of inherited guilt.

What made the story of Oedipus and his family such a great tragedy was that in the Greek culture of the time it was believed that the mistake of a father seals the fate of the children. It is without doubt one of the most famous examples of the problem of inherited guilt. Inherited guilt, a major theme of Greek tragedy, is basically irrational since it requires punishing the morally innocent. It made sense in the early days of Greek culture when the fundamental unit of society was the family so that all members of the family shared in the pollution developed by one. But by the sixth century BC the families were disintegrating, already being absorbed into the fabric of more complex communities. Why should a successful scoundrel spend his life in luxury while his children who did not share in the actions are forced to suffer the consequences?

Popular Orphic doctrine taught that there was a part of every person that was divine and eternal. This they called the soul or psyche. They taught that this part of a human being could leave the body. It was an ancient belief that may date back to early Siberian shamans. As an Orphic Shaman himself, Pythagoras was said to carry within his body the souls of two ancient shamans. What he did was to develop this theme into a new concept. That in every human being there existed a totally good and completely perfect immortal soul that was trapped into an evil body.

The way Pythagoras taught it was that every living thing was activated by a soul. Remember, though an Orphic preacher, he had been infected by Milesian rationalism. Thus this soul was the living divine spark of Anaximenes, his breath of life. Keep in mind that the living soul of Anaximenes was developed through purely rational reasoning. When Pythagorus merged this rational soul into essentially irrational Orphic beliefs he was attempting to develop a purely rational religion. He began with Anaximenes immortal soul which being eternal and divine was necessarily unchanging, and therefore had to be all good. He merged this with the itinerant immortal soul of the Orphics. He then made the claim that during life this absolutely good soul was trapped in a body that was constantly changing and therefore evil.

If we consider this along with the ancient idea borrowed from the advancing Persians that truth, knowledge and the good were connected with light, and ignorance and evil with darkness, we can see the rational thought that tied these things together. When the soul, which was air, a part of the Anaximenes divine fire, was trapped in the physical body, the presence of the material body obscured the light of truth and knowledge. Since the soul was immortal, When the body died it transmigrated to another. The way a man lived his life would affect where his soul transmigrated to. Depending on how he lived his life a man might become a donkey, a saint, or even a vegetable in his next life. The soul being finely divided air, was like the one, It was both divine and eternal.

All of these ideas were presented as a form of the traditional Greek orphic religion. His ideas, in general, did not take root in the east. Driven from his home, unaccepted in Ionia, he traveled to Croton in Italy where his ideas found fertile ground. From this grew a religion that was to become a source of ideas that would change the world. The Orphic tradition called for a ritual purification of the soul in preparation for death. The Pythagorean religion called for a purification of the soul through mathematics and reasoning. For the Pythagoreans a philosopher became more than a seeker after wisdom, he became a priest of the Pythagorean religion. Thus, the Ionian tradition taught that the underlying substratum of the universe was divine and eternal. The sensual world was the rational outcome of an eternal battle of opposites. Pythagoras taught that the underlying substratum of the universe was numbers and that the sensual world was the product of rational numerical harmony. Thus the Pythagorean religion included the worship of numbers and mathematical relationships. Twenty seven hundred years later the philosopher of science Sir Karl Popper said that though numbering systems were arbitrary, such things as the Pythagoreans were discussing and such modern forms as prime numbers, must exist in another world. They are not things we create, they are things we discover. In saying this he was expressing the kind of ideas that the Pythagorean religion was based on. What we find in the world may be constructed out the divine stuff, and certainly they believed, like the Ionians, that everything had a soul, but what is implied by experience and discovered through reasoning, that too was divine. The ultimate goal of every philosopher, then, is to partake of the divine. But this takes the evolving concept of the supreme cosmogenetic God another step because it links that god with the human soul through the power of human reasoning. Scientifically, the most significant of the Pythagorean concepts was that of "Harmony" of the body. Thus the first Greek school of medical theory was led by Alcmaion, a Pythagorean from Croton who taught that health was due to a delicate harmony among the balance of forces that exist within the body.