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disciple's lights and degree of initiation. Pythagoras replaced the soul-purging all-cures of competing sects, by an elaborate hierarchy of kathartic techniques; he purified the very concept of purification, as it were.
    At the bottom of the scale are simple taboos, taken over from Orphism, such as the interdiction of eating meat and beans; for the coarse-natured the penance of self-denial is the only effective purge. At the highest level katharsis of the soul is achieved by contemplating the essence of all reality, the harmony of forms, the dance of numbers. "Pure science" – a strange expression that we still use – is thus both an intellectual delight and a way to spiritual release; the way to the mystic union between the thoughts of the creature and the spirit of its creator. "The function of geometry," says Plutarch of the Pythagoreans, "is to draw us away from the world of the senses and of corruption, to the world of the intellect and the eternal. For the contemplation of the eternal is the end of philosophy as the contemplation of the mysteries is the end of religion." 8 But to the true Pythagorean, the two have become indistinguishable.
    The historical importance of the idea that disinterested science leads to purification of the soul and its ultimate liberation, can hardly be exaggerated. The Egyptians embalmed their corpses so that the soul might return to them and need not be reincarnated again; the Buddhists practised non-attachment to escape the wheel; both attitudes were negative and socially sterile. The Pythagorean concept of harnessing science to the contemplation of the eternal, entered, via Plato and Aristotle, into the spirit of Christianity and became a decisive factor in the making of the Western world.
    Earlier in this chapter I have tried to show how, by relating music to astronomy and both to mathematics, emotional experience became enriched and deepened by intellectual insight. Cosmic wonder and aesthetic delight no longer live apart from the exercise of reason; they are all inter-related. Now the final step has been taken: the mystic intuitions of religion have also been integrated into the whole. Again, the process is accompanied by subtle changes in the meaning of certain key-words, such as theoria – theory. The word was derived from theorio – "to behold, contemplate" ( thea : spectacle, theoris : spectator, audience). But in orphic usage, theoria came to signify "a state of fervent religious contemplation, in which the spectator is identified with the suffering god, dies in his death, and rises again in his new birth". 9 As the Pythagoreans canalized religious fervour into intellectual fervour, ritual ecstasy into the ecstasy of discovery, theoria gradually changed its meaning into "theory" in the modern sense. But though the raucous cry of the ritual worshippers was replaced by the Eureka of the new theorizers, they remained aware of the common source from which both sprang. They were aware that the symbols of mythology and the symbols of mathematical science were different aspects of the same, indivisible Reality. * They did not live in a "divided house of faith and reason"; the two were interlocking, like ground-plan and elevation on an architect's drawing. It is a state of mind very difficult for twentieth-century man to imagine – or even to believe that it could ever have existed. It may help to remember though, that some of the greatest pre-Socratic sages formulated their philosophies in verse; the unitary source of inspiration of prophet, poet and philosopher was still taken for granted.
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*
Hence the
short-cuts, or short-circuits, between different sets of symbols
in Pythagorean mystic number-lore, such as the correlation of odd
and even numbers with male and female, right and left; or the
magic quality attributed to the pentagram.
    It did not last long. Within a few centuries, the unitary awareness faded, religious and rational philosophizing split apart –