their
movements through space give rise to a sound, the harmony of the
spheres, unnoticed by us because we habitually hear it. They place the
sun in the centre of the system, round which, with the other planets,
the earth revolves. At this point the geocentric doctrine is being
abandoned and the heliocentric takes its place. As the circle is the
most perfect of forms, the movements of the planets are circular. They
maintained that the moon is inhabited, and like the earth, but the
people there are taller than men, in the proportion as the moon's
periodic rotation is greater than that of the earth. They explained the
Milky Way as having been occasioned by the fall of a star, or as having
been formerly the path of the sun. They asserted that the world is
eternal, but the earth is transitory and liable to change, the universe
being in the shape of a sphere. They held that the soul of man is merely
an efflux of the universal soul, and that it comes into the body from
without. From dreams and the events of sickness they inferred the
existence of good and evil daemons. They supposed that souls can exist
without the body, leading a kind of dream-life, and identified the motes
in the sunbeam with them. Their heroes and daemons were souls not yet
become embodied, or who had ceased to be so. The doctrine of
transmigration which they had adopted was in harmony with such views,
and, if it does not imply the absolute immortality of the soul, at least
asserts its existence after the death of the body, for the disembodied
spirit becomes incarnate again as soon as it finds a tenement which fits
it. To their life after death the Pythagoreans added a doctrine of
retributive rewards and punishments, and, in this respect, what has been
said of animals forming a penitential mechanism in the theology of India
and Egypt, holds good for the Pythagoreans too.

Of their system of politics nothing can now with certainty be affirmed
beyond the fact that its prime element was an aristocracy; of their rule
of private life, but little beyond its including a recommendation of
moderation in all things, the cultivation of friendship, the observance
of faith, and the practice of self-denial, promoted by ascetic
exercises. It was a maxim with them that a right education is not only
of importance to the individual, but also to the interests of the state.
Pythagoras himself, as is well known, paid much attention to the
determination of extension and gravity