The most distant region he called Olympus; the space between the fixed stars and the moon he called { ~GREEK SMALL LETTER KAPPA~}{ ~GREEK SMALL LETTER OMICRON WITH OXIA~}{ ~GREEK SMALL LETTER SIGMA~}{ ~GREEK SMALL LETTER MU~}{ ~GREEK SMALL LETTER OMICRON~}{ ~GREEK SMALL LETTER FINAL SIGMA~}; the space between the moon and the earth { ~GREEK SMALL LETTER OMICRON~}{ ~GREEK SMALL LETTER UPSILON WITH PSILI~}{ ~GREEK SMALL LETTER RHO~}{ ~GREEK SMALL LETTER ALPHA~}{ ~GREEK SMALL LETTER NU~}{ ~GREEK SMALL LETTER OMICRON WITH OXIA~}{ ~GREEK SMALL LETTER FINAL SIGMA~}. He, or at least his disciples, taught that the earth revolved on its axis, (though Philolaus taught that its revolutions were not round its axis but round the central fire). The universe itself they considered as a large sphere, and the intervals between the heavenly bodies they thought were determined according to the laws and relations of musical harmony. And from this theory arose the doctrine of the Music of the Spheres; as the heavenly bodies in their motion occasioned a sort of sound depending on their distances and velocities; and as these were determined by the laws of harmonic intervals, the sounds, or notes, formed a regular musical scale.
The light and heat of the central fire he believed that we received through the sun, which he considered a kind of lens: and perfection, he conceived to exist in direct ratio to the distance from the central fire.
The universe, itself, they looked upon as having subsisted from all eternity, controlled by an eternal supreme Deity; who established both limits and infinity; and whom they often speak of as the absolute { ~GREEK SMALL LETTER MU~}{ ~GREEK SMALL LETTER OMICRON~}{ ~GREEK SMALL LETTER NU~}{ ~GREEK SMALL LETTER ALPHA WITH VARIA~}{ ~GREEK SMALL LETTER FINAL SIGMA~}, or unity. He pervaded (though he was distinct from) and presided over the universe. Sometimes, too, he is called the absolute _Good_,--while the origin of evil is attributed not to him, but to matter which prevented him from conducting everything to the best end.
With respect to man, the doctrine of Pythagoras was that known by the name of the Metempsychosis,--that the soul after death rested a certain time till it was purified, and had acquired a forgetfulness of what had previously happened to it; and then reanimated some other body. The ethics of the Pythagoreans consisted more in ascetic practice and maxims for the restraint of the passions, than in any scientific theories. Wisdom they considered as superior to virtue, as being connected with the contemplation of the upper and purer regions, while virtue was conversant only with the sublunary part of the world. Happiness, they thought, consisted in the science of the perfection of the soul; or in the perfect science of numbers; and the main object of all the endeavours of man was to be, to resemble the Deity as far as possible.