The Secret Teachings of All Ages

After Pythagoras of Samos, its founder, the Italic or Pythagorean school includes among its most distinguished representatives Empedocles, Epicharmus, Archytas, Alcmaeon, Hippasus, Philolaus, and Eudoxus. Pythagoras (c. 580–500 B.C.) believed mathematics to be the most sacred and exact of all the sciences. He required all who came to him for study to be familiar with arithmetic, music, astronomy, and geometry. He placed special emphasis on living a philosophical life as a necessary requirement for attaining wisdom. Pythagoras was one of the first teachers to establish a community where all members provided mutual assistance to one another in the shared pursuit of the higher sciences. He also introduced the discipline of retrospection The practice of reviewing one's daily actions and thoughts in reverse order each evening to develop self-awareness. as essential to the development of the spiritual mind.

Pythagoreanism may be summarized as a system of metaphysical speculation concerning the relationships between numbers and the governing forces of existence. This school was also the first to explain the theory of celestial harmonics, or "the music of the spheres." The ancient belief that the movement of celestial bodies produces a divine harmony or musical frequency. John Reuchlin said of Pythagoras that he taught nothing to his disciples before the discipline of silence—silence being the first fundamental step of contemplation. In his work Sophist, Aristotle credits Empedocles with the discovery of rhetoric. Both Pythagoras and Empedocles accepted the theory of transmigration, Also known as reincarnation; the belief that the soul is reborn into different bodies. with the latter saying: "I was once a boy, then I became a girl; a plant, a bird, a fish, and I swam in the vast sea." original: "A boy I was, then did a maid become; a plant, bird, fish, and in the vast sea swum." Archytas is credited with the invention of the screw and the crane. He declared pleasure to be a "pestilence" because it opposed the self-control of the mind; he considered a man without deceit to be as rare as a fish without bones.

The Eleatic sect was founded by Xenophanes (c. 570–480 B.C.), who was notable for his attacks on the mythological stories of the universe and the gods found in Homer and Hesiod. Xenophanes declared that God was "one and without a physical body, spherical in substance and shape, and in no way resembling man; that He is all sight and all hearing, but does not breathe; that He is all things—mind and wisdom—not created but eternal, unable to suffer, unchanging, and rational." Xenophanes believed that all existing things were eternal, that the world was without beginning or end, and that everything created was subject to decay. He lived to a great age and is said to have buried his sons with his own hands. Parmenides studied under Xenophanes, but never entirely agreed with his doctrines. Parmenides declared the senses to be unreliable and reason to be the only standard of truth. He was the first to assert that the earth is round and he also divided its surface into zones of heat and cold.

Melissus, who is included in the Eleatic school, shared many opinions with Parmenides. He declared the universe to be immovable because, since it occupied all space, there was no place left for it to move to. He further rejected the theory of a vacuum in space. Zeno of Elea also maintained that a vacuum could not exist. Rejecting the theory of motion, he asserted that there was only one God, who was an eternal, uncreated Being. Like Xenophanes, he imagined the Deity to be spherical in shape. Leucippus held that the Universe consists of two parts: one full and the other a vacuum. From the Infinite, a multitude of tiny, fragmentary bodies descended into the vacuum where, through constant agitation, they organized themselves into spheres of matter.

The great Democritus expanded to a certain degree upon the atomic theory of Leucippus. Democritus declared the principles of all things to be twofold: atoms and the vacuum. He asserted that both are infinite—atoms in number, and the vacuum in size. Thus, all bodies must be composed of either atoms or vacuum. Atoms possessed two properties, shape and size, both characterized by infinite variety. The soul, Democritus also...