Pythagoras

(b. c. 570 BC)

Pythagoras was the son of Mnesarchus of Samos, but emigrated c. 531 BC to Croton in southern Italy. Here he founded a religious society, but was forced into exile and died at Metapontum. Membership of the society entailed self-discipline, silence, and the observance of various taboos, especially against eating flesh and beans. Pythagoras taught the doctrine of metempsychosis, or the cycle of reincarnation, and was supposed able to remember former existences. The soul, which has its own divinity and may have existed as an animal or plant, can, however, gain release by a religious dedication to study, after which it may rejoin the universal world-soul. Pythagoras is usually, but doubtfully, credited with having discovered the basis of acoustics, the numerical ratios underlying the musical scale, thereby initiating the arithmetical interpretation of nature. This tremendous success inspired the view that the whole of the cosmos should be explicable in terms of harmonia or number. The view represents a magnificent break from the Milesian attempt to ground physics on a conception of a prime matter, or undifferentiated basis shared by all things, and to concentrate instead on form, meaning that physical natures receive an intelligible grounding in different geometric structures. The view is vulgarized in the doctrine usually attributed to Pythagoras that all things are numbers. However, the association of abstract qualities with numbers reached remarkable heights, with occult attachments, for instance between justice and the number four, and mystical significances, especially of the number ten. Cosmologically Pythagoras explained the origin of the universe in mathematical terms, as the imposition of limit on the limitless by a kind of injection of a unit. Followers of Pythagoras included Philolaus, the earliest cosmologist known to have understood that the earth is a moving planet. It is also likely that the Pythagoreans discovered the irrationality of the square root of two: see Hippasus of Metapontum . See also harmony of the spheres.