Pythagoras by Raphael


On this page we set out the views of various writers concerning Pythagoras and pythagorean ideas.

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The significance of Pythagorean ideas


Best known today for the so-called Pythagorean theorem, the sixth-century BC Greek mystic and philosopher Pythagoras taught far more than geometry at the school, or ashram, he founded in Kroton, Italy. Widely traveled throughout Asia Minor as well as in ancient Egypt, Babylon, Persia and India, Pythagoras absorbed the sacred knowledge of the ancient world, and re-cast it in a form that would form the basis for modern science, philosophy, mathematics, and music theory. Upon his return to Greece, Pythagoras formed a spiritual brotherhood devoted to social equality, a vegetarian lifestyle, and the study of sacred teachings as a form of Yoga, to refine the mind and the soul in order to avoid re-incarnation, or the cycle of rebirth. The central concept of Pythagoras’ teachings, was harmonia, the Divine Harmony at the core of both cosmos and psyche, a concept derived from the religious tradition of Orpheus, but which was to lead to the teachings of Plato, and later to both the seven liberal arts of medieval education, the trivium and the quadrivium, and, eventually, to the development of empirical science in the seventeenth century. Now, as Buckminster Fuller states: “To be positive about the future you have to know a great deal.” Perhaps the knowledge required is re-integrated world-view based on the Pythagorean integration of the subjective and objective, Eastern and Western, branches of knowledge, which may once again point the way to a successful future.

The sixth century scene evokes the image of an orchestra expectantly tuning up, each player absorbed in his own instrument only, deaf to the caterwaulings of the others. Then there is a dramatic silence, the conductor enters the stage, raps three times with his baton, and harmony emerges from the chaos. The maestro is Pythagoras of Samos, whose influence on the ideas, and thereby on the destiny, of the human race was probably greater than that of any single man before or after him.

--Arthur Koestler, The Sleepwalkers (New York: Macmillan, 1968), p. 25

Pythagoras defies categorization: a primary thinker in philosophy, mathematics, music and cosmology, he may in fact be best thought of as one who challenges the legitimacy of categories. Anyone who conceives of Pythagoras as the inventor of a geometric theorem, the formulator of laws of music theory, and the utterer of cryptic aphorisms will miss the essence of his thought entirely, for the whole point of what he taught is the interrelatedness of all human knowledge.

--Jamie James, The Music of the Spheres: Music, Science, and the Natural Order of the Universe (New York: Grove Press, 1993), p. 23.

Pythagoras is sometimes described in histories of philosophy as a man who had two separate interests-a religious reformer, who taught the doctrine of transmigration and instituted a cult society, and a man of science who did much to lay the foundations of mathematics, that is to say of arithmetic, geometry, astronomy and music. Transmigration was, until very recent times, regarded by most modern Europeans as a rather crude and barbaric form of the doctrine of immortality. Also, it is not at once obvious to our minds that there is any connection between the immortality of the soul and mathematics. So the historian was disposed to dismiss the religious Pythagoras with brief and apologetic notice, and to concentrate on the scientific Pythagoras and his mathematical doctrine that the essential reality of things is to be found in numbers. But that is not the way to understand a great philosopher’s apprehension of the world. The vision of philosophic genius is a unitary vision. Such a man does not keep his thought in two separate compartments, one for weekdays the other for Sundays. We begin to understand Pythagoras when we see that the two sides of his philosophy meet in the conception of harmony-a conception that has a meaning both in the spiritual and the physical world. And the germ of this philosophy was a discovery in the field, not of arithmetic or geometry, but of music.

--F.M. Cornford, Before and After Socrates (Cambridge: Cambridge University Press, 1966), pp. 65-66.

If you listen to Werner Heisenberg lecturing about Pythagoreanism in his own work on the quantum theory, you will hear him emphasize that the basic building blocks of nature are number and pattern, that the universe is not made out of matter but out of music.  The historians of science I worked with in the University regarded Pythagoras as a magician, a shamanistic madman from the cults of the Near East; Yet both Whitehead and Heisenberg regarded him as a genius of the highest order who laid the foundation upon which our entire Western civilization is based.

--William Irwin Thompson, Darkness and Scattered Light (London: Anchor Books, 1978), p.110.

Pythagoras is said to have taught that the mathematical entities, such as numbers and shapes, were the ultimate stuff out of which the real entities of our perceptual experience are constructed. As thus baldly stated, the idea seems crude, and indeed silly. But undoubtedly, he had hit upon a philosophical notion of considerable importance; a notion which has a long history, and which has moved the minds of men, and has even entered into Christian theology. About a thousand years separate the Athanasian Creed from Pythagoras, and about two thousand four hundred years separate Pythagoras from Hegel. Yet for all these distances in time, the importance of definite number in the constitution of the Divine Nature, and the concept of the real world as exhibiting the evolution of an idea, can both be traced back to the train of thought set going by Pythagoras.

--Alfred North Whitehead, Science and the Modern World (Cambridge: Cambridge University Press, 1928), pp. 27-28.

None of Pythagoras' own work has survived, but the ideas fathered on him by his followers would be among the most potent in modern history. Pure knowledge, the Pythagoreans argued, was the purification (catharsis) of the soul. This meant rising above the data of the human senses. The pure essential reality, they said was found only in the realm of numbers. The simple, wonderful proportion of numbers would explain the harmonies of music which were the beauty of the ear. For that reason they introduced the musical terminology of the octave, the fourth, the fifth, expressed as 2:1, 3:1 and 4:3.

--Daniel Boorstin, The Discoverers, (New York: Random House, 1983), p. 298.

Pythagorean doctrine was all-inclusive in its intention and all-permeative in actual effect, and in some fields it retained its potency until well into the modern period. The notion of cosmic order and its corollaries, perhaps better known as universal harmony, stemmed from the school of Pythagoras in the sixth century B.C. It flourished throughout the classical period (most notably in the Academy of Plato and in the Roman circle of Neoplatonists around Plotinus), cross-pollinated with Stoics and Peripatetics, scattered seed as far abroad as the Hermeticists and the Cabalists and the Syrian syncretists and St. Augustine, and came to full bloom in the renaissance. . . Pythagorean cosmology, though withered, did not die until the acceptance of Newtonian science and Humian philosophy. . . In the meantime, however, the cosmic order first propounded by Pythagoras had provided the stimulus and the cohesion for the best Western thought through all the intervening centuries. And it must be mastered, I believe, if we wish to comprehend the art of those centuries.

--S.K. Heninger, Touches of Sweet Harmony; Pythagorean Cosmology and Renaissance Poetics, (San Marino CA: The Huntington Library, 1974), pp. 15-16.

. . . the Pythagoreans transformed the Orphic mystery cult into a religion which considered mathematical and astronomical studies as the main forms of divine worship and prayer. The physical intoxication which had accompanied the Bacchic rites was superseded by the mental intoxication derived from philo-sophia, the love of knowledge.It was one of the many key concepts they coined and which are still basic units in our verbal currency. . . .'Pure science' is another of their coinages; it signified not merely a contrast to the 'applied' sciences, but also that the contemplation of the new mysteria was regarded as a means of purifying the soul by its immersion in the eternal. Finally, 'theorizing' comes from Theoria, again a word of Orphic origin, meaning a state of fervent contemplation and participation in the sacred rites (thea spectacle, theoris spectator, audience).

Contemplation of the 'divine dance of numbers' which held both the secrets of music and of the celestial motions became the link in the mystic union between human thought and the anima mundi. Its perfect symbol was the Harmony of the Spheres-the Pythagorean Scale, whose musical intervals corresponded to the intervals between the planetary orbits; it went reverberating through 'soft stillness and the night' right into the poetry of the Elizabethans, and into the astronomy of Kepler.

It was indeed this sublimated form of Orphic mysticism which, through the Pythagorean revival in Renaissance Italy, inspired the Scientific Revolution. Galileo, Descartes, and Newton all regarded God as a kind of 'chief mathematician of the universe. Geometry existed before the Creation, is co-eternal with the mind of God, is God himself', wrote Kepler; and the other giants echoed his conviction. The 'oceanic feeling' of religious mysticism had been distilled into differential equations; the mind of the anima mundi was reflected in the rainbow colours of the spectroscope, the ghostly spirals of distant galaxies, the harmonious patterns of iron-filings around a magnet.

--Arthur Koestler, The Act of Creation (New York: The Macmillan Company, 1964), pp. 259-260.

Everyone finds a tremendous appeal in music because music arises from so fundamental a source that it is parallel to the structure of life and to that of the cosmos as a whole. This is why Pythagoras wrote that music and the universe of heavenly bodies are governed by the same mathematical laws. It is also why music has the power to resonate with every level of the awareness of the listener - mind, intellect, emotions and pure creative intelligence.

--Maharishi Mahesh Yogi. "Music and S.C.I."  M.I.U. Catalog 1974/75 (Los Angeles/Heidelberg: MIU Press, 1974), p. 247.