Pythagoras' Contribution

I. M. Oderberg

The stream of an ancient wisdom flows out of a remote antiquity. At times traces of its existence are observable while at others, when dogmatism prevails, the stream runs underground, its treasures in texts or fragments preserved in old cultures for future mankinds. In eras barren of spirituality, solitary individuals emerge out of the darkness like beacons.

One whose light has endured for millennia was Pythagoras, the Greek philosopher of the sixth century BC, best known in our school days as a mathematician and formulator of the theorem of the right-angled triangle. There was, however, another side to his teachings: that involving the development and training of character. While we do not have any of his own writings, those of his immediate students and later followers testify to the quality of his life and teaching that survived his personality.

Plato writes, for example, that there is no record of Homer

presiding, like Pythagoras, over a band of intimate disciples who loved him for the inspiration of his society and . . . the way of life which the Pythagoreans called after their founder and which to this day distinguishes them from the rest of the world . . . — The Republic, Book X, 600a, Cornford translation

Pythagoras was born in Samos and traveled widely in search of wisdom. He settled in Crotona, a Greek colony in Italy, about 530 BC, and soon attracted disciples who devoted themselves to the study of cosmology, science, and philosophy. They concentrated on ethical, moral, and social relationships, emphasizing personal character building, asceticism, moderation in all things, and communal service. After a time, there was a revolution in Crotona and the Pythagorean community dispersed. The transmission continued until approximately the middle of the fourth century BC. By then, some admixtures had crept in, as indeed had been the case earlier with the Orphic tradition. It may be said with some justice that Plato took up the torch in the "relay race" and, using whatever was still viable in both of these heritages, added to them his own quality, his whole presentation proving to be a major influence in Western civilization for more than two thousand years.

A particularly valuable book has been published very recently, collating all the material about the life and teachings of Pythagoras and Pythagoreanism still extant (The Pythagorean Sourcebook and Library: An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy, Phanes Press, Grand Rapids, Michigan, 1987). There have been many biographical and interpretive writings from antiquity onward. In previous years the sources, scattered through many volumes, were hard to find, but now are reachable between two covers! The major part of the book was compiled and translated by Kenneth Sylvan Guthrie, with additional translations by Thomas Taylor, the English Platonist, and Arthur Fairbanks Jr. The introduction by David R. Fideler, the editor, is an admirable guide for the reader to whom Pythagoras and his heritage may not be well known.

Citing Iamblichus' Life of Pythagoras, H. P. Blavatsky refers to Pythagoras' contacts with such Mystery schools as had survived into the sixth century BC: those at Byblus, Tyre, Syria, Egypt, Babylon, and others, adding India to the biographer's list.

Pythagoras' message focused, firstly, on the soul, and secondly, on the processes of the physical universe which he expressed in a mathematical system, numbers representing not only relationships but also ideas and entities. Our mathematical concepts are built more or less upon the foundation of Euclid's, but the Pythagorean view was richer and deeper, for number had a living reality that was qualitative rather than quantitative. This pointed to something to be experienced or, as the editor expressed it:

For them Number is not something to be used; rather, its nature is to be discovered. In other words, we use numbers as tokens to represent things, but for Pythagoreans Number is a universal principle, as real as light (electromagnetism) or sound — p. 21

And Fideler points out further that the great difference between modern and Pythagorean and Platonic science is to be found in the first being based on "Aristotelian" science or the investigation of things, while the latter is concerned with the investigation of principles as the collective cause of things.

For example, in the Pythagorean Tetraktys or Decad (1 + 2 + 3 + 4 = 10), the figure 1 refers to the essence of Divinity, the One, expressing itself through 2, duality, the first manifestation of spirit-matter after a rest period; the 1 and 2 produce 3, the animating "soul" of a cosmos or world order. The figure 4 refers to the unfolded cosmos in the physical aspect we perceive with our senses, and the 10 to the whole as a functioning organism. The components of the universe were thus viewed through the perspective of an all-embracing cosmology.

H. P. Blavatsky throws light upon the Pythagorean system by identifying it with the Hindu scripture Aitareya Brahmana of the Rig-Veda:

The harmony and mathematical uniformity of the double evolution — spiritual and physical — are elucidated only in the universal numerals of Pythagoras, who built his system entirely upon the so-called 'metrical speech' of the Hindu Vedas. — Isis Unveiled, 1:9

The Pythagorean philosophy was thus founded on the numerical or vibrational ground of reality. Pythagoras was credited throughout Greek antiquity with the invention of the musical scale derived from his discovery of the ratios of musical intervals which he demonstrated on a monochord. His "music of the spheres" — the individual vibratory notes which the moving planetary and stellar bodies emit — conforms to a harmonia, cosmic law as expressed through nature, a cosmic harmony. It has been said that we human beings can be "changed, improved, brought closer to divinity," if we allow the "sweet harmony" of the music of the spheres to influence our lives (See Touches of Sweet Harmony, Pythagorean Cosmology and Renaissance Poetics, by S. K. Heninger, Jr., 1974). In our time, music is limited to sound, composers and performers using melody, rhythm, and harmony according to their genius and inspiration. For Pythagoras, and Plato after him, the word music had deep philosophical overtones, being derived from the Muses, the nine goddesses who preside over the arts and learning.

The kinship of all entities in the cosmos as parts of a larger organism might have been the basis for the ethical conduct and morality of the Pythagorean communities. The members tried to conform their lives to the laws of the universe, every Pythagorean feeling his relationship with the all-permeating divine essence. This may have helped invest the Tetraktys with its sacred tone, for its utterance was regarded as their holiest oath.

As stated, the Tetraktys symbolized the first appearance of the cosmic Monad of consciousness and its emanation of successively materializing aspects of itself into the universe as we know it. The Tetraktys is sometimes depicted with and sometimes without an enclosing triangle. Within a triangle it can symbolize a universe; without a triangle it suggests an infinite number of such universes, each a manifestation of the all-pervading cosmic consciousness.

In his Life, echoing much older authors, Iamblichus states that Pythagoras spent some 22 years in Egypt studying with the priests. There is a glyph of Pharaoh in the tomb of Ramses IX showing the royal mummy leaning backward in a straight line, forming the hypotenuse of a right-angled triangle, with the classic proportions of 3:4:5. Ramses' tomb predates Pythagoras' visit to Egypt by many centuries, and we are indebted to R. A. Schwaller de Lubicz for the discovery of the Egyptian connection with the Pythagorean Golden Section, and the value of pi (3.1415 9 . . . ) (The Egyptian Miracle: An Introduction to The Wisdom of the Temple translated by Andre and Goldian VandenBroeck, pp. 101-3).

Both the vignette of Ramses IX and the number pi are symbols, but de Lubicz points out that the term symbol has been generalized in our time merely into analogy, failing thereby to provide an insight into transmission of spiritual teachings.

These rites, these dogmas, often hide ideas once reserved for a small number of initiates; their secret lies buried with them, yet it can be retrieved by those who study in depth the information of all kinds that survives concerning ancient beliefs and the ceremonies they prescribed. — Ampere, Essai sur la philosophie des sciences, cited by de Lubicz, p. 36.

The Egyptian image of Ramses IX as the hypotenuse percolated into Western civilization via Pythagoras' geometry. It was the Pythagorean mathematics and its sustaining philosophy that led de Lubicz to unraveling the inner meaning of the old Egyptian hieroglyphs and concepts. It seems like the completion of a circle: Pythagoras' studies in Egypt lead us back to the Egyptian heritage!

Who was Pythagoras? E. J. Urwick comparing the Platonic writings with Hindu metaphysical thought states that the latter is recognizable in the Pythagorean teaching. He reports a Vedantin claim that Pythagoras was "one of themselves," his name being the "Greek form of the Indian title, Pitta Guru, or Father-teacher" (The Message of Plato: A Re-Interpretation of the "Republic", p. 14). Urwick exposed many parallels in the two heritages, the Greek and the Hindu: an "upper" or "higher" science, and a "lower" one. The former, including astronomy ("sphaerics"), arithmetic, music, and dialectic, are termed by Plato "Pythagorean" in his Republic (Book VII, 521c-531c). These subjects are not what we mean by them today, which are covered by the classification "lower" sciences.

It would seem that, whereas Pythagoras dealt with the noumenal aspect of the universe and its activities and Plato taught similarly, we in our time deal with objective manifestations. We see everything through our own colored spectacles as separate entities and processes.

There is a strong temptation to summarize a large part of the material in Dr. Guthrie's book and Fideler's introduction, but a good note on which to close is the excerpt from Theon of Smyrna, a second century Pythagorean:

Unity is the principle of all things and the most dominant of all that is: all things emanate from it and it emanates from nothing. It is indivisible and it is everything in power. It is immutable and never departs from its own nature through multiplication (1 x 1 = 1). All that is intelligible and cannot be engendered exists in it: the nature of ideas, God himself, the soul, the beautiful and the good, and every intelligible essence, such as beauty itself, justice itself, equality itself, for we conceive of each of these things as being one and as existing in itself. (See p. xi, Theon of Smyrna: Mathematics Useful for Understanding Plato, by Theon of Smyrna, translated by Robert and Deborah Lawlor from the 1892 Greek/French edition of J. Dupuis, Secret Doctrine Reference Series, Wizards Bookshelf, San Diego, 1979.)

Summing up the rich contribution of Pythagoras and his school to the long line of inspiring instruction: they taught that the entire world exists through the harmonia among all its children. The Pythagorean view entailed so much more than a mere linking of material forms; rather it embraced all the qualities and possibilities latent as seeds in the heart of divinity.

(From Sunrise magazine, April/May 1988. Copyright © 1988 by Theosophical University Press)

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