The Ionian philosophers had been materialists in the sense that the chief accent of their inquiry was on the stuff from which the universe was made; the Pythagoreans' chief accent was on form, proportion and pattern; on the eidos and schema, on the relation, not on the relata. Pythagoras is to Thales what Gestalt philosophy is to the materialism of the nineteenth century. The pendulum has been set swinging; its ticking will be heard through the entire course of history, as the blob alternates between the extreme positions of "all is body", "all is mind"; as the emphasis shifts from "substance" to "form", from "structure" to "function", from "atoms" to "patterns", from "corpuscles" to "waves", and back again.
The line connecting music with numbers became the axis of the Pythagorean system. This axis was then extended in both directions: towards the stars on one side, the body and soul of man on the other. The bearings, on which the axis and the whole system turned, were the basic concepts of armonia: harmony, and katharsis: purge, purification.
The Pythagoreans were, among other things, healers; we are told that "they used medicine to purge the body, and music to purge the soul". 2 One of the oldest forms, indeed, of psychotherapy consists in inducing the patient, by wild pipe music or drums, to dance himself into a frenzy followed by exhaustion and a trance-like, curative sleep – the ancestral version of shock treatment and abreaction therapy. But such violent measures were only needed where the patient's soul-strings were out of tune – overstrung or limp. This is to be taken literally, for the Pythagoreans regarded the body as a kind of musical instrument where each string must have the right tension and the correct balance between opposites such as "high" and "low", "hot" and "cold", "wet" and "dry". The metaphors borrowed from music which we still apply in medicine – "tone", "tonic", "well-tempered", "temperance", are also part of our Pythagorean heritage.
However, the concept armonia did not have quite the same meaning that we lend to "harmony". It is not the pleasing effect of simultaneously-sounded concordant strings – "harmony" in that sense was absent from classical Greek music – but something more austere: armonia is simply the attunement of the strings to the intervals in the scale, and the pattern of the scale itself. It means that balance and order, not sweet pleasure, are the law of the world.
Sweetness does not enter the Pythagorean universe. But it contains one of the most powerful tonics ever administered to the human brain. It lies in the Pythagorean tenets that "philosophy is the highest music", and that the highest form of philosophy is concerned with numbers: for ultimately "all things are numbers". The meaning of this oft-quoted saying may perhaps be paraphrased thus: "all things have form, all things are form; and all forms can be defined by numbers". Thus the form of the square corresponds to a "square number", i.e. 16=4×4, whereas 12 is an oblong number, and 6 a triangular number:
Numbers were regarded by the Pythagoreans as patterns of dots which form characteristic figures, as on the sides of a dice; and though we use arabic symbols, which have no resemblance to these dot-patterns, we still call numbers "figures", i.e. shapes.
Between these number-shapes unexpected and marvellous relations were found to exist. For instance, the series of "square numbers" was formed simply by the addition of successive odd numbers:
and so forth:
The addition of even numbers formed "oblong numbers", where the ratio of the sides represented exactly the concordant intervals of the musical octave:
2 (2 : 1, octave) + 4 = 6 (3 : 2, fifth) + 6 = 12 (4 : 3, quart)
In a similar manner, "cubic" numbers and "pyramidal" numbers were obtained. Mnesarchos had been a gem engraver, so Pythagoras in his youth must have been familiar with crystals whose form imitated those of pure number-shapes: quartz the pyramid and double-pyramid, beryl the hexagon, garnet the dodocaeder. It all went to show that Reality could be reduced to number-series and number-ratios, if only the rules of the game were known. To discover these was the chief task of the Philosophos, the Lover of Wisdom.
An example of the magic of numbers is the famous theorem, by which alone Pythagoras is consciously remembered today – the visible peak of the submerged iceberg. * There is no obvious relationship between the lengths of the sides of a right-angled triangle; but if we build a square over each side, the areas of the two smaller squares will exactly equal the area of the larger. If such wonderfully ordered laws, hitherto hidden from the human eye, could be discovered by the contemplation of number-shapes, was it not legitimate to hope that soon all secrets of the universe would be revealed through them? Numbers were not thrown into the world at random; they arranged themselves into balanced patterns, like the shapes of crystals and the concordant intervals of the scale, according to the universal laws of harmony.
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*
Ironically, Pythagoras seems to have had no complete proof of the Pythagorean theorem.
3. "Soft Stillness and the Night"
Extended to the stars, the doctrine took the form of the "Harmony of the Spheres". The Ionian philosophers had begun to prise open the cosmic oyster, and to set the earth adrift; in Anaximander's universe the earth-disc no longer floats in water, but stands in the centre, supported by nothing and surrounded by air. In the Pythagorean universe the disc changes into a spherical ball. 3 Around it, the sun, moon and planets revolve in concentric circles, each fastened to a sphere or wheel. The swift revolution of each of these bodies causes a swish, or musical hum, in the air. Evidently each planet will hum on a different pitch, depending on the ratios of their respective orbits – just as the tone of a string depends on its length. Thus the orbits in which the planets move form a kind of huge lyre whose strings are curved into circles. It seemed equally evident that the intervals between the orbital cords must be governed by the laws of harmony. According to Pliny, 4 Pythagoras thought that the musical interval formed by earth and moon was that of a tone; moon to Mercury, a semi-tone; Mercury to Venus, a semi-tone; Venus to Sun, a minor third; Sun to Mars, a tone; Mars to Jupiter, a semi-tone; Jupiter to Saturn, a semi-tone; Saturn to the sphere of the fixed stars, a minor third. The resulting "Pythagorean Scale" is si, do, re bemol, fa, sol, la bemol, do – though the accounts of the scale given by different writers vary slightly.
According to tradition, the Master alone had the gift of actually hearing the music of the spheres. Ordinary mortals lack this gift, either because they are from the moment of birth, unknowingly but constantly bathed in the celestial humming; or because – as Lorenzo explains to Jessica – they are too grossly constituted:
... soft stillness and the night
Become the touches of sweet harmony ...
Look how the floor of heaven
Is thick inlaid with patines of bright gold;
There's not the smallest orb which thou behold'st
But in his motion like an angel sings ...
Such harmony is in immortal souls;
But, whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it. 5
The Pythagorean dream of musical harmony governing the motion of the stars never lost its mysterious impact, its power to call forth responses from the depth of the unconscious mind. It reverberates through the centuries, from Kroton to Elizabethan England; I shall quote two more versions of it – with a purpose that will become apparent later. The first is Dryden's well-known:
From harmony, from heavenly harmony,
This universal frame began:
When nature underneath a heap
Of jarring atoms lay
And could not heave her head,
The tuneful voice we heard from high:
Arise, ye more than dead.
The second is from Milton's Arcades:
But els in deep of night when drowsiness
Hath lockt up mortal sense, then listen I
To the celestial Sirens harmony ...
Such sweet compulsion doth in music ly,
To lull the daug
hters of Necessity,
And keep unsteddy Nature to her law,
And the low world in measur'd motion draw
After the heavenly tune, which none can hear
Of human mould with grosse unpurged ear.
But, one might ask, was the "Harmony of the Spheres" a poetic conceit or a scientific concept? A working hypothesis or a dream dreamt through a mystic's ear? In the light of the data which astronomers collected in the centuries that followed, it certainly appeared as a dream; and even Aristotle laughed "harmony, heavenly harmony" out of the courts of earnest, exact science. Yet we shall see how, after an immense detour, at the turn of the sixteenth century, one Johannes Kepler became enamoured with the Pythagorean dream, and on this foundation of fantasy, by methods of reasoning equally unsound, built the solid edifice of modern astronomy. It is one of the most astonishing episodes in the history of thought, and an antidote to the pious belief that the Progress of Science is governed by logic.
4. Religion and Science Meet
If Anaximander's universe reminds one of a Picasso painting, the Pythagorean world resembles a cosmic musical box playing the same Bach prelude from eternity to eternity. It is not surprising, then, that the religious beliefs of the Pythagorean Brotherhood are closely related to the figure of Orpheus, the divine fiddler, whose music held not only the Prince of Darkness, but also beasts, trees and rivers under its spell.
Orpheus is a late arrival on the Greek stage, overcrowded with gods and demigods. The little we know about his cult is clouded in conjecture and controversy; but we know, at least in broad outlines, its background. At an unknown date, but probably not much before the sixth century, the cult of Dionysus-Bacchus, the "raging" goat-god of fertility and wine, spread from barbaric Thracia into Greece. The initial success of Bacchism was probably due to that general sense of frustration which Xenophanes so eloquently expressed. The Olympian Pantheon had come to resemble an assembly of wax-works, whose formalized worship could no more satisfy truly religious needs than the pantheism – this "polite atheism" as it has been called – of the Ionian sages. A spiritual void tends to create emotional outbreaks; the Bacchae of Euripides, frenzied worshippers of the horned god, appear as the forerunners of the mediaeval tarantula dancers, the bright young things of the roaring 'twenties, the maenads of the Hitler youth. The outbreak seems to have been sporadic and shortlived: the Greeks, being Greeks, soon realized that these excesses led neither to mystic union with God, nor back to nature, but merely to mass-hysteria:
Theban women leaving
Their spinning and their weaving
Stung with the maddening trance
Of Dionysus! ...
Brute with bloody jaws agape
God-defying, gross and grim,
Slander of the human shape. 6
The authorities seemed to have acted with eminent reasonableness: they promoted Bacchus-Dionysus to the official Pantheon with a rank equal to Apollo's. His frenzy was tamed, his wine watered down, his worship regulated, and used as a harmless safety-valve.
But the mystic craving must have persisted, at least in a sensitivised minority, and the pendulum now began to swing in the opposite direction: from carnal ecstasy to other-worldliness. In the most telling variant of the legend, Orpheus appears as a victim of Bacchic fury: when, having finally lost his wife, he decides to turn his back on sex, the women of Thrace tear him to pieces, and his head floats down the Hebrus – still singing. It sounds like a cautionary tale; but the tearing and devouring of the living god, and his subsequent rebirth, is a leitmotif that recurs in Orphism on a different level of meaning. In Orphic mythology, Dionysus (or his Thracian version, Zagreus) is the beautiful son of Zeus and Persephone; the evil Titans tear him to pieces and eat him, all but his heart, which is given to Zeus, and he is born a second time. The Titans are slain by Zeus' thunderbolt; but out of their ashes man is born. By devouring the god's flesh, the Titans have acquired a spark of divinity which is transmitted to man; and so is the desperate evil that resided in the Titans. But it is in the power of man to redeem this original sin, to purge himself of the evil portion of his heritage by leading an other-wordly life and performing certain ascetic rites. In this manner he can obtain liberation from the "wheel of rebirth" – his imprisonment in successive animal and even vegetable bodies, which are like carnal tombs to his immortal soul – and regain his lost divine status.
The Orphic cult was thus in almost every respect a reversal of the Dionysian; it retained the name of the god and some features of his legend, but all with a changed emphasis and different meaning (a process that will repeat itself at other turning points of religious history). The Bacchic technique of obtaining emotional release by furiously clutching at the Now and Here, is replaced by renunciation with an eye on after-life. Physical intoxication is superseded by mental intoxication; the "juice that streams from the vine-clusters to give us joy and oblivion" now serves only as a sacramental symbol; it will eventually be taken over, together with the symbolic swallowing of the slain god and other basic elements of Orphism, by Christianity. "I am perishing with thirst, give me to drink of the waters of memory", says a verse on an Orphic gold tablet, alluding to the divine origin of the soul: the aim is no longer oblivion but remembrance of a knowledge which it once possessed. Even words change their meaning: "orgy" no longer means Bacchic revelry, but religious ecstasy leading to liberation from the wheel of rebirth. 7 A similar development is the transformation of the carnal union between the King and the Shulamite into the mystic union of Christ and his Church; and, in more recent times, the shift of meaning in words like "rapture" and "ravishment".
Orphism was the first universal religion in the sense that it was not regarded as a tribal or national monopoly, but open to all who accepted its tenets; and it profoundly influenced all subsequent religious development. It would nevertheless be a mistake to attribute too much intellectual and spiritual refinement to it; the Orphic purification rites, which are the hub of the whole system, still contain a series of primitive taboos – not to eat meat, or beans, not to touch a white cock, not to look in a mirror beside the light.
But this is precisely the point where Pythagoras gave Orphism a new meaning, the point where religious intuition and rational science were brought together in a synthesis of breathtaking originality. The link is the concept of katharsis. It was a central concept in Bacchism, Orphism, in the cult of the Delian Apollo, in Pythagorean medicine and science; but it had different meanings, and entailed different techniques in all of them (as it still does in the various schools of modern psychotherapy). Was there anything in common between the raving Bacchante and the aloof mathematician, the fiddle of Orpheus and a laxative pill? Yes: the same yearning for release from various forms of enslavement, from passions and tensions of body and mind, from death and the void, from the legacy of the Titans in man's estate – the yearning to re-light the divine spark. But the methods of achieving this must differ according to the person. They must be graded according to the disciple's lights and degree of initiation. Pythagoras replaced the soul-purging all-cures of competing sects, by an elaborate hierarchy of kathartic techniques; he purified the very concept of purification, as it were.
At the bottom of the scale are simple taboos, taken over from Orphism, such as the interdiction of eating meat and beans; for the coarse-natured the penance of self-denial is the only effective purge. At the highest level katharsis of the soul is achieved by contemplating the essence of all reality, the harmony of forms, the dance of numbers. "Pure science" – a strange expression that we still use – is thus both an intellectual delight and a way to spiritual release; the way to the mystic union between the thoughts of the creature and the spirit of its creator. "The function of geometry," says Plutarch of the Pythagoreans, "is to draw us away from the world of the senses and of corruption, to the world of the intellect and the eternal. For the contemplation of the eternal is the end of philosophy as the contemplation of the mysteries is the end of religion." 8
But to the true Pythagorean, the two have become indistinguishable.
The historical importance of the idea that disinterested science leads to purification of the soul and its ultimate liberation, can hardly be exaggerated. The Egyptians embalmed their corpses so that the soul might return to them and need not be reincarnated again; the Buddhists practised non-attachment to escape the wheel; both attitudes were negative and socially sterile. The Pythagorean concept of harnessing science to the contemplation of the eternal, entered, via Plato and Aristotle, into the spirit of Christianity and became a decisive factor in the making of the Western world.
Earlier in this chapter I have tried to show how, by relating music to astronomy and both to mathematics, emotional experience became enriched and deepened by intellectual insight. Cosmic wonder and aesthetic delight no longer live apart from the exercise of reason; they are all inter-related. Now the final step has been taken: the mystic intuitions of religion have also been integrated into the whole. Again, the process is accompanied by subtle changes in the meaning of certain key-words, such as theoria – theory. The word was derived from theorio – "to behold, contemplate" (thea: spectacle, theoris: spectator, audience). But in orphic usage, theoria came to signify "a state of fervent religious contemplation, in which the spectator is identified with the suffering god, dies in his death, and rises again in his new birth". 9 As the Pythagoreans canalized religious fervour into intellectual fervour, ritual ecstasy into the ecstasy of discovery, theoria gradually changed its meaning into "theory" in the modern sense. But though the raucous cry of the ritual worshippers was replaced by the Eureka of the new theorizers, they remained aware of the common source from which both sprang. They were aware that the symbols of mythology and the symbols of mathematical science were different aspects of the same, indivisible Reality. * They did not live in a "divided house of faith and reason"; the two were interlocking, like ground-plan and elevation on an architect's drawing. It is a state of mind very difficult for twentieth-century man to imagine – or even to believe that it could ever have existed. It may help to remember though, that some of the greatest pre-Socratic sages formulated their philosophies in verse; the unitary source of inspiration of prophet, poet and philosopher was still taken for granted.