Contents of the book
About this book
1. The Maze Within and Around us
Asia, Africa & Greece
2. A Turning World
3. The Gift of the East
4. The worlds that Pythagoras saw
Qualities of Greekness
6. Architecture of mind
7. Freedom from Sacred Texts
8. Clarity, Poverty and Nakedness
9. Catching the Voice
10. A first Encounter with Pythagoras
11. Three Words
14. Animals and Souls
15. Pythagoras and Heracleitus
16. Alignment and the Theorem
17. The Shape of the World and the Cosmos
18. The Push of the Cosmos
Problems with Pythagoras
19. Pythagoras in Italy
20. Who was Pythagoras?
21. The Historians and their Pythagorases
22. The curse of Fragmentariness
23. The Soul as Work of Art
24. Pythagoras and our Garden of Eden
Epilogue: Truth and Beauty
After-thoughts & Appendices
i. Celestial harmony and Ancient music
ii. Pythagoras, Lao Tzu and Confucius
iii. Proof by Rearrangement of the Pythagorean Theorem
Maps & Illustrations
Notes, Aknowledgements & Credits
Sources & Select Literature
The Gift of the East
‘Oranges and Green Oranges’ - Song Dynasty silk fan painted in ink and colour:
(?) Lin Chun, early 12th century: National Palace Museum, Taipei.
The story of the West begins with our debt to the East. Even as the day starts the East is at our breakfast table: the orange – prince of hybrids, from the foothills of the Himalaya, known in China for two and a half millennia and brought by Portuguese merchants into Europe in the late 15th century; the tea and porcelain likewise originally from China; the glassware, first perfected in Mesopotamia and Egypt; the coffee from the Horn of Africa, via Arabia and Turkey, and the sugar first brought from South East Asia by the Arabs into Europe through Sicily. Through the window where the morning sunlight enters are gardens: cultivated tulips, magnolias, peonies, rhododendrons, camellias, dozens of varieties of plants, all life-enhancing, all with ancient origins deep in the mountains or plains of Anatolia, Central Asia or China. Our cotton and linen clothes, made from plants first cultivated and fabrics first woven in ancient Egypt and Mesopotamia, and the silk which has given its name to the arteries that connected the West with China. Yet more comes to mind in looking around the room: wine, made from an exuberant, fruiting climber first brought to the Mediterranean from the Caucasus and Persia in Neolithic times. Olive oil and olives, from the Middle East in the same period. The generous chicken and her eggs from India and Southeast Asia. In later history, the first lemons and citrus fruits, rice, aubergines, even pasta – almost all brought by the Arabs into Sicily from Persia. Almonds, pistachios, pepper, a thousand spices and flavours. Yoghurt, yoga; precious stones and jewels; the sound of the flute and the music of stringed instruments... If we take them all away, what is left?
It is hard to conceive of our lives, our clothes and the food we eat without feeling chastened by our millennia-long debt to Asia. But it is not solely a story of luxuries, spices and perfumes; it is about the essential and commonest things which we take for granted in our lives, even the religious affiliations we may have – Jewish, Christian, Moslem, Buddhist, Hindu, whatever – all of which are Asian in origin. Without the things that it has taken from the East, the whole nature of our existence in the West would be unthinkably different.
In ways both obvious and subtle, Western culture has been sustained and shaped by the East – by the abundance, the imagination, and also by the awareness of beauty which has flowed out of Asia. But the relationship is not just one of giving and taking alone: it is more complex. The West has crucially processed whatever it has taken from Asia over the centuries, transforming it and often humanising it profoundly. We will observe this very same process in how Pythagoras transforms what he learns from the East...
Out of India
Extent of the Persian Achaemenid Empire under Darius I (500 BC) - from Libya to the Indus Valley and Western Himalaya, and from the (former) Aral Sea to the Straits of Hormuz.
From both Egypt directly, and from Babylon through the intermediary agency of the Persian Empire, Greece had long drawn deeply on the advanced knowledge of calculation and computation, and the superior technology of engineering, hydraulics and surveying of these already very ancient cultures. This was what they had to offer in abundance. But we have no clear evidence that either Egyptian or Babylonian thinkers had ever attempted to synthesise and integrate their impressive grasp of calculation, astronomic data, medical and musical practice into a philosophy which aspired to unify them. It was this synthesising capacity, in particular, which was the signal contribution of the Greek mind, as embodied particularly in the person of Pythagoras.
Greece had learnt her sculptural and architectural skills from Egypt; her geometry, arithmetic and calculation from Babylon; and, side-stepping Egyptian hieroglyphic script and Babylonian cuneiform, had sensibly adopted the flexible, phonetic alphabet of the Phoenicians, increasing its potential notably by the addition of vowel symbols. All three of these cultures stand as godparents to the new, emerging Greece. But there was one thing that – because of its strategic position in Asia – only Babylon could offer: and that was a conduit for the thinking that came from deeper within the East, namely from India. We would be only picking up half the story of Pre-Socratic and early Greek philosophy, if we were to neglect the powerful influences that are entering the West from India.
How is this possible? India is a very long way away from the islands and ports of the Aegean Sea. This is true: yet it lies at the other end of a vast arc of territory, stretching from Asia Minor through to the borders of today’s Afghanistan and the Indus Valley, most of which the Persian emperor, Cyrus the Great, as Herodotus related, brought under his own single control, while his successors, Cambyses II and Darius I, annexed the remainder. Both Hellenic Asia Minor (which included Miletus, Ephesus and Sardis, the former capital of the kingdom of Lydia) and the borderlands of the Indian sub-continent found themselves all of a sudden held within the same political entity, and this remarkable situation lasted for a crucial half-century, from the early campaigns of Cyrus in the 540s through to Darius’s ill-fated invasion of Greece in 490, which culminated in his defeat at Marathon. The court of these three Persian emperors – Cyrus, Cambyses and Darius – was, by design, highly multi-cultural; and so it was that, in both the Persian imperial capital itself and in the regional capital of Babylon, the intellectual and spiritual worlds of Greeks and Indians met and enjoyed contact, half way between their two geographically very distant poles...
Up until the collapse of the Roman Empire in the 5th century of this era, there was constant contact between India and the West. Eusebius, quoting Aristotle’s pupil Aristoxenus, even cites a conversation which is said to have taken place between Socrates and a visiting Indian guru. Maybe fanciful; but not impossible. The contacts were closer than we might imagine; and they were later given huge impetus by Alexander’s conquest of Persia in the 4th century BC. The cities which were founded in Bactria and in the upper Indus Valley following his campaigns there, were free to form mixed Hellenic-Buddhist communities; and it was this that helped to create the earliest visual and plastic arts of Buddhist culture.
The picture which emerges is one of profound cultural interpenetration over a considerable area of the surface of the globe. For much of this commerce of ideas Persia was the intermediary, and even though Greece and Persia were at times implacable foes, their cultures were nonetheless deeply linked. There were many Greeks who worked for the court of the Persian emperors in positions of trust: engineers (Mandrocles of Samos), military advisors (Histiaeus of Miletus), explorers (Scylax of Caryanda), sculptors (Telephanes of Phocaea) and physicians (Democedes of Croton). And these are just the ones we know by name. The syncretism that evolved was not just oxygen for the awakening intellectual culture of Greece in Pythagoras’s time, it was a force that shaped its content through the meeting of ideas and minds between Persia’s far West and its far East, which now stretched even into India.
The journeys Pythagoras undertook – to whatever extent we wish to accept they happened – are a metaphor for the discovery of the encompassing world by the human mind, and of the search for a structure underlying our existence in it. In him, the journeys become the thinking...
Architecture of mind
The Temple of Hephaistos (or ‘Theseion’), Athens, mid 5th century BC;
drawn by James Stuart and Nicholas Revett, 1794.
Perhaps the most enduring gift of all those bequeathed to posterity by the early Greek mind was the gift of simplification – a cutting away of the irrelevant and the illogical, and a seeking out of the universal and essential instead. A pursuit of structure. A Doric or Ionic temple is the physical embodiment of that spirit. Orderly, unpretentious and immediately comprehensible, it is fundamentally a simple idea – even though its eventual refinements may possess considerable subtlety. The temple structure has no complex forms: its interior is plain and subdued; its exterior is a paradigm of unity, clarity and symmetry. Its success throughout all of history as an architectural model to be copied reflects the success of the Greek way of thinking both about the cosmos and about the proper functioning of society. Structure, clarity and balance are pre-eminent in both.
Architecture is the visible and material expression of a way of thinking: yet at the same time it also actively shapes our thinking. It is in a constant and living dialogue with the mind. We create the outdoor and indoor spaces we inhabit, and those spaces in turn create ways of being and thinking in us. Buildings themselves have helped to fashion our attitudes towards the divine, to death and to the exercise of power. They also illustrate how thought structures vary fundamentally between different cultures and different periods. John Ruskin observed that, unlike the written histories of a particular age, buildings never fail to tell the truth about the epochs and the minds which created them.
Bold projects of architecture dominated the horizon of Pythagoras’s native Samos during his lifetime, as we have seen, and it is not merely coincidental that, among his peers, Pythagoras is perhaps the most ‘architectural’ thinker in the way he envisions his cosmos as a geometric and harmonised structure. In the period in which he was a child in Samos, the grandest temple of the Greek world was being constructed on the edge of his city, soon to be followed by competing projects at Ephesus and at the Oracle of Apollo at Didyma on the mainland of Asia Minor opposite. These buildings were to change the course of Western architecture, just as his own observations were to alter the thinking of those who came after him. In seemingly very little time, the conception of a temple-building had evolved out of all recognition from its clumsy predecessors, transforming itself from chrysalis to butterfly – mirroring the rapidity of development in thinking and philosophy under way in the same geographic area. It is not easy to explain the speed and degree of such architectural development: much has to do with Samos’s close commercial and political ties with Egypt, and what the island’s merchants had seen there. There was also the ingenuous desire simply to emulate, or even outdo, the greater and older culture of the Egyptians. But, once again, it is the transformation that Egyptian ideas of building design undergo when they take root in the Aegean world that is so significant...
Sound and Silence
Oak tree at the site of the Oracle of Zeus at Dodona.
The ear of Antiquity was more finely attuned to pure sound than ours. The greater silence of its world shaped a different mind. At the ancient sanctuary of Zeus at Dodona in the mountains of Epirus, oracles were revealed by the sound of acorns dropping into bronze bowls from a sacred oak tree: these bowls were of varying sizes and would have given rise to different pitches of resonance and durations of sound before reverting again into silence. In the intervals of silence, the rustling of the tree’s leaves would also be listened to attentively. Visitors and pilgrims would sit for long, waiting to hear these sacred sounds. They did this not out of foolishness or ignorance, but because, by listening, they put themselves into a receptive state of mind. Receptivity is fundamental for the relation to experience which Pythagoras advocates: wisdom and insight are things that we cannot go and get, but rather we receive them – like house-guests, asked or unasked, or like swallows that may or may not choose to nest beneath our eaves.
Our contemporary and more simplistic conception of an oracle is that you go to it, ask a worldly question and sit and wait for an answer from a divine source, transmitted through some strange and particular medium. This, at least, is the image of them that has been common since the time of the first written accounts. But the coming of literacy itself taught us to think in these more mechanistic and reductive ways: writing seeks, and lives by, explanation. Oracular sites are not explainable as mechanisms, which is why we do not wish to have them today. They were places for learning receptivity, where the simple act of waiting and listening – not listening for something, just plain listening – was often revelatory. This perhaps sheds light on one of the most revealing precepts of the Pythagorean School which the philosopher is said to have founded towards the end of his life in Croton in Southern Italy, that novices should pass their first five years in silence. This, at least, is what Iamblichus tells us. Imagine: no words (in the context of the School at least) for five years.
In an age when background noise was almost non-existent and birdsong was vividly present, where distant horns communicated simple messages across the open landscape or announced the arrival of a military force, where the powerful resonance of gongs marked ritual moments or the thinner sound of the reed-pipe a funeral, and when the human voice in song was to be heard wherever there was humanity, pure and simple sound was a richer and more meaningful experience. This is the quality of sound to which a person of Pythagoras’s era was accustomed, and it helps to explain how it was possible that his single most important philosophical idea arose from the consideration of sound...
Animals and Souls
Ancient rhyton (a pouring cup for ceremonial drinking) in the shape of a dog’s head, with decoration attributed to the Brygos Painter, working in Athens c.490-470 BC; Museo Nazionale Etrusco di Villa Giulia, Rome.
Humans and animals: what a chequered history lies there. Some of it good; most of it terrible. We live in the midst of nature and yet we are often as orphans in its world. The collective memory of exploitation, disturbance and invasion of territory has meant that we terrify most of the rest of creation and we are unable to get close to it even when we want to. Yet when we do establish close relations with animals it can be a source of wondrous curiosity to us. The simplest thing done for an animal can bring an unexpected, almost disproportionate, sense of joy or gratification. Why ever should we not have meaningful relations with animals? The pity is that we don’t have more.
Those few historically constructive relationships that we have formed with animals through history – with the horse in so many parts of the world, with the dog since time immemorial, with the elephant in South Asia, the camel and the falcon in Arabia – have come about through a strange concoction of fear, persistent inculcation, mutual benefit and mutual receptivity. Like children these creatures awaken in us a range of reflex feelings. Unlike children, however, these animals to which we are close can, if they wish, at any moment do us mortal harm; yet miraculously they don’t, unless provoked, because the bonds between us are felt by them,at least,to be somehow inviolable. Much of our own purpose in desiring to be close to them is utilitarian. Yet, once such a relationship is established, a sense of our kinship with them starts to break upon our consciousness. At that point the uneasy question arises as to whether, behind their animal eyes, lies the repository of a soul.
This question held a fascination for Pythagoras, as we have seen. In that one surviving anecdote about him which dates from his own time, he gives us an insight into his thinking both about the soul and about animals...
The transmigration of the soul from incarnation to incarnation and the wheel of constant rebirth appears to have been an idea so widely permeating the beliefs of much of Asia at that time, that it comes as a surprise to realise that it could possibly have seemed unusual or funny to the Aegean Greeks of the 6th century BC...
Standing Buddha, from Gandhara, 1st century.
(Musée Guimet, Paris).
This striking example of the style of sculpture which emerged in the Upper Indus Basin, in the area of Gandhara on the borderlands of modern-day Afghanistan and Pakistan, during the 1st century BC exemplifies perhaps the most felicitous and beautiful conjunction of Asian and European aesthetic in the history of world art. It speaks eloquently of the movement of artistic ideas and styles across great distances and spans of time. The Gandharan artists were of an unusual heredity – a mixed Greek and Asian descent: they lived in the communities which had been seeded by Alexander the Great, and in the cities that he had founded during his sweep through the Persian Empire into Asia two centuries earlier. This remarkable hybrid gave crucial form and style to the first figurative visual art of Buddhism which had, up until then, been strictly abstract and symbolic in nature: at the same time it endowed it with a poignant humanity. In Gandhara, the Buddha appears as a human person for the first time in the history of art; furthermore, he appears dressed as a Greek teacher or philosopher. Through the long history of their interaction both in the realm of ideas and of art, the East has given sustenance to the West, and the West at other times to the East. Such is the intricate fabric of the world’s artistic and intellectual history.
The Buddha as Greek philosopher: the Greek philosopher as Spiritual Guru. Two ideas from different parts of the world that became superimposed in one resonant image. In the same way, when perceptions from quite different sources and arising from opposite areas of the field of human experience come together – from within us and without, arising from a spiritual awareness inside of us and meeting with an observation of the world around us – the synergy and harmony they create can take us by surprise. As the musical demonstration of Pythagoras had shown, when two or more tones sound in perfect harmony (either together or sequentially), their beauty and their effect upon us is greater, by far, than the simple sum of their individual elements. It is for this reason that harmonía is central to everything that Pythagoras said and believed. We know instinctively when an intuition within us overlaps and resonates with a reality we perceive outside. It transforms what we see and how we see it. We cannot say in words what that sensation is, but we know it when we encounter it. This is the reason for which Pythagoras laid words and explanations aside and allowed the simple acoustic experiment to speak for itself. Those who understood what it meant, understood. Those who didn’t see any significance in it – well, in another life, they would have the opportunity to understand perhaps.
Pythagoras is a horizon. He was the first mind we know of in the West to think in a truly integral manner about our world, our place within it, and its place within the cosmos. He was the first person to talk about all this without resorting to myth, anthropomorphic deities or allegorical narrative. And he was the first person to show how it was beauty that gave meaning to this whole – the beauty of underlying harmony and of a universal mathematical order. Others such as Anaximander and Thales before him had spoken abstractly of the design of the cosmos, but they did not choose to explore the participation of the human soul within it; while others such as Hesiod and Pherecydes had spoken in an allegorical manner about humanity within the cosmos, but without relating it to a rational cosmic structure. The perceptions of Pythagoras, for sure, built upon those of his older contemporaries. Yet we like to consider him as one of the creators, in his time, of a quite new way of thinking; and, although the reality is more complex, for convenience we conceive of that way as characteristically ‘Western’ because of the primacy he gave to number and geometry in his conception of the ordered cosmos. This laid important ground for the prevalently scientific method we use to understand our world today. But unlike his predecessors, Pythagoras was unable to leave aside from his enquiry the participation of the human soul. In this way he shows how great a part of his instinct remained within the sphere of what we would consider to be ‘Eastern’ thinking whose roots went deep into Asia and Ancient India. He was, in short, a creation of both East and West...