Pythagoras and Western Magic

Pythagoras and Western Magic
John Michael Greer

Nowadays, Pythagoras of Samos is usually remembered as the discoverer of the so-called “Pythagorean theorem” on the relationship of the sides of a right triangle – a theorem that was known in Babylonia more than a thousand years before he was born.1) Behind his place as a footnote in the history of geometry, however, looms a larger and substantially stranger reputation. He has been credited with major discoveries in mathematics and musical theory as well as geometry, and has a crucial place in the development of Greek philosophy; in fact, the word “philosopher” itself was apparently his invention.2) At the same time, the school he founded was at least as much a religious sect as it was a philosophical movement, with teachings about reincarnation, ethical precepts and a sizeable collection of ritual taboos binding its members. Furthermore, Greek and Roman writers — in tones that range from reverence to mockery — reported claims that Pythagoras himself performed miracles, foretold the future, and recounted his own previous lives dating back to before the Trojan War.3)

It's little wonder that modern historical scholarship has veered awkwardly about when dealing with Pythagoras and his place in the history of ideas. For most of the last three centuries, the usual approach to the man and his thought has been to dismiss everything unacceptably magical about him as an encrustation of legends from the declining years of classical civilization.4) In this way Pythagoras has been squeezed into an early but honored place in the line of progressive thinkers that forms the origin myth of the modern world. In recent years, discomfort with this sort of mythic history has given rise to another, equally mythic, in which Pythagoras is pictured as a shamanic figure, an inheritor of archaic traditions from the Greeks' Indo-European roots or a borrower of practices from the Greek world's less civilized neighbors.5) Both these views, of course, take for granted the same historical mythology of progress; the quarrel is simply whether magic belongs to the early parts of the story, as a primal inheritance not yet outgrown, or later on as a sign of a society-wide loss of nerve, one more aspect of the ancient world's failure to live up to modern expectations.

The critical problem with both these images, though, is that the early Classical Greek magic that can be glimpsed through the lens of the early Pythagorean school can be adequately explained in neither way. As the evidence shows clearly enough, archaic magical practices were indeed involved in the Pythagorean phenomenon, but these were not simply being handed down unchanged. They were being reshaped {16} and reinterpreted in terms of a new language, the language of philosophy — and this was happening during the years in which that new language was first being created.

The high magic of the ancient world was thus neither an outdated relic from past ages or a late product of cultural decline. It came into being in the first flowering of classical culture, as part of the same broad impulse, and it continued to develop in scope and sophistication throughout the centuries when the classical world was at its height. In the same way, and at the same time, as the tools of reasoned discourse were first being applied to human experience of the natural world to create something akin to science, they were also being applied to a range of other human experiences to create the foundations of the high magic of the West.

In that development, the role of Pythagoras was a crucial one. He seems to have been the first major figure in the intellectual history of the West to combine magic and philosophy, and a number of the elements that were central to his own synthesis — including a mystical analysis of number focused on the first ten natural numbers, the use of the pentagram as a magical symbol, theories of reincarnation and of cosmic harmony, and others — have remained part of the core of Western high magic ever since.

Pythagoras was born around 570 BCE,6) to an engraver named Mnesarchos and his wife Pythais, on the island of Samos off what is now the coast of Turkey. Samos at that time was near the height of its wealth and influence as one part of a thriving belt of Ionian Greek settlements on the eastern shores of the Aegean. The years of Pythagoras' birth and early childhood were the years when construction began on the great Temple of Hera at Samos, which Herodotus ranked as one of the three greatest engineering projects in the Greek world. The great lyric poet Anacreon was a Samian, and Pythagoras' contemporary; on the mainland a short distance away was the city of Miletus, where Thales and Anaximander were founding the first major tradition of Greek natural science during Pythagoras' youth. Trade links and political contacts linked Samos with Egypt, the city-states of Phoenicia and the rich kingdoms of Asia Minor.7) It was a propitious setting for the birth and youth of a philosopher.

Of his early life no real information survives, although it's clear that he received the normal Greek schooling of the time–gymnastike, athletic training, and mousike, instruction in literature, music and the arts. Like most men of his time, he studied with a number of teachers in his youth, but only one of them seems to have left a lasting impression. {17}

This was Pherecydes of Syros, according to ancient testimonies the first Greek ever to write a book in prose rather than verse. Tradition recounts that he had studied secret writings from Phoenicia. Whether this is true or not, the handful of surviving quotes and summaries of his book, The Seven-Hollows Mingling Of The Gods or Origin Of The Gods, reveal a vision of the cosmos at odds with most of the myths and speculations of mainstream Greek culture.8) Three divine powers existing from eternity — Chronos or Time, Zan or Zas (an alternate form of Zeus), and Chthonie, the earth-principle — are said to govern the universe in Pherecydes' account. Chronos creates fire, water and air from his seed, mingles them in five “hollows” or “nooks” from which a generation of gods is born, and then fights a battle with the serpent-god Ophioneus, winning the crown of heaven and casting Ophioneus into the sea. Zas weds Chthonie and gives her a robe embroidered with lands and seas, and she takes the name Ge (“Earth”); the robe also appears on a winged oak tree, which may be another manifestation of Chthonie. There was undoubtedly much more that has not survived.

This mythic cosmogony was not the only basis for Pherecydes' later reputation. A story repeated in numerous sources reports that once, upon drinking water from a well, he predicted that there would be an earthquake within days, which duly happened; one wonders if he had learned that turbidity or dissolved gases in groundwater can predict seismic activity. Similarly, he was said to have seen a ship making for harbor, commented to his companions that it would not reach land safely, and looked on as a cloudburst followed and swamped the ship. A solsticemarker on Syros was also credited to him. All this sounds very much like the work of a perceptive student of nature, but any attempt to classify Pherecydes as some sort of proto-scientist must also deal with the mythic vision of his book, and with the fact that Pherecydes was also apparently the first Greek to teach the doctrines of reincarnation and the immortality of the soul.9)

According to one ancient writer, it was after hearing Pherecydes speak on these latter themes that Pythagoras decided to become a philosopher rather than an athlete.10) The story may be apocryphal, but the impact of Pherecydes' ideas on his student was substantial enough to give it some degree of plausibility. Certainly there is every reason to think that Pythagoras retained a good deal of affection for the older philosopher; during his final illness, years later, it was Pythagoras who cared for him and arranged for his burial when he finally died.

Aurelius Augustinus, the same writer who described the effect of Pherecydes on Pythagoras' career plans, commented also that Pythagoras was “not contented with the philosophy of the Greeks, which then hardly existed or at any rate was most obscure.”11) To a young man hungry for learning, the merchant fleets that linked the harbor of Samos with the ends of the ancient world offered one obvious way to go past the limits of his own culture. It was a way that people from the Greek {18} world had begun to take in significant numbers in the generation or two before Pythagoras. Polycrates, an important citizen of Samos who would make himself ruler of the island a few years later, had traveled to Egypt and was a friend of the Egyptian Pharaoh Ahmes-sa-neith, whom the Greeks called Amasis; Pythagoras asked Polycrates for a letter of introduction, got it, and set out on the first of his journeys. According to his biographer Iamblichus, he was then twenty-two years old.12)

Accounts of his journeys vary from biographer to biographer, but most agree that he spent time studying in Egypt and Babylon. What exactly he learned there is anyone's guess. Both these ancient civilizations were in the last years of their existence, and it's fairly clear that in Egypt, at least, much of the cultural and scholarly richness of the past had already been lost. Attempts to trace precise details of Pythagorean lore to Egyptian or Babylonian sources have had equivocal results.13) It seems likely, though, that much of what Pythagoras later taught came from materials he gathered in his travels.

It should also be noted, though, that certain mystical strains in Greek culture had much to contribute to the Pythagorean synthesis. The movement known as Orphism was central here. There are any number of scholarly questions and disputes about the nature, sources and history of the Orphic movement, and it's not even certain that Orphism as such existed during Pythagoras' time.14) Certainly, though, there were a range of mystical teachings in circulation when Pythagoras was born, many of them associated with the mystery initiations of the Greek world. Porphyry describes a visit by Pythagoras to at least one of these, the Cretan mystery of the Idaean Dactyls, and later writers point to a number of identities between Orphic and Pythagorean traditions.15)

His wanderings finally brought him to Crotona in what is now southern Italy, where he spent most of the last half of his life. There he founded a hetairia — a half-religious, half-political body — around his teachings, which apparently held political control over most of the Greek colonies in Italy for much of a century. At some point around 500 BCE, apparently as a result of political troubles, he moved from Crotona to Metapontum, where he died a short time later.

Egyptian, Babylonian, and Orphic or proto-Orphic teachings played important roles in Pythagoras' education, if the biographers are to be believed, and there is some plausibility to the claim. Certainly echoes of all these elements can be found readily, from the earliest records onward, in the system of thought that went under his name. Some of his more enthusiastic biographers credit Pythagoras with an even wider range of travels, studies and initiations, but this seems to be more an {19} attempt to have him corner the market on wisdom than anything else; in this category must be placed Iamblichus' claim that Pythagoras studied under the Druids, for example.

The same sort of enthusiasm in a modern context has decked Pythagoras out with the attributes of a shaman, and as this point of view still commands a certain amount of respect it is probably necessary to deal with it here in detail. It has been pointed out, with some supporting evidence, that several of the tribal peoples to the north and east of the Greek homeland seem to have practiced something not too much unlike shamanism of the classic Siberian type; it has been suggested, with somewhat less justification, that certain Greek myths that can be linked to these peoples are fundamentally shamanistic in nature; it has been claimed, finally, that a handful of figures in the early history of Greek philosophy make more sense if they are reinterpreted as “Greek shamans,” and some sweeping claims have been made on this basis.16)

The problems with these claims are twofold. On the one hand, the word “shamanism” has come to be used with quite a bit of recklessness in recent years, even - in fact, especially — in academic circles. Properly speaking, it refers to a group of highly specific traditions and practices common to many of the native peoples of Siberia and the Americas.17) Those traditions and practices are far from universal. There are plenty of magicians, healers, ritualists and diviners around the world, in and out of tribal cultures, who do their work in radically different ways. For their part, the figures lumped together as “Greek shamans” — although some of them do indeed seem to have been involved with magical practices — have only a small fraction of the characteristics that define shamans in the most accurate sense of the word.18) To paper over the very substantial differences with a single term is to dilute that term itself to the point of meaninglessness; if “shamanism” means anything magical in the broadest sense, why not simply use the word “magic” instead?

The other side of the difficulty lies in the notion that these “shamanic” traditions in ancient Greek culture have to be traced back to non-Greek peoples in order to explain their existence. It's hard not to see the unspoken assumption at work here, which is that magical practices were foreign to the Greeks. With this assumption, though, we are back in the realm of modern mythology. From the Renaissance onward, attempts have been made to force the ancient Greeks onto a Procrustean bed of pure rationality, but these simply won't work; abundant evidence shows that magical practices were as deeply embedded in ancient Greek culture as they have been in all other human societies, including our own.19) It is certainly true that important figures in the history of Greek philosophy seem to have been involved with magical practices, but there is no need to call on shamanism to explain that fact. The magical traditions of Greek culture are ample explanation all by themselves. {20}

This point has implications central to our theme, though, because these Greek magical traditions are themselves linked, clearly and directly, to the currents of Greek mystical spirituality that underlay Pythagoras' own achievement. For example, Orpheus, the “father of initiations” and eponymous founder of the Orphic movement, was equally the dominant figure in the legendary lore of ancient Greek magic. Throughout the history of the classical world, his name was quite literally one to conjure with.20) Equally, the powers of the underworld who were central to the mystery cults were the powers most often invoked in Greek magical workings.

We happen to know a fair amount about these latter, because ancient Greek magicians had the archeologically useful habit of writing their spells on thin sheets of lead and dropping them into wells, springs, fresh graves, and other points of access to the underworld. As a result, more than fifteen hundred of these katadesmoi — “binding tablets” is a good English equivalent - have been uncovered over the last several centuries. The similarities between the language of these texts and surviving Bacchic and Orphic literature are unmistakeable, and it's unlikely to be an accident that the earliest binding tablets discovered so far, at Selinus in Sicily, were deposited in a temple with important links to the mystery cults.21)

Attempts have of course been made to raise the usual modern barricades between religion and magic in these cases, but here again this can't be justified by the evidence. On the contrary, it's clear — just as with the Egyptian and Babylonian traditions Pythagoras apparently studied — that the Greek traditions that went into the making of the Pythagorean synthesis were ones in which magic, mysticism and religion were blended to the point of fusion.

It's in this context that the miracles attributed to Pythagoras in the ancient sources need to be assessed. These are, in their own way, a crucial part of the story. Very few historical figures of ancient times were credited with so many wondrous deeds, but a thread of the miraculous runs through the biographies of many of the central figures of our story; by itself these tales prove nothing, but they can serve as markers for patterns of thought and action that carry much more in the way of meaning.

What were the miracles credited to Pythagoras? To modern eyes, at least, they make odd reading. According to his biographers, he appeared at the same hour of the same day in two towns more than a hundred miles apart. He tamed a savage bear by the power of his voice and converted it to vegetarianism, and instructed an ox to give up eating beans, a commandment it kept for the rest of its life. While walking on the seashore, he came across fishermen hauling in full {21} group of friends, the river itself called out, “Hello, Pythagoras!” He called an eagle down from the sky to be petted, and bit a poisonous snake to death. He recounted not only his own past incarnations but those of other people as well. He calmed storms, stopped high winds and banished a plague; and when he stood up among the spectators at the Olympic Games, the people around him saw that one of his thighs was made of gold.22)

Strange though these accounts may seem, they follow patterns that can readily be traced elsewhere in Greek culture. Quite a number of figures in the classical world, in fact, were credited with such a mastery of wild animals, of the forces of nature, and of the fabric of space and time; notable among these is Orpheus himself, whose lyre-playing called wild beasts and rivers to heel. Near-contemporaries of Pythagoras such as Empedocles of Acragas were credited with similar feats, as were several later figures such as Apollonius of Tyana and Jesus of Nazareth. Also worth considering is the intriguing comment of Apollonius Paradoxographos that Pythagoras “first studied mathematics and numbers, but later also indulged in the miracle-mongering of Pherecydes.”23)

The common feature of all these accounts is that they were attributed to people who were involved with magic. Miracles such as these, in fact, were the stereotypical powers of the most respected class of magician in the classical world, the theios aner or “divine man.”24) Every important figure in the history of Greek and Roman magic is the subject of similar or identical tales, although few of them collected legends in such profusion. When miracle stories of this sort appear in accounts concerning a classical figure, therefore, it's worth looking into the possibility that the figure in question either was a magician or was thought to be one.

Certainly Pythagoras was thought to be a magician, by later Pythagoreans as well as by their enemies. Was he one? Until recently, as mentioned earlier, most scholars rejected this idea with a good deal of heat, claiming that these legends and their uncomfortable implications were the product of the “decadent” thought of later centuries. In point of fact, though, accounts of the miracles of Pythagoras were widely known in the Greek world by the early fourth century BCE, little more than a century after his lifetime.25) They can be found among the very earliest references to Pythagoras and his teaching. It's hard to imagine that such claims would have gathered so quickly around him unless there was something to attract them. This is not to say that Pythagoras necessarily performed any of these miracles, what it does say, and clearly, is that he was seen – in his own lifetime, or very shortly thereafter — as the kind of person who could be expected to do so, or in other words that he was seen as a magician.

Another kind of evidence points in the same direction, from a very different standpoint. Near the end of the sixth century BCE, when Pythagoras was probably {22} still living, the philosopher Heraclitus accused him of manufacturing a wisdom of tricks and swindles out of other people's learning.26) This language is striking, for it echoes the standard rationalist dismissal of magic in ancient Greek writings — the claim that magic was all a matter of trickery and outright fraud. In the later literature on Pythagoras, this same sort of argument appears at much greater length; a story recounted by Hermippus, for example, has Pythagoras faking a descent into Hades with the assistance of his elderly mother!27) Here again, it's hard to imagine such accusations clustering around Pythagoras unless there was something to attract them, and as we've seen, theres good reason to believe that that “something” was magic.

To turn to the teachings of Pythagoras themselves, though, is to venture onto slippery ground. A few points are generally admitted — the idea that he taught some form of reincarnation, for example, is too widely attested to be challenged by more than a few modern scholars, and it's agreed equally that his teachings had a substantial ethical element, and dealt in some way with numbers. Beyond such generalities, though, matters become difficult.

The crux of the problem here, as with the related teachings of Orphism and the mysteries, is the secrecy practiced by the first generations of Pythagoreans. The earliest public account of Pythagorean teachings appeared in the writings of Philolaus of Crotona in the late fifth century BCE, which survives only in fragments quoted by other authors. The few fourth-century sources — Aristotle's book On the Pythagoreans, the writings of the Pythagoreans Philolaus of Crotona and Archytas of Tarentum, and a handful of others — have suffered a similar fate. As a result, the total corpus of surviving evidence for the original Pythagorean teachings could be made into a fairly slim pamphlet. On this scanty foundation, a succession of modern writers have built up various edifices of speculation, or simply brushed the whole matter aside as unimportant or undecidable.

Still, neither of these extremes is necessary. The surviving evidence does point in certain directions with a fair degree of clarity, and it's possible to trace at least some of the outlines of the Pythagorean teachings in their early forms. Some of these forms almost certainly go back to Pythagoras himself; others are likely to have been evolved later on; all of them are relevant to the Pythagorean tradition as it developed in later centuries, and to the important links between that tradition and the origins of Western high magic.

We can outline what is known about the early teachings under three headings: the bios Pythagorikos or Pythagorean disciplines of daily life, the akousmata, and the mathematical sciences on which Pythagoras' later reputation came to rest.28) {23}

To the ancient Greeks, the most striking feature about the early Pythagoreans was the distinctive way of life they followed, and which they claimed to have received from Pythagoras himself. “Pythagoras was especially revered for this,” comments Socrates in Plato's Republic; “his followers even now use the term “Pythagorean Way of Life,” and they stand out among the rest of men.”29) The more sardonic eyes of Athenian comic playwrights noted the same sense of distinction, and made regular use of it; the wandering Pythagorean ascetic, grubby, threadbare and arrogant, is a stock figure of the Middle Comedy.

These comic portrayals, in fact, provide among the best outlines of the bios Pythagorikos in ancient writings. Pythagoreans appear in them as barefoot, longhaired, shabbily dressed, and stiff with dirt because their way of life forbids them from using the public baths. They will not touch meat or wine, and live on vegetables and plain water. They follow such an ascetic life, the playwrights suggest wryly, because this is the best they can manage. When one character in a play by Aristophon announces that he has been to the underworld and seen that the Pythagoreans alone are permitted to feast with Pluto, another retorts that Pluto must be a very easy-going god if he dines with such ragamuffins.30)

How much of this ascetic stance actually originated with Pythagoras himself is hard to say for certain, but there is good evidence that much of the bios Pythagorikos dates back to the earliest phases of the movement. Many of the same characteristics mocked by the poets of the Middle Comedy are also identified as Orphic customs, and many of them are also reflected in the akousmata, which certainly come from the oldest stratum of Pythagorean tradition. While the extreme poverty mentioned in the comic portrayals was at least partly a function of their context - the Pythagoreans in fourth-century Athens were refugees from the final collapse of the political side of the movement — many of the other features are likely to be original.

One thing that apparently does not belong to the earliest forms of the tradition, though, is the vegetarianism that was mentioned (and mocked) over and over again in comic references. The akousmata, as we'll see, establish a wide range of food prohibitions; certain kinds of fish and certain animal organs, as well as beans, are not to be eaten. This implies, however, that other kinds of meat are not forbidden, and in fact there is a substantial body of early references that picture Pythagoras and the early Pythagoreans as eaters of meat.31) What prompted the change is anyone's guess, but it's possible that contacts between Pythagorean and Orphic circles in the years after Pythagoras' death are involved. {24}

A second element of the earliest stratum of Pythagorean teaching is a collection of brief, enigmatic maxims or sayings called akousmata, “things heard,” or symbola, “symbols” or “passwords.” These can be grouped into two broad classes, which correspond to a large degree with the other two elements of the traditions surveyed here: one, the larger of the two, passes on rules for daily life closely linked to the bios Pythagorikos, while the other communicates fragments of a wisdom tradition that includes myth, proverbial lore, cosmology, and certain elements of the mathematical sciences. To the first class belong akousmata such as these:

Do not wear a ring with the image of a god.
Do not eat from a whole loaf of bread.
Do not roast what has been boiled.
Do not eat heart or brains.
Do not speak in the dark.
Do not step over a yoke.
Do not sit on a bushel.
Do not stir the fire with a knife.
Do not travel by the public highways.
Abstain from beans.
Abstain from those fish which are sacred.
Put on the right shoe first, but wash the left foot first.
Enter temples and perform sacrifices barefoot.
Do not help a person to unload, only to load up.
To the second, smaller class, belong these:
The Isles of the Blest are the Sun and the Moon.
The sea is the tears of Cronus.
The Great and Little Bears are the hands of Rhea.
The planets are the dogs of Persephone.
The most just thing is to sacrifice.
Old age is decrease, youth is increase.
A friend is a second self.
The truest thing is number.
The oracle at Delphi is the tetraktys, which is the song the Sirens sing.32)

Most of these are baffling at first glance, but there are several keys that unlock their meanings. First of all, as scholars have been pointing out since the third century BCE, a good many of the akousmata of the first kind closely parallel popular superstitions and the precepts of Greek oracles and mysteries. Like the Orphics, the Pythagoreans adapted these traditional rituals of purity for new roles as part of a lifetime discipline, and enshrined them in maxims of a kind well suited for oral transmission. {25}

Second, a number of akousmata of the second kind appear to be remnants, similarly suited for an oral tradition, of a very specific kind of lore. The sayings that link the Sun and Moon with the Isles of the Blest, for example, or polar constellations with the hands of the goddess Rhea, draw connections between the visible heavens and the structures of Greek mythology - connections that are highly reminiscent of the starlore of Babylonia, which Pythagoras is said to have studied. These akousmata may well be the remnants of a much more developed system of mythic astronomy using Greek images in place of Babylonian ones.

Finally, it's by no means certain that the akousmata should be read only in terms of their most obvious meanings. As early as 400 BCE, Anaximander of Miletus had already written a book exploring hidden interpretations in the akousmata.33) The discovery of the Derveni papyrus, an allegorical commentary on Orphic poetry from the fourth century BCE, shows that the same sort of interpretation was going on in Orphic circles within a century or so after Pythagoras' death.34) Later still, the akousmata were generally explained by various schemes of moral allegory: for example, the prohibition against stirring the fire with a knife was said to mean that one should refrain from stirring up the anger of powerful men, and that against eating hearts was interpreted as an injunction not to worry excessively.

Many of these interpretations show the unmistakeable marks of late classical philosophy and religious thought, but it's quite possible that even in the beginning there was a hidden dimension to the meaning of the akousmata, one concealed under the proverbial Pythagorean silence. What that dimension might have comprised is impossible to guess, but the possibility of its existence opens up unexpected doors. In magical traditions rooted in the Pythagorean movement, certainly, the same sort of enigmatic communication on multiple levels came to play a central role.

Finally, there is the matter of the mathematical sciences in early Pythagoreanism. Later accounts made the four sciences of the medieval quadrivium — arithmetic, geometry, music and astronomy — central to Pythagoras' achievement; as the theorem bearing his name bears witness, the same habit of interpretation remains in place in our own culture. This approach to the early Pythagorean tradition has some validity, but it becomes misleading if taken in any simplistic way. There is a fair amount of evidence that Pythagoras and the early Pythagorean school devoted much of their efforts to the study of number, and to the ways number and numerical relationships serve as deep patterns for music and astronomy, but it's equally clear that these efforts went in directions that have little to do with mathematics in the typical modern sense of the word. {26}

The mathematical sciences, in something like their modern sense, were adopted wholesale by later figures in the Pythagorean tradition, and this has done a good deal to cloud the point. It's perfectly true, for instance, that such later Pythagorean figures as Nicomachus of Gerasa (active in the second century CE) have important roles in the history of ancient mathematics, but it's by no means certain that Pythagoras himself did. Certainly the earlier and more reliable sources say very little about this aspect of his work, and his name does not appear among classical lists of famous mathematicians until after the Pythagorean revival of the first few centuries of the common era redefined him in its own terms.35)

What sets the Pythagorean approach to number apart from mathematics in the modern sense is that it treats numbers as symbols, with meanings that go beyond pure quantity. From a Pythagorean perspective, the difference between two numbers — say, one and two — was not simply that two is twice as large as one. Each of these numbers is at the center of a cluster of symbolic meanings; it has its own character, its own personality, and its own relationships to the world of human experience.

It was from this standpoint that the early Pythagoreans, as well as many of their philosophical descendants in later times, pursued the study of number. A certain amount of mathematical knowledge in the modern sense did come out of their inquiries, especially in number theory and music. Still, it's a mistake to see this, as some modern writers have done, as evidence for a “scientific” attitude in the Pythagorean movement. There are many ways to use numbers in human thought, and many of them - including those central to the Pythagorean approach — have little in common with the sense of number as abstract quantity that seems like sheer common sense to so many people today.

Surviving references, many of them from Aristotle's lost work on the Pythagoreans, tell us something about what their symbolic understanding of number was like. We learn among other things that all numbers are born from the interaction of limit and the unlimited, opposite powers that are equivalent in some sense to odd and even, unity and plurality, male and female, and a range of other polarities. One, which is not a number but the source of all number, is mind and being; two is opinion; four, the first square number, is justice, being equal times equal; seven is opportunity, and also the virgin goddess Athena, because it is neither a factor nor a multiple of any of the other numbers from two to ten. Ten itself is the number of perfection, and embraces the whole nature of number.36) Numbers beyond ten were of far less importance, and since the number 10 is itself the sum of the first four numbers — 1+2+3+4 = 10 — the entire world of number, and the perfection of the whole universe, is contained in the numbers one through four. This became the basis for the central Pythagorean diagram, the tetraktys. Like most of their mathematical patterns, it was typically laid out on the ground with pebbles, {27} in the form shown below:

"The tetraktys, which is the song the sirens sing." A tetraktys formed in four rows as an upward pointing triangle of circles: 1, 2, 3, 4

“What is the Oracle of Delphi?” asks one of the most significant of the akousmata, and answers: “The tetraktys, which is the song the sirens sing.” What song that was, fortunately, is preserved in later documents, which point out that the tetraktys contains within itself the proportions governing the basic harmonies of music: 1 to 2, the octave; 2 to 3, the perfect fifth; 3 to 4, the perfect fourth; and the difference between fifth and fourth, which is a single whole tone.37) These same musical intervals, in turn, give rise to the “music of the spheres” — one of the most enduring of all Pythagorean concepts, the idea that each of the planets produces by its movement a musical tone that can be heard by the wise, bringing mathematics, music and cosmology into a single unity.

A saying preserved in several of the sources describes the tetraktys as “the fount and root of visible Nature.” What other connections Pythagoras may have found between this pattern and the natural world is anyone's guess, though texts from the Pythagorean revival of later centuries have plenty to offer. The same blending of symbolism, science and philosophy that appears in the tetraktys, however, is equally common all through the surviving remnants of early Pythagorean thought.

These, then, were the teachings — or some of them — that Pythagoras passed on to his students in the years after his arrival in Crotona: a fusion of Greek mythology and mystery teaching, Babylonian mathematics and starlore, and Egyptian theology, transformed by the presence of Greek philosophy in one of its earliest forms but still deeply rooted in the mythic world of its sources. All of these characteristics, each of these specific sources, and a fair number of the core ideas of the synthesis Pythagoras created from them, would go on to become central features of the tradition of Western high magic.

For all that, magic itself is the one thing that cannot be proved to exist as a subject of teaching in the earliest phases of the Pythagorean tradition. As we've seen, Pythagoras himself was understood as a magus from a very early period on; all the sources from which his synthesis was drawn have magic as a central element; the tradition in its later forms was as often as not part and parcel of explicitly magical systems. There is even evidence that Pythagoras himself and his Thracian {28} disciple Zalmoxis both underwent symbolic journeys to the underworld, journeys that were interpreted by later sceptical writers as hoaxes but may well have originally had a serious ritual context.38) Of magical teachings by Pythagoras himself, though, the only trace from before the common era is a mocking description by the comic playwright Timon, quoted by Diogenes Laertius:

Pythagoras, who often teaches
Precepts of magic, and with speeches
Of long high-sounding diction draws,
From gaping crowds, a vain applause.39)

What those “precepts of magic” might have been the surviving evidence does not even allow us to guess. As a result, it may well be that — barring the discovery of new documentary information — the original expressions of Western high magic may remain a permanent mystery.

{29}

{31}

Barnes, Jonathan, ed. and trans., Early Greek Philosophy (London: Penguin, 1987).

Burkert, Walter, Lore and Science in Early Pythagoreanism, trans. Edwin L. Minar Jr. (Cambridge, MA: Harvard UP, 1972).

De Santillana, Giorgio, and Hertha von Dechend, Hamlet's Mill (Boston: Davide R. Godine, 1977).

De Vogel, C.J., Pythagoras and Early Pythagoreanism (Assen: Van Gorcum, 1966).

Faraone, Christopher A., and Dirk Obbink, eds., Magika Hiera: Ancient Greek Magic and Religion (Oxford: Oxford UP, 1991).

Guthrie, K. S., comp. and trans., The Pythagorean Sourcebook and Library (Grand Rapids, MI: Phanes, 1987).

Guthrie, W. K. C., Orpheus and Greek Religion (London: Methuen, 1952).

Kingsley, Peter, Ancient Philosophy, Mystery and Magic: Empedocles and Pythagorean Tradition (Oxford: Clarendon, 1995).

Minar, E. L., Early Pythagorean Politics in Practice and Theory (Baltimore: Waverly, 1942).

Neugebauer, Otto, The Exact Sciences in Antiquity (Princeton: Princeton UP, 1952).

Philip, J. A., Pythagoras and Early Pythagoreanism (Toronto: U. Toronto P., 1966).

Schibli, Herrmann S., Pherekydes of Syros (Oxford: Clarendon, 1990).

Smith, Morton, Jesus the Magician (San Francisco: Harper & Row, 1978).

Von Fritz, Kurt, Pythagorean Politics in Southern Italy (NY: Columbia UP, 1940).

{32}


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1)
Neugebauer (1952), 35.
2)
This claim appears in Iamblichus' hagiographical biography of Pythagoras — see Guthrie (1987), 70 - but is generally accepted by modern scholars.
3)
The primary sources for the life of Pythagoras include four ancient biographies, collected in translation in Guthrie (1987), and a wide range of other sources, very few classical figures are as well attested. See Diels and Kranz (1951-2) for collected testimonia.
4)
This approach still remains standard in most histories of philosophy and mathematics. See also Philip (1966).
5)
For Pythagoras as shaman, see especially Burkert (1972).
6)
The dates of Pythagoras are conjectural, based on contradictory material from ancient sources. The dates used here are those proposed by de Vogel (1966); see also the discussion in von Fritz (1940), 47-67. The following account of his life is largely based on the biographies by Porphyry and Diogenes Laertius, taking into account issues raised by Burkert (1972), de Vogel (1966), Kingsley (1995), and Philip (1966).
7)
Philip (1966), 173-175; see also Herodotus, Book 3.
8)
For Pherecydes, see especially Schibli (1990), which includes the known fragments of and references to his work.
9)
Based on the reconstruction in Schibli (1990), 128-9.
10)
Quoted in Schibli (1990), 159.
11)
Ibid.
12)
This is implied (although not stated) by the chronology in Iamblichus, see von Fritz (1940), 47-9.
13)
Most of these, such as the writings of R. A. Schwaller de Lubicz and his disciples, tend to mistake the possibility of a Pythagorean interpretation for proof that this interpretation is valid. See de Santillana and von Dechend (1969) for similar logical mistakes in a more academic context.
14)
schol. lit on Orphism
15)
For Porphyry, see Guthrie (1987), 126; for later parallels, see Kingsley (1995).
16)
See, among others, Meuli (1935), Dodds (1951) and Burkert (1972).
17)
Eliade (1964) remains the standard work on the subject.
18)
Philip (1966) 159-162
19)
See Faraone (1992) and Kingsley (1995) among many others.
20)
Guthrie (1952), 17-19.
21)
For katadesmoi, see Gager (1992). For the temple at Selinus, and its relation to the earliest known binding tablets, see Gager (1992), 117 and 138-142, and Kingsley (1995), 242-244
22)
Sources for the miracles attributed to Pythagoras include the biographies by Porphyry (23-30) and Iamblichus (61, 134 and 140-143), as well as writings by Aelian, Plutarch, and others. See the summaries in Burkert (1972), 141-147, and Kingsley (1995), 289-316.
23)
Apollonius, Marvelous Stories 6, quoted in Schibli (1990).
24)
For the distinctions among classical concepts of the magician, see Smith (1978).
25)
See Burkert (1972), 137-147, and Kingsley (1995), 289-316.
26)
Heraclitus B81, quoted in Diogenes Laertius; see Guthrie (1987), 142.
27)
Quoted in Diogenes Laertius; see Guthrie (1987), 152.
28)
The outline of Pythagorean teaching given here is largely based on Philip (1966) and Burkert (1972), which reach nearly opposite conclusions on the basis of much the same evidence. Philip's Pythagoras is a proto-philosopher, Burkert's a shaman; most of the divergence between these two images can be resolved readily by recognizing Pythagoras as a magician, and thus intermediate between the two. I have also taken note of the criticisms in Kingsley (1995).
29)
Republic 600a.
30)
For Pythagoreans in the Middle Comedy, see Burkert (1972), 198-201.
31)
Burkert (1972), 180-185.
32)
The akousmata appear in numerous sources. See Burkert (1972), 166-192; a standard collection may be found in Guthrie (1987), 159-162
33)
See Kingsley (1995), 112-126, and Burkert (1972), 166 and 172.
34)
Kingsley (1995), loc. cit.
35)
See Philip (1966), 76-133.
36)
Burkert (1972), 465-482; see also Porphyry, in Guthrie (1987), and Waterfield (1988).
37)
See, for example, Guthrie (1987), 317-319. For a later and far more complex version of the same symbolism, see Nicomachus (1994).
38)
Primary sources are Diogenes Laertius, Guthrie (1987) 152, and Herodotus 4.96. See also Burkert (1972), 154-159.
39)
Diogenes Laertius, in Guthrie (1987), 150.