The Music of Pythagoras (12 page)

Having come to the conclusion not only that numbers, but the specific numbers 1, 2, 3, and 4 and the ratios between them were the primordial organizing principle of the universe, Pythagorean thinking moved in other directions, some of which seem strange and primitive, but it is not surprising that they overestimated the simplicity of the rationality they had glimpsed and were too expectant of immediate applications and results. They were not unlike the earliest followers of Jesus, coming away from what was for them a transforming experience and trying to apply it to the everyday world, thinking all would be resolved soon. The Pythagoreans had discovered a new road to “truth.” Great thinkers thought about truth and proposed answers. Only a shaman—and many regarded Pythagoras as what we today would call a shaman—was sure he had the answer. In fact, Pythagoras and his followers
did
, but they traveled their new road weighted down with ancient baggage. Still in the age of oracles, divination, and mystic utterances, with its preconceptions about the universe and nature,
their naive conception of the world carried over into a naive conception of the power of numbers.

T
HE HALCYON DAYS
in Croton lasted thirty years. Iamblichus’ biography included long lists of names, which he probably got from Aristoxenus, of Pythagoras’ first followers, who sat at his feet, heard his teaching, argued points and worked out problems with him, played with the pebbles, and experimented with the
kanon
and with hanging disks. Was the young physician “Alcmaeon” really one of them? Was there actually a “Brontinus” who was husband and/or father of Theano? Were “Leo” and “Bathyllus” real people? And what of the “Pythagorean women,” about whom nothing is known but their names on these lists? Frustratingly, there is no specific surviving information about how the new coinage affected the economy or, except the story of Milo’s defeat of Sibaris, about Pythagorean leadership in Croton and the surrounding territory, what offices the Pythagoreans held, or exactly in what capacity they wielded their power—only that they did wield it and that the results were by most accounts beneficial to the region. What is clear is that in about 500
B.C
., three decades after Pythagoras arrived in Croton, hostility among the populace and perhaps a coup within the ranks of his followers brought it all to an end. The information is confused and contradictory, with common themes being others’ suspicion that Pythagoras and his followers were either becoming too powerful politically or aspiring to too much power—and, oddly, an unusual respect for beans.

According to Diogenes Laertius, Pythagoras was visiting with friends in Milo’s home when someone deliberately set fire to the house. The arsonists were either Crotonians who feared that Pythagoras might “aspire to the tyranny” or envious, disgruntled people who thought they should have been included in this gathering but had not been deemed “worthy of admission.” Pythagoras escaped but was captured and killed when he avoided crossing a bean field and took a longer way around. He must have decided, Diogenes Laertius said, that death was preferable to trampling on beans or speaking with his pursuers. About forty of his companions died as well.

Diogenes Laertius was interested in conflicting accounts, so he also reported a story he got from Hermippus, portraying Pythagoras and his “usual companions” in a militaristic light. They had joined the Agrigentine army to fight the army of Syracuse. The Syracusans put them to
flight and captured and killed Pythagoras as he was making a detour around a bean field. Being less squeamish about trampling on beans did not help his companions. About thirty-five were caught and burned at the stake in Tarentum, accused of trying to set up a rival government in opposition to the prevailing magistrates.

Diogenes Laertius showed he had a rather macabre sense of humor by casting part of this story into verse in another of his “jesting epigrams.”

Alas! alas! why did Pythagoras hold

Beans in such wondrous honor? Why, besides
,

Did he thus die among his choice companions?

Here was a field of beans; and so the sage
,

Died in the common road of Agrigentum
,

Rather than trample down his favorite beans
.

Two other endings to the story came through Diogenes Laertius from the trustworthy Dicaearchus and Heracleides Ponticus; in these, Pythagoras escaped his pursuers but died soon thereafter in Metapontum of self-imposed starvation.
^*

Porphyry gave a more detailed description of what supposedly happened, based on Aristoxenus, naming names and filling in the gaps in the other stories, and Iamblichus had some of the same specifics. According to this fuller account, the huge success of Pythagoras and his associates, and particularly their role in the administration and reform of the cities, aroused envy, most notably and ominously from one Cylon. He was a wealthy community leader of impeccable breeding, but also of a “severe, violent and tyrannical disposition,” and he controlled a large group of loyal supporters. He had a high opinion of himself, “esteemed himself worthy of whatever was best,” and assumed he would be welcomed to the Pythagorean fellowship. When Cylon approached Pythagoras, “extolled himself,” and tried to converse, Pythagoras peremptorily “sent him about his business.” Pythagoras, Porphyry pointed out, “was accustomed to read in the nature and
manners of human bodies the disposition of the man.” Cylon did not take the rebuff gracefully. He assembled his cronies and instigated a conspiracy against Pythagoras and his followers. According to Iamblichus it took some time for Cylon to bring his plans to fruition because of the Pythagoreans’ power and the trust placed in them by the citizens of the various cities. Accounts more sympathetic to Cylon had him as the leader of a group that opposed the oppressive ultra-conservatism of the Pythagoreans.

Iamblichus suggested that Hippasus—who invented the demonstration of the musical ratios using the disks of different thicknesses—may have played a subversive role. Before Cylon’s attack, Hippasus was, according to Iamblichus, one of a faction, among the insiders, who disagreed with Pythagoras and the more orthodox members of the school. He urged Pythagoreans who were playing prominent roles in governing the cities to adopt more democratic policies. He may have attempted to stir up popular feeling against Pythagoras’ leadership, playing into Cylon’s hands.

W. K. C. Guthrie described, with good understanding of human nature, the complicated political situation that probably contributed to the death or exile of Pythagoras:

This combination of forces seems to have been due on the one hand to popular discontent with the concentration of power in the hands of a few, coupled with the ordinary man’s dislike of what he considers mumbo-jumbo, and on the other to the native aristocracy’s suspicion of the Pythagorean coteries, whose assumption of superiority and esoteric knowledge must at times have been hard to bear.
²

Porphyry took the longest and most dramatic version of the story from Dicaearchus. Pythagoras was with his friends in Milo’s house when Cylon’s men set it afire. Pythagoras’ most devoted followers threw themselves into the flames to make a bridge with their bodies for the elderly sage to cross and escape. He and a remnant of survivors then tried to reach the city. Fleeing along the road, the others were gradually picked off by their pursuers, but Pythagoras, protected by them as much as possible during their flight, managed eventually to make his way to the harbor of Caulonia and from there to Locri. The Locrians refused him
sanctuary. Perhaps they sensed that the days of Pythagorean preeminence had come to an end and feared retribution from Cylon if they sheltered him. Or perhaps they feared Pythagoras himself, for, as the story goes, their message to him as they turned him away was that they admired his wisdom but liked their present condition and way of life and did not wish to change.
^*
In any case, the story has it that they sent some old men to intercept him before he could reach their gates and tell him that the Locrians would give him food and supplies but he must “go to some other place.” Pythagoras sailed to Tarentum, then back to Croton. The Crotonians also sent him away. Everywhere, as Porphyry reported Dicaearchus’ words, “mobs arose against him, of which even now the inhabitants make mention, calling them the Pythagorean riots.” In Dicaearchus’ account, Pythagoras eventually found asylum in the temple of the Muses in Metapontum, where he starved himself to death, grieving for the friends who had perished trying to save him.

The people of Metapontum prefer another ending. According to the tradition in that city, after Pythagoras arrived as a refugee from Croton, he settled down and established a school. After his death, his house and school were incorporated into a temple of Hera. Fifteen columns and sections of pavement from that temple still remain today in Metapontum, called the Palatine Tables, because knights (paladins) in the Middle Ages assembled there before setting off on the Crusades. In the first century
B.C
., when Cicero visited Metapontum, people could still identify the house where they believed Pythagoras had lived. Cicero wrote about how moved he was when he visited it.

Porphyry lamented that most of what Pythagoras taught died with him and his closest followers. “With them also died their knowledge,” he wrote, “which till then they had kept secret except for a few obscure things which were commonly repeated by those who did not understand them.” Iamblichus wrote that the cities hardly mourned Pythagoras at all or took much notice of what had happened, though in truth they had lost “those men most qualified to govern.” “Then science died in the breasts of its possessors, having by them been preserved as something mystic and incommunicable.”

Sixth Century
B.C
.

I
N THE FIRST OR EARLY SECOND
century
A.D
., Plutarch, the author of the famous
Parallel Lives
, and his team of researchers tried to find the earliest reference connecting Pythagoras with the “Pythagorean theorem.”
^*
They came upon a story in the writing of a man named Apollodorus, who probably lived in the century of Plato and Aristotle, that told of Pythagoras sacrificing an ox to celebrate the discovery of “the famous figure of Pythagoras.”
^†
Plutarch concluded that this “famous figure” must have been the Pythagorean triangle. Unfortunately Apollodorus was no more specific than those words “the famous figure of Pythagoras”—which probably indicates that it was so famous he had no need to be.

A modern author could also write “the famous figure of Pythagoras” and be as certain as Apollodorus apparently was that no reader would think of anything but the “Pythagorean triangle.” Even nonmathematicians
can often recall the “Pythagorean theorem” from memory: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. For millennia, anyone who had reason to know anything about this theorem thought Pythagoras had discovered it.

For many who learned the formula in school and always thought of it only in terms of squaring numbers, rather than involving actual square shapes, it came as an almost chilling revelation when Jacob Bronowski in his television series
The Ascent of Man
attached a square to each side of a right triangle and showed what the equation really means. The space enclosed in the square “on the hypotenuse” is exactly the same amount of space as is enclosed in the other two squares combined. The whole matter suddenly took on a decidedly Pythagorean aura. Clearly this was something that might indeed have been discovered and is true in a way that does not require a trained mathematician or even a mathematical mind to recognize. In fact, using numbers is only one of several ways of discovering it and proving it is true.

Bronowski pointed out that right angles are part of the most primitive, primordial experience of the world:

There are two experiences on which our visual world is based: that gravity is vertical, and that the horizon stands at right angles to it. And it is that conjunction, those cross-wires in the visual field, which fixes the nature of the right angle.
¹

Bronowski did not mean that experiencing the world in this way necessarily leads immediately, or ever, to the discovery of the Pythagorean theorem. Indeed, all over the ancient world, long before Pythagoras,
right angles were used in building and surveying, and right triangles appeared decoratively.
^*
Without drawing tools, a draftsman can produce right triangles, and a skilled draftsman can produce right triangles that no human eye can see are not absolutely precise—this without knowledge of the Pythagorean theorem. Just as tuning a harp is an “ear thing”—and was, long before anyone understood the ratios of musical harmony—the use of right triangles in design was an “eye thing.” Such judgments of harmony, figures, and lines are intuitive for human beings, and the mathematical relationships that lie hidden in nature and the structure of the universe often manifest themselves in the everyday world in useful ways long before anyone thinks of looking for explanations or deep relationships.