Chapter 8
THE MISSION
In the age of Leucippus and Democritus, and even before them, lived those called Pythagoreans, who applied themselves to the study of mathematics and were the first to advance that science; and, penetrated with it, they fancied that the principles of mathematics were the principles of all things.
—Aristotle, Metaphysics A.5
Lysis woke up abruptly, his heart thumping, his forehead covered with sweat. He had been dreaming of fire—again. Only this time the dream had seemed so real he could have sworn he had felt the scorching heat on his face and heard the screams, people yelling as if in pain, crying for help. He was an optimist by nature, used to looking at the bright side of things, but lately he had become possessed with a feeling that those dreams forebode some imminent calamity. The time was the second year of the 71st Olympiad, or 495 BC.
Could my dreams be a warning from the gods? He wondered. It was a while since he had sacrificed to Hera, the queen of the Olympian gods. When he worshipped at her temple situated in a promontory overlooking the Ionian Sea near the city of Croton, in Magna Graecia, he would leave wheat and barley and cheese cakes as offerings. He knew that the cow was the animal especially sacred to the goddess, but the killing of animals was forbidden in the fraternity—the sect, as outsiders called it—as was the eating of animal flesh. As prescribed by the Master, he would enter the temple from the left and wearing a clean garment in which no one had slept, because sleep, just as black or brown, indicates slothfulness, while cleanliness is a sign of fairness and justice in reasoning.
He wished he could travel to Delphi to consult the oracle about his dreams, but right now he had to attend to a more pressing affair. The Master had sent for him concerning “an urgent matter of the utmost importance,” as Zalmoxis, the Master’s servant, had put it when he delivered the message the night before.
Lysis came from the city of Tarentum, situated on a rocky peninsula north of Croton. As a young man he had traveled to Croton to listen to a sage by the name of Pythagoras who had arrived in the city from abroad. Tall and graceful in speech and gesture and blessed by nature with unsurpassed intelligence, the well-traveled foreigner had made a strong impression on the Crotonians and rapidly won their esteem, to the point that the governing council of elders had invited him to give lectures also to the younger men and the women. Such was the man’s reputation that people from far and wide, including magnates and kings, came to hear his eloquent discourses.
“Observe the crowd gathering at some public spectacle,” Pythagoras would tell the audience, “and you will see men of all descriptions and views. One hastens to sell his wares for money and gain; another exhibits his bodily strength for renown; but the most liberal assemble to contemplate the landscape, the beautiful works of art, the specimens of valor, and the customary literary productions. So also in the present life men of manifold pursuits are assembled. Some are influenced by the desire for riches and luxury; others, by the love of power and dominion, or by an insane ambition for glory. But the purest and more genuine character is that of the man who devotes himself to the contemplation of the most beautiful things, and he may properly be called a philosopher. The survey of the whole heaven and of the stars that revolve therein is indeed beautiful, when we consider their order, which is derived from participation in the first intelligible essence. But that first essence is the nature of Number and numerical ratios that pervades everything, and according to which all those celestial bodies are arranged elegantly, and adorned fittingly. Similarly beautiful is devotion to erudition. The desire for something like this is philosophy.”
He would also teach that the soul is immortal, and that after death it transmigrates into another human or mammalian animal body. For this reason people must abstain from eating flesh, lest they unwittingly should devour their own parents, or children, or friends in some altered shape. Beans too were forbidden for various reasons, but especially because they were believed to be a temporary receptacle for the transmigration of souls, perhaps due to their resemblance to human testicles.
“Do not defile your bodies with impious food,” he would urge the crowd. “We have corn; we have apples weighing down the branches, and grapes swelling on the vines. There are flavorsome herbs and vegetables that can be cooked and softened over the fire, and there is no lack of flowing milk or thyme-scented honey. The earth, prodigal of its wealth, offers us food that can be procured without slaughtering or bloodshed.”
Pythagoras was a native of the island of Samos, in Ionia, a Greek colony on the western coast of the Aegean Sea. Around the middle of the sixth century BC, the once thriving and opulent Ionians had fallen under the yoke, first of the Kingdom of Lydia, then of Persia. At a time when the victorious days of Athens and Sparta were yet to come, the glory of the Hellenic spirit was kept alive by the Greeks who settled in southern Italy. Following the Persian conquest, many eminent Ionians migrated there, attracted by the freedom and prosperity of the Greek cities that dotted the lower part of the Italian boot. One of these newcomers was Pythagoras. Soon after arriving in Croton, he founded an ascetic and secretive society, part scientific school, part religious community, devoted to the study of numbers, which he considered to be “the source and the root of all things.” Out of reverence, the members of the sect never referred to Pythagoras by name but as “the Master” or “that Man.”
Lysis had joined the Pythagorean fellowship and in time had become a mathematiko, or “student,” the higher of the two classes of disciples. These learned the more elaborate aspects of geometry, astronomy, and other sciences from Pythagoras himself. The akousmatikoi, or “auditors,” on the other hand, were limited to hearing summarized lectures without detailed explanations given by one of the Master’s disciples.
The Pythagorean disciples’ daily program began with solitary morning walks to some quiet place, such as a temple or grove. They walked alone because they considered it inappropriate to engage in conversation or mingle in a crowd before having attained inner serenity.
After their morning walk they met in groups, in a temple or some other peaceful place, to discuss the Master’s teachings or listen to lectures. Next, they turned their attention to the health of the body. Most of them raced, while others wrestled or exercised by jumping with weights.
They lunched on honey and honeycomb and bread made of millet or barley. In the afternoon they resumed their walks in parties of two or three, reviewing the teachings they had received and the precepts they had learned, after which they visited the bath house to cleanse themselves for the evening rituals.
Following their ablutions they gathered in the common dining room, where Pythagoras performed libations and fumigations in honor of the deceased and the gods. They represented the gods not by anthropomorphic images but as the sphere, the divine receptacle in form and nature similar to the Universe. These rituals he repeated three times, because the tripod was the symbol of Apollo’s prophetic powers.
For supper they ate raw or boiled vegetables and herbs, cheese cakes, grapes and dry figs, very rarely fish and never beans or animal meat, and they drank wine. The evening ended with the reading aloud of some of Pythagoras’ precepts and maxims, such as: Do not devour your heart (meaning, we ought not to afflict ourselves with grief and sorrow). Do not poke the fire with a sword (Do not provoke a man in anger). Do not negligently enter into a temple, nor adore carelessly. Always sacrifice and adore barefoot. Make thy libations to the Gods by the ear (Beautify thy worship with music). To the celestial Gods sacrifice an odd number, but to the infernal, an even (To God consecrate the indivisible soul; offer the body to hell). Leave not the least mark of the pot on the ashes (After reconciliation, forget the disagreement). Help a man to take up a burden, but not to lay it down (Encourage not idleness but virtue). Write not in the snow (Do not trust your precepts to persons of an inconstant character). After which they separated and went home.
As Lysis knew well, certain Crotonians were hostile to the fraternity and capable of base and treacherous acts, just like Hipparchus, a former disciple of the Master, who had philosophized indiscriminately and publicly when the very first thing the Master taught was that his doctrines should be preserved in silence and under no circumstances revealed to the profane. He had since been expelled from the fraternity and a symbolic tomb had been built for him with “Let him be declared dead” written on it.
Still worse had been the fate of another sacrilegious disciple, Hippasus, who had divulged the secret of the incommensurable quantities to those unworthy to receive it. So indignant with him was the Divine Power that it unleashed a terrible storm while he was sailing at sea, and the impious perished when his ship was wrecked on the sharp reefs of the Ionian coast.
Two line segments are said to be incommensurable (i.e., without common measure) if the ratio of their lengths cannot be expressed as a fraction n/m of integers n, m. The Pythagoreans were the first to discover that the diagonal of a square is incommensurable with its side. Put another way, if the side of the square measures, say, n centimeters, then the diagonal is not an exact number of centimeters; and the same is true regardless of the unit of length used. In practice, a “common measure” of any two segments can always be found, within the limits of precision, by choosing the unit of length sufficiently small. This empirical fact may have led to the belief that segments were always commensurable.
How the Pythagoreans, or rather some unknown Pythagorean, discovered the existence of incommensurable lengths has been the subject of much speculation. But a passage in Aristotle suggests a possible argument leading to the result: Aristotle says that the diagonal cannot be commensurable with the side because if it were, then the notions of odd and even numbers would coincide. The argument hinges on the early Pythagoreans’ conception of a line segment as made up of a finite number of points and the fact that their geometry was based on the natural numbers.
Suppose then that we construct a square whose side has an odd number k of points. How many points does its diagonal have? Say that the number of its points is n. The unknown Pythagorean must have deduced that n should be even, because according to his Master’s famous theorem, n2 = k2 + k2, so the square of n equals 2k2, which is even, and only even numbers have even squares. But, on the other hand, n would have to be odd, because if n is even, its square must be a multiple of 4, which 2k2 isn’t.
At this point the Pythagorean would have been at a loss to make sense of a number that was at the same time even and odd—a logical impossibility. (For the Pythagoreans, whether a number was even or odd was important, as this property was related to other, nonmathematical ideas.) And so, our unknown Pythagorean—we imagine him young and blond, with a sharp intellect and a predisposition for inquisitive speculation—would have concluded that the diagonal had no number! It could not have occurred to him that the way out of the paradox was to realize that the length of the diagonal was a new kind of number we now call irrational (i.e., not expressible as a ratio n/m of two integers). We write this number as 
k, where (the square root of 2) is the (irrational) measure of the diagonal using the side of the square as unit of length.
From the vantage point of our present-day knowledge, we can hardly imagine the anguish and despair the discovery of incommensurable quantities might have caused the Pythagoreans. Apart from the fact that it dealt a blow to their tenet that “all is number and proportion,” inasmuch as mathematics was for them a description of reality, they may have glimpsed in this discovery a contradiction at the heart of reality itself. So terrible a truth had to be hidden at all costs. What if they had stumbled upon some forbidden knowledge the gods never intended humans to posses? Who knows what unspeakable punishment might befall them? Wasn’t Hippasus’ death at sea a retribution from the divinities for having revealed the secret?
On the other hand, the mind of the unknown Pythagorean must have been blessed by the gods themselves, for he had not merely discovered a new truth, he had done it by the power of reasoning alone in what is probably one of the first examples of a mathematical proof. The mathematics of his predecessors in Babylonia or ancient India is rich in arithmetic and geometric facts; but these are only stated, never proved by means of a logical argument. It is the presence of proofs from first principles or axioms that sets Greek mathematics apart, in particular those in Euclid’s Elements, which became the standard for mathematical rigor for nearly two millennia.
Among the most prominent citizens of Croton was a wealthy aristocrat by the name of Cylon, a man with a disposition to take offense easily and to react violently, and who would not stop at anything to achieve his ends. As he considered himself worthy of whatever was best, he deemed it his right to be admitted to the Pythagorean fellowship, and he therefore went to see Pythagoras for that purpose.
Those wishing to enter the fellowship had to pass a certain initiation test, which could take up to one year to complete. But prior to the admission test Pythagoras would study their manners, their gait, and the motions of their whole body, for he considered these as visible signs of the invisible tendencies of the soul, such as the potential to engage in serious studies or the ability to cope with the rigors of an ascetic life.
It did not take very long for Pythagoras to discern Cylon’s true nature, and to tell him in no unclear terms that his admission to the fellowship was out of the question. The rejected applicant took this as a great affront and became furious, and, just as Lysis feared, devised a vindictive scheme to get back at Pythagoras and his disciples.
His opportunity came following the defeat and capture by Croton of its rich and luxurious neighbor, the city of Sybaris, on the Gulf of Tarentum, after a ferocious battle. For many years the Crotonians had enjoyed peace and prosperity. But the people had changed, and they were no longer content with the old magistrates and the original form of government. After the capture of Sybaris, the dissatisfaction of many with the way the conquered land had been divided provided a pretext to challenge the existing constitution. Lysis had been present at the assembly where changes to the constitution had been debated, such as opening the magistracy to every citizen. When this was opposed by the Pythagorean Democenes, Cylon took the opportunity to mount an attack on the fraternity. In a long and fiery speech he accused the Pythagorean philosophy of being a conspiracy against democracy.
After Cylon’s defamatory tirade had aroused the masses, the plebeian Ninon had followed with his own calumnies, pretending he had penetrated the secrets of the Pythagoreans. A scribe had then begun to read from a book given to him by Ninon entitled Sacred Discourse: “Friends are to be venerated in the same manner as gods, but others are to be treated as brutes.” A series of other lies and fabrications had followed: that Pythagoras had praised Homer for calling a king a shepherd of the people—an implicit approval of aristocracy in which rulers are few, while the implication is that the rest of men are like cattle; that beans should be scorned because they are used in voting (voters signified their approval or disapproval of a candidate for public office by placing a light-colored or dark-colored bean in an urn, respectively), whereas the Pythagoreans selected officeholders by appointment; that to rule should be an object of desire, because it is better to be a bull for a day than an ox for life; and that the people should remember that when they raised their right hand to vote, that same hand was rejected by the Pythagoreans, who were aristocrats.
The purpose of the joint attacks by Cylon and Ninon had been clear: to stir up the Crotonian people against the Master and his disciples. The worst is still to come, thought Lysis; there is no telling to what extremes Cylon might go to seek revenge, and now he has the masses on his side. He feared that a revolt against the Pythagoreans was in the making. It was no doubt on this account that the Master wished to see him.
When Lysis arrived at the house he was greeted on the porch by Myia, Pythagoras’ eldest daughter. “The Master awaits you,” she said, as she held open the large door leading into a high-walled inner courtyard. As Lysis walked across it he passed the altar dedicated to Zeus Herkeios, “the protector of the walled courtyard,” on his way to the andron, or reception room.
Zalmoxis was standing in the small antechamber. Without speaking a word, he pointed to the adjacent room, whose only light came from the courtyard through a small window high on the wall. Lysis stood in the doorway, waiting for a signal to step inside. His eyes, slowly adjusting to the darkness, could barely make out the long-haired figure of the old man in the immaculate white chiton, an ankle-length tunic, sitting on a wooden bench at the opposite end of the room.
“Come in and be seated, my loyal friend,” said Pythagoras at last. He had been studying Lysis’ expression. “I see troubling thoughts crossing your mind.”
“You see right, Master,” replied Lysis.
He sat down on a low stool before speaking again.
“Cylon is in a vindictive mood. He has aroused the assembly against the fraternity and violence may result.”
“To act inconsiderately is part of a fool,” was Pythagoras’ calm response.
But Lysis had still another source of concern: “I have been having some disturbing dreams of late, premonitory dreams, I believe. I fear for your life, Master.”
“Don’t forget that death is appointed to all . . .” And then he added, in a tone that had suddenly become mellow: “I have had some premonitions of my own, and they are the reason I have sent for you, Lysis, my most faithful and dependable friend.”
Lysis’ only reaction was a slight bow of the head. He was flattered by the compliment but would not let his expression show it.
“What I shall ask you to do is known to my daughter Myia, but to no one else, not even to my wife Theano or any of my most intimate friends. No other person besides us three shall be let in on the secret; no one, that is, until the right man comes along.”
He stroked his white beard in a pensive manner, increasing the dramatic effect his words were having on Lysis.
“The Providence has spared me so far,” Pythagoras resumed, “but I have now received some signs from the gods that my soul will soon journey away from my tired body and migrate to another one in order to accomplish a mission of the utmost importance, and I need your help to carry it out.”
As he spoke, he rested his left hand on an object that had been lying on the bench beside him but that only now Lysis remarked: a metal cylinder, of the kind used to keep papyrus scrolls.
“It’s all written here, in this scroll,” said the old man, tapping on the metal case, “and I must absolutely avail myself of it on my return among the living.” There was a short pause before he added: “You are to follow my instructions to the letter, lest this precious document should be lost or, even worse, fall into the wrong hands.”
Pythagoras then instructed Lysis to keep the scroll in a safe place and guard it jealously, and to make arrangements so that, upon his death, its safekeeping be transferred to his son, or daughter, or wife, or a trusted friend. This person would have to promise allegiance by taking the Pythagorean Oath: “I swear by he who revealed to our soul the Tetraktys, that most sacred symbol, the source of all our wisdom and the perennial root of Nature’s fount.” The new keeper was to pass the document on to his own descendants, who would hand it down to theirs and so on from generation to generation.
The successive keepers would enjoy the protection of Apollo, but they should be warned that the wrath and the curse of the god would fall upon them should they neglect their duties as custodians of the precious manuscript, break its protective seal, or otherwise put in jeopardy the success of Pythagoras’ mission. The passing of the scroll from one keeper to the next should continue, perhaps for a long time, until the reincarnation of Pythagoras was ready to carry out his mission. The Providence would then send a signal to the current keeper to deliver the scroll to him.
Lysis had been listening attentively to the Master. He was proud to have been chosen as custodian of the scroll but realized the heavy responsibility that had befallen him. Although he wished the Master would tell him a bit more about the nature of the mission, he did not dare to ask. But he felt that one particular point required further clarification: “When the appropriate time comes, how, among all men, will the custodian of the scroll recognize the Master?”
Pythagoras seemed annoyed by the question, as if his disciple should have known the obvious answer. But there was no sign of irritation in his voice when he replied, fixing Lysis as he spoke: “He will be an extraordinarily gifted man, eminently versed in the secrets of Number, of whom many wonderful things will be persistently related.”