Archimedes went out into the courtyard, splashed his face with some water, and sat down against the wall, hands dangling limply from his upfolded knees. He was not sure what he believed about an afterlife. Like most educated Greeks, he found the stories his own people told about the gods and the Underworld totally incredible, but to replace those stories he had only contradictory reports from the teachings of the philosophers. The soul was the true Platonic Form, immortal and unchangeable, struggling through the shadow play of the world, reborn many times until it could find its way back to the God who had made it. The soul of the Wise was king, and by virtue might attain eternal union with the Good. The soul was a handful of atoms, born with the body, disintegrating with that body's death, and the gods lived apart from the world and had no interest in it. What was he to believe?
It hadn't mattered much, before.
After a while, he went upstairs and took out his abacus and compasses. He drew a circle in the sand: that was immortal and unchangeable. Its end was its beginning, and it defined the total of all angles. The ratio of its circumference to its diameter was forever the same number: three and a fraction. What that fraction was, though, was impossible to calculate. Less than a seventh. Try to define it further, and it slipped away from you, more precise than your measurement, infinitely extendable, infinitely variable. Like the soul. Like the soul, it could not be comprehended by reason.
That thought was comforting.
He inscribed a square in the circle, then an octagon, and began calculating in earnest.
When Arata came up about three hours later, she found her son crouched over the abacus, sucking the hinge of his compasses. Scratched into the sand was a multi-sided polygon, circumscribed by a circle and filled with a tangle of superimposed reckonings.
"Dearest," she said gently, "the neighbors have started to arrive."
It was traditional for friends and neighbors to pay their respects to the dead as soon as possible, and for the family to greet them dressed in black, with hair cut short in mourning. Arata's hair was freshly cropped, and she had draped about herself a black cloak bought many years before for her mother's funeral and worn infrequently since. Philyra, too, was dressed in mourning; even the slaves were prepared. But Archimedes still wore the good tunic he had put on that morning, and his hair hung in tangles over his forehead. Faced with his mother's summons, however, he merely took the compasses out of his mouth and said, "It's more than ten seventy-firsts and less than a seventh."
Even if the evening light hadn't shown clearly the dry trails of tears across his cheeks, Arata would have known better than to mistake his absorption for lack of feeling. She crouched down beside him as quietly as though he were a wild animal she was trying not to startle. "What is?" she asked.
He gestured with the compasses at a point on the diagram where the circle's circumference was cut by its diameter. The letter [Phi] had been written in the angle between them. "That." There was a silence, and then he said, "People often say it's three and a seventh, but it's not. It's not a rational number at all. If I could draw more sides to the polygon, I could approximate it more closely, but no one can ever calculate it absolutely. It goes on forever."
Arata regarded the circle and the scratched figures. Phidias would have understood them. That thought had just become painful. "Why does it matter?" she asked.
He stared blindly at the circle. "Some things do go on forever," he whispered. "If some part of us wasn't like them, would we be able to understand that?"
At that she saw the reason for his calculations, and, strangely, found comfort in them. Her husband too had loved and believed in these infinite things, and now he was with them. She put an arm about her son's shoulders, and for a moment they were both quite still. Then Arata sighed. "Dearest," she said resolutely, "you're the head of the family now. You must change and come down and greet the neighbors."
Archimedes dropped the compasses and put his hands over his face. He did not want to speak to anyone.
"You must," Arata insisted. "He was always so proud of you. Let everyone see that he left a son who honors him."
Archimedes nodded, pulled himself to his feet, and went with her. The black cloak she found for him had been his father's. Putting it on made him shudder.
Several of the neighbors, alerted by the commotion earlier in the day, were already gathered in the courtyard. Archimedes greeted them courteously, and they responded with condolences, then went to pay their respects to the body. Phidias, washed, dressed in his best clothing, and garlanded with herbs and flowers, lay on the sickroom couch facing the door, eyes closed, one thin hand clutching a honey cake as an offering to the guardian of the realms of the dead. Archimedes gazed at the corpse with a curious sense of indifference. This formal object had nothing to do with the astronomer, the solver of puzzles, the musician who had brought him up.
Philyra had already seated herself at the head of the couch and begun playing a dirge upon the kithara; as the women of the neighborhood arrived they sat down next to her and joined in, either singing or simply keening, so that the room filled with the thin moaning of grief. Arata sat down on a chair next to the couch, but made no sound, and covered her head.
Archimedes wondered if there were more people he should inform of the death. Phidias had been an only child, but Arata had a brother, and there were friends. Should he ask his mother about it? It seemed better not to disturb her. What about the funeral? In this hot weather it would have to take place next day. He supposed he should be arranging wood and incense for the pyre, and seeing about a funeral feast. Did he have money for it all? Presumably the shopkeepers would give him credit.
It seemed unbelievably strange to be worrying about such things, with his father lying there dead.
He went back into the courtyard, and was relieved to see Marcus returning from the public fountain with a heavy amphora of the water the visitors would need to ritually purify themselves from the contact with death. "Marcus," he whispered, hurrying over to him, "who should we send to about this?"
"Your mother's already informed everyone," said Marcus. Archimedes blushed, ashamed that Arata should have had to worry.
The visitors kept arriving all evening. When it began to grow dark, the slaves found torches and set them up in the courtyard and by the door. They had just been lit when Archimedes became aware of a commotion in the street outside- and then Hieron came through the open door, followed by his secretary. The unexpected appearance of the lord of the city caused an alarmed ruffle in the now-crowded courtyard, but Hieron ignored the stir and walked straight to Archimedes. "My condolences," he said, shaking hands. "You have lost a father who was one of the best men in the city, and your grief must be great."
Archimedes blinked, fiercely pleased by such a public declaration from such a source. The neighborhood had always liked Phidias- but it had always laughed at him, too. "Thank you," he replied. "I do grieve for him, very much."
"It would be your shame if you did not," said Hieron.
Like any other mourner, he went on to the sickroom to view the body; when he entered, the women were so startled that they stopped keening, and there was a sudden, profound, reverberating silence. Once again, Hieron ignored the effect he produced, and he bowed his head respectfully to the dead. "Phidias, farewell!" he said. "I always regretted that I could not study with you longer. May the earth be light upon you!" Then he went up to Arata, who was still sitting veiled beside her husband's body. "Good lady," he said, "your loss is great. But I trust that the outstanding promise shown by your son is some comfort to you."
Arata was utterly speechless. She clutched her cloak tightly against her breast and nodded wordlessly. Hieron nodded back, in farewell, and withdrew.
Back in the courtyard, he turned again to Archimedes. "Please," he said, "allow me to show the esteem in which I held your father, and the respect I have for you, and permit me to provide for the funeral. If you agree, my slaves and the resources of my house are at your dis
posal."
"I, uh," stammered Archimedes, almost as speechless as his mother. "I, uh- thank you."
Hieron smiled. "Good. Just tell my secretary Nikostratos here what you want, and he'll see that it's arranged for you." He gently directed Archimedes toward the secretary with a pat on the arm, and turned to go. Then he turned back again. "Oh," he added, "it struck me that you haven't yet been paid for that astounding catapult you built. I'm ashamed that I can't possibly pay as much as such a fine machine is worth, but Nikostratos has something for it. I wish you joy!" With that he gave his hands a perfunctory ceremonial wash in the water which stood ready by the narrow door, then stepped out into the night.
Archimedes looked at the secretary. Nikostratos, a bland-faced, nondescript man in his thirties, burdened with a heavy satchel, looked back. "Do you wish to tell me what arrangements you want now, sir?" he asked.
"Uh- yes," said Archimedes, keenly aware of the astonished neighbors. "Um- I suppose we should go into the dining room."
Marcus fetched lamps for the dining room, then stood listening while the secretary jotted down the requirements for the funeral. He added up the bill in his own mind as they proceeded: wood, incense, wine and cakes for a hundred- Archimedes said sixty at first, but the secretary thought this too mean. It was not going to come to less than twenty-five drachmae, Marcus concluded, and would probably be considerably more. The king was not going to save money by paying for a funeral and skimping on a catapult. And Marcus doubted that Hieron meant to skimp on the catapult either, despite his words about not paying as much as it was worth. He just wished he knew why the king of Syracuse was putting himself out to flatter and conciliate a catapult engineer.
When the funeral requirements had been fixed, the secretary took out an olive-wood box, which he set down before Archimedes. "The money for the catapult," he stated. "Can I ask you to sign for it?"
Archimedes looked at it vaguely and asked, "How much is it?"
"Two hundred and fifty drachmae," replied the secretary matter-of-factly. He pulled a ledger out of his satchel.
Archimedes stared, then lifted the lid from the box. New-minted silver which had been packed to the rim spilled out onto the dining table. He shook his head. "It was supposed to be fifty!" he protested. "And the king said that-"
"I was instructed to say that if the catapult were priced according to its value, it should be a thousand," said Nikostratos.
Archimedes stared at him for a long moment in silence. Then he looked down and picked up one of the coins which had fallen onto the table. Hieron's face, diademed and smiling, had been stamped in profile on the obverse. He studied it. A number of things he had seen and heard without really paying attention fell into place. He had always known that he was exceptional as a mathematician, but he'd thought that at mechanics, which were merely a hobby to him, he was only ordinarily good. But he realized now that Epimeles had not been flattering him: the Welcomer really was the best catapult built in Syracuse in twenty years. That pivot- that was something nobody had thought of before. The reason the workshop slaves had laughed was that he hadn't realized that. Eudaimon had been not merely short-tempered, but jealous. Kallippos had really believed that it was impossible to move a ship single-handed.
He was the best engineer in the city, and what his mind and hands could shape was so powerful that the king himself was now trying to cultivate him. This piece of silver, shining in his hand, was a tribute to his power. It was deeply satisfying, but at the same time frightening. The Roman army might soon be arriving to lay siege to Syracuse, and his own abilities would be in the first line of defense against it. The danger at once seemed much closer, and much more real.
He took fifty drachmae out of the box, then pushed the box itself back toward Nikostratos. "Tell the king I thank him for his generous offer," he said, "but I will take the price agreed, and no more."
Nikostratos was genuinely surprised- a strange sight, in such a dry man. He tried to push the box back. "This is the sum the king instructed me to pay you," he protested. "He won't want it back!"
Archimedes shook his head, "I am Syracusan; I don't need to be paid extra to defend Syracuse. I will take the agreed price for the catapult because my family needs it, but I will not profit from my city's urgent need by taking more."
The secretary stared. Archimedes took the ledger out of his hands and found the entry- "To Archimedes son of Phidias, for the one-talent catapult for the Hexapylon, 250 dr." He crossed out "250 dr" and wrote above it, "50 dr., as agreed," and signed his name.
Nikostratos suddenly smiled widely. "The gods have favored Syracuse," he said quietly. He took back his ledger and the olive-wood box, and put both away. Still smiling, he murmured his good nights and departed.
Archimedes looked at Marcus, who still stood watching by the door. "I suppose you disapprove of that?" he said challengingly.
But Marcus grinned widely and shook his head. "Not me," he said. "If a man isn't willing to fight for his own city, he deserves slavery."
And you, Marcus thought to himself, have just refused to be bought.
9
Four days later, Delia watched Agathon set out sour-faced and hurrying on some errand of the king's. Then she walked up to the great double door of the mansion on the Ortygia, opened it, and stepped through.
It was as easy as that: open the door and step out into the street. Nothing there, she told herself, to cause this pounding of the blood in her ears, this sense of vertigo that slowed her footsteps as she started down the road. There was nothing dangerous in what she was doing- it was just that she had never done it before.
Never before walked through that door without someone in attendance upon her. Never before set off, telling no one, for an appointment of which the household would not approve.
It was a shocking thing. She should not do it; of course she should not. But ever since the demonstration, her pretense that her interest in Archimedes was no more than that of a patroness in a potentially useful servant of the state had been vanishing like water into sand. She was chagrined at how completely she had been deluding herself. And yet, she was sure that at first she had not been pretending. When she first met the man she had simply been intrigued by him- but that had changed. It was ridiculous! She had seen him three times, spoken to him twice, played music with him once- and she felt that if she allowed him to slip away she would regret it all her life.
She had written him a note: I must speak with you. Meet me at the fountain of Arethusa tomorrow at the tenth hour. I wish you well. She had addressed it to "Archimedes, son of Phidias, at the catapult workshop," sealed it with one of Hieron's seals- he kept several about the house- and set it in a pile of the king's letters which were about to be distributed through the city. It had been fearfully easy. It was still easy: the end of a working day, the streets of the Ortygia as full as they ever were, and herself easing her way down the street, inconspicuous among the others, swathed in a voluminous cloak of linen with a fold pulled modestly over her head to conceal her face. Of course, nobody had been trying to prevent her leaving the house: nobody had ever imagined that she would do such a wanton, shameless, and disloyal thing as to arrange an assignation with a young man.
When the possibility of what she was doing had first occurred to her, she had striven to force it from her mind. It would be wickedly self-indulgent and disloyal to return all her brother's kindness to her with nothing but callous ingratitude and shame. The king's own sister went whoring after an engineer, the gossip would say. She promised herself that she would do no such thing. She did not love Archimedes- she barely knew him. She could certainly live without him!
And yet, and yet… in a way, not knowing him was the worst of it. It was as though she had been walking all her life along the same narrow streets and then, unexpectedly, at the top of a hill, glimpsed a unfamiliar and breathtaking vista. Perhaps the new prospect was as narrow and confined as the old streets when you were inside it- but if she never explored it, she wo
uld never know. That was the thing that gnawed at her: not to know, to marry some nobleman or king and have children and grow old, never knowing what she had missed.
In the end she told herself that if she did know him better, she would probably discover that she didn't much like him. Then she could go home and settle to her lot in life, not perhaps content, but at least untroubled by wild suppositions of how much better things could have been. This small, this easy, disobedience, wasn't much to pay for peace of mind, was it? And she would not do anything with the man. He wouldn't dare take liberties with her. They would talk a bit, and then she would see how silly she was being, and go home.
She had never been so frightened in her life. But she walked on resolutely toward the fountain of Arethusa.
She had chosen the fountain for three reasons: it wasn't far from her brother's house; it wasn't far from the catapult workshop; and it was enclosed by a small garden which could provide some cover for a private conversation, while remaining public enough to give her a sense of security. She did not at all believe that as soon as she was alone in private with Archimedes he would leap on her like a maddened satyr, but she had been warned of the wickedness of men and the dangers of impropriety so often that she wanted to feel that someone would hear her if she shouted. So she walked into the garden with one eye on the passersby she might have to call on: two guardsmen sharing a drink under a date palm; a couple of girls sitting on the ground by a myrtle bush; a pair of lovers kissing under a rose trellis. The girls would all be whores: respectable girls didn't sit about in public like that- like her. She tugged a fold of her cloak farther over her head, to hide herself from curious eyes.
The fountain itself was a large oblong basin of dark water, shaded by pines. The sweet water welled up silently from its depths. Tall, feathery-topped papyrus reeds grew in the shallows, a gift from Ptolemy of Egypt; in all Europe, the papyrus grew only here. Above one side of the basin towered the city wall, and at the far end, white and lovely, a statue of the nymph Arethusa gazed upon her fountain. Flowers garlanded the base of the statue, and coins gleamed in the water's depths: offerings to the protectress of Syracuse.
The Sand-Reckoner Page 19
