"Archimedes got bored with them," Marcus replied at once. "He always loses interest in his machines once he's got them working. He'd rather spend his time drawing circles- or, excuse me, cuboids. Of course, other people started making water-snails too, copying them from ours as well as they could. But still, everyone knew it was Archimedes' invention, and we were everyone's first choice of builder. We could have made a fortune, we could have! Instead, as soon as my master could afford to do geometry again, he found an enterprising fellow who was willing to pay a hundred drachmae for the design, handed our order book over to him, and went back to Alexandria to draw circles. I tell you, I could weep when I think of it. But listen! That's what happened the last time Archimedes applied himself to making machines. Now he's going to do it again. I'll bet on him against any engineer King Hieron ever heard of. You taking the bet?"
"Can I see this water-snail?"
Marcus grinned. "Certainly." Then, as the soldier moved toward the wicker basket, he added, "But I charge two obols for a demonstration."
Straton stopped in annoyance, one hand on the basket's lashings. "Your master lets you do that?"
"He lets me look after the money," said Marcus coolly. "Weren't you listening?"
Straton studied the slave a moment, then laughed. "All right!" he exclaimed. "I'm sorry I laughed at your master and insulted your loyalty. You're a good slave."
"I am not!" declared Marcus fiercely. "I'm freeborn, and not slave enough to forget it. But I'm honest. You taking that bet or not?"
"Twenty drachmae to a stater? Your master to be offered his predecessor's job within six months?"
"That's right."
Straton considered. It was an interesting bet. And despite what the slave had said, he thought he'd win. The slave was, after all, loyal to his master, and the master hadn't looked all that impressive to Straton. Ten to one was good odds. "All right," he agreed. "I'll take it."
Archimedes himself appeared as they were shaking hands on it. He was holding a torch, which flickered brightly in the growing dark, and a small boy followed him leading a donkey. Straton gave his new acquaintance the look of appraisal normally reserved for racehorses, and was reassured. No, this tall and gangling young man in a dirty linen tunic and shabby cloak did not look like a formidable genius. He was much in need of a haircut, a shave, and a bath, one knee was covered with blood while the other was dirty, and his face had a vague and vacant expression. The Egyptian stater, thought Straton, was pretty safe.
They loaded the chest on the donkey- the donkey was unhappy about it- and confirmed that they would meet next day. Archimedes handed the torch to Marcus, and the little party clip-clopped off down the road.
"What were you shaking hands about?" Archimedes asked his slave as they turned to climb the hill to the other side of the Achradina.
Marcus gave a self-satisfied smile. "I made a bet with that soldier. Going to get back that stater you gave him."
Archimedes looked at him with concern. "I hope you don't lose your money."
"Don't worry," said Marcus, "I won't."
2
The Achradina was an old quarter. The first Greeks to colonize Syracuse had settled on the promontory of Ortygia, and Ortygia- a grand region of temples and public buildings prudently fortified and garrisoned- was still the seat of the government. The Achradina had formed early, though, when the houses and shops of the growing city overflowed the crowded citadel and sprawled messily along the shore. When the city grew again, in wealth and power, the New Town had been laid out inland for the rich, while the Tyche quarter, a straggle of buildings along the road north, had become the place of settlement for the poor. The Achradina belonged to the old middle class. Narrow-streeted and dirty, bordered by the walls which guarded the city from attack by sea, it was the heart of Syracuse- dark, crooked, and full of secret delights.
Archimedes crossed it joyfully. A city-state customarily inspired in her citizens the most intense and passionate sense of patriotism and civic pride, and though Archimedes had always been something of a misfit in his own city, still every dusty cross-roads seemed to him to be shining with the glory of Syracuse. Each step, too, took him closer to home. Eagerly he marked off each familiar landmark: the small park with its bedraggled plane trees; the baker's shop around the corner where the family had bought its bread; the public fountain with its statue of a lion, which had supplied water for the household. A scent of herbs and roast meat wafted from the cookshop down the road, where he'd often run to fetch an evening meal if for some reason one hadn't been prepared at home. Nikomachos' house; Euphanes the Butcher's shop, with his house on top of it… and finally, there it was. Archimedes stopped in the street and gazed in silence at the front of featureless mud brick and the weathered wood of the single door. His chest began to hurt and his eyes stung. At one time this house had defined what was meant by a house. It had been the only house that mattered, the center of the universe, that container for everything that was important in his small world. And it was still true that all the people he loved most were behind that door.
He wished they lived in Alexandria.
Marcus raised the torch and likewise gazed at the house, remembering the first time he'd seen it, when Phidias had led him back from the slave market in chains. Not home, he reminded himself fiercely, though uncertain why he was denying the joy that hovered at the edge of his awareness. Just the house where I am a slave. For a moment he remembered his own home in the hills of central Italy, his own parents. He shoved them quickly from his mind: probably dead now, anyway. Some of the bricks on Phidias' house were crumbling, he noted, and the roof needed retiling. Not surprising. He himself had been the only man in the household, unless you counted the masters, and you couldn't count them, not when it came to retiling roofs. The place must have been running down. He had work ahead of him.
Gelon the Baker's son, who'd come to look after his father's donkey, shuffled his feet and asked, "Is this it?"
They unloaded the donkey, set the chest down, and sent the baker's son home with his father's beast, handing the child the torch to light his way. In the soft summer darkness Archimedes took a deep breath and knocked upon the door.
There was a long silence. Archimedes knocked again, and at last the door cracked open and a woman peered anxiously out, the lines in her worn face deeply shadowed in the light of the lamp she held. "Sosibia!" cried Archimedes, breaking into an enormous smile, and the housekeeper gaped, then screamed, "Medion!" — the diminutive ending of his proper name, his family nickname, which he hadn't heard for three years.
The reunion was as noisy and as joyful as anything Archimedes had pictured to himself. His mother, Arata, came running and flung her arms around him. His sister, Philyra, seized him as soon as his mother let go. "You've grown up!" he told her, and held her at arms length to admire her. She had been thirteen when he left: now sixteen and a young woman, she had not, in fact, changed much. Still straight and thin, gawky and bright-eyed, with her unruly brown hair pulled into a knot behind her head. She knocked his hands away so she could hug him.
"You haven't!" she replied. "You're as much a mess as ever!" Sosibia and Sosibia's two children hovered grinning and exclaiming in the background. But there was an absence. "Where's Papa?" asked Archimedes, and the noise died.
"He's too ill to stand," Philyra said, into the sudden quiet. "He hasn't been able to get out of bed for months." Her voice was heavy with reproach. For months she had tended their father and watched him waste away, while Archimedes, the darling and only son, lingered in Alexandria.
Archimedes stared at her, stricken. He had known that his father was ill. For a couple of months that awareness had lurked in the back of his mind, putting a wash of anxiety over all his preparations for coming home. But despite that, he had expected to find his father much as he had left him. He would have reckoned illness to be a persistent cough, a bad back, chronic indigestion. He had not expected a deforming monster to have moved into the house and pinned his father to his
bed.
"I'm sorry, my darling," said his mother gently. She had always been the family peacemaker, the voice of calm practicality. She was shorter than her children, wide-hipped, broad-browed; there was more gray in her brown hair than her son remembered. "I'm afraid it will be a great shock for you to see him. You can't have realized how ill he is. But I thank the gods you're safely home at last."
"Where is he?" asked Archimedes in a hoarse whisper.
Phidias's sickbed had been placed in the room Archimedes remembered as his mother's workroom. It was at the opposite end of the small courtyard which opened onto the street and formed the center of the house. The stairways to the bedrooms on the upper floors were steep and narrow, and a ground-floor room was much more convenient for an invalid. When Archimedes crossed to the old workroom, he found a lamp lit and his father sitting up and looking eagerly toward the door: he had heard the commotion, and was impatiently awaiting his son's appearance. Archimedes faltered on the threshold. Phidias had always been tall and thin; now he was skeletal. The whites of his eyes had turned yellow, and they stared out of deep hollows; his skin, too, was yellowish, and crumpled and dry. Most of his hair had fallen out, and what remained was white. When he stretched out his arms toward his son, his hands trembled.
Archimedes went through the door in a rush, dropped to his knees beside the bed, and threw his arms about his father's emaciated frame. "I'm sorry!" he choked. "I didn't… if I'd known…"
"Archimedion mine!" exclaimed Phidias, and folded his stick-like arms about his son. "Thank the gods you're home!"
"Oh, Papa!" cried Archimedes, and burst into tears.
In the courtyard, Marcus dragged the luggage in out of the street and shut the door. When he turned back to the house, Sosibia caught his shoulders and kissed him lightly on the cheek. "You're welcome back, too!" she said softly. "I wish it were to a happier house."
He looked at her in surprise, touched despite himself. He and Sosibia had never been friends. When they first met, her chief concern had been to make it clear that though he might have been purchased to replace the household's previous manservant, she had no intention of allowing him to take the dead man's place in her bed. Marcus had not at first understood her (he had been eighteen at the time, fresh from Italy and almost Greekless), but when at last he did, he in turn had made it clear that the very idea of sleeping with a plain, fortyish household slave disgusted him. This unanimity about sleeping arrangements had not, obviously, led to any feelings of goodwill, and for years they feuded, Sosibia sneering at Marcus as a crude barbarian, and Marcus disdaining Sosibia as a servile old woman. Now she was welcoming him back. "Well," he said gruffly, "it's good to be here."
There was a silence, and then he nodded to the two children, who stood behind their mother, watching- Chrestos, a boy of fifteen, and thirteen-year-old Agatha. "You two have grown," he commented. Another reason not to be welcome, he thought privately. Four adult slaves was too many for one middle-class household: now that Marcus was back, it was quite likely that Chrestos would be sold. But Sosibia had not acknowledged this uncomfortable prospect, so he ignored it as well. "When we came up to the house, I thought to myself that there'd be a lot of work waiting for me," he said instead. "I'd forgotten we have another man about the place now."
Chrestos grinned. "Welcome home, Marcus," he said. "You're welcome to do my work if you want to!"
His little sister laughed, slipped forward suddenly, and gave Marcus a shy kiss on the cheek. "Welcome home!" she whispered.
Not home, Marcus reminded himself, but some part of him was still glad. The first year of his slavery had been a nightmare he still sweated to remember, but that nightmare had ended in this house, and he had waked again to a world governed by sane rules. "It's good to be back," he repeated gruffly.
There was another silence, and then Marcus jerked his head at the doorway on the other side of the small courtyard and asked, "Is the old man dying?"
Sosibia hesitated, then made a gesture against evil and nodded. "Jaundice," she said resignedly. "He can't eat now, poor man: he lives on barley broth and a little honeyed wine. It won't be much longer."
Marcus reflected on Phidias. A kind man; an honest, hardworking citizen; a loving husband and father. A good master. He might resent the man for that last, but it was not Phidias' fault that he himself was a slave. "I'm sorry," he said sincerely; then added, in a harsh voice, "The gods made us mortal. It will come to us all."
"He has lived well," said Sosibia. "I pray the earth receives him kindly."
Archimedes stayed with his father for half an hour, retreating when the dying man fell asleep. He himself had no interest in anything more that night. Sosibia and his mother made up the bed in his old room, and he lay down and sought oblivion in sleep.
He woke early next morning, and lay for a while looking at the patterns the rising sun made upon the wall beside his bed. The window shutter was of wickerwork woven in a crisscross pattern and covered the whitewashed plaster with bars and triangles of orange light. As the sun rose higher, the light grew paler and the triangles shifted and widened. They slid from the wall onto his bed, where they lay in bright profusion over the sheet, like tiles of fresh ivory.
His eyes stung. In Alexandria he had purchased a game for his father, a set of ivory tiles cut into squares and triangles. They could be fitted together to form a square, or arranged to make a ship, a sword, a tree, or any of a hundred other figures. The puzzle was a geometer's delight. He'd liked it, so he'd been sure his father would too. Gifts given to his father now were destined for the grave. That fact was an enormity so devastating that it left him feeling as if half his soul had been removed.
When Archimedes was growing up, Phidias had been the one person who really understood. It had often seemed to Archimedes that everyone else had a blind spot in the middle of the head. They could look at a triangle, a circle, a cube- but they couldn't see it. Explain it to them, and they couldn't understand. Explain the explanation, and they stared and wondered aloud why you thought that was so wonderful. Yet it was, unspeakably wonderful. There was a world there, a world without material existence but luminous with pure reason, and they couldn't see it! Only Phidias had seen it. He had shown it to Archimedes, taught him its ways and its rules, and joined in with all his exclamations of amazement. As Archimedes grew older, they had gone on to explore the other world together. They had been co-conspirators, laughing together over an abacus, arguing together about axioms and proofs. They had walked together into the hills on clear nights, to observe the rising and setting of the stars and take sightings of the altitude of the moon. Only the two of them, out of all Syracuse, were at home in the invisible world. Others- even the closest and best loved of others- were forever outsiders.
It had been Phidias who suggested that Archimedes go to Alexandria. "I went when I was your age," he said, "and I heard Euclid himself lecture. You must go." He had sold a vineyard he could not afford the loss of, parted with a slave he could not easily do without, so that his son could study mathematics at the world's greatest center of learning. And Alexandria had been everything Phidias had promised- but it had been more, as well. For the first time, Archimedes had found others who understood, and some of them were young men of about his own age. It was the first time in his life he hadn't felt like a freak; the first time he'd been free to open up his mind outside his own house. So he had tossed it open to embrace the sky, and the ideas came in- thronging, pushing for attention, scattering, battling, seething, dancing together. He had felt like a fish raised in a garden pond, suddenly discovering the vastness of the sea. It was a liberation more intoxicating than anything he had ever imagined.
At the end of the first year, Phidias had started to write letters asking, "When are you coming home?" and Archimedes had not known how to answer them. Instead he had written to tell his father about Aristarchos' hypothesis that the earth went around the sun, about Conon's work on eclipses, about the Delian problem, and the attempts made
by various geometers to square the circle. And Phidias had replied in kind- amazed and enthusiastic, full of arguments and proofs- but somewhere in his every letter, there the question would be again: "When are you coming home?" Archimedes had known- oh, with perfect clarity! — that his father missed him terribly; that Phidias now had no one to share his ideas with, no one to understand him. But he had not wanted to go home.
Then, early in the spring, Phidias' last letter: "A war has started with Rome, and I am not well. I have had to stop teaching. Archimedion dearest, you must come home. Your mother and your sister need you." Your mother and your sister. Phidias himself had needed Archimedes long before, but for himself he had made no demands- only asked that one pleading question, persistently ignored.
This time the question was a command, and could not be ignored. Archimedes had slowly and reluctantly gone about the business of selling the furniture he'd bought in Alexandria, finding another tenant for the rooms he rented, disposing of a few machines he'd built and some of the tools he'd bought to make them. He had welcomed every delay. When his ship finally set sail for Syracuse, he had wept to see Alexandria dwindle behind him. Those tears seemed shallow now: the grief that lay before him would be much deeper.
The door to his room opened, and Philyra looked around it. She saw that he was awake, and came in.
Philyra was almost seven years younger than her brother, but tended to behave as though she were seven years older. She was a confident, outspoken, no-nonsense sort of girl; she'd been popular at her school and was well thought of in the neighborhood. She was very fond of her brother, but found him hopelessly vague and dreamy, much in need of firm management. She now advanced on him purposefully with a length of yellow cloth folded over her arm- towel or blanket or clothes, he wasn't sure. He sat up in bed, drawing up his long legs to make space for her, and she sat down and regarded him critically. He became uncomfortably aware that he was naked under the sheet, that his bare skin was blotched with fleabites, that his jaw and neck were scruffy with unshaved beard and his hair was dull with dirt. In daylight, too, he could see more clearly how she'd changed since he saw her last, how her body had filled out and rounded. Here in the house she was wearing only a light linen tunic, and it clung to her breasts revealingly. He felt abruptly embarrassed in front of her.
The Sand-Reckoner Page 3