The Sand-Reckoner

by Gillian Bradshaw

  But the thought of going to Hieron, of admitting what she'd been doing and what she wanted to do, of facing his anger- or, worse, his bewildered pain- appalled her.

  She also had no idea whether Archimedes wanted to marry her. She felt sometimes that he loved her, sometimes that he must despise her as shameless- it was shameless, the way she'd thrown herself at him! Did he really want to go to Alexandria? Did she want to be the chain that kept him in Syracuse? She was afraid to see him again, afraid that if she suggested this impossible scheme he would turn it down.

  In the end she'd decided to talk to his sister, to see if she couldn't discover what he thought about her. That had been a disaster. Philyra didn't appear to have heard anything about her, good or bad, and, what was more, had disliked her. She wasn't sure why, though she supposed she'd mishandled the interview; she often did. And Queen Philistis disapproved of the invitation, though she'd had to concede that it was perfectly proper. She had stayed in the room the whole time Philyra was there, frowning whenever Archimedes was mentioned. Philistis disapproved of Archimedes generally- a conceited young man, she thought, who was being treated with altogether more honor than he deserved, and who had had no business disturbing her husband at the end of particularly exhausting day and making accusations of deceit. Hieron thought it important to cultivate the man, so Philistis was cooperating, but she did not like it.

  And now here was Archimedes himself, rumpled and tired and staring sadly into the basin of the fountain, while around him the early-morning light cast fresh shadows through the leaves of the garden.

  Delia stepped forward, and he looked up. He blinked at her vaguely, without surprise, his mind still fixed on whatever he had been contemplating in the water.

  "Good health!" she said, struggling to keep her voice steady. "What brings you here so early?"

  At that he grimaced, scrunched up his shoulders, and got to his feet. "Nothing pleasant," he told her unhappily. "My slave Marcus helped two Roman prisoners to escape. One of their guards was killed, a man I knew, a good man."

  "Oh, by the gods!" she exclaimed with concern; then added quickly, "I'm sure my brother doesn't blame you for something your slave did."

  He shook his head, but remained hunched unhappily. "He's being locked up in the prisoners' place- Marcus, I mean- though Hieron has implied he'll be exchanged or released with the other Romans. I- feel ashamed."

  "It's not your fault if a slave does something wicked!"

  He shook his head. "Not like that at all! I never really noticed Marcus before. He was always just there. But he's really quite an extraordinary man. He's actually a Roman citizen, and the reason he helped those men escape was that one of them is his brother. He could have escaped as well, but he didn't because he didn't want to betray Syracuse. And I realized that that's exactly like him. He had an obligation to his brother and an obligation to Syracuse, so he fulfilled both as well as he could, and then stood there expecting to die for it. He didn't even complain about it. He's always been absolutely honest and scrupulous. I should have noticed. But I don't notice people, even when they're under my eyes. All I notice is mathematics." His voice had filled with disgust.

  She did not know what answer to make to this. She went over to the fountain and sat down on its rim. "I suppose mathematics is rational, and people aren't," she said. He gave a rueful snort. "You know the song of the Sirens?

  " 'Halt your ship and stay to hear our song.

  For sailor none in his black ship has gone from listening to our honey-voiced call but goes his way delighting, knowing more…

  For we know as many things as come to pass upon the fertile Earth.' "

  His voice lowered, and he continued:

  " 'So they cried with lovely voice and clear and I wished with all my heart to hear and commanded my friends to set me free… instead they bound me with more chains.'

  "Mathematics is a siren. It's probably just as well that most of the world has its ears stuffed with wax and can't hear her. I'm saying this now as though I'm ashamed of it, but I won't change. The moment she sings to me again, I'll ignore everyone and everything else."

  She was silent for a long moment, thinking about him, and about herself, and about her brother. Then she repeated slowly, "Chains. Do you know, Hieron talked about chaining you to Syracuse. Do you hate it?"

  He did not answer at once. He had thought that morning that Hieron was summoning him as though he were a slave, and he'd been surprised by his own sense of outrage and betrayal. He had not realized how much he had started to believe that he would stay in Syracuse and work with the king. With the king; that was the point. Not for him. He had been more or less resigned to being under another man's command when he'd thought it unavoidable, but that resignation had been crumbling as he came to appreciate his own power. The way Hieron had tried to manipulate him had impressed him. He hadn't liked it, but it had been interesting, as elegant in its way as a geometrical proof, and it had seemed to him a clear indication that the king genuinely preferred persuasion to decree. And he had begun to like Hieron himself- the subtlety, the quick perception and efficient action, the good humor. And then there was Delia. She was worth staying in Syracuse for, if he could get her, and he had begun to wonder if he might. After all, Hieron had promised him almost anything.

  But was that only another trick? The position Hieron had been inventing for him had impressed him as something more than the kind of straightforward contract he could get in Egypt, but what if it was something less? What if it was only a counterfeit meant to cheat him? Would he be a friend of the king, an adviser, on an equal footing- or would he be a hired servant?

  "I am deeply in your brother's debt," he said at last, slowly, "and I suspect that's where he wants me. But there's nothing he's given me yet that I can't repay- not even Marcus' life. What I can make is worth a great deal, so I don't mind. Chains. Well." He frowned down at his own flat, big-boned wrists as though contemplating shackles. "Sirens eat people. Odysseus only heard them and lived because of those chains. Maybe I need them. Maybe I ought to be tied to a city, and to people who aren't mathematical. And there'd be chains anywhere. If King Ptolemy does offer me a job, it will be because of water-snails and catapults, not pure mathematics. So really all I can choose is whose chains, and how heavy."

  "So you are still thinking of going to Alexandria!" she asked.

  He looked up at her and groaned. "Oh, don't! Everyone's been quarreling with me about that."

  "I don't want you to go!" she said unwarily, and then crimsoned.

  He caught her hand, and her neat, strong flute player's fingers clenched upon his own. "Delia," he began urgently, then stopped, not knowing what he wanted to say. They gazed at each other for a long moment, not in any rapture of love but simply trying desperately to judge the other's will, the other's mind.

  "I want to ask you this, then," he said at last. "Is there any chance you could be responsible for my staying?"

  Her blush darkened. "Hieron might…" she whispered. "He might… no!" She had promised herself that she would not try to force Hieron's agreement; that she would not return all his kindness with this- this insult. She looked away and tried again. "I can't…" She became aware that she was still clutching Archimedes' hand, and stopped, tears of shame springing to her eyes. That was how much strength of mind she had: trying to give up the man, she couldn't even let go of his hand. She shook her head and cried despairingly, "I can't!"

  "It's not up to you," came his voice beside her. "It's up to your brother. I'll talk to him."

  She risked looking back at him, and saw that his face was alight with joy. He had understood enough: her mind.

  "He did promise me anything except the Museum," he told her reasonably. "And I never expected the gods to favor me as far as this. Why not ask for more? The worst that can happen is that he says no. I'll ask him. I'll find a good time and ask him. When the three-talenter is finished. I'll ask him then."

  13

  Marcus was
literally put in his brother's place, in the middle of the three sheds at the quarry, with Fabius' leg irons clamped about his own ankles. The other prisoners were astonished when he arrived, and suspicious of his account of himself. He did not much care, and spent most of his first day in prison asleep. The guards woke him around noon, when they chained each prisoner to the next as part of the newly increased security. The sawn-through planks of the shed wall had been replaced even before he arrived, and another two guards now took their place in each shed, at the far end, where they could keep an eye on everything the two on the door might miss. Marcus did not much care about that, either. He did not much care about anything. He supposed he ought to feel glad and excited- it seemed that he might, after all, be a free man again and still live- but he was too exhausted. The sheer effort it would take to adjust to his own people again, even if they didn't kill him, appalled him. He ate the meal the guards brought him and went back to sleep.

  He woke with a sensation of being watched and sat up abruptly. Archimedes was squatting at the end of his mattress, hands hanging over knees and an anxious expression on his face. On all sides the other prisoners were watching the visitor with impassive suspicion, and a guard was hovering nervously a few paces away. In the dimly lit shed it was hard to tell, but Marcus thought that it was evening.

  "I'm sorry to wake you," said Archimedes.

  "I've been asleep all day," replied Marcus, embarrassed. He did not know what to say; the other seemed almost a stranger to him. Yet he knew Archimedes as intimately as he knew Gaius: he had watched him grow from childhood to manhood, and they had shared lodgings and short money in a foreign land. But though he had only rarely thought of Archimedes as his master, his own slavery had always defined the relationship between them, and now by Hieron's judgment he had never properly been a slave at all. With that tie cut, he could only flounder in a sea of shapeless emotions.

  "I, uh, brought you some things," Archimedes said, as embarrassed as Marcus. He set a bundle down on the end of Marcus' mattress.

  Marcus saw at once that the bundle's wrapping was his own winter cloak. He drew it over and unknotted the corners. Inside was his other, winter tunic, a terra-cotta statue of Aphrodite he'd bought in Egypt with money from the water-snails, and some other small knickknacks he'd picked up over the years. There was also a small leather bag that chinked and a long oblong case of polished pine. He stared at the case, then picked it up and opened it: it held Archimedes' tenor aulos. The hard sycamore wood was darkened about the stops, polished with use. He looked up in shock.

  "I, uh, thought maybe you could teach yourself to play it while you're here," said Archimedes. "It would be something to do while you're waiting to be exchanged."

  Marcus picked up the flute; the wood was water-smooth in his hands, and warm. "I couldn't, sir," he said. "It's yours."

  "I can buy another. I can afford one, after all. And you have a good sense of pitch; it's a shame to waste it. I don't know why you never learned an instrument before."

  "It's not a Roman thing to do," Marcus told him helplessly. "My father would have beaten me if I'd asked it."

  Archimedes blinked. "Because of all the jokes about flute boys?"

  "No," said Marcus, in a low voice. "No- he'd say it was unmanly to waste time studying music. He'd say that music is a luxury, and luxury corrupts the soul. He tolerated it at work, or as an amusement, but he always said that the only studies worthy of a man are farming and war."

  Archimedes blinked again, trying to accommodate his mind to this bizarre idea. Greeks too believed that luxury corrupted, but Greeks didn't consider music a luxury. It was an essential: without it men were not fully human. "Do you not want it, then?" he asked, giving up.

  Marcus ran one calloused thumb along the flute, then whispered, "I do want it, sir"- and his heart suddenly rose. Going back to his own people need not mean giving up everything he'd learned. Why shouldn't he play the flute? He had never agreed with his father anyway! "Thank you."

  Archimedes smiled. "Good. I've put three reeds in the case. They should last you a little while. If you're here for a long time, I'll bring more- or you can get your guards to buy some. And when you're able to manage this one, you'll want a second flute. You can decide for yourself what voice it should be. There's some money." He gestured vaguely at the leather bag.

  "Thank you," said Marcus again. "Sir, I'm sorry."

  Archimedes shook his head quickly. "You couldn't abandon your own brother."

  Marcus met his eyes. "Perhaps not. But I did abuse your trust and put you in danger. I think Fabius would have killed you if he'd realized who you were when you came in. I should never have brought him to the house, and never have given him the knife. So- I'm sorry."

  Archimedes looked down, his face going red. "Marcus, my trust deserved to be abused. Do you remember when we came back to Alexandria after making the water-snails? How I told you to take all the money back to our lodgings? My friends said later that I was an idiot to trust you with so much, but it had never even occurred to me that you might steal it."

  Marcus snorted. "It occurred to me!"

  "Did it? Well, why not? After all, it would have been freedom and independence. But you didn't. You took it home, and then nagged me for days to make me put it in a bank. And what I meant to say was, I had no right to trust you that far. It was arrogant. I had never done anything to earn that sort of loyalty. As a master I was negligent and careless. Yet I relied on you absolutely, and never considered that you deserved any credit for not failing me. So- I'm sorry, too."

  Marcus felt his own face go hot. "Sir…" he began.

  "You don't need to call me that."

  "I was in your debt for a great many things even before this morning. Music is one of them; mechanics is another. Yes, that is a debt. I don't think I've ever enjoyed any work as much as I enjoyed making the water-snails. Since this morning I owe you even more. If I'd been anybody else's slave, I would have been flogged and sent to the quarries. The king treated me leniently because you pleaded for me- you know that as well as I do. I have no way to repay what I owe. So don't burden me with your apologies as well."

  Archimedes shook his head, but did not respond. After a moment he changed the subject and asked, "Do you want me to show you how to play that flute?"

  There followed a short lesson on how to play the aulos: fingering, breathing, the positions of the slide. Marcus played a few wobbly scales, then sat stroking the silken wood. Its touch was a promise for the future, and gave him unexpected hope.

  Archimedes cleared his throat uncomfortably. "Well," he said. "They're expecting me at home. If you need anything, send me word." Marcus opened his mouth, and Archimedes said urgently, "Don't! You've been a member of my household ever since I was a child. Of course I want to help you if I can."

  Marcus realized suddenly why he had felt so numb. He was losing home and family for the second time in his life.

  "Please tell them at the house," he whispered, "that I'm sorry. And tell Philyra I hope she will be very happy, with Dionysios or whoever she marries. I wish you all much joy."

  Archimedes nodded and got to his feet. "I wish you joy, Marcus." He turned to go.

  The sight of him turning away suddenly filled Marcus with an almost panic-stricken urgency. Something between them was unresolved, and the thought of being left with that undigested lump of emotions terrified him. He jumped to his feet with a clank of irons, and called "Medion!" — then bit his tongue, realizing that he had used the family nickname for the first time.

  Archimedes didn't appear to notice the slip. He looked back at Marcus inquiringly, his expression just visible in the growing dark.

  For a moment Marcus did not know what to say. Then he held out the flute. "Could you play me that tune you played last night?" he asked.

  Slowly, Archimedes reached out and took the instrument. He adjusted the slide. "I really need the soprano as well," he said apologetically. "It won't be the same without it." But he s
et the flute to his lips and at once began the same sweet dancing tune which had filled the courtyard the night before.

  Everything in the shed seemed to hold its breath. One of the guards, who had gone to fetch a lamp, came back with it and stood silent in the aisle listening. All around the eyes of prisoners gleamed in its light, drawn into the dance, and then bewildered by the inexplicable grief that crept into the tune. The melody was clearer on a single aulos, the shifts of tempo and mode more precise. There was the same sense of disintegration, and the same almost miraculous resolution. At last the same sad march faded softly into silence. Archimedes stood for a moment with his head bowed, looking at his fingers on the stops.

  "And now I wish you joy," said Marcus, quietly into the quiet.

  Archimedes looked up, and their eyes met. The unresolved thing between them solved itself, and the ties severed. Archimedes smiled sadly and handed the flute back to Marcus. "May you indeed find joy, Marcus Valerius," he said, stumbling a little on the alien family name.

  "And you, Archimedes son of Phidias," said Marcus. "May the gods favor you."

  Archimedes walked home from the quarry through the dark streets slowly. He did not want to think about Marcus, so he thought about the tune he had played. A farewell to Alexandria, he'd called it. He did not like the way his mind seemed to be making up itself about Alexandria, without consulting him. Even before Delia. If Delia…

  He lost himself for a moment in the memory of kissing Delia, then went on, more grimly. What he needed to know was whether Hieron saw him as an ally or as a valuable slave.

  The test was Delia. Hieron might refuse his permission for the match for many good reasons, but if the request was viewed as an affront, he'd do better going to Egypt if he had to slip out of Syracuse in disguise.

  In the house there were lamps burning in the courtyard, and the family was waiting: Arata and Sosibia spinning, little Agatha winding wool, Philyra playing the lute, Chrestos sitting in the doorway doing nothing in particular. Archimedes had not been home all day, though he had sent one of Hieron's slaves to the house to tell the family what had happened, and to tell Chrestos to pack up all of Marcus' things and bring them to him at the catapult workshop. He had not wanted to talk to his family: not about Marcus, and not about Delia- yet. Now they were all waiting to talk to him.