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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.