The Sand-Reckoner

by Gillian Bradshaw

  "Is this going to work?" whispered Marcus nervously.

  Archimedes looked at the anxiety on his face, and for the first time felt a quiver of doubt. He looked at the ship, at the spider-web of rope between it and himself, mentally reviewing his mechanical advantage. It was sound, it should work. It should- but what if a pulley jammed? What if a rope thread jammed a wheel, or a tooth on one broke? Things did break. Had he made enough allowance for the weight of the rope itself?

  Everyone was watching him. Oh, Apollo, if he failed, with everyone watching him…

  "It's going to work," he told Marcus, with all the resolution he could muster. It should. There was a stool he'd sat on while he was working the system out; he went over and pulled it out from the shade of the ship shed, into the bright sun where everyone could see it, and sat down. "Just coil the rope up when I hand it to you," he ordered Marcus, and took hold of the rope.

  Sitting down was bravado, really; it would have been easier standing up. He had allowed for an effort of one talent, but as he started pulling he suspected that he had not made enough allowance for the weight of the rope itself. Still, he might have to dig his heels in, but he could do it. Hand over hand, he slowly but steadily drew the rope; back and forth the rope wove through the pulleys, reducing the load again and again by the distance it traveled until it was commensurate with his effort.

  The ship shuddered on the slipway, then began to glide forward. It did not jerk or pitch, but moved so smoothly that at first the watching crowd just murmured, uncertain whether it really was moving at all. Then, unsteadily at first, from a few throats, but growing, came a roar of delighted wonder. Beside him, Archimedes heard Marcus laughing. Seven tons of ship and thirty men were drawn up by a single pair of hands and the power of one mind.

  Archimedes drew the ship up as far as the ship shed, then dropped the rope and stood up. The crowd was still cheering. He turned toward them: a sea of faces, with a purple patch before them that was the king. His arms were trembling from the strain of pulling, and he felt suddenly dizzy. Nobody had ever cheered for him before. He had expected to feel triumph, but he was suddenly afraid. Under this acclaim he felt exposed, freakish. It was not really such an exceptional thing. The principles had always been there, unchangeable as stars. He had simply applied them. "O Apollo!" he whispered, as though he were genuinely begging the god for help.

  Marcus caught his shoulder. "Wave to them!" he whispered, and Archimedes waved: the cheers redoubled. He shook his head angrily.

  "Sir," said Marcus, "your cloak."

  Archimedes shook his head again and began walking back toward the king without it.

  As he drew closer, he noticed first his sister's face. Philyra's cloak had fallen off her head and one arm, her hair was tousled, and she was radiant. Then, next to her, he saw Delia, still applauding, her eyes glowing with pride. His irrational dread suddenly lifted, and he grinned back at both of them. Philyra gathered up her skirts and ran over to him, laughing. "Medion!" she exclaimed, flinging her arms around him. "It was unbelievable!"

  He put an arm around her, but said nothing, and kept walking until he was facing the king.

  Hieron's face too had lit with sheer delight, and as soon as Archimedes was within reach, he seized one surprised hand in both his own and shook it. "You really could move the earth, couldn't you?" he asked, grinning.

  "With another world to stand on," replied Archimedes, "anyone could."

  The king laughed, still shaking the hand. Then his eyes flicked to the system of pulleys and he let go. "Can I try it?" he asked.

  Archimedes blinked and looked back at the ship, from which the guardsmen were now leaping. "It will have to be pushed down the slipway the hard way," he said apologetically. "And I'll have to, uh, move some of the wheels."

  Hieron at once turned to the guardsmen: "Dionysios!" he shouted. "Get some volunteers and push it back down again! I'm going to pull it up this time!"

  "I want to!" shouted little Gelon, running to his father.

  "You can help me," conceded the king, scooping the boy up. "Come on, Archimechanic, you can tell us where to pull."

  The ship was moved up and down the slipway so many times that eventually the foreman of the shipyard came up and begged the king not to wear out the keel of a perfectly good vessel. The king moved it; Dionysios moved it; people fought their way through the crowd to take turns hauling on the rope. Archimedes explained the principle of the pulley so many times he lost count. It wasn't until some time had passed that he realized that he had not seen Kallippos since he first took hold of the rope. He glanced around, looking for the engineerand noticed Chrestos, just arrived flushed and out of breath at the edge of the crowd. Archimedes stared in consternation, then thrust his way through the startled mob to where the slave was standing.

  "What's happened?" he demanded. "Did my mother send you?"

  The boy was so out of breath from running that he couldn't speak, but he nodded.

  "This is your slave?" asked Hieron quietly.

  Archimedes stared at him blankly: he had not noticed the king following him. Then he nodded. "I asked my mother to send him," he said, "if my father…"

  "She says…" panted Chrestos, "come… as fast as you can."

  The world went cold, even in the hot sun. Time seemed to slow down.

  "You may borrow my horse," said the king.

  Archimedes met the king's eyes, and felt a spasm of wild gratitude at the way his situation had been understood without explanation. "I can't ride," he choked out through a tight throat. "I'll run. Lord, my sister…" He wasn't even sure exactly where she was; she'd been beside him, but he realized now that she'd gone off some time before with Marcus and Agatha. Probably she was sitting down in the shade somewhere, but where? She could not run, not in that thick cloak and long tunic, but she should come home now too, if their father was… She should not be abandoned on the docks.

  "I will see to it that your sister gets home as quickly as possible," Hieron said evenly.

  "Thank you!" exclaimed Archimedes passionately. He turned and began pushing his way through the crowd that had trailed eddylike after the king. As soon as he had a space of clear cobbles before him, he broke into a run.

  Philyra was sitting inside one of the ship sheds on a coil of rope, disconsolately eating the picnic she'd expected to share with her brother. Outside the noise of the crowd bubbled on, festive but with a wildness to it. She felt as though her life had suddenly become dislocated from everything it had been before. She told herself firmly that it was good, it was wonderful that Archimedes was really going to succeed in his new career, that there was no reason for the apprehension that had tightened her stomach and taken away her appetite for the food. But her first exhiliration and pride were irrevocably gone. Things were going to be different now, and she was realizing that she'd liked them as they were.

  A soldier came into the ship shed, then stopped abruptly. Philyra grabbed the hot cloak she'd taken off when she sat down, relieved at the way Marcus at once jumped up and stood between her and the soldier.

  "Is this lady the daughter of Phidias the Astronomer?" asked the soldier, speaking correctly to Marcus rather than addressing an unmarried girl directly.

  Marcus nodded warily.

  "Please come with me," said the soldier.

  Philyra hurriedly draped the cloak around herself while the slaves heaped the food back into the basket, and they followed the soldier out onto the sunlit quay.

  The ship was being eased back into the water and the crowd was beginning to disperse. The soldier led them over to a crimson-cloaked officer and saluted. "This is the lady, sir!" he said, and Philyra modestly held a corner of her cloak up before her face. The officer was the one who'd come to the house once, the captain of the Ortygia garrison- Dionysios, that was the name. "The king wishes to speak with you, lady," he told her, his tone respectful. "Please come with me."

  Philyra glanced nervously about, looking for her brother. He was now
here to be seen. Beside her, Marcus was scowling.

  King Hieron was standing beside his white charger. His son was in the saddle, looking pleased with himself, while his wife and the lady in red- the king's sister, someone had said- waited by the litter. Hieron came forward when Philyra was led up and inclined his head graciously. "Lady," he said solemnly, "I am very sorry to be the bearer of bad news. Your brother has been summoned back to his house: it seems that your father's illness has taken a sudden turn for the worse."

  Philyra dropped her veil, forgetting modesty, and stared at Hieron in shock.

  "I have promised him that I would see to it that you were conveyed home as quickly as possible," the king went on. "And my inestimable wife has kindly offered to take you in her litter. If you and your slave girl would get in, she will drop you off at home on her way back to our own house."

  Philyra swallowed, looking at the queen. Philistis came over and took her hands graciously. "I am so sorry that you should receive such terrible news in public," said the queen sincerely.

  Philyra bobbed her head, remembered her manners, and vaguely murmured, "Thank you, O Queen." She went over to the litter and climbed in. Agatha followed her, trembling, and then the queen and the king's sister.

  Marcus watched the slaves pick the litter up and set off. He felt sick with apprehension, whether for Phidias or Philyra he could not say. No one was paying any attention to him; the king mounted his horse behind his son, the soldiers fell into line, and the royal party set off for the Ortygia. Marcus settled the food basket on his arm and began to walk away. He went slowly at first, but as he left the docks his steps grew longer and longer, and when he reached the house in the Achradina he was running.

  Hieron reached his own house before Marcus could make the longer journey on foot. As soon as he did, the king turned to his doorkeeper. "Kallippos needs to speak to me," he said. "Find him for me, and tell him so."

  Before the chief engineer could be found, however, Delia returned with the queen, and went at once to see her brother.

  Hieron had retreated to the library, where Delia found him reading. He looked up quickly when she came in, then put his scroll aside and moved his feet so that she could sit down. "Did they arrive in time?" he asked.

  Delia nodded. "But he wasn't conscious," she added. "They had their own doctor there, and he said it might be hours, and might be any minute. The… wife of Phidias came out to thank us for bringing her daughter home. Philistis offered her any help they wanted, on your behalf, and she thanked us, but said they didn't need any help."

  Hieron snorted. "Well," he said, after a minute, "I'm glad they were in time." He picked up his book again.

  "What are you going to do about Archimedes?" demanded Delia in a low voice.

  He set the book down again. "Keep him," he said fiercely. "Keep him if I possibly can, no matter how much he costs. Zeus! You saw it. It was a game to him, moving that ship: when he understood how the rest of the world regarded it, he was shocked. He's as good as an extra army to any city lucky enough to own him."

  "But what are you going to do?"

  He shook his head. "I don't know. I've always thought the legends make King Minos sound a most appalling fool, but at the moment I can find some sympathy for the man. He had the most ingenious mind in the world at his disposal, and he didn't want to lose it. So he locked up its owner in a tower. It didn't work, but I can understand why he was tempted to it!"

  "You're not planning to lock Archimedes up!" cried Delia. It was more a command than a question.

  "Herakles!" exclaimed Hieron, looking at his sister in surprise. "Not if you're going to strangle me if I do."

  Delia flushed. Her protectiveness surprised her as well. But that morning she had watched Archimedes do the impossible, and she had forgotten all caution in the wave of delighted pride. Surely she was entitled to feel proud, since she had discovered him? And to feel responsible as well, if her brother's notice threatened him. "You're not, are you?" she asked more quietly.

  "No, I am not," said Hieron. "Minos was a fool. You don't get people to work for you by locking them up in towers, particularly when they're a great deal cleverer than you are yourself. Daedalus, you remember, simply devised an impossible means of escape and flew away. I don't think Archimedes could fly, but after today I wouldn't like to bet that he couldn't if he really applied his mind to it."

  Delia relaxed. "You worried me," she complained, and at last took the offered space on the couch.

  Hieron was gazing at her thoughtfully. "You like him," he stated.

  She blushed again. "I discovered him," she said. "I… feel responsible. I don't want him hurt."

  Hieron nodded, as though this made perfect sense. "I promise you, I won't hurt him. To tell the truth, I think it would offend the gods if I did. It would be like smashing a priceless work of art. I've never seen anything like him."

  "I will not take orders from him," said a voice in the doorway, and they both looked up to see Kallippos standing there. The royal engineer was disheveled and sweat-stained, and his feet were covered with dust: he had been walking. He glared angrily at Hieron. Delia jumped nervously to her feet.

  Hieron simply smiled. "Kallippos, my friend," he said, "I'm glad you've come. Shall we go into the dining room and have a cup of chilled wine?"

  "I won't take orders from him," repeated Kallippos, as though Hieron had not spoken. "I'm not Eudaimon, King. I don't just copy, I think. I won't let somebody else do my thinking for me. I'm too old and my family's too good to stand being that man's subordinate. I resign."

  "I was afraid you were going to say that," said Hieron. "Now, my friend-"

  "You arranged it!" shouted Kallippos furiously. "You invited him to do something impossible, and asked me to say he couldn't. Well, I said it: I don't deny it. And I was wrong. But I am not going to take orders from some flute boy from a mud house in the back streets of the Achradina!"

  "I don't ask you to," said Hieron.

  "Hah!" sneered the engineer. "You may make his position officially equal to mine, but we both know you intend him to be my superior."

  "I have no intention of appointing Archimedes son of Phidias to the position of royal engineer," declared the king. "May the gods destroy me if I do."

  Kallippos stared for a moment in astonishment, then shouted, "Then you're out of your mind! You saw what that boy did! Do you think I could have done that? I couldn't even have done the catapult!"

  "My friend!" protested Hieron. "You are the finest engineer in the city's employ, and if you left, I could not replace you. For you to resign now, when we are threatened with all the terrors of siege, would be a disaster for the whole of Syracuse. How can you contemplate such a thing? Archimedes is young and inexperienced. I know your quality, and I never expected you to work under him. Before the demonstration I thought it might be possible to appoint him as engineer with a rank equal to yours. Now I see that this is quite impossible. I repeat, I am not going to appoint him to a salaried position at all."

  Kallippos opened his mouth to speak, then shook himself. "King," he said, trying again. "Don't you understand that he's better than I am?"

  "My friend," said Hieron, "I know perfectly well that he has Apollo and all the Muses taking turns to breathe into his ear. But his natural home is Alexandria, and any job I gave him he would eventually come to regard as a prison. So I am not going to give him a job. For what he makes for the city, he will be paid, and generously, but what he actually does will be up to him: that will please him far more than any position I could offer. He is not, and never was, your rival. You are an engineer, and a very good one: he is a mathematician who happens to make machines occasionally. All I want you to do is to join me in asking him to assist in constructions for the good of the city where we judge he has a contribution to make. Now, do you want to come into the dining room, wash your feet, and have a cup of chilled wine?"

  Kallippos stared at Hieron for another long minute. Then he made a slow, snort
ing noise, half laugh, half sigh, wholly relief. Delia saw that he had not in the least wanted to resign, but had felt that he had no other option. "Yes," he said now, starting to smile. "Yes, O King. Thank you."

  Delia watched the two men go out, then sat back down on the couch, heavily. She knew her brother well enough to understand that Hieron had not said quite what Kallippos thought he had. Hieron had known that Kallippos was too proud to agree to become another man's subordinate- especially when the other man was younger and of a less distinguished family. Now he had arranged matters so that Kallippos would be content to ask Archimedes to "assist" with particular problems- and, no doubt, take all the "advice" he was given. Eudaimon, too, had been brought "in hand." There remained only Archimedes himself to bring under the yoke- and that would not be done in the way she'd feared. She should have realized that her brother would never do anything so crude as bind a man to an iniquitous contract of employment. The kind of chains he preferred were both subtler and stronger, forged in a gray area between manipulation and beneficence, put on with gifts and received with gratitude. But what sort of chains he might find for Archimedes she could not guess.

  Phidias died at about four in the afternoon, without regaining consciousness. Arata had watched him all morning with growing concern, and at noon, when his breath seemed to be failing, sent for her children. All through the long hot afternoon the family sat together about the bedside, while Phidias' breath stopped, then started, then stopped again. When the end finally came, they did not at first recognize it, and waited for some time for the frail gasping to resume. Eventually it became clear that it would not. Archimedes covered his father's face, and the women of the household began to beat their breasts and raise the high-pitched ritual keening.