The Sand-Reckoner

by Gillian Bradshaw

  In the King's house, Hieron was sitting in the doorkeeper's lodge, feet up on the arm of the couch, sipping a cup of cold water and discussing the evening with Agathon, as was his custom after a dinner party. He listened to his guests, his doorkeeper listened to his guests' slaves, and afterward they compared notes; it was a technique that had often proved valuable. The doorkeeper had revealed that the slave of one of the officers was worried that his master had been drinking too much, while one of the councillors had been spending a great deal of money lately.

  "And Archimedes' slave?" asked the king. "Anything useful from him?"

  Agathon snorted. "I think somebody must have noticed that we were asking about his master. He arrived determined that he, at any rate, was not going to tell us anything. Once the music started he slunk off and hid in the garden so that he wouldn't have to talk to anyone. But he was claiming to be a Samnite, and he's quite plainly a Latin."

  "You're sure of that?"

  "Oh, yes. His name's Marcus, and when he found out that Aristodemos' slave is a real Samnite, he was horrified." Agathon gave a cackle of laughter. "He had to pretend he'd forgotten how to speak Oscan, and he was such a poor liar it was pitiable."

  The king frowned. "Has he had access to the workshops?"

  "I'll check it," said Agathon at once. "But he's been in Phidias' household for thirteen years, and my impression is that he's loyal to his master."

  Hieron nodded thoughtfully and took a sip of water. "Probably no use," he said. "But one never knows. Keep an eye on him."

  "Yes, sir," said Agathon. He watched his master for a moment, then said, "And you, sir? What did the guests think about the war?"

  Hieron stretched and sat up. "We did not discuss it."

  Agathon raised his eyebrows. "That must have been difficult."

  Hieron grinned. "Not too much so. Archimedes discussed ideal mechanics from the eggs through to the turbot. After that the other guests were perfectly happy to talk about anything nonmechanical. It needed very little steering."

  Agathon cleared his throat nervously. "Sir…" He stopped.

  "What?" asked Hieron.

  When Agathon did not answer, the king leaned forward smiling and said, "Do you want to talk about the war, Aristion?"

  It was an old nickname- the diminutive of "best" for Agathon's proper name, which meant "good." The slave plucked courage from it, met his master's eyes, and said, "What's going to happen, sir?"

  Hieron sighed. "Whatever is fated, my friend. But what I hope for is that once the Romans have blunted their teeth on our defenses they'll offer me better terms than they offered at Messana."

  Agathon sat silent for a long moment. It was stark hope, and severely limited. "There's no hope from the alliance, then," he said at last. "No hope of victory."

  "There is always hope," replied Hieron evenly, "but I don't expect anything, no. Carthage has not made terms with Rome and has not moved openly against us, and as long as that's true I will continue to speak in public as though she were our steadfast ally. But the Carthaginians had a fleet which was supposed to be guarding the straits, and it notably failed to stop the Romans from crossing to Sicily. And while we were besieging Messana, the Romans negotiated with me and with the Carthaginians- separately. When I suggested to my allied commander that I send someone to observe his negotiations and he send someone to observe mine, he turned me down. And when the Romans attacked us, the Carthaginians did nothing. The enemy had two legions, Agathon- ten thousand of the fiercest fighters in the world. They quick-marched out of the city and attacked our siege works. We threw them off and chased them halfway back to the walls. If the Carthaginians had attacked the Romans in the flank as they retreated, it would have been a real victory. But they did nothing- nothing! Drew up their troops to defend their own camp, and stood watching. Oh, afterward Hanno sent a messenger congratulating me on my victory and explaining that he had not had time to arrange his forces, but it was perfectly clear from that battle how Hanno intends to fight this war. He hopes to use us to weaken the Romans and the Romans to break us, and to claim Sicily for Carthage when all is done. So I disengaged under cover of darkness and came home- Don't repeat any of this, Agathon, my dear. I will call Carthage my ally as long as there is any chance of her remaining so. And there may be something to be done at Carthage. There are always factions: I have some friends there and Hanno has some enemies."

  "What terms did the Romans offer at Messana?" asked Agathon bleakly. They both knew that without Carthaginian help, the best Syracuse could hope for was survival.

  "The same that they offer their Italian 'allies,' " replied Hieron dismissively. "We accept a garrison and send troops to aid them in their war. Oh, and pay five hundred talents of silver, to compensate the Romans for their trouble and expense in making war upon us. Highly unpleasant man, Appius Claudius." He took another sip of water. "Any comments?"

  Agathon sighed unhappily and rubbed his nose. "They're saying in the city that the Carthaginians have betrayed us."

  Hieron gave a rueful snort. "Didn't take them long to work it out! They're not panicking though, I hope?"

  "No, sir. They've seen you behaving as though there's nothing to worry about, and they still hope. I suppose you're right not to confirm their fears."

  "I'm so glad you approve! Shall I tell you what my hopes for this city's survival rest upon?"

  Agathon nodded silently. Hieron looked down into his half-empty cup of water and said softly, "Walls, Agathon. Walls and catapults. The Romans are almost unbeatable on an open field, but they don't have much experience in siege work. Let them lay siege to Syracuse and die before our walls. Let them understand how much it will cost them if they want to break us. Then let them give us some terms we can accept." He emptied the cup.

  "So that's why you're so interested in Archimedes son of Phidias."

  "I'd be interested in him under any circumstances," said Hieron, getting to his feet and setting the cup down. "If I weren't interested in having the best engineers available, I wouldn't deserve to be king. But I admit, at the moment it cheers me just to see the fellow. The Romans aren't used to big catapults, and even a one-talenter will frighten them- as much as they can be frightened by anything in war, which I suppose isn't much." He yawned, stretching, and added lightly, "He plays the flute well, too."

  8

  Phidias' illness had taken a turn for the worse again. He slept most of the time, and it was hard to rouse him; when he did wake, he was often confused and could not understand where he was or what was wanted of him. To Archimedes' grief, he did not seem to appreciate even that the catapult had passed its trial and that his son was in a position to provide for the family. Hieron's personal physician had indeed come to visit him, but apart from leaving a drug which Phidias could take if he was in any pain, had done nothing the family's own doctor hadn't done already. "There is no hope of a cure," he had said.

  Archimedes could not stop himself from hoping anyway. Every morning and evening he would go into the sickroom to see his father. He would try to start a conversation, and when that failed he would simply sit, doing calculations or playing music while Phidias slept.

  On the morning two days after the dinner party, the day of the demonstration, he went into the sickroom as usual and found his father asleep. He sat down on the couch, took the skeletal hand in his own, and brushed back the thin white hair. "Papa?" he said. Phidias woke and smiled up at him in silence.

  "I'm going down to the docks now," he told his father. "I'm doing a demonstration of mechanics for the king."

  The brittle hand clenched suddenly on his own. "Don't go away!" Phidias begged.

  "It's only for an hour or two," said Archimedes.

  "Don't go away to Alexandria, please, Medion!"

  "Papa! I'm not, I won't. I'm just doing a demonstration at the docks. I'll come home and check on you afterward."

  "Don't go away again, please!" whispered Phidias, as though he hadn't heard; then, more softly still, "Lo
ok after your mother and sister for me."

  "I will, Papa," Archimedes said. "I promise."

  He stayed where he was for a few more minutes, and eventually the tight grip on his hand relaxed, and his father went back to sleep. He stood up very gently so as not to wake him, then stood looking down at the yellow face soberly. Was it imagination, or was there a translucent quality to the skin, a gasp to the shallow breath, which had not been there before?

  Arata came in. Archimedes had invited her to come watch the demonstration, and she had put on her best gown preparatory to going, but at the sight of her husband's face she pulled her chair out from the wall and sat down to keep watch over him. "I don't want to leave him this morning," she told her son. "You take Philyra."

  Archimedes did not protest. He said only, "Send Chrestos to fetch me if… if he asks for me, or if anything happens. I don't care about the king: I'll come."

  Arata nodded, and Archimedes bent to kiss her forehead, then went out into the courtyard.

  Philyra was already waiting, bright-eyed and impatient in her best tunic and cloak. Archimedes thought she needn't have bothered with the tunic, since it was invisible apart from the border around the hem: Philyra was respectably swathed in cream-colored wool from head to foot, and her face was already pink with the heat- unless it was excitement. Marcus and young Agatha, waiting beside her, both looked considerably more comfortable in plain linen tunics. Agatha was going because it was genteel to have a lady's maid, and Marcus was carrying a basket with some refreshments.

  "Medion!" exclaimed Philyra, "You're not wearing that cloak!" It was the linen one.

  "I'm not going to be able to wear any cloak to do the demonstration," objected Archimedes. "You can't haul on a rope in a cloak. So I thought…"

  Philyra shook her head firmly. Marcus, grinning, set down the basket, ran upstairs, and came back with the yellow cloak. Archimedes swore under his breath, but put the thing on, and the party set out.

  When they were approaching the docks, the streets grew crowded, with large numbers of people jostling along in the same direction as themselves. Archimedes eyed them dubiously. "Is something happening?" he asked a plump waterseller.

  "Haven't you heard?" replied the waterseller. "One of the king's engineers thinks he can move a ship single-handed."

  "But…" said Archimedes, blinking. "Are all these people coming to see that?"

  " 'Course," said the waterseller reprovingly. "Should be quite a sight."

  "But- but how do they all know?" asked Archimedes.

  "It was posted in the marketplace," replied the waterseller. "What's it to you?"

  "I'm the engineer," said Archimedes bemusedly, wondering who had posted it.

  "So you're Archimedes son of Phidias!" exclaimed the water-seller, looking him up and down disappointedly. "I thought you'd be older."

  Philyra gave a laugh of delighted astonishment and took her brother's arm. "Medion, you're famous!"

  The quayside, when they reached it, was crowded with people standing about talking, eating, and drinking and pointing out to one another the ship Archimedes had selected. This was by no means the largest ship in the king's fleet, but it was nonetheless indisputably a ship: a fat single-masted transport about seventy feet long. It had been drawn up out of the water and its sides curved upward from the stone slipway twice as high as a man. Philyra stopped when she saw it, stared a moment, then looked at her brother anxiously. So did Marcus. They had both accepted Archimedes' assurances that his system would work, but now they were faced with an object larger than their house, the project suddenly appeared totally impossible.

  "Can you really move it?" asked Philyra.

  But he was surprised that she could doubt it. "Oh yes!" he exclaimed. "It only weighs about twelve hundred talents unloaded, and I've given myself a mechanical advantage of fifteen hundred. I'll show you!"

  The area about the ship was in the process of being roped off to protect it from the crowd, but the sailors doing the roping recognized Archimedes and allowed his party through. He had just begun explaining the system to Philyra when there was a blare of trumpets, and they looked up to see the king arriving. First came a file of guards, led by an officer on horseback. The shields slung over their backs gleamed with color, and their helmets and spear points shone in the sun. Behind them came the king, riding upon a magnificent white horse and robed in purple. He was accompanied by Kallippos, on a tall bay, then followed by trumpeters, and by a covered litter carried by eight slaves. The crowd cheered and applauded, and- eventually- made way for him. Philyra clutched Archimedes' arm with excitement as the royal procession drew to a halt before them.

  The litter was set down, and the passengers climbed out: first the queen, purple-cloaked like her husband; then the little boy, Gelon, also in purple and looking hot. Lastly a dark-haired girl climbed out and stood a moment straightening a cloak of very fine crimson cotton worked with gold stars. Archimedes stood up straighter, grinning with pleasure. So Delia had come to see his demonstration! She was even prettier than he remembered. He tried to meet her eyes, wondering how he could thank her for her message. But when he finally caught her gaze, she returned his smile only with a cold flat stare.

  Philyra had no real idea who the girl in red was, but she thought she would float up in the air with pride when the whole royal party came over to shake hands with her brother. She was aware of the watching crowd talking about them, pointing Archimedes out to one another as the son of Phidias the Astronomer, the Alexandrian-educated engineer who had offered to do something impossible.

  Kallippos shook hands with Archimedes very brusquely, then at once strode off to inspect the system of pulleys, leaving Archimedes glancing nervously after him.

  Queen Philistis smiled graciously at Philyra when Archimedes introduced her. "I believe we've met before," she said. "You won prizes for music at your school, didn't you, child? Your whole family is much gifted by the Muses, it seems."

  Philyra blushed. She had indeed won prizes for music, and the queen had handed them out, but she hadn't expected Philistis to remember.

  Delia merely gave Philyra a look of black-eyed disdain. Under the disdain, she was troubled. When she had first noticed that Archimedes had a girl on his arm, she had suffered a perplexing moment of indignation- followed by relief as she noticed the strong family resemblance between the two, and remembered that he had a sister. Such feelings were, she knew, entirely inappropriate- no, lunatic! It didn't matter if Archimedes had a girl or a boy or half a dozen strumpets. He was nothing to her, and that was how she wanted it. She transferred the disdainful look to him, and he blinked in confusion.

  "And that's the ship you're going to move, is it?" asked the king. "Herakles!"

  As Philyra had, he surveyed the height and length of it, then looked at the gangling young man beside him. The disparity between the two seemed insurmountable. The king silently approved his decision to have the time of the demonstration posted in the marketplace. If the fellow failed, as seemed likely, the public nature of that failure would make his own forgiveness of it appear more magnanimous, and strengthen his hold on the man. Of course, it would also make the failure more humiliating- but that couldn't be helped, and failure had sharp teeth whether or not anyone else saw it bite.

  The little boy, Gelon, also stared at the ship, then at Archimedes. He did not usually like going to public functions with his mother, but when his father had explained what this one involved, he'd been eager to come. "You're going to move that all by yourself?" he asked.

  Archimedes grinned and tugged his cloak straight. "Certainly."

  "You must be strong!" said Gelon admiringly.

  "I don't need to be," said Archimedes happily. "That's the point. There are two ways to move something heavy. One is to be very strong, the other is to use a machine. Do you see those pulleys?"

  A spider web of rope ran between the front of the nearest ship shed and the stone mooring posts on the quay: running through pulleys atta
ched to pulleys, reversed around tackle blocks, attached to other pulleys, run about the axles of toothed wheels, reversed again, and attached to more pulleys. Kallippos was standing by the mooring posts, counting them.

  "That's my machine," said Archimedes. "Do you know how a pulley works?"

  "You pull on it," said Gelon authoritatively.

  "That's right. You pull on a rope which travels twice as far as the load moves, so it takes you half as much effort. By using enough pulleys you can move any load with any effort. But maybe we should see first whether strength will move the ship. Lord King, since you've brought along so many of your guardsmen, perhaps they'd like to push?"

  Hieron had brought some thirty guardsmen along with him, under the command of Dionysios. (Archimedes looked for Straton among them, but for once did not find him.) The men were perfectly happy to set down their spears, brace themselves against the ship's sides, and push. Faces crimson with effort, feet skidding on the slipway, they struggled for a while without success, then gave up. The watching crowd groaned in sympathy. Archimedes' grin broadened. "Dionysios!" he called. "Can I give you and your men a ride?"

  Dionysios looked starkly disbelieving, and the guardsmen shook their heads pityingly. But when Archimedes hurried over to the ship and pulled down the boarding ladder, they hauled themselves aboard. Dionysios went last. He looked at Archimedes, began to say something, then shook his head and climbed in after his men.

  "Me too!" shouted little Gelon, running down onto the slipway. When Hieron nodded his consent, Archimedes helped the child onto the ladder. Dionysios caught the little boy's hand when he was halfway up and lifted him the rest of the way. Gelon ran at once to the ship's prow and climbed onto the figurehead to wave to his father and mother.

  Archimedes took a deep breath, then went to the thick rope which emerged from the pulleys and fastened it to the ring he had fixed securely to the ship's keel. He gestured for Marcus to follow him and made his way to the place where the other, thinner end of the rope emerged from its long and convoluted passage. He could feel the crowd watching him; closer at hand, the engineer Kallippos was staring at him, face tight with the same indefinable expression it had worn when they last parted. He tried to ignore them all, and took off his cloak; the sweat evaporated from his bare arms and damp tunic with a sudden delicious coolness. He handed the heavy folds of the yellow wool to Marcus.