The Sand-Reckoner

10

Archimedes had walked most of the way back to the Achradina before he even noticed that he'd left the Hexapylon. Then he stopped in the middle of the dusty road and looked up at the sky. Light. Because of what he had made, thirty or forty men who had seen the light that morning would never see it again. No- more than that. Thirty or forty were only what Good Health had killed; the Welcomer had accounted for some too. To say that they had been foreigners bent on conquest was surprisingly little comfort. They were dead, and he had shaped their death for them, devising it with great cunning from wood, stone, and the hair of women.

He had never believed that a man's head could be knocked off like that, and now something inside him had revolted. If he put the hand of his mind to catapults, it went numb and dead. Some part of him wanted nothing more to do with such things. Trying to force it there by loyalty and will was like trying to wrestle a donkey through a door. And yet the city still needed every defense he could contrive for her. Her enemies were camped before her gates, and if they got in everyone within her would suffer. What had happened that day would only make the rest of the Roman army angry.

He sat down in the dust of the roadside and covered his face. He thought of Apollo, who had "come like night" upon the Greeks at Troy, and caused the funeral pyres to burn night and day. There was nothing to be gained by praying to such a god, so he did not pray. He thought instead of cylinders. They began as cylinders of catapult strings, but altered suddenly into abstract cylinders, ideal in form. A section cut through a cylinder at a right angle to its axis was a circle. He imagined that circle, then rotated it to form a sphere which his imaginary cylinder precisely enclosed. Diameters, centers, and axes whirled through his mind, forming a pattern that was fascinating, complex, bewitchingly beautiful.

He realized with a shock that he had not thought about any problem in geometry since his father died. He had sworn to Phidias that he would never give up mathematics for catapults, and yet he had been devoting himself absolutely to the engines of death. He took his hands off his face and stared at the dust beside him. Nice, even dust. He felt about at the roadside, discovered a twig, and began to sketch.

Archimedes was not home by suppertime, so the women of the familywho disapproved of the hours he'd been working- sent Marcus to the Hexapylon with orders to fetch the master home whether the catapult was ready or not. Marcus set out in a hurry, hungry and impatient; he took a shortcut through the back streets and up the edge of the Epipolae plateau, missed his master, and arrived on the main road just as the Roman prisoners were marched past on their way into the city.

News of the assault had yet to penetrate the Achradina, and it was not at first clear to Marcus what this procession was. The people of the Tyche quarter, the poor inhabitants of the dirty shacks, had gathered along the road to watch, and Marcus made his way into the line to see what they were staring at. A double file of Syracusan soldiers, marching to the flute, enclosed an unsteady line of men in plain tunics who carried stretchers laden with wounded. Marcus surveyed them in surprise, then asked the man nearest him what was happening.

The man, an elderly goatherd, spat and replied, "Romans- and may the gods grant that we see the rest of them the same way!"

Marcus looked back at his countrymen in shocked silence. They had been disarmed, but they were not bound, and the injuries of the wounded had been tended; only the expression of bewildered shame on each face betrayed their status. The question "How?" formed in his throat, but he did not utter it, aware as never before of the accent that would mark him out.

The procession of stretchers passed, and was followed by a small group of walking wounded. Afterward it seemed utterly inevitable to Marcus that the third man among them should be his brother Gaius.

Gaius had his right arm in a sling, and his tunic, unpinned on the right shoulder, showed that his chest was bandaged as well. His face was white with pain, but he walked steadily- until his eyes, brushing blindly over the faces that watched him, snagged on Marcus'. Then he stumbled. The Syracusan soldier next to him caught his good arm to stop him falling, and Gaius gasped and stood still, sweating and shuddering with pain from some injury that had been jolted. His eyes, recovering before the rest of him, sought out Marcus again, in amazement and disbelief.

Marcus stared silently back. A part of him seemed to be standing somewhere beyond them both, observing the meeting; another part burned and froze with shame. Gaius had no doubt believed him dead. He should have been.

"Marcus?" whispered Gaius; Marcus could not hear his name, but recognized its shape on his brother's lips. He did not respond; instead he made himself glance over his shoulder as though to see who this stranger could be speaking to.

The Syracusan soldier beside Gaius asked him, in Greek, if he could walk. Gaius replied, "I not speak Greek," and began walking again. As he passed Marcus he glanced back, his expression stunned.

Marcus forced himself to watch the rest of the procession, though his legs were shaking. He was astonished that no one turned to him and asked, "Why was that man staring at you?" He realized later that that meeting of eyes, which for him had burned like the sun, must to others have appeared as nothing more than the blank stare of a wounded man encountering the curious gaze of an onlooker.

When the noise of flute and marching feet had faded away down the road, and the small crowd had dispersed, Marcus went on toward the Hexapylon, then stopped and sat down on a stone at the edge of the road. His mind was in such a chaos of shame and astonishment and excitement that it was several minutes before he was aware of any one thought or feeling. Gaius, alive and in Syracuse! Gaius had seen him, knew he was here. What was he to do?

"Marcus?" said a voice just beside him. He looked up with a guilty start and found the guardsman Straton standing over him. He stared stupidly: it was not anyone he'd expected.

"I thought it was you," said Straton. "What's the matter? You look ill."

Marcus forced himself to stand and struggled to collect his wits. "I ran too fast for the heat," he said. "I'll be fine in a minute. Are you coming from the Hexapylon?"

Straton nodded. "Taking a message back to the Ortygia," he explained. "Did your master leave something at the fort?"

"Isn't he there?" asked Marcus, surprised.

Straton was equally surprised. "He left hours ago! Isn't he home?"

When Marcus explained his own errand, the soldier blew out his cheeks and rolled his eyes. "I hope nothing's happened to him!" he exclaimed. "The king wouldn't trade him for a battalion, and rightly so. Those catapults of his are worth one. You heard the Romans assaulted the walls?"

"I saw the prisoners on the road," replied Marcus cautiously.

Straton grinned. "All that's left of two maniples," he said proudly. "The catapults did that. You should have seen the two-talenter!" He punched a palm with a fist. "Ten or more of them down with every stone! What a test-firing! The rest of them are camped out there, thinking about it. If they have any sense they'll leave Syracuse alone now."

"What will happen to the prisoners?" asked Marcus, still too shaken to wonder if such a blunt question was wise.

Straton, however, had forgotten all about Marcus's dubious nationality and was too preoccupied with triumph to be suspicious. "They'll be locked up in the Athenian quarry," he said. "The king gave orders that they're to be treated well; I'm sure he has plans for them. He wanted prisoners.- Do you suppose your master's all right?"

"He's probably stopped to draw circles," said Marcus. "He does that sometimes." He turned from the Hexapylon and began walking back along the road into the city.

Straton followed, spear slung across both shoulders. "Will he be able to make a three-talenter?"

"Yes."

"What about a four-talenter?"

"Probably."

"A five-talenter?"

Marcus glared. "You've heard him yourself! He can build them as big as wood and iron and strings will stand. That's probably a lot bigger than anybody wants. But iron will give out before Archimedes' ingenuity does."

Straton laughed. "I believe you! He earned me a month's pay when he moved that ship. I boast now about knowing him."

Marcus grunted. Archimedes' fame had been growing ever since the demonstration. All the shopkeepers and neighbors had become remarkably polite. Marcus didn't like it: they always asked about catapults. Marcus imagined a two-talent stone smashing into his brother's arm, and winced.

Straton kicked a loose stone in the road, then said, "There was a matter my captain asked me to sound you out about, if I could. Your master's sister: is she promised to anyone?"

Marcus' head lifted with a jerk and he stared at the soldier. Straton gave an embarrassed grin and hefted his shoulders. "See," he said, "the captain's not married. He noticed your young mistress, and thinks she's charming. He's a fine man, and the king thinks highly of him. It would be a good match."

"The house is in mourning," said Marcus.

"Well, yes," conceded Straton. "The captain really just wants to know if it's any good him talking to your master when the period of mourning is over."

Marcus imagined Philyra marrying Dionysios son of Chairephon. A good match. An officer with a responsible position and the king's favor, not too old, well liked by his subordinates… musical, too. He thought of Dionysios singing while Philyra's angular body folded about the lute- thought of her low voice that blended with the swift intricacies of the music, her hip outlined against the thin tunic, her hair, her smile, her bright eyes- gone? Out of the house, out of his life.

He had always known she would go one day. Stupid to have thought about her as he had; stupid to feel now this utter desolation. Stupid to worry about a future he might not live to see.

He realized on the last thought, with a chill of pure dread, that he did mean to do something about Gaius.

"She's not promised to anyone," he forced himself to admit- then, despite everything, found himself adding, "But in Alexandria Archimedes talked about marrying her to one of his friends. He wasn't head of the household then, and couldn't arrange it, but he may want to now. I don't know."

"A friend in Alexandria?" demanded Straton, startled.

Marcus nodded solemnly, disgusted but unable to stop himself. He was not exactly lying, but he wasn't telling the truth, either. "A Samian called Conon, a student at the Museum. He and Archimedes each thought the other the cleverest mathematician alive. Conon's of very good family, and rich, but he would have been happy to forgo a dowry in order to call Archimedes brother."

That was all true- but Conon's wealthy and distinguished father had been far less romantic. He had long before arranged for his son to marry a Samian girl of his own class as soon as she came of age. The talk of brotherhood had never been more than daydreams.

"Archimedes can't be planning to go back to Alexandria!" exclaimed Straton.

"He can go where he likes!" replied Marcus sharply.

"B-but- the war!" stammered Straton.

"It won't last forever."

Straton chewed his lip, and Marcus knew that he was thinking of catapults- of the biggest catapults in the world being built in Alexandria instead of in Syracuse. He realized suddenly that the king had thought of that from the first, and saw the purpose of those obscure manipulations.

"A loyal citizen…" began Straton, then stopped: he had just seen Archimedes.

They had followed the road down from the heights now and reached the edge of the Achradina. It was dusk, but there was still enough light to read by. Archimedes was sitting at the edge of a small public square, folded up like a grasshopper in the middle of a patch of dry ground, chewing the end of a stick and staring at the dust before him. His black mourning tunic was hitched up, exposing thin thighs, and he looked like a delinquent schoolboy.

An elderly woman who'd been drawing water at the fountain in the square noticed them staring and paused beside them. "He's been there for hours," she confided in an anxious whisper. "Drawing in the dust. We think he must be possessed by a god. I pray it's not a bad omen!"

"It's geometry," Marcus informed her. "It's true about the god." He walked over, stopped when he reached the diagrams scrawled across the ground, and called, "Archimedes!"

"Unnh?" replied his master absently.

"It's time to come home," said Marcus firmly. "Your mother and sister sent me to find you."

Archimedes raised one hand in a wait-a-minute gesture. "Jush let me work thish out," he said indistinctly around the stick.

Straton had followed the slave cautiously; now he gazed down at the thicket of endlessly repeated cylinders and spheres, letters and lines that were scraped into the dry ground. "What are you trying to do?" he asked wonderingly.

Archimedes took the stick out of his mouth, glanced up, then returned his eyes to the diagram before him as though this extraneous presence had not registered. "I'm trying to find the ratio between the volumes of a cylinder and an enclosed sphere," he said dreamily. "It isn't straightforward. If I could only…"

"Sir," said Marcus, "it's getting dark."

"Oh, leave me alone!" exclaimed Archimedes irritably. "I'm doing this!"

"You can do it at home."

Archimedes jumped suddenly and unexpectedly to his feet. "I told you to leave me alone!" he shouted, glaring into Marcus' surprised face. "If it were some god-hated machine I was working on, you would have obeyed me, wouldn't you? But this is only geometry, so you interrupt. Slaves can interrupt geometry, but kings keep quiet when it's catapults!" He lashed out furiously with the stick, and broke it with a crack against his slave's arm. "Catapults! They're lumps of god-hated wood and some strings. They're graceless and they kill people. This is wonderful and beautiful! You never understand thatany of you!" He turned the furious glare onto Straton as well. "Geometry is more perfect than anything ever seen with the eyes. That ratio was true before we were all born, will still be true when we're all dead, and would still be true if the earth had never been createdeven if no one ever discovers what it is. It matters- we're the ones who don't!"

He stopped, breathing hard. The other two looked back at him in bewilderment; Marcus was rubbing his arm. Archimedes met their gaze for a moment, then looked down at the calculations at his feet, perfect and unsolved. His rage began to trickle away, and he shuddered. What he'd said was true- but they would never, could never, understand it. For a moment he felt fully the pain of his isolation, as he had not felt it for years- not since he was a little boy, and had first understood that all the things he found most wonderful were to the rest of the world mere confusion. He longed for his father, and then, wistfully, remembered Alexandria, house of Aphrodite where existed all things that anyone could desire, magnet of the mind.

"Even if that's true," said Marcus at last, "you can't calculate in the dark."

Archimedes gave a small groan of despair, dropped the end of his broken stick, and walked silently away.

Straton swallowed as he watched the tall black figure slouch off, shoulders hunched and head hanging. "Is he often like that?" he asked Marcus.

The slave shook his head. "No," he said dazedly. "I've never seen him like that before. I suppose it's the war, and his father dying."

The soldier nodded, relieved. "Enough to upset anyone. You'd better go look after him. We need his catapults, whether he thinks they're worthless or not."

They walked in silence as far as the door of the house in the Achradina. There Archimedes stopped, staring blankly at the worn wood. He didn't want to go in. Everything that had happened since he returned from Alexandria seemed to be falling into a kind of a shape inside him- his father's death, the king's favor, Delia- everything. He realized that he needed to see the king, now, while the force of what he felt still armored him against fear and respect.

"Sir?" said Marcus, and he shook his head.

"Tell them I'm going to speak to King Hieron," he commanded, and turned on his heel. Marcus called again, "Sir!" but he paid no attention and strode angrily on.

It was night, and when he reached the citadel the streets were quiet, with no sound but the crickets calling and, far off, the sound of the sea. He made his way rapidly to the king's house, knocked determinedly, and told the surprised doorkeeper, "I would like to speak to King Hieron."

Lamplight deepened the severe shadows of Agathon's face as he gave the visitor a look to crush stone. "It's late," he said.

"I know," replied Archimedes, "but see if he'll speak to me anyway."

The doorkeeper snorted angrily, but nodded. He shut the door; only the sound of his sandals clacking away across the marble floor provided any assurance that he was indeed going to check whether his master would speak to the visitor. Archimedes leaned wearily against a column in the porch and waited. Presently the door opened, and the doorkeeper looked out, more disapproving even than before. "He will see you," he admitted reluctantly, and beckoned Archimedes in.

Archimedes followed him into the mansion, past the marble antechamber and directly into the dining room. Two lampstands provided a strong soft light, and the remains of a late supper were spread over the table. Hieron was reclining on his couch, while his wife and sister sat either side of him in chairs, as was the custom for a private family meal. Archimedes stopped just inside the door, nodded to the king and his family in greeting, then crossed his arms and rubbed an elbow uncomfortably. He became aware that he was dressed only in the plain black tunic, and that it was covered with dust and oil and not fit at all for a king's house; that he was tired and overwrought and was probably going to say something stupid. Delia's eyes were wide with surprise. He tried not to think of her as he'd last seen her, flushed from kisses and flute-playing, laughing as she untied her cheek strap. She had warned him, then tried to retract her warning: who knew how far she could be trusted? Next to her the queen looked almost as disapproving as the doorkeeper.

"Good health!" said the king, smiling. "Won't you sit down and have a cup of wine?"

Archimedes sidled to the nearest couch and sat down on it; one of the slaves at once filled a cup with watered wine and set it before him.

"What was it you wanted to see me about?" asked Hieron.

Archimedes cleared his throat, his eyes on the king's. "What is it you want of me?" he asked quietly.

Hieron's bright pleasantness faltered. He sat up, swinging his legs off the couch, and regarded Archimedes assessingly. Then he said evenly, "You know that you are exceptional."

Just what Delia had said. Archimedes nodded once, quickly.

"What do you think a king wants of an exceptional engineer?" asked Hieron, lifting his eyebrows quizzically.

Archimedes gazed at him for a moment longer, baffled again. Then his eyes dropped to the table in front of him. "I have a… method of analysis," he said. "A way of thinking about geometrical problems mechanically. It doesn't provide proofs, but it helps me understand the properties of things. I think of plane figures as consisting of a set of lines, and then I see if they balance. This is a bit like that. The way a king treats an exceptional engineer- if I think of that as a triangle, then the way you've treated me is more like a parabola of equal base and height. The two don't balance."

"Don't they?" asked Hieron.

"No," said Archimedes. He dipped his finger in the cup of wine and carefully traced a parabola on the tabletop: a tall humped curve. Then he traced a triangle inside it, point touching the curve's peak, corners at its edges. It was instantly clear that the two would indeed not balance. Archimedes looked up, meeting the king's eyes again. "The area of the parabola is four-thirds that of the triangle," he said. "I worked it out myself."

Hieron craned his neck to see, and his quizzical look reappeared. "You don't like getting a third more than you expected?"

Archimedes made a small dismissive gesture with his hands. "I simply want to understand what I am dealing with. The properties of parabolae are different are from the properties of triangles."

"Are you accusing my husband of deceit?" interrupted the queen angrily. "After all his kindness to you? What…"

Hieron raised his hand, and she stopped. Husband and wife looked at each other a moment. Then Philistis sighed. She got to her feet, went to her husband, and brushed back his hair gently. "Don't let him upset you," she ordered.

Hieron smiled affectionately and nodded, and she kissed him and swished out of the room.

Delia scrunched herself deeper into her chair, telling herself fiercely that she had an interest here. Hieron didn't know how much of one, but she had a legitimate interest, too. Hieron showed her that he had noticed with an ironic glance, but made no comment. He looked back at Archimedes in silence and made a go-ahead gesture with one hand.

"You asked me to do that demonstration," said Archimedes. "And it was you who had it posted in the marketplace, wasn't it?"

Hieron nodded fractionally.

"They all cheered when it worked," Archimedes went on slowly, "and since then things have been different. I didn't notice at first, but they have been. I was warned"- he did not glance toward Delia- "that I should be more cautious if my demonstration went well than if it went badly, but I didn't understand. I thought it meant to watch the contract- only I haven't been given one. What has happened is that now people know who I am. If I start to do something, they run about to help. People I don't know call me by a nickname which you gave me. Everyone has heard what you said at my father's wake, and how you paid for his funeral- out of respect for me. Everyone has heard, too, that you thought that first catapult I made was worth a thousand drachmae, even though your man only said as much to me in private. You've arranged for me to be famous, haven't you? As an engineer, as an… archimechanic."

"You would have been anyway," said Hieron, "in time."

"You arranged for it to happen at once," replied Archimedes. "And you arranged it so that Eudaimon does what I say and Kallippos follows my advice. Even though they have titles and contracts with the city and I don't, still somehow or other my standing is higher than theirs. You tried to give me money the same way, too- something extra for something undefined. Something that doesn't come from the city, but belongs to me- because I am a great engineer. But I never chose to be a great engineer. That status, like the fame, is something you arranged."

"Very well," said Hieron, in an absolutely neutral voice, "you've noticed all this. What do you think I want of you?"

Archimedes blinked at him for a long minute, then said slowly, "I think you do want only what a king wants of an exceptional engineer. But for some reason you don't think I'll give it to you, so you're trying to… to maneuver me into a room to which only you have the key. And if I go in, you'll lock the door behind me, and I won't be able to get out again."

Hieron looked at him for another moment- then shook his head and gave a long sigh of acknowledgment and disgust. "Oh, Zeus!" he exclaimed. "I've botched it, haven't I? I should have remembered that you're more intelligent than I am." He hitched himself forward in his seat and slapped the table. "But look, I can't lock you into anything, because- unfortunately! — there is no room to which only I have the key. Your parabola has the same base and height as your nice straightforward triangle. I want only what a king wants of an engineer- that you should build things for me- and in return I can offer only what kings have to give- money and status."

Archimedes' cheeks had flushed with anger. "You were fixing that 'Archimechanic' name onto me as though you were title-tagging a book! In a year or so, if I tried to claim that I'm really a mathematician, everyone would laugh at me and tell me to get on with my real work. My own family would start hiding the abacus. I swore to my father on his deathbed that I would never give up mathematics, and you-"

"No!" cried Hieron urgently. "May the gods destroy me if that's what I intended! I know you only build machines to get the money to do mathematics, and the main reason I haven't offered you a contract is to leave you free to do just that."

"Then what is the point of all your arrangements?" demanded Archimedes.

"To keep you in Syracuse! When Ptolemy of Egypt offers you a position at the Museum, I wanted everyone you know- from your own household through to the man who sells you vegetables- to tell you fervently that you must not accept, that for you to leave Syracuse would be treachery to the city that gave you birth. If I'd really succeeded, you wouldn't even have found a Syracusan ship willing to carry you to Alexandria, and you would have had to stay for very shame. I swear by all the gods, though, that beyond that I intended nothing for you but wealth and honor. Right now you're upset because you've seen what your catapults can do to people, and I understand that- I do, I hate killing, too! But if you think about it when you're calmer, you'll see that nothing I have done is going to oblige you to abandon mathematics. Nothing! With the enemy at our gates, no one can think of anything but war, but I pray to all the gods that we will have peace again, and then there will be space for better things."

Archimedes blinked at him stupidly for a long time. "Why are you so certain that Ptolemy will offer me a job?" he asked at last. "He has some very clever people in Alexandria already."

"He'll want you for exactly the same reasons I want you!" said Hieron impatiently. "I don't think you appreciate yet how exceptional you are. You think that compound pulleys and screw elevators are just things anybody else would have used to solve the engineering problems you were faced with. And they are- now. Now they seem obvious to everyone. But last month they weren't, because they hadn't been invented."

"But- pulleys are used all the time!" protested Archimedes. "And screws have been used to hold things down for ages."

"So it's perfectly natural to use one pulley to turn another, and a screw to lift things up? Certainly. Only nobody ever did. Only somebody who's happier with the theory of screws and pulleys than with the objects themselves could have adapted them like that. You approach engineering through mathematics- and mathematics is probably the most powerful tool ever employed by the human mind. I knew that before I met you, and when I heard about you I suspected at once that you were going to prove exceptional. Ptolemy had Euclid for a tutor, and he knows the value of geometry even better than I do. Probably the only reason he hasn't offered you a job already is that the problems you were working on in Egypt were so extremely advanced that only about half a dozen men in the world were capable of understanding them, and Ptolemy's head of Museum didn't happen to be one of that half-dozen. But even so, you would probably have been offered a post this summer, if you hadn't come here instead. You have planted your fame in Egypt now, though it's taken a little while to grow. A ship's captain I spoke to recently told me about an irrigation device invented by one Archimedes of Syracuse which obliges water to flow uphill."

"It doesn't, exactly," muttered Archimedes. "You have to turn it."

He sat for a moment, contemplating what Hieron had just told him, stunned by it. The unbreachable walls he had sensed closing about him had turned out to be low enough to vault over. The power he possessed could bring him not merely wealth and the favor of kings, but freedom as well. The sea lay before him, and it was his sole choice what course to set on it!

He looked back at Hieron and managed an unsteady smile. "Thank you for telling me this," he said.

"I wouldn't have," replied the king sourly, "if you weren't on the point of working it out for yourself. I still want to keep you. I can't offer the Museum, but anything else you might expect to find in Egypt is yours for the asking."

Archimedes grinned. He picked up his cup of wine and drank it off thirstily, then stood up. "I'll bear that in mind."

"Do!" said Hieron sharply. "And bear in mind, too, that when Alexandria takes the best minds from all over the world, the rest of the world is impoverished. Syracuse is your own city. She is a great and beautiful city, and fully deserves the love of all her children."

Archimedes hesitated, looking at the king with curiosity, then replied impulsively, "That calculation about the areas of a parabola and a triangle- it was the parabola I was interested in when I did it. Not the triangle."

For the first time Hieron was thoroughly taken aback. He stared at Archimedes in honest and straightforward astonishment.

Archimedes grinned again, and for the first time since he'd come into the room his eyes flicked over to meet Delia's, with a look as though he were sharing a joke with her. "I wish you joy," he said to them both, and departed the room with a swagger.

The following morning Archimedes set off for the catapult workshop at the usual time, looking tired but determined. Marcus watched him go, then silently let himself out of the house and set off in the opposite direction, toward the Athenian quarry.

The quarries of Syracuse lay within the city wall. The plateau of Epipolae was composed largely of limestone, a great dry island lying upon the coastal shelf. Its southern, city side broke off in steep cliffs, and into these the Syracusans had cut a series of quarries for building stone. The Athenian quarry was the most famous of these. It took its name from its use nearly a hundred and fifty years before as a prison for the seven thousand Athenian prisoners of war taken at the conclusion of their city's disastrous attempt to subdue Sicily. Within its limestone walls the Athenians had suffered horrors, the living crowded in a narrow pit together with the dead. Many had died, and their bones lay still beneath the quarry floor.

There was nothing in the appearance of the place now to speak of its grim history. The morning sun was just rising above the overhanging cliffs, casting deep cool shadows, and at the quarry sides a thick tangle of cistus and juniper covered the rock spoil with a canopy of sweet-scented green. There was a stone wall across the quarry entrance, however, and the only gate was guarded. Marcus walked boldly up to the gate and wished the guards good health.

The guards- there were six of them- looked back at him suspiciously. "What do you want, fellow?" asked their leader.

"I'm the slave of Archimedes son of Phidias," replied Marcus- and noticed the sharpening of interest as the name was recognized. "He wanted me to check the quarries to find which has the best stone for catapult shot."

At this, suspicion was completely swept away. "Is he building a three-talenter?" asked the youngest man eagerly.

"He starts it this morning," said Marcus. "It'll probably be ready in six or seven days."

"Zeus! A three-talenter!" exclaimed the young guard happily. "More than a man's weight! Imagine that hitting you!"

Marcus forced himself to grin back. "They're going to call it 'Wish You Joy,' " he said.

All the guards laughed. They reminded one another of the names of the other new catapults at the Hexapylon, and punched the air as they recalled how well they had performed.

"But why does the archimechanic want you to check the quarries?" asked the man in charge- not suspiciously, but with genuine puzzlement.

"Think about it," said Marcus. "You can get stone for thirty-pound shot anywhere, but a three-talent boulder is a big piece of rock. If it's flawed or uneven it may not fly straight. So Archimedes told me to go out to all the quarries and check which one would be best for the size of ammunition he needs." He dug into the leather sack he carried and produced a hammer and chisel. "He told me to bring him back a couple of samples, too."

The guards' leader took the hammer and chisel and examined them thoughtfully. Marcus waited, trying to keep his face blank, trying not to think about what he was doing or what he was about to do. He was already in trouble if news of this visit got back to Archimedesthough not in as much trouble as he would be in if it continued.

"I can't let you take this in," said the guards' leader regretfully. "We have Roman prisoners in this quarry. I can't risk something like this falling into their hands."

"Romans?" asked Marcus, tension giving his voice a strained note that passed well as surprise. "Here? Well, bad luck to them!"

"You're an Italian, aren't you?" said the guards' leader.

"A Samnite," agreed Marcus. "And a slave because of Rome. But a Syracusan for the last thirteen years. What's the king going to do with these Romans, then?"

The guards shrugged. "He wants them for something," said the leader. "They get the best of food and the king's own doctor is attending their wounded. He's in there now, in fact."

"With some guards?" asked Marcus.

"Of course!" exclaimed the young guardsman, shocked at the thought of the king's own doctor going unguarded among enemies. "There's a half-file of us here."

Marcus grunted. "Well, bad luck to the Romans anyway!" he said. "Can I go in and check the quarry, even if I can't take samples? I may be able to tell straight off that the stone's no good for my master's catapult."

"Of course," said the guards' leader, smiling. "Your master's welcome to any help we can give his catapult. Good health to him!" And he gestured to his men to unlock the gate.

The youngest guardsman accompanied Marcus into the quarry. The eastern part of the quarry floor was still in shadow, but the morning sun shone warmly on an empty expanse of stone. "Where are the Romans?" asked Marcus.

The guardsman gestured toward the north face of the cliff, where a collection of sheds nestled under an overhang. "In there," he said disgustedly. "Nice and comfortable, out of the sun."

Marcus scrutinized the sheds. There were three of them: long, low, windowless buildings which had probably been set up to house a slave workforce when the quarry was in use. He could make out guards on the doors. "You've only got two people on each shed!" he objected.

"All we need," replied the guardsman. "Most of the Romans are wounded, and we've put leg irons on the rest. All the men on the sheds have to do is let prisoners up to use the latrines. If you want to look round, I'll just tell them who you are, so they don't bother you." He crunched off across the quarry floor to explain Marcus's presence to the other guards.

Marcus made his way slowly about the perimeter of the quarry, ostentatiously examining the spoil heaps and occasionally picking up a chunk of limestone and putting it in his sack. When he was finally approaching the sheds, he was relieved to see the king's doctor come out of the nearest, accompanied by three guards.

The doctor noticed him, recognized him, and came over to ask what he was doing; Marcus explained. The doctor sighed and shook his head sadly. "At times I wish catapults had never been invented!" he exclaimed. "The injuries they produce- but it's for the good of the city. I wish you joy!"

Marcus waited until the man was well on his way back to the gate, then walked slowly up to the shed. The guards were at the far end and were not watching him, but his stomach was so tight that he thought he would be sick. He reached the wooden wall and leaned against it, trembling. There was a gap in the rough planking; he set his eye to it and gazed in.

The only light inside was what shone through the many gaps in the uneven walls, and it took a little while for his eyes to adjust. The building had a dirt floor, and in winter would have been cold and drafty, but it was comfortable enough for the Syracusan summer. About thirty men were within it, some of them lying very still on straw mattresses on the ground, but some, in leg irons, gathered together in little knots, talking or playing dice. Marcus made his way silently along the space between the cliff and the back of the shed, shielding his eyes from the light to preserve their adjustment to the dimness and checking each prisoner in turn, but it was soon clear that none of them was Gaius.

He waited until both the guards at the shed door were facing into the building, watching the prisoners, then glided out from behind the wall of the first shed and crept on to the next. He found another gap in the planks and peered through it.

He spotted Gaius at once, about halfway along the shed and on his own side of it, lying on his back on a mattress with his injured arm across his chest. Marcus made his way noiselessly along the side of the shed toward his brother. He could hear the guards at the door beyond talking, and his skin prickled with tension. He told himself that even if they did notice him, he could explain himself by saying he was simply curious to see the prisoners. But his skin prickled anyway. It was not really the guards he was afraid of.

When he had reached Gaius he knelt in silence for several minutes, inches away behind the thin planking, watching through a crack. Gaius was awake, his eyes open and staring darkly at the ceiling. His tunic was loose about his waist, and his chest was wrapped in bandages.

Marcus tapped lightly on the wall. Gaius' head turned slowly, and their eyes met.

Gaius sat up, bracing himself against the wall, trying to see more of his brother than showed through the crack. "Marcus?" he whispered. "Is it really you?"

"Yes," whispered Marcus. He was trembling again. The Latin word, sic, tasted strange in his mouth. For a long time he had spoken Latin only in his dreams, and to use it now made him feel that he was dreaming still.

"Marcus!" repeated Gaius. "I thought you were dead. I thought you died at Asculum!" On his right, his neighbor looked around at the raised voice, though the man on his left was asleep.

"Softly!" hissed Marcus. "Don't look at me; the guards may notice. Just sit with your back to me and keep your voice down. Right. Now, I've got some things for you-"

"What are you doing here?" whispered Gaius, sitting stiffly against the wall with his back to his brother. "What are you doing alive?"

"Being a slave," replied Marcus flatly. The man to Gaius' right was still listening, he noticed. He was not looking any more than Gaius was, but the expression on his face showed that he was listening intently. He was a lean, thin, dark man with something dangerous-looking about him; his head was bandaged, but he didn't seem to be otherwise injured, and his feet were imprisoned in irons.

"How?" demanded Gaius in a furious whisper. "Nobody was enslaved at Asculum! King Pyrrhus returned all his prisoners without ransom."

"He returned all his Roman prisoners," Marcus corrected him. "The other Italians were offered for ransom, and if nobody ransomed them, they were sold. There were a couple thousand people enslaved, Gaius. Not 'nobody' by any…" He found he could not remember the Latin for "reckoning" and fumbled to a halt.

"No Romans!" Gaius pointed out angrily.

"One at least," said Marcus bitterly. "Gaius, don't be stupid. If nobody told you what happened, you must have guessed. I deserted my post in battle. I was frightened, and I ran."

Gaius gave a jerk of pain. Roman did not desert their posts. A Roman who did would be beaten to death by his comrades. Even at Asculum, where the legions had tasted defeat at the hands of King Pyrrhus of Epirus, most of the Roman troops had been so afraid of the punishment for flight that they resisted to the death, and made Pyrrhus' victory so expensive that it cost him his campaign.

"Our square broke," said Marcus bluntly, "and most of the men died. I knew that the survivors would list me as one of the ones who ran. So after the battle I said I was just an allied Latin, or a Sabine or a Marsian, or anything except a Roman. I wasn't returned, and of course nobody ransomed me. I was sold to a Campanian, a vulture who was following the war about picking up scraps, and he sold me to a private citizen here in Syracuse."

"Oh, gods and goddesses!" whispered Gaius.

"It's what I chose," said Marcus in a harsh voice. "I wanted to live."

There was a long, wretched silence, a silence fully as bad as anything Marcus had imagined beforehand. There was nothing either of them could say. He had preferred life as a slave to death as a Roman, and for that there was neither condolence nor excuse.

"How are things at home?" he asked at last.

"Mother died eight years ago," said Gaius. "Valeria married Lucius Hortensius and has three daughters. The old man's still in charge at the farm, though his chest is bad." He hesitated, then added quietly, "I won't tell him you're alive."

There was another silence. Marcus thought of his mother dead, his sister married, his father… his father would not learn of his disgrace. Good, good, good; the thought of the old man's rage still made him cringe inside. He wished that it were his father who was dead, that he could have gone back to his mother- and was ashamed of the thought.

"Thank you," he said finally. "I've come to help you. I've brought you some things."

"Can you help me get out?"

It was exactly what Marcus had expected his brother to say, and he sighed. "You're better off where you are, Gaius! The king"- he used the Greek title- "wanted prisoners, and that means he wants an exchange for something. You'll be safest staying here until you're exchanged. And your arm's broken, isn't it?"

"My arm and my collarbone," said Gaius flatly. "And three of my ribs. Can you help me escape?"

"Was it a catapult?" asked Marcus unhappily. It seemed ridiculously important to know whether it was his own master's contrivance which had injured his brother.

"Yes, of course it was," replied Gaius impatiently. "May the gods destroy it!"

"What size?"

Gaius started to glance around, then remembered that he should not do this and leaned his head back against the wall. "Marcus, all I noticed was that it hit me! There were catapult stones everywhere, and some of them were enormous. Why does it matter?"

Marcus didn't reply. "I've brought you some money," he said instead. "If you put your left hand up against this crack I'll pass it through. Your guards will probably buy things for you, for a cut. It's twenty-three drachmae."

"Twenty-three!" exclaimed Gaius in a strangled voice. "How did you- Marcus, your master will notice it's missing!"

Marcus remembered suddenly how scarce silver coin was in Rome, remembered with a shock how his family had bartered for almost everything, and used the heavy bronze as for almost everything else. When he was sixteen, twenty-three drachmae would have seemed a fortune. It was plain that to Gaius it still did.

"It's my own money," said Marcus. "I've never stolen yet, though I will if I must to help you. This isn't as much as you think- a month's wages for a soldier. But it may be useful."

Gauis set his hand against the crack, and Marcus fed the coins through. "What are these?" whispered Gaius, watching the silver fall into his palm. "They're… strange."

"They're Egyptian," replied Marcus. "We spent a few years in Alexandria. Don't worry- they're the same weight as Syracusan, and people here will take them."

Gaius said nothing, only stared at the silver, and Marcus remembered a time when Alexandria had been remote as the moon. It had ceased to seem that even before he visited it. At Syracuse one met ships from all over the Greek-speaking world, and he had grown used to the idea of traveling even before he'd traveled himself. But in central Italy people hadn't traveled much. Gaius had never traveledexcept, of course, with the army. He had enrolled in the legions for the Pyrrhic War, and had presumably gone home to the family farm afterward, enrolling again for the Sicilian campaign. Marcus was oppressed by confusion and disquiet. It was quite wrong that he, a slave and coward, should feel superior to his elder brother.

"I have a saw and a knife as well," Marcus said, the confusion adding to the harshness in his voice. "And a coil of rope, but I think they're better left out here. If you decide you want them, I'll hide them." He did not really want to help Gaius escape- he sincerely believed that his brother was safest where he was- and yet he could not refuse to help. Besides, he could be wrong. The prisoners might yet be executed, or murdered by a Syracusan mob furious at some Rome atrocity.

"How did you get in here?" asked Gaius. "How did you get the guards to allow you to bring in saws and ropes?"

"They didn't know I had 'em," replied Marcus. "Though they did take my hammer and chisel. I told them I was on an errand for my master. They know my master, so they let me through. I told them I'm Samnite, too, so that they wouldn't suspect me of wanting to help. Now, listen. I can invent another errand and come again if you need me, but if I do it too much, someone will start to suspect. So it's better if I don't come again soon, and I need to know now: are you going to try to escape?"

"Can you pass the saw in?" interrupted the man on Gaius's right.

"Who are you?" demanded Marcus.

"Quintus Fabius," replied the other. "Friend and tentmate of your brother. He's not going to get out without someone to help him."

"You're safer staying where you are!" warned Marcus.

"We'll get out if we can," said Gaius. "I don't care to find out what the tyrant of Syracuse wants prisoners for."

"There's nothing wrong with King Hieron," said Marcus. "He's cleverer than a fox and more slippery than an eel, but he's not cruel."

"He's a Sicilian tyrant!" protested Gaius in astonishment. "He cooks his enemies alive in a bronze bull!"

Marcus gaped. "Don't be ridiculous!" he exclaimed, recovering a little. "He's never put a single citizen to death, let alone cooked one alive. It was Phalaris of Akragas who had the bull- a man who lived centuries ago and in another city."

There was a bewildered silence, and then Gaius said, "I heard that Hiero"- he used the Latin form of the name- "had a hundred of the wives and children of his enemies impaled on stakes."

Marcus realized that his brother had undoubtedly heard dozens of stories of Syracusan atrocities. The Mamertini would have told some when they asked for Roman help, and more would have sprung up among the legions as they prepared for war. The Senate must have known the tales were false, but had said nothing.

"You heard a brazen-faced liar," snapped Marcus in disgust. "A stinking bandit who wanted an excuse for his own crimes."

"How can you be so sure?"

"Gaius, I live here! I've met Hieron, been to his house! If anything remotely similar had happened, I'd know about it. King Hieron has never killed or injured any citizen- which is more than the people you've come to Sicily to help can say!"

"You've gone very Greek," said Fabius quietly.

"I don't have to have gone Greek to say that the Mamertini are a tribe of bandits!" replied Marcus heatedly. "We put our own people to death for doing what they did- but you've come to fight and die for that bunch of filthy Campanian murderers." He stopped himself, swallowed a lump of anger, and went on, more moderately, "But what I meant to say is, if you think you need to escape because King Hieron's likely to harm you, think again. You'll be well treated until he exchanges you. Things are likely to be much worse if you try to escape than if you stay where you are."

"I mean to escape anyway," said Gaius, "if I can."

Marcus sighed again: it was no more than he'd expected. "I can probably manage to get two out of the city," he said, "but no more."

"Can you pass us the saw?" asked Fabius.

Marcus passed in the saw, though he had to take the handle off to get it to fit through the crack. Fabius tucked it under his mattress.

"With this and your knife and rope we can get out," he said. "Hide them under a rock beside this plank. You wouldn't happen to have noticed how many guards there are, and where they're posted?"

"Half a file," said Marcus. "Six on the gate, two on each of the sheds. Presumably the other six are on the wall, though I didn't see them when I came in. Don't even think of going up the cliff: it overhangs. The spoil heap by the west edge of the wall is probably your best chance: it's high, and it's overgrown pretty thickly and can give you cover while you wait for a sentry to turn his back. If you get out, come to our house, and I'll get you out of the city. All I ask is that you wait at least three nights first. If you come at once, somebody's bound to remember that I was here, and know where to look for you: a few days will give them a chance to forget. And Gaius needs the time to recover his strength, anyway."

He gave careful instructions on how to find the house. "The brick on the left side of the doorframe about halfway up is crumbled," he finished. "You can't mistake it. I'll find an excuse to sleep down in the courtyard, starting in three nights' time, and if you come at night I'll let you in secretly. If you don't come- and I tell you again, I think you'd do better to stay where you are! — I'll come back in ten days with some more money."

"Whose house is it?" asked Fabius.

"You're not to ask for it!" said Marcus. "That would give everything away."

"I just want to know," said Fabius. "Who's this master of yours that all the guards know, who goes to visit the king?"

"His name's Archimedes," admitted Marcus. "He's an engineer."

"The catapult maker!" said Gaius, turning his head to stare through the crack.

"Don't look!" growled Marcus. "Yes, he makes catapults."

"They were telling us about him at the fort. They showed us one of the catapults and said he was building an even bigger one."

Marcus said nothing.

"They said that the next one would be the biggest catapult in the world. They said it was bound to work, because his catapults always work. They said it was no use hoping to take Syracuse by storm, because Syracuse has the greatest engineer in the world. He's your master?"

"If you come to his house," Marcus said suddenly, between his teeth, "you're not to harm him. You have to swear that to me."

Silence. "It would be better for Rome if a man like that were dead," said Fabius slowly.

"You're not coming into the house unless you swear not to harm him," said Marcus. "I'm not having anyone in that house hurt."

Again, silence. "He's treated you well?" asked Gaius at last, with a mixture of bewilderment and shame. Marcus should never have been in the position where it mattered how a master treated him.

"Oh, may I perish!" muttered Marcus. "He trusts me. And- and he ought to exist. Someone like that- there aren't any others like that, not even in Alexandria. He can do anything- make water flow uphill, move a ship single-handed, tell you how many grains of sand it would take to fill the universe. It's not better for anybody when a man like that is dead. It means that there are a lot of things which the human race could do once and suddenly can't anymore." He stopped, utterly sick with confusion. He felt suddenly that he must have died without noticing: the Marcus who had run away at Asculum would never have thought the sort of things that were in his mind now.

Again there was a silence. Then Gaius said resignedly, "I swear that I will not harm him. May all the gods and goddesses destroy me if I do."

"I also swear it," muttered Fabius.

"Then come when you will," said Marcus, "and I will help you as much as is in my power."