The Sand-Reckoner

by Gillian Bradshaw

  "He was a true Roman," agreed Gaius proudly.

  The brown eyes fixed him, uncomprehending and angry. "Oh? The people who killed him called themselves true Romans. If they were, he wasn't."

  "Appius Claudius isn't a man, let alone a Roman!" exclaimed Gaius hotly.

  "You can't disown him that easily!" replied Archimedes. "The Roman people elected him and followed him. His successors are now obliging my city to pay for the war he and his friends started and forced upon us, the war that isn't over yet. Rome hasn't disowned him, and nor can you! Your people murdered Marcus. Gods! Barbarians!"

  Gaius flinched, though Fabius, adding the last phrases to his translation, merely looked contemptuous. Behind them, the guardsman from the Euryalus, who had stood watching the two Romans with his spear balanced on guard, grinned. Archimedes looked back down at the flute, trying to calm himself. He fingered the dry wood, and remembered Marcus stroking it. Marcus had never had time to learn it properly. Waste, waste, stupid waste!

  "I loved my brother," said Gaius slowly. "And I wanted…"

  He hesitated. He did not know how to speak to this man. He wished Archimedes had indeed been the white-bearded sage of his imaginings; he would have known then how to conduct himself. This young man, this foreigner who angrily condemned his own people, confused Gaius, muddling his reactions. He remembered the two voices in the dark courtyard of the house in the Achradina: this one, quick, drink-slurred, questioning and commanding; and the other voice, now silenced. He had been unable to tell then, and could not tell now, what connection bound them, what history of emotions they assumed. He took another step forward and squatted in front of the figure on the stool, trying to meet the eyes, silently raging against the need to pause, and wait at each phrase for Fabius to alter his words and render them comprehensible; longing for direct communication.

  "I did not have much time to talk to Marcus last year," he said. "A little while when we escaped; a little while more before and after the trial. But he did talk a little about Egypt, and about you and your household, and about… about Greek things. Mechanics, mathematics- things I have no knowledge of. I do not know very much about what he was like, the last years of his life. I want to know. I lost him when he was sixteen, and almost half his life is missing for me. Please, tell me what you can. I ask it as a favor, as the brother of a man who was your slave, and for whom, it seems, you had some affection."

  Archimedes sighed, still fingering the flute. "What can I say? He was, as you say, my slave, and for most of the time I knew him I took him entirely for granted. One does not ask a slave what he's thinking or feeling: one just expects him to get on with his work. My father bought him when I was about nine. We paid a hundred and eighty drachmae for him- it was during the Pyrrhic War, and slaves were cheap. We had a vineyard then, and we needed a worker to help get in the vintage, and a farm- the tenants mostly managed it on their own, but we usually tried to help with the harvest, as one does. So your brother did that, and he did the heavy work at the house, and occasionally helped the neighbors. Marcus hated being a slave- I think I always did know that- but I think apart from that he wasn't unhappy. He lived in the house with me and my parents and my sister and our other slaves. My father was a gentle man and a good master. Your brother didn't seem to dislike his work, and he enjoyed other things. We always played a lot of music, and when we went out to concerts and the theater we usually chose Marcus to carry things, because we knew he enjoyed music. Machines, too- yes, he did like them. I was always building them, and he was always interested in them. He'd help hammer and saw, and he'd make suggestions- tell me that what the next hoist needed was a way to fix it halfway up and so forth, and then when I'd worked out how to make it do that, he'd grin about it. So we liked each other."

  "When I was nineteen, my father gave Marcus to me, and we went off to Alexandria for three years. I was not a good master. Marcus would say, 'Sir, we're out of money,' and I'd say, 'Oh well,' and forget about it, leaving him to sort out how we were to live without it. He was very resourceful and always amazingly honest. When he took money out of my purse- he had to, I never remembered to give it to him- he'd always tell me how much and for what, even though I never paid the least attention, and he always used to remind me who I owed money to. And he used to mend clothes and make sandals himself, and he'd do odd jobs for the tradesmen in exchange for this and that we needed. He never complained. But he never liked Alexandria- at least, that was the impression I had. He was always telling me we ought to go home. But the last year we were in Egypt I designed a machine to lift water, and he told me once that he'd enjoyed building that more than any other work he'd ever done."

  "The water-snail," said Gaius.

  Archimedes smiled at the word, which, being Greek, needed no translation. "I'm not surprised that he told you about that: he loved that machine. We didn't make them for long. I got tired of them. He was furious with me about it; he kept telling me we could make a fortune with the god-hated things. He never saw the point of geometrynot that he admitted to me, anyway."

  "He seems to have…" Gaius hesitated: told you what to do a lot hovered on his lips, but he was afraid of offending, and changed it to "… spoken his mind to you freely."

  Archimedes snorted. "He always spoke his mind freely. That's what he died for, isn't it?" He looked back at the flute, and continued, "When the war started, we came home. He was… unhappy about the war. We didn't know he was Roman- if anyone asked, he'd say he was Sabine or Marsian or Samnite or whatever- but we knew he had some loyalties to Rome. He kept swearing, though, that he would never do anything to harm the city or our house." Archimedes paused, then added, "Of course, he would have been even more unwilling to harm Rome. And you know how quickly he decided to help you. But afterward he kept saying that he was sorry he had abused my trust. And he was very sorry over the man you killed escaping- a fine man, and a friend." He raised his head and looked directly at Fabius. "If you are the Fabius who was with him that night, he said he was wrong to have given you a knife. And he said that he thought you would have killed me if you'd known who I was."

  Fabius looked back a moment in silence; he did not translate the addition. "It was our duty to escape if we could," he said at last. "As for the other, yes, I would have killed you. We had heard of your catapult-making, and I thought you were likely to cost Rome dearly. As you have. Many men are dead, and the peace we achieved has gained us little, because of you and your catapults. I do not say you were wrong to defend your city, but I would have been right to defend mine."

  "No one was attacking Rome," Archimedes pointed out coldly. "Your reasoning puts the bully on the same level as the victim who fights back. I find it fallacious. Nor do I understand how your consul could justify putting a brave and loyal man to death merely for speaking his mind."

  Gaius had been listening to this incomprehensible exchange anxiously, and now cleared his throat nervously. Fabius resumed his translation with the complaint against the consul. Gaius Valerius looked away with an uneasy hunch of the shoulders that reminded Archimedes suddenly and painfully of his brother.

  "The consul was a weak man angry," said Gaius. "As soon as he found out who Marcus was, he had him arrested and tried. He was the judge and the principal accuser. Nobody would have put Marcus to death for what happened at Asculum. Not even at the time- he was sixteen when it happened, and he'd been in the legion only three weeks! But our father had taught us to expect harsh punishments, and Marcus was always hard on himself: he'd convinced himself that he deserved to die, and he'd expected to. But even Claudius couldn't rely on Asculum after so many years. The big charge he had was that Marcus had dishonored the Roman name. Through accepting slavery, you see, and through saying that the Romans were wrong to attack Syracuse."

  "And he wouldn't lie and say he thought they were right?" asked Archimedes, with resignation.

  Gaius nodded wearily. "I think he meant to. But when it came to the point, he was angry, and he didn't. The consul had
accused him of other things as well. Foul things."

  Archimedes looked at him, frowning, and Gaius went on reluctantly, "Of prostituting himself to Greeks. To King Hieron, and to you, among others." Archimedes flushed angrily, and Gaius went on hastily, "Stupid accusations, but he had no way to refute them, except to get angry. So he got angry, and did not tell any lies, and the consul sentenced him to death."

  Gaius reached over to the flute case and took something else from it: a fat black flask about the size of a child's fist, empty. "I was very glad that he had this," he went on, low-voiced. "The legions knew that Marcus was innocent- but since the beating had to take place, the fact that no one wanted to strike only meant that it would last longer. But in the morning, when they went to take him out of the tent where they were keeping him, he was already dead. He had this with him, this and the flute. Your gifts, weren't they?"

  Archimedes shook his head. "Only the flute," he said soberly. "That was from Hieron. He told me that he'd given it to Marcus, just in case."

  Gaius looked at him in surprise and doubt, then ran a finger around the top of the flask. "A gift from the king of Syracuse? I am indebted to the king. But I don't understand how King Hieron knew Marcus, or why he bothered."

  "He knew your brother through me," replied Archimedes. "And he wanted Marcus to come back to Syracuse after the war and be his Latin interpreter. It would have been a good position, and Marcus would have filled it very well. Hieron told me about it. Your news will grieve him too." Archimedes got to his feet, holding the flute carefully in both hands. "It is waste, and nothing but waste. I don't know what your people will do to the world."

  Gaius rose too, and bowed his head in a gesture that was neither denial nor acceptance. "Marcus was a Roman," he said. "I would ask you, sir, to remember that of us as well. But I don't want to quarrel with you. I am grateful for your kindness in speaking with me, and grateful also for your kindness to my brother while he lived. He admired you greatly."

  Archimedes shook his head angrily. "I did not realize how exceptional your brother was until too late," he said. "I am much to blame. I hope it is some consolation to you to know that even as a slave he earned the respect of those around him." He hesitated, trying to think if there was anything else he should say, then realized that the visitors must have had a long walk from their camp, and asked them if they would like some wine.

  They thanked him and agreed that they would, indeed, like something cold to drink. Archimedes started back toward the main part of the house; as he did, Fabius gestured at the lead-lined box in the center of the workroom and asked uneasily, "What is that machine? A new kind of catapult?"

  "May all the gods and heroes forbid it!" Archimedes exclaimed vehemently.

  He had never been so sick of anything in his life as he was of catapults. He'd lost track of how many he'd built: one-talenters, two-talenters, three-talenters, three-and-a-half- and four-talenters. And arrow-firing catapults, with particularly long ranges and particularly large bolts. Outworks to the walls had come as something of a relief. The nasty little surprises he and Kallippos had invented for any siege machine that did get close to the wall had seemed like the comedy tacked onto the end of a tragic cycle at the theater. There was a long list of other things that could be done, with time and supplies, if the war went on, and he was infinitely glad to have escaped them- for the time being, anyway. His relief at the peace had been as great as that of anyone in the city. "That is a water-aulos," he told Fabius happily. "Or it will be, when I finish it."

  "A what?" asked Fabius confusedly.

  Archimedes' eyes lit. "A water-aulos. See, you fill the tank with water, and you put this hemisphere in it." He hooked the holed basin off the tank's corner and held it, upside down, in the empty cistern. "And then you have one pipe coming down to this opening here, and another coming out from here, which is shut off unless you press the keys to open the valves- the valves are the cleverest part- and you pump the air in with the bellows. The water pressurizes the air, so that when you release it through the pipes, it produces a good volume of sound." He put the basin back over the corner of the tank. "I'm waiting for the pipes from the bronzesmith."

  "But what is it for?" asked Fabius.

  "It's a musical instrument!" said Archimedes in surprise. "I said it was a water-aulos, didn't I? My wife wants one."

  "A musical instrument!" exclaimed Fabius, and shook his head wonderingly. "So peace has already reduced the greatest of engineers from the making of catapults to the making of flutes as an amusement for women!"

  Archimedes stared at him in complete bewilderment for a moment, then went red. "Reduced?" he repeated furiously. "Catapults are stupid, god-hated lumps of wood which throw stones to kill people! I hope I never touch another of the filthy things in my life! This will sing with a voice like gold to the glory of Apollo and the Muses. This is as much superior to a catapult as… as…" He fumbled for a comparison, then gestured impatiently at the abacus, "… as that is to a pig!"

  "But I don't know what that is, either!" said Fabius, amused.

  "A calculation of the ratio between the volumes of a cylinder and an enclosed sphere," replied Archimedes with cold precision. He edged back toward it, and looked down, frowning. "Or an attempt to calculate it, anyway." The way into the problem, and the answer to it, had eluded him.

  "But what use is that?" asked Fabius, coming over to look down at the drawings scratched in the sand: spheres and cylinders labeled endlessly with letters; letters repeated down the sides in inexhaustible calculations, in curves, in straight lines, in figures balanced and not balanced. So much intelligence, he thought, to be squandered upon air!

  "It doesn't need a use," declared Archimedes, still looking down at his diagram. In his mind, a circle slipped up the line of the cylinder, its height the diameter, then revolved at the mid-point to form the sphere: perfect, more perfect than anything on earth. "It simply is." He studied his calculations and saw that they would get him nowhere. He picked up a flattened piece of wood and carefully smoothed the blind alley out.

  "What are you saying?" asked Gaius in Latin. Fabius had translated nothing about the water-aulos: he had no idea what a "valve" was, or "pressurize," and he suspected that the words simply didn't exist in Latin.

  "The box in the middle of the room is part of a musical instrument," said Fabius. "I said it was a sad descent from catapults to that, and he took offense. He said that music was nobler than war, and that this"- he gestured at the box of sand- "is nobler than anything."

  As the dead end vanished into the sand, Archimedes saw suddenly the path along the spinning of the circle to the truth. Breathlessly he hooked the stool over with his foot and picked up his compasses. "Just a minute," he said to the visitors. "I've just seen something. Just go into the house and have a drink; I'll join you… in a minute."

  The others looked at him in surprise, but he was already oblivious to them. The compass marked out its precise reckonings in the fine sand, and his face following it was rapt, intense, joyful. For the first time in his life, Fabius felt the foundations of his own certainties tremble. This mind was not bent upon air. The suddenly quiet room was filled with something that made the hair stand up along his arms, something that existed for no human use. Perspective altered dizzyingly, and he wondered what his own use was to a universe. Unaccountably afraid, he ducked his head and backed away.

  When Delia came into the workroom a couple of hours later, she found Archimedes sitting on the ground, resting his head on the stool and gazing fondly at the abacus. "Dearest?" she said gently.

  He raised his head and beamed at her. "It's three halves!" he told her.

  She came over and knelt beside him, putting an arm about his shoulders. They had been married since January, and she was beginning to feel that she was going to be very good at estate management but would never understand geometry at all. "The ratio is?" she asked, trying to take an interest.

  He nodded, and swept a hand toward the thicke
t of calculations. "It all comes out so perfectly," he wondered. "A rational number, after all that. So exact, so… perfect!"

  He was so happy that she hardly liked to disturb him. But after a moment she said, "I heard that there were two Romans here earlier. What did they want?"

  The happiness vanished. He looked around in alarm. "By the god! I said I'd join them in just a minute. Are they…?"

  "They left some time ago," said Delia sourly. "Melias said they talked to you, and then you sank out of sight into the abacus, so he gave them a drink, and they went. What did they want?"

  He told her, sadly, and showed her the battered flute. "Though all Gaius Valerius really wanted was to hear about his brother," he finished. "I liked him. He was like Marcus, very straightforward and honorable. The other one, Fabius, was a true Roman. He thought it was a reduction to go from catapults to music!" He rubbed angrily at another spot of corrosion on the reed clamp. "Marcus told me once that the Romans don't think music a fit subject for serious study at all. He said that his father would have beaten him if he'd asked to learn the flute. He wanted to learn it anyway. But they didn't give him the chance."

  She put her arm around him again, remembering the slave who had sat in the dark garden, listening to the music. She could not remember his face, but she was sorry he was dead. Sorry mostly for Archimedes' sake, but a little for the slave's sake as well. "I pray the earth is light upon him," she said.

  He turned toward her, put both arms around her and kissed her, then held her, feeling the shape and warmth of her against his chest, a comfort for every grief. When he asked Hieron for her, he had not known that it was even possible to feel for a woman what he felt now. From the first day of their marriage, she had astonished him. It now seemed to him that she was best at everything he was worst at, that, like the second leg of a compass or the second flute of a pair, she completed him.