The Sand-Reckoner

by Gillian Bradshaw

  Arata, with her usual patience and clear sense of priorities, first asked him if he'd eaten, and when he admitted that he had not, took him into the dining room and sat him down with a plate of fish stew. But Philyra, red-eyed and sniffing, sat with her elbows on the table as she watched him eat, the slaves hovered anxiously, and even his mother was frowning with anxiety. He gave up and started telling them about Marcus after the first few mouthfuls.

  "Will he be all right?" asked Philyra, biting at her fingernailsa habit which her mother had striven to break, and which only reemerged when she was deeply unhappy.

  "I hope so," was all Archimedes could say. "Hieron said he's welcome to answer anything the Roman general asks him. And his brother is there to speak up for him. I would think he'd be all right." But he was not altogether certain of it. Marcus ought to be all right- but he was so uncompromisingly honest. He had not prayed for the destruction of Rome for a Tarentine mercenary; he would not pray for the sacking of Syracuse for a Roman consul.

  But perhaps the Roman consul would not ask it. Marcus would be returned in company with eighty other prisoners, and his brother would, presumably, be in the army to welcome and protect him. He ought to be all right.

  "They're barbarians," said Philyra, blinking at new tears. "They might do anything to him! Can't he just come back to us? It wasn't his fault- you did tell the king that, didn't you, Medion? I mean, it was his own brother, or he wouldn't have…"

  "The king has already been very lenient," said Arata quietly. "For your brother's sake, Philyrion. We can't ask more. After all, a man was killed because of what Marcus did."

  Archimedes cleared his throat unhappily, then said, "When I saw Marcus just now he, uh, said to tell everyone that he was sorry and that he wished us all much joy. And he said he hoped you would be very happy, Philyrion, with Dionysios or whoever you marry."

  Philyra pulled her torn nails out of her mouth and stared, and he realized that he hadn't told her about Dionysios.

  "Dionysios only offered last night," he said defensively. "I was going to tell you this morning."

  He told her about Dionysios then. There was considerable discussion of the man and his offer, and eventually it was agreed that Archimedes would invite the captain to dinner so that the rest of the family could have a look at him. But when the others went to bed, Philyra sat for a while alone in the courtyard under the stars, playing upon the lute, and it was not Dionysios who filled her thoughts.

  "I don't want you to think ill of me," Marcus had told her, only the night before. "Whatever happens, please believe that I've never wanted any harm to this house."

  She did believe it; she did not think ill of him. That morning his quiet admission had redefined courage for her. She realized that she no longer thought of him as a slave, and that when she thought of him as a free man, it was as a man she loved. A brave man, honorable and proud, who had- she could see it now- loved her.

  "Remember once," she sang, carefully picking the strings of the lute,

  "Remember when,

  I told you this holy word?

  'The hour is fair, but fleet is the hour,

  The hour outraces the swiftest bird.'

  Look! It's scattered to earth, your flower."

  She suspected that for the rest of her life, when she remembered him it would be as something that went tragically wrong- an appointment missed, a letter mislaid, a person misunderstood with devastating and irremediable consequences. Already it was too late to retrieve what had gone by; the flower's spent petals were scattered to earth. She played on for a while, then put the lute away and went to bed.

  That night a Roman force attacked the Syracusan seawall under cover of darkness. The extra guards Hieron had posted saw the stealthy movements against the gleam of the sea, however, and sounded the alarm. The Romans were inside catapult arc of fire when they were discovered, but so close to the cliff that it was easy to drop catapult shot directly onto them from the walls. A few hundred weight of stones were followed by some catapult fire canisters, which exploded and splattered the attackers with burning pitch and oil, so that the scene was lit by the burning clothes and bodies of the men who occupied it. Many of the Romans jumped into the sea to escape the fire, and were swept off their feet by the strong currents and drowned. The remainder fled. In the morning it could be seen that they had brought ropes and ladders, which had been woefully short for the height of the cliffs, and which now littered the rubble at the cliff foot, together with the bodies of the dead- and a few more wounded prisoners for the quarry.

  The following night, the Romans left. The Syracusans keeping watch from the north wall saw the camp settling itself for the night in the evening, and the campfires glowed throughout the hours of darkness, but in the morning the army was gone, and only the fires remained, with the neat rows of flattened grass where the tents had been pitched.

  Hieron sent out scouts to track them. He sent out a letter to the Carthaginian commander as well, writing it in his own hand, because it was still too early in the day for his secretary to have arrived at the house. He warned General Hanno that the Romans might now be heading in his direction, and offered to attack them in the rear if the Carthaginians could engage them. He had sent a similar message when the Romans first appeared outside Syracuse, inviting the Carthaginians to a similar feat, but there had been no response.

  As he sealed the letter he wondered how long it would take for the Carthaginians to realize that, faced with an enemy like Rome, they needed Syracuse whole and strong and on their side. Stupidity, he thought, pressing his favorite signet into the wax that fixed the red cord binding of the letter. The Roman campaign, too, was one of blatant stupidity- if the Carthaginians had appeared in their rear, they would have been in a very sorry state. And they had left Messana only lightly guarded, with most of their supplies and all the ships that had carried them from Italy: if the Carthaginians stormed that in their absence, the whole army would be forced to surrender. It was a stroke Hieron was much tempted to himself: load his army onto his own ships, take them up the coast, sail into the Messanan harbor with some big catapults mounted on naval vessels and some incendiaries, fire the Roman ships, and storm the city!

  Yes, but to do it would weaken Syracuse while the Romans were too close to her for comfort, and who knew how the Carthaginians would react? They still wanted Messana themselves. The last thing Hieron could afford to do was drive them into open alliance with Rome.

  They might well have some kind of understanding with Rome already. Perhaps the reason they were doing nothing at present was that they'd promised not to interfere in any Roman campaign against Syracuse. Still, even if such a promise had been made, Appius Claudius was an awful fool if he trusted it. Just as Hanno was a fool to let what might be his only opportunity for victory slip by. Hieron's envoy had returned from Carthage with the news that the Carthaginian senate was growing impatient with their general. It was very stupid of Hanno to think that he had time to do nothing. Stupidity; it was altogether a stupid, blind, and pointless war, and Hieron felt a sick certainty that it was far from over. He tossed the sealed letter onto his desk and clapped his hands to summon a messenger.

  When the messenger came in, Agathon was with him, holding a bundle of the day's other letters. The messenger took the king's letter, vowed to deliver it to General Hanno within three days, saluted, and marched out. Agathon watched him go, then set the other letters down on Hieron's desk. Hieron picked them up and glanced through them; the doorkeeper busied himself in trimming and lighting one of the lamps on the stand beside the desk, even though it was morning. Hieron paused and looked up at his slave inquiringly.

  Agathon gave his sour smile. "You said you wanted to see any letters to Archimedes that came from Alexandria," he remarked. "One came yesterday. I had the customs official divert it." He pulled a small, thin-bladed knife out of his belt and began warming the end in the lamp flame.

  Hieron looked down to the bottom of the sheaf, found the relev
ant letter, and handed it to him. He and Agathon had been in the habit of intercepting other people's letters long before he became king, and if he'd ever had any tremors of conscience over it, they had long since faded.

  Agathon carefully slid the hot knife between the parchment and the wax of the seal, then handed the letter to the king with a bow. Hieron sat back and read it. Reading aloud was the usual custom of the age, but Hieron, to his slave's disappointment, read almost silently, barely moving his lips.

  Conon son of Nikias of Samos to Archimedes son of Phidias of Syracuse sends greetings.

  Dearest [Alpha]…

  Hieron frowned slightly: "Dearest Alpha." Had the writer chosen that form of address because it was the first letter of Archimedes' name- or because it was the number one?

  Dearest Alpha, you've been gone less than a month, and I swear by Delian Apollo it seems years, and empty years, too, with nothing but wet afternoons in them. I never hear a flute but I think of you, and there's not one person who's had anything remotely intelligent to say about tangents of conic sections ever since you went away. Diodotos was blathering on about hyperbolae the other day, and I told him what you'd said about the ratio, and he swelled up like a frog and asked me to prove it. And of course, I couldn't, though I gave him a list of propositions instead. He came back later saying he'd proved one, but he hadn't. I'll tell you more about that later.

  The main thing I want to say is, I have a job at the Museum, and you can have one too! In fact, it's thanks to you that I now have my perch in the Muses' bird cage. The king has been investing in the most enormous engineering works at Arsinoitis, and when he went up to have a look at them, apparently the first thing he saw was a water-snail. "What is it?" asked the king. "By Zeus, I never saw anything like it in my life!" And shortly afterward, Kallimachos…

  The poet? wondered Hieron. The head of the Library of Alexandria?

  … Kallimachos himself came knocking at my door in a great sweat and said, "You're a friend of Archimedes of Syracuse- where is he? The king wants to meet him." So I told him you'd gone back to Syracuse, and he swore by Hades and the Lady of the Crossroads (and several other divinities I wasn't sure about; poets can't even swear like other people these days) and took me to meet the king instead. Ptolemy was amazingly civil to me, and gave me dinner, and we talked. Kallimachos was there, too, but he just sat and picked his fingernails and made eyes at the slave boys. The man's incapable of talking about anything but literature and boys. The king, though, knows quite a lot of mathematics- you know Euclid was his tutor. He said it was quite true about Euclid saying there was no royal road to geometry, he was there at the time. And he was very interested when I told him about eclipses, and asked me when the next one would be. That's nothing to do with what I'm writing you about, though. After we'd talked for a bit, and I'd told him some more about you (you can believe I sang your praises, Alpha!), he said he wished he'd known it sooner, and he asked me to write to you and invite you to come back and take a job at the Museum, with a big salary and everything. Then he offered me a job too (Diodotos is perfectly green about that) but it's you he really wants. I think it's really engineering he's after- he kept telling me how wonderful the water-snail is, and when I showed him my dioptra he wanted to buy it, and laughed and said he didn't blame me when I said I'd sooner sell my house and the cloak off my back. I warned him, though, that you weren't interested in doing any more water-snails, and he said that was fine. I know you like making machines if it isn't the same thing all the time and it doesn't interfere with geometry. Write to him, or to me if you prefer, and he'll send you the letters of authorization at once. Please, Alpha, come back quick! Why be poor in Syracuse when you can be rich in Alexandria? You could bring your family here if you're worried about them. It's much safer, anyway, with none of your garlic-eating barbarian armies about. As for me, I am pining away in your absence, or I would be if I didn't keep eating Dora's cakes to console myself. The Museum banquets are on a Homeric scale, too.

  The proposition Diodotos says he proved is this…

  There followed several pages of abstruse geometrical reasoning, which Hieron skipped. He read the warm farewell at the close, and the still warmer hope that the writer would see the recipient "soon, by Hera and all the immortals!" Then he refolded the letter and set it down with a sigh.

  "Well?" asked Agathon.

  "King Ptolemy is offering him the Museum," said the king resignedly.

  Agathon picked the letter up and squinted at it. "It's not the royal seal," he observed.

  "No," agreed Hieron. "The offer comes through a friend- a close friend, from the sound of it. But I don't think there's any doubt that it's genuine. Ptolemy was evidently much impressed by an irrigation device. I'll have to ask Archimedes how it works." He waved a hand at the letter. "You'd better seal that up again and return it."

  "You don't want it to go missing?"

  Hieron shook his head glumly. "He'd realize. I just want to see the reply." He turned back to his other letters. They were mostly business notes from within the city, but one caught his eye. He held up a hand to check Agathon just before the door-keeper left. "Note from Archimedes himself," he said; then, glancing through it, "He says the three-talenter will be ready in another three days, and he invites me to stop at his house on my way back to the city after the test-firing, either for dinner or simply for wine and cakes."

  "He wants something," said Agathon flatly.

  "Good!" replied Hieron. "He can have it." He tapped the invitation against his desk. "That other letter- delay it, until I've seen what he wants. Tell whoever was taking it to say it was mislaid or forgotten about until he came to clear the ship."

  Agathon looked at his master dubiously. "Don't you think you're spending more on this man than he deserves?"

  Hieron gave him an exasperated look. "Aristion," he said, "think a minute. I was toying earlier with the idea of a naval assault on Messana. If I wanted to do that, I would need to lash ships together and build artillery platforms- each stable for the weight of catapult or they'd come to bits when the shooting started. And I would need counters to the Messanan harbor defenses, which means I'd need somebody to reckon their distance and strength before we reached them. Then I'd need siege ladders- and they'd have to be the right height or we'd have a lot of men dead for nothing. I'd need battering rams that were strong enough to do the job and light enough to move in quickly. In other words, the whole success or failure of such a raid would depend upon my engineer. Now, Kallippos is good, but I wouldn't gamble my whole fleet on his getting it right. With Archimedes, it would be no gamble. Top-quality engineering can make the difference between victory and defeat. No, I do not think I am spending too much on it."

  "Oh," said Agathon, abashed.

  "You and Philistis," Hieron went on, smiling, "don't like Archimedes because you think he's been disrespectful to me."

  "And he has been!" said Agathon warmly. "The other morning-"

  "Aristion! If somebody came and arrested you, I'd be disrespectful!"

  Agathon, who had not thought of it this way, grunted sourly.

  "He has, in fact, treated me exactly as I would wish. And he told me I was a parabola. I think that's the most unusual compliment I've ever been given. I might have it engraved upon my tomb."

  "If you say so," replied Agathon, who had no idea what a parabola was and remained unconvinced. After a moment he asked, in a low voice, "And the naval assault?"

  Hieron shook his head, turning back to his letters. "Can't do it without knowing where the Romans are and what the Carthaginians would do if it worked. But it's still true about top-quality engineering. If it hadn't been for our catapults, the Romans would still be camped by the north wall and living off our farmers' lands."

  The three-talenter wish you joy was installed in the Hexapylon precisely on time. Archimedes was not pleased with it. It was heavy to pivot, the loading mechanism was finicky, and the range was, he felt, short of what it could have been. Every
one else was delighted with the machine, however- the biggest catapult in the world! — and at the test-firing that afternoon a great cheer arose when the first massive stone crashed into the field where Romans had died only the week before. The king's son, Gelon, had asked to go with his father to see the spectacle, and his shrill cheer rose above all the others.

  All the way back to the city the little boy talked excitedly to Archimedes, leaning down from the saddle of his father's horse to offer his own ideas for improving the defenses of Syracuse. Archimedes, who was sidling toward the moment when he must ask the king for his sister's hand in marriage like a dog toward a scorpion, found the child's chatter both an irritation and a relief. At least it was easier than talking to Hieron. Even if he hadn't been oppressed by the awful imminence of his outrageous request, Archimedes would have found Hieron's company wearing, for the king kept trying to persuade him to borrow a horse. Archimedes regarded horses as large, dangerous, bad-tempered animals that were very likely to throw you off and trample you, and he stayed on his own feet.

  The house near the Lion Fountain had been prepared for the royal visit almost out of recognition. Arata and Philyra had been horrified to learn that Archimedes had invited the king to have cakes and wineit had been shocking enough to have such an eminent person turn up at the wake, but at least then there'd been no necessity of providing entertainment proper to the guest's station. Since Hieron could not be uninvited, however, they had set to work to uphold the family honor. The house had been swept, freshly daubed, and garlanded, and all the laundry boards and buckets removed from the courtyard, which looked quite empty and rather desolate. Sesame cakes purchased from the finest confectioner in Syracuse were oozing honey onto the best Tarentine pottery plates in the dining room, and wine from the best vintner trembled darkly in the antique red-figure mixing bowl. The slaves had been provided with new clothes, and when Hieron arrived, they stood scrubbed and uncomfortable by the door to meet him. The king, looking at them, saw that he was going to have to work at it if the visit was to be a success.