The Sand-Reckoner Read online

  Archimedes had in fact noticed a Protean quality to Marcus' nationality in the past. The slaver who sold him had called him a Latin, but Marcus himself had sometimes claimed to be a Sabine and sometimes a Marsian. Archimedes had no idea what the truth was- but he knew Latins, Sabines, and Marsians were all part of the Roman alliance. Disgust was swallowed entirely by alarm: Marcus might well be sent to the state quarries for the duration of the war. Given the conditions under which quarry slaves were kept, he'd be lucky to leave them alive. "Marcus is a Samnite," he declared firmly. "And he's been in the family for years. My father bought him when I was nine years old. Do you think I'd smuggle an enemy into my own city? If you want to accuse me of something, do it in front of a magistrate."

  The Tarentine gave Archimedes a hard look before turning his assessing stare back on Marcus; Marcus stared back with the same unruffled impassivity he had adopted from the first. The soldier shifted his grip on his spear and commanded, "Say, 'May the gods destroy Rome!' "

  Marcus hesitated, then raised both hands to heaven and said loudly, "May the gods destroy Carthage, and grant victory to lovely Syracuse!"

  The soldier whipped his spear up and around in a whistling blur; the shaft caught Marcus under his raised arm and knocked him sideways into Archimedes. Archimedes gave a yelp, nearly fell off the quay, and dropped to all fours, skinning his knee on the stones. Marcus fell on top of him with a grunt.

  Archimedes was aware of a thick silence as he struggled to get back to his feet. He could feel Marcus on top of him shaking- whether with rage or with fear he couldn't guess. Then the slave's weight shifted and slid off, and Archimedes scrambled up. Marcus remained kneeling on the quay, right hand pressed against his left side where the spear shaft had caught him. Archimedes could feel blood trickling down his own shin. For a moment he was so angry he wanted to hit the soldier: what right did this foreigner have to knock him down on the docks of his own city? He took a deep breath and reminded himself that the soldier was a foreign mercenary, to be treated with great caution; that the soldier was armed and he wasn't; and that he did not want Marcus in trouble. "Why did you do that?" he demanded, struggling to swallow his rage. "He may not have said what you told him to, but he prayed for victory for the city!"

  "He prayed for the destruction of Carthage," said the Tarentine. He was flushed now, and a bit breathless: he'd gone further than he'd meant to. Hitting slaves was one thing; knocking over freeborn citizens quite a different one. His comrade and the customs official were staring at him with distaste.

  "Don't we all?" said Archimedes. Carthage had been the enemy of Syracuse since the city's founding nearly five centuries before.

  "Carthage is our ally," said the soldier.

  Archimedes was too astonished even to remember the caution needed with mercenaries. He looked from the Tarentine to the other soldier, then to the customs official. "Carthage?" he repeated disbelievingly.

  The other soldier and the official looked embarrassed. "You hadn't heard?" said the official.

  Archimedes shook his head numbly. He supposed that, in a way, it was a natural development. Carthage and Syracuse had long fought for the possession of Sicily, and the Carthaginians were undoubtedly as dismayed as the Syracusans by the intrusion onto the island of the rising power of Rome. Perhaps it was right that two old enemies should unite against a new common threat. But- Carthage! Carthage, which had tortured to death the entire male population of the city of Himera; Carthage, which worshiped gods that required her to burn her own children alive; Carthage, the crucifier, the deceiver, the enemy of the Greeks! "Has our tyrant really sworn a treaty with Carthage?" he asked.

  "Our king," the Tarentine corrected him quickly. "He calls himself king now."

  Archimedes just blinked. "Tyrant" to a Syracusan was the natural title for an absolute ruler: it implied no condemnation. If Syracuse's present tyrant wanted to call himself a king, that was his right, but it seemed a bit pointless.

  "King Hieron hasn't sworn anything," the official said defensively.

  "He's no fool," added the second soldier, for the first time speaking above a whisper and revealing his own accent- to Archimedes' relief- as the inimitable growl of the back streets of Syracuse. "If Carthage wants to help our shining city against Rome, she's welcome to, but King Hieron won't trust that sackarsed lot, and I say, well done! He's agreed to a joint military operation against the Romans, nothing more." He gave the Tarentine a disgusted look: it was quite clear that he thought that a prayer for the destruction of Carthage in no way deserved a blow.

  Marcus grunted, and Archimedes remembered what he was supposed to be doing. "We hadn't heard anything about this alliance in Egypt," he said stiffly. "I'm sorry if Marcus offended you, but he thought he was praying for a Syracusan victory."

  The official and the Syracusan soldier both nodded, accepting the explanation, relieved that Archimedes had tacitly agreed to forget the blow. The Tarentine, however, only scowled. Marcus might have prayed for a Syracusan victory, but he had not prayed for the destruction of Rome. The man's dark eyes returned to the slave, who was still kneeling on the quay, head bowed, rubbing his bruise. Something flickered behind the scowl: the desire to hurt and humiliate.

  Archimedes too was keenly aware of his slave's evasion. He cleared his throat. "If you really believe that Marcus is a Roman- though why you should expect a Roman to be a slave I don't know- we can go see whoever is responsible for deciding about such things," he offered. "On the other hand…" He dug into his purse and pulled out two silver staters- two-drachma pieces, each one worth more than a day's wage for a mercenary. "It's getting late, and I want to go home to my family, not hang about the magistrates' courts." He held out the coins toward the Tarentine: they gleamed in his palm, fresh-minted silver stamped with the head of King Ptolemy of Egypt.

  The Tarentine just stared at them. The Syracusan soldier, however, hurried over and took the coins with a grin. The customs official also hurried over, sucking his teeth. He looked a question at the Syracusan. The Syracusan grinned again and declared easily, "We'll split it three ways."

  The Tarentine gave Archimedes a black glare. But the other two were happy to take the money and forget about Marcus, and he didn't quite dare override them. "You can't split two staters three ways!" he snapped instead.

  Archimedes forced himself to smile, though the effort nearly choked him. "Of course you can," he said. "It makes eight obols each if you do. But here." He pulled out another coin, identical to the first two. "Good luck to the defenders of the city!"

  The Tarentine snatched the coin with a look of pure hatred and strode off toward the nearest gate. His comrade shrugged, gave Archimedes a look of apology, and turned to the customs official with the other two staters. Archimedes limped over to Marcus.

  "Are you hurt?" he asked.

  Marcus rubbed his bruise once more, then shook his head. He got slowly to his feet, scowling. "May the gods destroy that Tarentine filth in the worst way!" he muttered. "Three staters tipped into the sewer!"

  Archimedes slapped him across the face, anger and relief adding force to the blow. "You worthless lump!" he exclaimed in a vehement whisper. "You might have been sent to the quarries! Why didn't you say what he told you to?"

  Marcus looked away, now rubbing the slap. "I'm not his slave," he declared.

  "Sometimes I wish you weren't mine, either!"

  "Sometimes I do too!" replied Marcus, looking back and meeting his master's eyes.

  Archimedes let out his breath in a hiss. "Well, you nearly got away from me there, didn't you? That fellow wanted you chained up cutting stone till the war ended, whatever your god-hated nation is, and you certainly did everything you could to encourage him. Herakles! I should have let him take you! Why couldn't you have called him 'sir' and lowered your eyes when he talked to you, like a good slave?"

  "I'm freeborn," said Marcus sullenly. "I've never crawled to you and your father, so why should I crawl to some Tarentine without a house o
r half acre to his name?"

  "You and your free birth!" exclaimed Archimedes in disgust. "I'm freeborn and a citizen, and I don't quarrel with mercenaries." He was on the point of adding, "Anyway, I don't know why I should believe in your free birth, when you can't decide whether it's free Sabine or free Samnite!" when he noticed that the customs official was walking off while the remaining soldier stood listening. He swallowed the words. They were pointless, anyway. No one born to slavery could ever have been as obstinate, awkward, and proud as Marcus.

  "There wouldn't have been any trouble if we'd been seen first," growled Marcus, still defending himself. "They wouldn't've had time for it. And we would have been first, if you hadn't been too busy drawing circles to pay attention." He glanced at the scuffed and scratched quayside and corrected himself: "Drawing cubes."

  "Cuboids," said Archimedes wearily. He gazed at the half-eradicated drawings, then started, grabbed at his belt, and exclaimed, "I've lost my compasses!"

  Marcus glanced around and quickly retrieved the compasses from the ground beside the luggage. Archimedes seized them gratefully and began checking them for damage.

  "That thing looks sharp," said the Syracusan soldier, coming over. "Lucky you dropped it. If it'd been in your belt when Philonides knocked you down, it would've speared you. That leg all right?"

  Archimedes blinked, then glanced at his grazed knee. It had stopped bleeding. "Yes," he said. He put the compasses through his belt.

  The soldier snorted at this piece of folly, but offered to help with the luggage. The guardsman was, Archimedes noticed, about his own age, a wide-shouldered man with a close-clipped curly beard and a pleasant, shrewd-eyed face. For all his whispered jokes to his comrade earlier, he seemed genuinely to want to be friendly now. Archimedes accepted the offer.

  With Marcus carrying one end of the chest, the soldier the other, and Archimedes trying rather ineffectually to help in the middle, they started toward the gate. "Thanks for the money," said the soldier. "My name's Straton, by the way, son of Metrodoros. When you come to enlist, mention me and I'll see that you're looked after."

  Archimedes blinked again, then remembered the customs official's assumption that he'd returned to fight for his city. He was silent for a moment. He had no plans to enlist; on the other hand, some advice from a friendly source in the city garrison would be very welcome. "I, uh, wasn't planning to enlist, exactly," he said hesitantly. "I, uh, thought the king would want engineers. Do you know how I should go about asking for a job as one?"

  Straton glanced at the wicker basket strapped to the chest- the big bucket! — and smiled to himself. "You know anything about catapults and siege engines?" he asked.

  "Um, well," said Archimedes, "I never actually made one. But I know how they work."

  Straton smiled again. "Well, you can talk to the king about it, of course," he said. "He might want people. I don't know."

  Marcus laughed. The soldier's smile vanished, but he said nothing.

  "Is King Hieron in the city now?" asked Archimedes earnestly.

  King Hieron, Straton informed him, was off with the army, besieging the city of Messana. The man in charge in Syracuse was the king's father-in-law, Leptines. Straton wasn't sure whether Archimedes should approach Leptines or whether he'd do better to go north to Messana and speak to the king himself. He'd ask around. Would Archimedes like to meet him the following evening, for a drink? He'd be posted to the docks again all day, but his shift finished at dusk, and they could meet at the gate. Archimedes thanked him and accepted the invitation.

  They had passed the gate by this time, and they set the heavy chest down in the narrow dirt street on the other side. "Where are you going?" Straton asked.

  "Other side of the Achradina," Archimedes supplied at once. "Near the Lion Fountain."

  "You don't want to carry this all that way," said Straton authoritatively. "Gelon the Baker down the road has a donkey he'd loan you for a few coppers."

  Archimedes thanked him and went off to see about the donkey. Marcus started to sit down on the chest; Straton caught his arm. "Just a minute!" he said sharply.

  The slave's face went blank, and he stood perfectly still, making no effort to retrieve his arm from the other's grip. The two men were much of a height, and they looked directly into each other's eyes. It was beginning to get dark, and behind them the new guard shift was closing the sea gate of Syracuse.

  "I'm not Philonides," said the soldier quietly, "and I don't beat other men's slaves, but you deserve a thrashing. I don't care what sort of Italian you are, but just at the moment the city doesn't like any of your nation, and if we'd gone to a magistrate, you wouldn't have escaped without a beating at the least. Your master got you out of a nasty hole there- and in return you were insolent to him. I don't like to see a slave laugh at his master. Plenty of other people feel the same way, and some are like Philonides."

  Marcus had relaxed as he realized that he was in trouble for his conduct rather than his nationality. "When did I laugh at my master?" he asked mildly.

  Straton's hand tightened on the slave's arm. "When he said he wanted to be an army engineer."

  "Oh, then!" replied Marcus calmly. "It was you I was laughing atsir."

  Straton stared in offended surprise, and the corner of the slave's mouth twitched. He was beginning to enjoy this.

  "You were laughing at him from the moment you set eyes on him," he said. "And when he said he'd never made a catapult, you made up your mind he doesn't know a thing about them, didn't you? Let me tell you this: if Archimedes makes catapults, and if King Hieron's half as clever as he's supposed to be, then whoever the king has making catapults at the moment is out of a job. Do you gamble?"

  "Some," said Straton, puzzled now.

  "Then I'll lay you a bet on it. Ten drachmae to the stater he gave you- no, make that twenty! I bet you that if my master becomes an engineer for the king, then whoever's in charge of whatever he's set to do will be demoted or unemployed within six months, and Archimedes will be offered his place."

  "You have twenty drachmae?"

  "I do. Before you decide about the bet, you want to hear how I got it?"

  Straton stared suspiciously a moment, then gave a snort of concession. "All right." He let go of the slave's arm.

  Marcus leaned back against the chest. "We went out to Alexandria three years ago. My master's father, Phidias, sold a vine-yard to pay for the trip: he'd been to Alexandria himself as a young man, and he wanted his son to enjoy the same opportunity. Archimedes did enjoy it, too- Herakles, he did! They have this big temple to the Muses in Alexandria, with a library-"

  "I've heard of the Museum," said Straton with interest. "Myself, all I know is how to read, and that badly, but I've heard that the scholars of the Museum of Alexandria are the most learned men on earth."

  "It's a lunatic asylum," said Marcus disgustedly. "Full of a lot of Greeks drunk on logic. My master raced in to join them like a lost lamb that's finally found its flock. Made a lot of friends, did geometry all day, sat up drinking and talk, talk, talking all night; didn't ever want to go home to Syracuse. You saw fit to tell me I deserve a thrashing for the way I talk to my master: let me tell you, I've earned the right to talk to him anyway I like! I could've stolen every copper he had and run off with it, anytime, and he wouldn't even have noticed until three days later. Instead, I looked after him and tried to make one drachma do the work of two. Phidias had given us money to last us a year- though with the prices they charge in Alexandria, it wouldn't have. First we spent that, and then we spent our return fare, and then we bartered and borrowed and sold bits and pieces, and then, after two years in the city, we were flat out of cash and in debt. I kept pointing this out to Archimedes until he finally paid attention and agreed to do some machine-making."

  Marcus paused. "That's a common story, isn't it, apart from the geometry? Young man away from home for the first time, running wild in a big foreign city, faithful slave wringing his hands and saying, 'Oh, sir, r
emember your poor old father and come home!' All right, but here's where it gets uncommon. My master builds machines. Not ordinary machines, but machines so cunning and ingenious you could travel the world from one end to the other and never see anything like them. That's how we lasted two years in Alexandria: whenever we were short, he'd put something together and I'd go sell it. He'd been playing around with that for a while"- Marcus jerked his head at the wicker basket behind him- "but he'd never got around to seeing if anyone wanted a full-size one. Now he took it to a rich man we knew who'd recently acquired an estate in the Nile Delta and was looking for ways to improve his land. Zenodotos looked at the water-snail and fell in love- and that shows sense, because the water-snail is the most amazing machine Archimedes ever built, the most amazing machine I've ever seen in my life. Zenodotos instantly ordered eight of the things at thirty drachmae apiece. He agreed to supply us with all the equipment and the labor we needed to make them, as well as our keep while we were working and the traveling expenses to and from his estate."

  "So we went up to his estate and set to work. When we got the first water-snail finished, people started coming around to have a look at it. Now in Egypt they've been irrigating since the creation of the world. They thought they knew everything there is to know about raising water- but nobody had ever seen anything like a water-snail. And everybody- I tell you, everybody- who had a bit of land in the Delta wanted one. I put the price up to forty drachmae, then to sixty, then to eighty: it made no difference. People still queued up to buy. And then, of course, the rich men in the queue didn't want to wait. They started coming up to me and slipping me a drachma and saying, 'See that your master does my order first.' That is where I got my money: selling the shavings of Archimedes' ingenuity."

  "If it was so profitable, why aren't you still building water-snails?" asked Straton skeptically.