The Sand-Reckoner
Page 7
Marcus opened it, and Archimedes stumbled in, smelling of wine.
He had not stayed at the Arethusa for the inevitable conclusion of the evening. His father's impending death had shriveled up desire, and whatever their other talents, the Arethusa's flute girls hadn't played the flute very well. It had set his teeth on edge to listen to them. In another situation, he might have offered to play himself and let them just dance, but to have made the offer then would have invited the lewdest of ribaldry. So he had done calculations until his companions were provided for, then excused himself with apologies, paid the reckoning, and come home.
"Can you fetch me a light?" he asked Marcus breathlessly, pushing the flute girls' wreath of wilted parsley farther back onto his head. "I need to write something down."
Philyra jumped up and hugged him, but he shook her off hastily. "Careful!" he exclaimed. "You'll smear it!"
Marcus gave a snort and hurried off.
"Smear what?" she demanded.
"Some calculations I was doing. Marcus! Is there anything to write with?"
"You were doing calculations?" Philyra asked in bewilderment.
He nodded; the gesture was revealed by the sudden glow of the lamp Marcus had just returned with. Archimedes held his left arm toward the light: it was covered with figures sketched in lampblack.
"Medion!" exclaimed Philyra in horror. "It's gone all over your new cloak!"
"Don't worry," he said reassuringly, "I can still read it."
Since Marcus had not brought anything to write with, Archimedes picked up the laundry board, found a lump of chalk, and began to copy the figures from his arm. "I'm going to have to correct most of these when I can look at a smaller catapult," he told the other two, busily writing. "I couldn't remember most of the dimensions to scale them up. But this should be close enough to let me order the wood, which will speed things up."
"You got the job," observed Marcus with satisfaction, and Archimedes nodded absently, frowning at his chalked calculations.
"I thought the man you were seeing tonight was just a soldier!" exclaimed Philyra.
"Oh," said her brother vaguely, "yes. But he asked about who I should talk to and his captain wanted to see me. They really do want engineers. I'm to build stone-hurlers, starting with a one-talent machine."
"What's the pay?" demanded Marcus.
"Uh? To be arranged. Nothing, until the first catapult is complete. But there doesn't seem to be anyone else in the city at the minute who can build big stone-hurlers, and the captain said that they're what the tyrant wants most, so I think it will be good. I'm seeing Leptines the Regent about it tomorrow morning."
"Oh, Medion!" cried Philyra, torn between delight and exasperation. "You must give me your cloak at once. You can't go see the regent all covered in lampblack!"
"You can't start doing laundry at this time of night!" protested Marcus.
Archimedes glanced up, finally realized that his sister had been waiting for him, and blinked. "Philyrion darling," he said firmly, "you should be in bed." Then he noticed the kithara she was clutching and added, "It's too late for music, too. But tomorrow night we can have a concert."
"To celebrate your new job!" said Philyra, happily dismissing the state of his cloak. "Mama and Papa will be so pleased!"
The following morning Archimedes reported his success to his parents; they were, as his sister had expected, pleased. After the first unanswerable questions about pay, however, Phidias asked wistfully, "And will it leave you much time for study?"
"I don't know," replied Archimedes awkwardly. He did not want to admit to his father that he foresaw scholarship squeezed to the edges of his life. "I think- I think not right at the moment, Papa. Because of the war. I will do everything I can to make sure I still have time to talk with you."
"Oi moi, the war!" sighed Phidias. "I pray that our king finds some way to get us out of it soon. It will be a bad war, my Archimedion, a very bad war. Our lovely city is like a dove in the pit with two fighting cocks. I am glad that I at least won't have to see what happens to her. My dear boy, you must look after your mother and your sister for me!"
Archimedes took his father's trembling hand. "I will," he promised solemnly. "But I hope, Papa, that King Hieron does find some way out of the war. They say he's a wise man: he may yet bring peace."
"He's ruled well," Phidias conceded- reluctantly, for he had always supported the city's turbulent longings for democracy. Even Hieron's enemies, however, had to admit that he had ruled well. He had come to power eleven years before in a bloodless military coup, and had since governed with moderation, humanity, and a strict regard for the law- much to the surprise of the citizens, who did not expect such behavior from a tyrant.
"Yes, I pray you're right," Phidias went on, then smiled at his son. "I am glad you're back," he said tenderly. "I was afraid to think what would happen to the house, left headless while the city was at war. You go devise some weapon to destroy our enemies, child. And make sure you get a good price for it!"
"Yes, Papa." Archimedes kissed his father's cheek, kissed his mother, who was attending the sick man, then went out into the courtyard.
Philyra was there, trying to clean his cloak. She had brushed it, beaten it, and poured boiling water on it, and had succeeded only in spreading the oily lampblack more widely. She rolled her eyes at her brother distractedly. "You're going to have to wear something else," she told him.
"It's too hot for a cloak anyway," he replied.
Marcus appeared at the foot of the stairs, carrying an old cloak of plain Egyptian linen. "That has wine stains on it!" snapped Philyra impatiently.
"But you can fold the edge over so they don't show," Marcus replied, suiting action to words.
Archimedes groaned, but spread out his arms and allowed his sister and his slave to drape the linen cloak around him, insisting only that the drape go under rather than over his right arm- "It's more dignified worn over both shoulders!" protested Philyra; "It's also hotter!" replied Archimedes. The other two stood back, assessing whether he looked fit to be presented to the king's father-in-law. Archimedes, however, looked at Marcus thoughtfully.
He had been debating whether to take Marcus along to help with the catapult-making. Marcus could undoubtedly be useful at it. He'd helped with the water-snails and with dozens of less successful machines: he knew how to follow technical instructions. He was strong, quick, and handy with a saw or a hammer. On the other hand- on the other hand, Marcus clearly still had some loyalties to the people the catapults were to be employed against. And the catapult-making would take him in and out of the military workshops and the arsenal- the most vulnerable and strategically important buildings in Syracuse. If someone lit a fire in them…
"Marcus," said Archimedes, "I want you to stay here and see if my mother wants anything done around the house."
The slave's face went blank. He had foreseen this problem, but he hadn't expected his master to have foreseen it as well. "You don't want me to come with you, sir?"
Archimedes shook his head. "You're not Samnite," he explained quietly.
Marcus stood for a moment frowning at him. He was not sure whether he felt relieved, because he was not required to construct devices that might injure his own people, or hurt, because his master thought him capable of treachery. He could feel Philyra's eyes on him, full of shocked accusation: did she really believe he'd be happy to see her city fall to Rome, her brother killed, and herself raped and enslaved? At last he said, "Sir, I swear that I would never do anything to injure this city or this house. May the gods destroy me in the worst way if I'm lying!"
"I believe you, since you swear it," said Archimedes. "But I think it would be better, all the same, if you stayed home."
Marcus hunched his shoulders. "Very well, sir."
Archimedes slapped him on the shoulder. The linen cloak, which was too short to hold its drape properly with the edge folded over, fell off. Archimedes redraped it again awkwardly and set off.
"What difference does it make?" growled Marcus. "I'm not a citizen anywhere. Anyway, what kind of claim does this city have on me to begin with? No one has ever pretended I came here of my own free will." He was a little surprised at his own honesty. "I've sworn I won't do anything to injure the city. Archimedes took my word for it. Isn't that good enough?"
"You know what sort of people the Romans have come to Sicily to help?" demanded Philyra.
Marcus again hunched his shoulders unhappily. The Romans had come to Sicily to help the city of Messana against Syracuse. Messana, however, was a robber state, the home of bandits. More than twenty years before, a group of Italian mercenaries, Campanians, had been posted to the city as a garrison by a previous tyrant of Syracuse; tempted by Messana's wealth, they had taken advantage of the chaos when the tyrant died to seize the city for themselves. They had murdered all the men and taken the women and children as their slaves. Calling themselves Mamertini- "the sons of Mars"- the Campanians had gone on to raid or exact protection money from the neighboring towns, all of which were under Syracusan protection. Syracuse had made war on the bandits sporadically, as Carthage and her own affairs allowed, but with little success- until Hieron rose to power. He had defeated the Mamertini in the field and laid siege to Messana itself. To save themselves, the Campanians had appealed to both the great powers of the West- to Carthage and to Rome.
Carthage had responded first. Always happy to frustrate Syracuse, she had sent a garrison to Messana. But the Carthaginian intervention had provoked a response from the new mistress of Italy. Rhegium, just across the straits from Messana, had fallen to Rome only six years before: Rome was unwilling to allow her African rival to control Messana. She sent her own expedition to the Mamertine city. The Mamertini preferred a Roman garrison to a Carthaginian one- they were Italians, too, after all- and expelled the Carthaginians. Syracuse, which had wanted nothing except to rid herself of a long-standing nuisance, suddenly found herself allied to Carthage and at war with Rome.
"I don't think the Romans should have come to Sicily," muttered Marcus. "It's a bad cause, a bad war. The Mamertini don't deserve any help." He looked back at Philyra's suspicious eyes and declared with sudden fervor, "Mistress, please believe me. I will never betray this house while I live."
Her suspicion changed to puzzled surprise, and he saw that he'd said the right thing, and smiled.
All through the walk to the Citadel, the linen cloak kept slipping. Like all cloaks, it had weights in its bottom corners to help it drape, but with the end folded over this was simply not enough. At the gates to the citadel Archimedes gave up, shook it out, and draped it around himself again, this time with the stains showing. He brushed ineffectually at the new dust patches collected on the walk, then strode through the gates, past the temple of Apollo, and on into the heart of the Ortygia.
King Hieron's house was not a palace. It was a large and elegant mansion, set in a leafy quarter of the citadel, near the Council House. It didn't even have any guards outside it, and Archimedes hesitated in the columned porch, wondering whether to knock on the door or wait for Dionysios outside. He glanced up and down the wide street. It was empty in the quiet morning light, so he knocked.
A middle-aged man in a red tunic opened the door at once and looked at him disapprovingly. "Your business?" he demanded.
"I, um," faltered Archimedes, "I was to see the regent this morning. Dionysios son of Chairephon told me to speak to him about a job. I'm a, um, engineer."
"Catapults," said the middle-aged man dismissively. "Your name is Archimedes? Very well, you're expected. Captain Dionysios is with the regent now, but they're busy. You'll have to wait."
Archimedes was ushered into the house and conducted to a vaulted anteroom which opened onto a garden. There were benches about the marble walls, and he sat down on one. The middle-aged man vanished back the way they'd come, leaving Archimedes to wonder if he was a doorkeeper; if so, he was a very abrupt and exalted one. But perhaps that's what slaves were like in kings' houses. Archimedes sighed and looked down at the marble floor. He scuffed it with a sandal, then took from his purse the piece of papyrus on which he'd fair-copied his calculations from the previous night, plus a few interesting thoughts he'd had that morning and wouldn't mind working on further. He wished he'd remembered to bring a pen and ink. He was looking about for something to use instead when he heard the sound of a flute.
Tenor aulos, he decided at once, set to the Lydian mode, playing a variation on a theme from an aria by Euripides. He listened to it intently for a couple of minutes: the player was good. The tune came to an end; there was a pause; and then the music began again, this time with a peculiarly breathy sound, skirting about the verge of dissonance. He grinned to himself: he recognized that sound. An aulos had a metal slide inside it which allowed a player to cover some of the fingerholes, and thus to play several different modes upon one instrument. This player had opened the slide which separated the fingerings of the Lydian and Hypolydian modes and was trying to play the notes between them. Archimedes had once tried the same thing himself. It had required some very tricky part-fingering, and it still hadn't worked.
He got to his feet and slouched out of the antechamber into the garden, following the music. He knew another way of playing those intermediate notes; he owed it to a fellow aulist to share it.
A passage led through a colonnade from the first garden into a second one. A fountain decorated with carved nymphs stood under a grape arbor, and there were roses flowering. On the edge of the fountain sat the flute player: a girl a year or two older than Philyra. Her black hair was caught up in a silver net, and she was wearing a rose-colored tunic fastened with a silver belt. But her hairnet was disarranged by the leather strap most aulists wore to support their cheeks during a long session, and she was so intent on her playing that she didn't notice Archimedes' arrival: she was a real aulist, not a decorative one. He wondered who she was. By her dress she was rich, but she was too young to be the king's wife and too old to be his daughter. Somebody's concubine, he decided. He coughed to attract her attention.
She lowered the aulos and frowned at him, irritated by the interruption. Her eyes were very black. In a moment, he thought, she'd tell him to go back to the public part of the house.
"It doesn't work," said Archimedes quickly. "But if you take your baritone aulos and set it to the Dorian mode, you can get the right effect if you avoid the B-flat."
Interest replaced the irritation in her eyes. She picked up a second aulos from the rim of the fountain beside her: it was an alto. "My other one's this," she said.
"Then set that to the Lydian mode and the tenor to the Dorian! But Lydian doesn't mix with Hypolydian, part-finger it as you will. When I tried it, I sounded even worse than you did."
She grinned. "Thank you for the compliment! Dorian's better?"
"Try it!"
"I will!" The girl shifted the slide on her tenor aulos, setting the instrument to the Dorian mode. She set the alto to the Lydian, raised both, and began to play the Euripides variation again. Her eyebrows rose; she played on to the end of the piece, shifting from one aulos to the other, from one mode to its neighbor, scattering the notes, bittersweet and sad. When she finished she set the flutes down and looked at him in surprised triumph. "You're right!" she exclaimed, and they grinned at each other.
Then she wiped the mouthpieces and asked, "Are you a professional?"
"What? Oh, flute player. No. I'm a mathematician." Then he bit his lip and corrected himself. "Engineer. I'm to see the regent about building some catapults."
"Catapults!" she exclaimed. "I wouldn't have expected someone who makes machines to be musical."
He shrugged. "Actually, it's a help. You have to tune them by ear."
"Catapults?"
"Mm, the strings. If a catapul
t's two sets of strings are out of tune with each other, the machine will shoot crooked when you come to fire it."
She laughed. "What do you do to tune them? Pluck them and tighten the key, like a lyre?"
"Exactly! Except you twist the strings, not the key. You have to use a windlass and wedges."
"I like that! The stringed instruments: lyre, kithara, harp, luteand catapult. I suppose big ones have a low pitch, and small ones a high pitch?" He nodded, and she laughed again. "Somebody should write a catapult chorus," she declared. "For scorpions, ten-pounders, and thirty-pounders." She raised the auloi to her mouth again and piped a mad dance on three widely separated notes.
Archimedes grinned. "A friend of mine is trying to build an air-powered catapult," he said. "It could play the flute part. But I'm afraid that all it does is go bang, very loudly, so maybe it should be percussion."
"Oh, no!" she exclaimed, lowering her auloi and putting a hand over her mouth. "An air-powered catapult? Where was this, Alexandria?"
He laughed in surprise. "Yes!"
"It would be! They'll do anything in Alexandria. Since you've been there, tell me: I heard somebody there has built a machine which allows you to play thirty auloi simultaneously. Do you know-"
But Archimedes had broken into delighted laughter. "That's Ktesibios!" he exclaimed. "The same friend who's making the air-powered catapult. He calls the instrument a water-aulos. I helped him with it!"
The girl pulled off her cheek strap and put her instrument down. Her hair, disturbed from its net, dropped black curls around her face. "Does it work?" she demanded. "The- the multiple aulos, I mean. I don't see how it possibly can!"
"It's not really thirty auloi," Archimedes told her. "It's thirty pipes, but they only play one note each. Each is a different length, see, like the reeds in a syrinx. To sound them, you press a key which opens a valve in the bottom of the pipe. Air is forced up into the pipe by the pressure of water in a tank underneath. That's why it's called a water-aulos. See, you have this inverted hemisphere submerged in the water, and two tubes which-"