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 thicket 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.
Even with war, even with siege, even with catapults they had been so happy.
He thought, painfully, of Marcus dead; Marcus burned, and the smoke rising from the funeral pyre high into the sky above Syracuse. Perhaps he had seen it, and not known what it was. He had noticed Marcus little enough in life.
Marcus had done his best to fulfill all his obligations honorably, and had died in their contradictions without complaint. He himself, no better a man, had everything to make himself joyful. By what calculation could those shapes be made to balance? Archimedes sighed and glanced down at the small riddle he had solved, the perfect ratio, already dwindled in his estimate.
And yet, that ratio was perfect still. Perfect, and known. It rested whole in his mind, needing no use, sufficient in its existence. Like the soul. But unlike the soul, comprehended.
