Gillian Bradshaw: The Sand-Reckoner

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.