younger and of a less distinguished family. Now he had arranged matters so that Kallippos would be content to ask Archimedes to 'assist' with particular problems- and, no doubt, take all the 'advice' he was given. Eudaimon, too, had been brought 'in hand.' There remained only Archimedes himself to bring under the yoke- and that would not be done in the way she'd feared. She should have realized that her brother would never do anything so crude as bind a man to an iniquitous contract of employment. The kind of chains he preferred were both subtler and stronger, forged in a gray area between manipulation and beneficence, put on with gifts and received with gratitude. But what sort of chains he might find for Archimedes she could not guess.
Phidias died at about four in the afternoon, without regaining consciousness. Arata had watched him all morning with growing concern, and at noon, when his breath seemed to be failing, sent for her children. All through the long hot afternoon the family sat together about the bedside, while Phidias' breath stopped, then started, then stopped again. When the end finally came, they did not at first recognize it, and waited for some time for the frail gasping to resume. Eventually it became clear that it would not. Archimedes covered his father's face, and the women of the household began to beat their breasts and raise the high-pitched ritual keening.
Archimedes went out into the courtyard, splashed his face with some water, and sat down against the wall, hands dangling limply from his upfolded knees. He was not sure what he believed about an afterlife. Like most educated Greeks, he found the stories his own people told about the gods and the Underworld totally incredible, but to replace those stories he had only contradictory reports from the teachings of the philosophers. The soul was the true Platonic Form, immortal and unchangeable, struggling through the shadow play of the world, reborn many times until it could find its way back to the God who had made it. The soul of the Wise was king, and by virtue might attain eternal union with the Good. The soul was a handful of atoms, born with the body, disintegrating with that body's death, and the gods lived apart from the world and had no interest in it. What was he to believe?
It hadn't mattered much, before.
After a while, he went upstairs and took out his abacus and compasses. He drew a circle in the sand: that was immortal and unchangeable. Its end was its beginning, and it defined the total of all angles. The ratio of its circumference to its diameter was forever the same number: three and a fraction. What that fraction was, though, was impossible to calculate. Less than a seventh. Try to define it further, and it slipped away from you, more precise than your measurement, infinitely extendable, infinitely variable. Like the soul. Like the soul, it could not be comprehended by reason.
That thought was comforting.
He inscribed a square in the circle, then an octagon, and began calculating in earnest.
When Arata came up about three hours later, she found her son crouched over the abacus, sucking the hinge of his compasses. Scratched into the sand was a multi-sided polygon, circumscribed by a circle and filled with a tangle of superimposed reckonings.
'Dearest,' she said gently, 'the neighbors have started to arrive.'
It was traditional for friends and neighbors to pay their respects to the dead as soon as possible, and for the family to greet them dressed in black, with hair cut short in mourning. Arata's hair was freshly cropped, and she had draped about herself a black cloak bought many years before for her mother's funeral and worn infrequently since. Philyra, too, was dressed in mourning; even the slaves were prepared. But Archimedes still wore the good tunic he had put on that morning, and his hair hung in tangles over his forehead. Faced with his mother's summons, however, he merely took the compasses out of his mouth and said, 'It's more than ten seventy-firsts and less than a seventh.'
Even if the evening light hadn't shown clearly the dry trails of tears across his cheeks, Arata would have known better than to mistake his absorption for lack of feeling. She crouched down beside him as quietly as though he were a wild animal she was trying not to startle. 'What is?' she asked.
He gestured with the compasses at a point on the diagram where the circle's circumference was cut by its diameter. The letter [Phi] had been written in the angle between them. 'That.' There was a silence, and then he said, 'People often say it's three and a seventh, but it's not. It's not a rational number at all. If I could draw more sides to the polygon, I could approximate it more closely, but no one can ever calculate it absolutely. It goes on forever.'
Arata regarded the circle and the scratched figures. Phidias would have understood them. That thought had just become painful. 'Why does it matter?' she asked.
He stared blindly at the circle. 'Some things do go on forever,' he whispered. 'If some part of us wasn't like them, would we be able to understand that?'
At that she saw the reason for his calculations, and, strangely, found comfort in them. Her husband too had loved and believed in these infinite things, and now he was with them. She put an arm about her son's shoulders, and for a moment they were both quite still. Then Arata sighed. 'Dearest,' she said resolutely, 'you're the head of the family now. You must change and come down and greet the neighbors.'
Archimedes dropped the compasses and put his hands over his face. He did not want to speak to anyone.
'You must,' Arata insisted. 'He was always so proud of you. Let everyone see that he left a son who honors him.'
Archimedes nodded, pulled himself to his feet, and went with her. The black cloak she found for him had been his father's. Putting it on made him shudder.
Several of the neighbors, alerted by the commotion earlier in the day, were already gathered in the courtyard. Archimedes greeted them courteously, and they responded with condolences, then went to pay their respects to the body. Phidias, washed, dressed in his best clothing, and garlanded with herbs and flowers, lay on the sickroom couch facing the door, eyes closed, one thin hand clutching a honey cake as an offering to the guardian of the realms of the dead. Archimedes gazed at the corpse with a curious sense of indifference. This formal object had nothing to do with the astronomer, the solver of puzzles, the musician who had brought him up.
Philyra had already seated herself at the head of the couch and begun playing a dirge upon the kithara; as the women of the neighborhood arrived they sat down next to her and joined in, either singing or simply keening, so that the room filled with the thin moaning of grief. Arata sat down on a chair next to the couch, but made no sound, and covered her head.
Archimedes wondered if there were more people he should inform of the death. Phidias had been an only child, but Arata had a brother, and there were friends. Should he ask his mother about it? It seemed better not to disturb her. What about the funeral? In this hot weather it would have to take place next day. He supposed he should be arranging wood and incense for the pyre, and seeing about a funeral feast. Did he have money for it all? Presumably the shopkeepers would give him credit.
It seemed unbelievably strange to be worrying about such things, with his father lying there dead.
He went back into the courtyard, and was relieved to see Marcus returning from the public fountain with a heavy amphora of the water the visitors would need to ritually purify themselves from the contact with death. 'Marcus,' he whispered, hurrying over to him, 'who should we send to about this?'
'Your mother's already informed everyone,' said Marcus. Archimedes blushed, ashamed that Arata should have had to worry.
The visitors kept arriving all evening. When it began to grow dark, the slaves found torches and set them up in the courtyard and by the door. They had just been lit when Archimedes became aware of a commotion in the street outside- and then Hieron came through the open door, followed by his secretary. The unexpected appearance of the lord of the city caused an alarmed ruffle in the now-crowded courtyard, but Hieron ignored the stir and walked straight to Archimedes. 'My condolences,' he said, shaking hands. 'You have lost a father who was one of the best men in the city, and your grief must be great.'
Archimedes blinked, fiercely pleased by such a public declaration from such a source. The neighborhood had always liked Phidias- but it had always laughed at him, too. 'Thank you,' he replied. 'I do grieve for him, very much.'
'It would be your shame if you did not,' said Hieron.
Like any other mourner, he went on to the sickroom to view the body; when he entered, the women were so startled that they stopped keening, and there was a sudden, profound, reverberating silence. Once again, Hieron ignored the effect he produced, and he bowed his head respectfully to the dead. 'Phidias, farewell!' he said. 'I always regretted that I could not study with you longer. May the earth be light upon you!' Then he went up to
