Jack was living with a small group of English clerics in Toledo. They were part of an international community of scholars that included Jews, Muslims and Arab Christians. The Englishmen were occupied translating works of mathematics from Arabic into Latin, so they could be read by Christians. There was an atmosphere of feverish excitement among them as they discovered and explored the treasure-house of Arab learning, and they had casually welcomed Jack as a student: they admitted into their circle anyone who understood what they were doing and shared their enthusiasm for it. They were like peasants who have labored for years to scratch a crop out of poor soil and then suddenly move to a rich alluvial valley. Jack had abandoned building to study mathematics. He had not yet needed to work for money: the clerics casually gave him a bed and any meals he wanted, and they would have provided him with a new robe and sandals if he had needed them.

Raschid was one of their sponsors. As an international trader he was multilingual and cosmopolitan in his attitudes. At home he spoke Castilian, the language of Christian Spain, rather than Mozarabic. His family also all spoke French, the language of the Normans, who were important traders. Although he was a man of commerce, he had a powerful intellect and a wide-ranging curiosity. He loved to talk to scholars about their theories. He had taken a liking to Jack immediately, and Jack dined at his house several times a week.

Now, as they began to eat, Raschid asked Jack: “What have the philosophers taught us this week?”

“I’ve been reading Euclid.” Euclid’s Elements of Geometry had been one of the first books translated.

“Euclid is a funny name for an Arab,” said Ismail, Raschid’s brother.

“He was Greek,” Jack explained. “He lived before the birth of Christ. His work was lost by the Romans but preserved by the Egyptians-so it comes to us in Arabic.”

“And now Englishmen are translating it into Latin!” Raschid said. “This amuses me.”

“But what have you learned?” said Josef, the fiancé of Raya.

Jack hesitated. It was hard to explain. He tried to make it practical. “My stepfather, the builder, taught me how to perform certain operations in geometry: how to divide a line exactly in half, how to draw a right angle, and how to draw one square inside another so that the smaller is half the area of the larger.”

“What is the purpose of such skills?” Josef interrupted. There was a note of scorn in his voice. He saw Jack as something of an upstart, and was jealous of the attention Raschid paid to Jack’s conversation.

“Those operations are essential in planning buildings,” Jack replied pleasantly, pretending not to notice Josef’s tone. “Take a look at this courtyard. The area of the covered arcades around the edges is exactly the same as the open area in the middle. Most small courtyards are built like that, including the cloisters of monasteries. It’s because these proportions are most pleasing. If the middle is bigger, it looks like a marketplace, and if it’s smaller, it just looks as if there’s a hole in the roof. But to get it exactly right, the builder has to be able to draw the open part in the middle so that it’s precisely half the area of the whole thing.”

“I never knew that!” Raschid said triumphantly. He liked nothing better than to learn something new.

“Euclid explains why these techniques work,” Jack went on. “For example, the two parts of the divided line are equal because they form corresponding sides of congruent triangles.”

“Congruent?” Raschid queried.

“It means exactly alike.”

“Ah-now I see.”

However, no one else did, Jack could tell.

Josef said: “But you could perform all these geometric operations before you read Euclid-so I don’t see that you’re any better off now.”

Raschid protested: “A man is always better off for understanding something!”

Jack said: “Besides, now that I understand the principles of geometry I may be able to devise solutions to new problems that baffled my stepfather.” He felt rather frustrated by the conversation: Euclid had come to him like the blinding flash of a revelation, but he was failing to communicate the thrilling importance of these new discoveries. He changed tack somewhat. “It’s Euclid’s method that is the most interesting,” he said. “He takes five axioms-self-evident truths-and deduces everything else logically from them.”

“Give me an example of an axiom,” Raschid said.

“A line can be prolonged indefinitely.”

“No it can’t,” said Aysha, who was handing round a bowl of figs.

The guests were somewhat startled to hear a girl joining in the argument, but Raschid laughed indulgently: Aysha was his favorite. “And why not?” he said.

“It has to come to an end sometime,” she said.

Jack said: “But in your imagination, it could go on indefinitely.”

“In my imagination, water could flow uphill and dogs speak Latin,” she retorted.

Her mother came into the room and heard that rejoinder. “Aysha!” she said in a steely voice. “Out!”

All the men laughed. Aysha made a face and went out. Josef’s father said: “Whoever marries her will have his hands full!” They laughed again. Jack laughed too; then he noticed they were all looking at him, as if the joke was on him.

After dinner, Raschid showed off his collection of mechanical toys. He had a tank in which you could mix water and wine and they would come out separately; a marvelous water-driven clock, which kept track of the hours in the day with phenomenal accuracy; a jug that would refill itself but never overflow; and a small wooden statue of a woman with eyes made of some kind of crystal that absorbed water in the warmth of the day and then shed it in the cool of the evening, so that she appeared to be weeping. Jack shared Raschid’s fascination with these toys, but he was most intrigued by the weeping statue, for whereas the mechanisms of the others were simple once they had been explained, no one really understood how the statue worked.

They sat in the arcades around the courtyard in the afternoon, playing games, dozing, or talking idly. Jack wished he belonged to a big family like this one, with sisters and uncles and in-laws, and a family home they could all visit, and a position of respect in a small town. Suddenly he recalled the conversation he had had with his mother the night she rescued him from the priory punishment cell. He had asked her about his father’s relations, and she had said Yes, he had a big family, back in France. I have got a family like this one, somewhere, Jack realized. My father’s brothers and sisters are my uncles and aunts. I might have cousins of my own I wonder if I will ever find them?

He felt adrift. He could survive anywhere but he belonged nowhere. He had been a carver, a builder, a monk and a mathematician, and he did not know which was the real Jack, if any. He sometimes wondered if he should be a jongleur like his father, or an outlaw like his mother. He was nineteen years old, homeless and rootless, with no family and no purpose in life.

He played chess with Josef and won; then Raschid came up and said: “Give me your chair, Josef-I want to hear more about Euclid.”

Josef obediently gave up his chair to his prospective father-in-law, then moved away-he had already heard everything he ever wanted to know about Euclid. Raschid sat down and said to Jack: “You’re enjoying yourself?”

“Your hospitality is matchless,” Jack said smoothly. He had learned courtly manners in Toledo.

“Thank you; but I meant with Euclid.”

“Yes. I don’t think I succeeded in explaining the importance of this book. You see-”

“I think I understand,” Raschid said. “Like you, I love knowledge for its own sake.”

“Yes.”

“Even so, every man has to make a living.”

Jack did not see the relevance of that remark, so he waited for Raschid to say more. However, Raschid sat back with his eyes half closed, apparently content to enjoy a companionable silence. Jack began to wonder whether Raschid was reproaching him for not working at a trade. Eventually Jack said: “I expect I shall go back to building, one day.”