“But why?”

The president gestured to the side window, through which the small lake was visible. “Outside influence. The people see an alternative elsewhere that they believe will give them power and a voice, and they crave that. They think…”

He smiled, but it seemed more sad than amused. “They think the grass is greener on the other side of the Great Wall.” He shook his head. “But are the Russians better off now with their capitalism and their democracy? They were the first in space, they led the world in so much! And their literature, their music! But now it’s a land of pestilence and poverty, of disease and early death — you would not want to visit it, trust me. Yet it’s what our people desire. They see it and, like a child reaching out to touch a hot stove, they can’t help but want to grasp it.”

Zhang nodded, but didn’t trust his voice. Behind the president, through the big window, he could see the red tile rooftops of the Forbidden City and the perpetually silver-gray sky.

“My advisors made a fundamental error in their assumptions, though,” said the president.

“Excellency?”

“They assumed that the outside influences would always be able to get in. But Sun Tzu said, ‘It is of first importance to keep one’s own state intact,’ and I intend to do that.”

Zhang was quiet for a time, then: “The Changcheng Strategy was intended only as an emergency measure, Excellency. The emergency has passed. The economic concerns…”

The president looked sad. “Money,” he said. “Even for the Communist Party, it always comes down to money, doesn’t it?”

Zhang lifted his hands slightly, palms open.

And at last the president nodded. “All right. All right. Restore communications; let the outside flood in again.”

“Thank you, Your Excellency. As always, you’ve made the right decision.”

The president took off his glasses and rubbed the bridge of his nose. “Have I?” he said.

Zhang let the question hang in the air, floating with the incense.

Caitlin could always tell when they were pulling into her school’s parking lot: there was a large speed bump immediately after the right turn that made her mother’s Prius do a body-jolting up-and-down.

“I know you won’t need it,” her mom said, as she swung the car into the drop-off area near the main doors, “but good luck on the math test.”

Caitlin smiled. When she’d been twelve, her cousin Megan had given her a Barbie doll that exclaimed, in a frustrated voice, “Math is hard.” Mattel had made that model for only a short time before a public outcry had forced them to recall it, but her cousin had found one for her at a garage sale; they used to have a blast making fun of it. Caitlin knew Barbie was an impossible physical role model for girls — she’d worked out that if Barbie were life size, her measurements would be 46-19-32 — and the idea that girls might find math hard was equally ridiculous.

“Thanks, Mom.” Caitlin grabbed her white cane and computer bag, got out of the car, and walked to the school’s front door, but she was dragging her feet, she knew. Oh, she liked school well enough, but how … how mundane it seemed, compared to the wonders of the night before.

“Hey, Cait!” Bashira’s voice.

“Hey, Bash,” Caitlin said, smiling — but wondering, yet again, what her friend looked like.

Caitlin knew Bashira would be holding out her elbow just so, and she took hold of it so Bash could lead as they maneuvered down the crowded hallway. “All ready for the test?”

“Sine 2A equals 2 sine A cosine A,” said Caitlin, by way of an answer. They came to a stairwell — sounds echoed differently in there — and headed up the two half-flights of stairs.

“Good morning, everyone,” said Mr. Heidegger, their math teacher, once they entered the classroom. Caitlin had only Bashira’s description of him to go by:

“Tall, skinny, with a face like his wife squeezed it tight between her thighs.” Bashira loved saying risqué things, but she’d had no actual experience of such matters; her family was devoutly Muslim and would arrange a marriage for her. Caitlin wasn’t sure what she thought about that process, but at least Bashira would end up with someone. Caitlin often worried that she’d never find a nice guy who liked math and hockey and could deal well with her … situation. Yes, now that she was in Canada, meeting boys who liked hockey would be easy, but as for the other two…

“Please stand,” said a female voice over the public-address system, “for the national anthem.”

There wasn’t nearly as much pomp and circumstance in Canada, which was fine in Caitlin’s book. Pledging allegiance to a flag she couldn’t see had always bothered her. Oh, she knew the American flag had stars and stripes: they’d felt embroidered flags at the School for the Blind. But the synonym for the flag — the old red, white, and blue — had been utterly meaningless to her until, well, until yesterday. She couldn’t wait until she had a chance to sneak a peek at the Web again.

After “O Canada,” the test was distributed. The other students got paper copies, but Mr. Heidegger simply handed Caitlin a USB memory key with the test on it. She was skilled at Nemeth, the Braille coding system for math, and her dad had taught her LaTeX, the computerized typesetting standard used by scientists and many blind people who had to work with equations.

She plugged the memory key into one of her notebook’s USB ports, brought out her portable thirty-two-cell Braille display, and got down to work. When she was done she would output her answers onto the USB key for Mr. Heidegger to read. She was always one of the first, if not the first, to finish every in-class test and assignment — but not today. Her mind kept wandering, conjuring up visions of light and color as she recalled the incredible, joyous wonder of the night before.

After school, Caitlin and her mom drove to Toronto to pick up Dr. Kuroda. As soon as they got to the house, he had a shower — which, Caitlin imagined, was a relief to everyone. Then, after a steak dinner, which Caitlin’s dad had made on the barbecue, they got to work; it was Monday night, and Kuroda understood that his only opportunities to work with Caitlin during the week would be in the evenings.

Kuroda had brought his notebook computer with him. Caitlin, curious, ran her hands over it. When closed it was as thin as the latest MacBook Air, but when she opened it she was astonished to feel full-height keycaps rise up from what had been a flat keyboard. She’d read that lots of technology appears in Japan months or even years before becoming available in North America, but this was the first real proof she’d had that that was true. “So, what’s on your desktop?” she asked.

“My wallpaper, you mean?”

“Yes.” Caitlin had had her mom put a photo of Schrodinger — the cat, not the physicist — on as her wallpaper; even though she couldn’t see it, it made her happy knowing it was there.

“It’s my favorite cartoon, actually. It’s by a fellow named Sidney Harris. He specializes in science cartoons — you see his stuff taped to office doors in university science departments all over the world. Anyway, this one shows two scientists standing in front of a blackboard and on the left there are a whole bunch of equations and formulas, and on the right there’s more of the same, but in the middle it just says, ‘Then a miracle occurs…’ And one of the scientists says to the other, ‘I think you should be more explicit here in step two.’”

Caitlin laughed. She showed Kuroda her refreshable Braille display (the eighty-cell one she kept at home), and let him run his finger along it to see what it felt like. She also had a tactile graphics display that used a matrix of pins to let her feel diagrams; she let him play with that, too. And she demonstrated her embossing printer and her ViewPlus audio graphing calculator, which described graph shapes with audio tones and cues.