Jamil acknowledged the request with a hand signal and shifted his trajectory. It was almost a decade since he'd last played the game, but he still knew the intricate web of possibilities by heart: he could drain the two-ten harmonic into the three-ten, five-two and five-six modes-all with "good parity," peaks along the centre-line-in a single action.

As he pounded across the gra.s.s, carefully judging the correct angle by sight, increasing his speed until he felt the destructive beats give way to a steady force like a constant breeze, he suddenly recalled a time-centuries before, in another city-when he'd played with one team, week after week, for 40 years. Faces and voices swam in his head. Hashim, Jamil's 98th child, and Hashim's granddaughter Laila had played beside him. But he'd burnt his house and moved on, and when that era touched him at all now it was like an unexpected gift. The scent of the gra.s.s, the shouts of the players, the soles of his feet striking the ground, resonated with every other moment he'd spent the same way, bridging the centuries, binding his life together. He never truly felt the scale of it when he sought it out deliberately; it was always small things, tightly focused moments like this, that burst the horizon of his everyday concerns andconfronted him with the astonishing vista.

The two-ten mode was draining faster than he'd expected; the see-sawing centre-line dip in the wave was vanishing before his eyes. He looked around, and saw Margit performing an elaborate Lissajous manoeuvre, smoothly orchestrating a dozen transitions at once. Jamil froze and watched her, admiring her virtuosity while he tried to decide what to do next; there was no point competing with her when she was doing such a good job of completing the task Chusok had set him.

Margit was his opponent, but they were both aiming for exactly the same kind of spectrum. The symmetry of the field meant that any scoring wave would work equally well for either side-but only one team could be the first to reap the benefit, the first to have more than half the wave's probability packed into their goal. So the two teams were obliged to co-operate at first, and it was only as the wave took shape from their combined efforts that it gradually became apparent which side would gain by sculpting it to perfection as rapidly as possible, and which would gain by spoiling it for the first chance, then honing it for the rebound.

Penina chided him over her shoulder as she jogged past, "You want to leave her to clean up four-six, as well?" She was smiling, but Jamil was stung; he'd been motionless for ten or fifteen seconds. It was not forbidden to drag your feet and rely on your opponents to do all the work, but it was regarded as a shamefully impoverished strategy. It was also very risky, handing them the opportunity to set up a wave that was almost impossible to exploit yourself.

He rea.s.sessed the spectrum, and quickly sorted through the alternatives. Whatever he did would have unwanted side effects; there was no magic way to avoid influencing modes in other players'

territory, and any action that would drive the transitions he needed would also trigger a mult.i.tude of others, up and down the spectrum. Finally, he made a choice that would weaken the offending mode while causing as little disruption as possible.

Jamil immersed himself in the game, planning each transition two steps in advance, switching strategy halfway through a run if he had to, but staying in motion until the sweat dripped from his body, until his calves burned, until his blood sang. He wasn't blinded to the raw pleasures of the moment, or to memories of games past, but he let them wash over him, like the breeze that rose up and cooled his skin with no need for acknowledgement. Familiar voices shouted terse commands at him; as the wave came closer to a scoring spectrum every trace of superfluous conversation vanished, every idle glance gave way to frantic, purposeful gestures. To a bystander, this might have seemed like the height of dehumanization: 22 people reduced to grunting cogs in a pointless machine. Jamil smiled at the thought but refused to be distracted into a complicated imaginary reb.u.t.tal. Every step he took was the answer to that, every hoa.r.s.e plea to Yann or Joracy, Chusok or Maria, Eudore or Halide. These were his friends, and he was back among them. Back in the world.

The first chance of a goal was 30 seconds away, and the opportunity would fall to Jamil's team; a few tiny shifts in amplitude would clinch it. Margit kept her distance, but Jamil could sense her eyes on him constantly-and literally feel her at work through his skin as she slackened his contact with the wave.

In theory, by mirroring your opponent's movements at the correct position on the field you could undermine everything they did, though in practice not even the most skilful team could keep the spectrum completely frozen. Going further and spoiling was a tug of war you didn't want to win too well: if you degraded the wave too much, your opponent's task-spoiling your own subsequent chance at a goal-became far easier.

Jamil still had two bad-parity modes that he was hoping to weaken, but every time he changed velocity to try a new transition, Margit responded in an instant, blocking him. He gestured to Chusok for help; Chusok had his own problems with Ezequiel, but he could still make trouble for Margit by choosing where he placed unwanted amplitude. Jamil shook sweat out of his eyes; he could see the characteristic "stepping stone" pattern of lobes forming, a sign that the wave would soon converge on the goal, but from the middle of the field it was impossible to judge their shape accurately enough to know what, if anything, remained to be done.

Suddenly, Jamil felt the wave push against him. He didn't waste time looking around for Margit; Chusok must have succeeded in distracting her. He was almost at the boundary line, but he managed toreverse smoothly, continuing to drive both the transitions he'd been aiming for.

Two long lobes of probability, each modulated by a series of oscillating mounds, raced along the sides of the field. A third, shorter lobe running along the centre-line melted away, reappeared, then merged with the others as they touched the end of the field, forming an almost rectangular plateau encompa.s.sing the goal.

The plateau became a pillar of light, growing narrower and higher as dozens of modes, all finally in phase, crashed together against the impenetrable barrier of the field's boundary. A shallow residue was still spread across the entire field, and a diminishing sequence of elliptical lobes trailed away from the goal like a staircase, but most of the wave that had started out lapping around their waists was now concentrated in a single peak that towered above their heads, nine or ten metres tall.

For an instant, it was motionless.

Then it began to fall.

The umpire said, "Forty-nine point eight."

The wave packet had not been tight enough.

Jamil struggled to shrug off his disappointment and throw his instincts into reverse. The other team had 50 seconds, now, to fine-tune the spectrum and ensure that the reflected packet was just a fraction narrower when it reformed, at the opposite end of the field.

As the pillar collapsed, replaying its synthesis in reverse, Jamil caught sight of Margit. She smiled at him calmly, and it suddenly struck him: She'd known they couldn't make the goal. That was why she'd stopped opposing him. She'd let him work towards sharpening the wave for a few seconds, knowing that it was already too late for him, knowing that her own team would gain from the slight improvement.

Jamil was impressed; it took an extraordinary level of skill and confidence to do what she'd just done. For all the time he'd spent away, he knew exactly what to expect from the rest of the players, and in Margit's absence he would probably have been wishing out loud for a talented newcomer to make the game interesting again. Still, it was hard not to feel a slight sting of resentment. Someone should have warned him just how good she was.

With the modes slipping out of phase, the wave undulated all over the field again, but its reconvergence was inevitable: unlike a wave of water or sound, it possessed no hidden degrees of freedom to grind its precision into entropy. Jamil decided to ignore Margit; there were cruder strategies than mirror-blocking that worked almost as well. Chusok was filling the two-ten mode now; Jamil chose the four-six as his spoiler. All they had to do was keep the wave from growing much sharper, and it didn't matter whether they achieved this by preserving the status quo, or by nudging it from one kind of bluntness to another.

The steady resistance he felt as he ran told Jamil that he was driving the transition, unblocked, but he searched in vain for some visible sign of success. When he reached a vantage point where he could take in enough of the field in one glance to judge the spectrum properly, he noticed a rapidly vibrating shimmer across the width of the wave. He counted nine peaks: good parity. Margit had pulled most of the amplitude straight out of his spoiler mode and fed it into this. It was a mad waste of energy to aim for such an elevated harmonic, but no one had been looking there, no one had stopped her.

The scoring pattern was forming again, he only had nine or ten seconds left to make up for all the time he'd wasted. Jamil chose the strongest good-parity mode in his territory, and the emptiest bad one, computed the velocity that would link them, and ran.

He didn't dare turn to watch the opposition goal; he didn't want to break his concentration. The wave retreated around his feet, less like an Earthly ebb tide than an ocean drawn into the sky by a pa.s.sing black hole. The city diligently portrayed the shadow that his body would have cast, shrinking in front of him as the tower of light rose.

The verdict was announced. "Fifty point one."

The air was filled with shouts of triumph-Ezequiel's the loudest, as always. Jamil sagged to his knees, laughing. It was a curious feeling, familiar as it was: he cared, and he didn't. If he'd been wholly indifferent to the outcome of the game there would have been no pleasure in it, but obsessing over every defeat-or every victory-could ruin it just as thoroughly. He could almost see himself walking the line,orchestrating his response as carefully as any action in the game itself.

He lay down on the gra.s.s to catch his breath before play resumed. The outer face of the microsun that orbited Laplace was shielded with rock, but light reflected skywards from the land beneath it crossed the 100,000 kilometre width of the 3-toroidal universe to give a faint glow to the planet's nightside. Though only a sliver was lit directly, Jamil could discern the full disc of the opposite hemisphere in the primary image at the zenith: continents and oceans that lay, by a shorter route, 12,000 or so kilometres beneath him. Other views in the lattice of images spread across the sky were from different angles, and showed substantial crescents of the dayside itself. The one thing you couldn't find in any of these images, even with a telescope, was your own city. The topology of this universe let you see the back of your head, but never your reflection.

Jamil's team lost, three nil. He staggered over to the fountains at the edge of the field and slaked his thirst, shocked by the pleasure of the simple act. Just to be alive was glorious now, but once he felt this way, anything seemed possible. He was back in synch, back in phase, and he was going to make the most of it, for however long it lasted.

He caught up with the others, who'd headed down towards the river. Ezequiel hooked an arm around his neck, laughing. "Bad luck, Sleeping Beauty! You picked the wrong time to wake. With Margit, we're invincible."

Jamil ducked free of him. "I won't argue with that." He looked around. "Speaking of whom-"

Penina said, "Gone home. She plays, that's all. No frivolous socializing after the match."

Chusok added, "Or any other time." Penina shot Jamil a glance that meant: not for want of trying on Chusok's part.

Jamil pondered this, wondering why it annoyed him so much. On the field, she hadn't come across as aloof and superior. Just unashamedly good.

He queried the city, but she'd published nothing besides her name. n.o.body expected-or wished-to hear more than the tiniest fraction of another person's history, but it was rare for anyone to start a new life without carrying through something from the old as a kind of calling card, some incident or achievement from which your new neighbours could form an impression of you.

They'd reached the riverbank. Jamil pulled his shirt over his head. "So what's her story? She must have told you something."

Ezequiel said, "Only that she learnt to play a long time ago; she won't say where or when. She arrived in Noether at the end of last year, and grew a house on the southern outskirts. No one sees her around much. No one even knows what she studies."

Jamil shrugged, and waded in. "Ah well. It's a challenge to rise to." Penina laughed and splashed him teasingly. He protested, "I meant beating her at the game."

Chusok said wryly, "When you turned up, I thought you'd be our secret weapon. The one player she didn't know inside out already."

"I'm glad you didn't tell me that. I would have turned around and fled straight back into hibernation."

"I know. That's why we all kept quiet." Chusok smiled. "Welcome back."

Penina said, "Yeah, welcome back, Jamil."

Sunlight shone on the surface of the river. Jamil ached all over, but the cool water was the perfect place to be. If he wished, he could build a part.i.tion in his mind at the point where he stood right now, and never fall beneath it. Other people lived that way, and it seemed to cost them nothing. Contrast was overrated; no sane person spent half their time driving spikes into their flesh for the sake of feeling better when they stopped. Ezequiel lived every day with the happy boisterousness of a five-year-old; Jamil sometimes found this annoying, but then any kind of disposition would irritate someone. His own stretches of meaningless sombreness weren't exactly a boon to his friends.

Chusok said, "I've invited everyone to a meal at my house tonight. Will you come?"

Jamil thought it over, then shook his head. He still wasn't ready. He couldn't force-feed himself with normality; it didn't speed his recovery, it just drove him backwards.

Chusok looked disappointed, but there was nothing to be done about that. Jamil promised him,"Next time. OK?"

Ezequiel sighed. "What are we going to do with you? You're worse than Margit!" Jamil started backing away, but it was too late. Ezequiel reached him in two casual strides, bent down and grabbed him around the waist, hoisted him effortlessly onto one shoulder, then flung him through the air into the depths of the river.

Jamil was woken by the scent of wood smoke. His room was still filled with the night's grey shadows, but when he propped himself up on one elbow and the window obliged him with transparency, the city was etched clearly in the predawn light.

He dressed and left the house, surprised at the coolness of the dew on his feet. No one else in his street seemed to be up; had they failed to notice the smell, or did they already know to expect it? He turned a corner and saw the rising column of soot, faintly lit with red from below. The flames and the ruins were still hidden from him, but he knew whose house it was.

When he reached the dying blaze, he crouched in the heat-withered garden, cursing himself. Chusok had offered him the chance to join him for his last meal in Noether. Whatever hints you dropped, it was customary to tell no one that you were moving on. If you still had a lover, if you still had young children, you never deserted them. But friends, you warned in subtle ways. Before vanishing.

Jamil covered his head with his arms. He'd lived through this countless times before, but it never became easier. If anything it grew worse, as every departure was weighted with the memories of others.

His brothers and sisters had scattered across the branches of the New Territories. He'd walked away from his father and mother when he was too young and confident to realize how much it would hurt him, decades later. His own children had all abandoned him eventually, far more often than he'd left them. It was easier to leave an ex-lover than a grown child: something burned itself out in a couple, almost naturally, as if ancestral biology had prepared them for at least that one rift.

Jamil stopped fighting the tears. But as he brushed them away, he caught sight of someone standing beside him. He looked up. It was Margit.

He felt a need to explain. He rose to his feet and addressed her. "This was Chusok's house. We were good friends. I'd known him for 96 years."

Margit gazed back at him neutrally. "Boo hoo. Poor baby. You'll never see your friend again."

Jamil almost laughed, her rudeness was so surreal. He pushed on, as if the only conceivable, polite response was to pretend that he hadn't heard her. "No one is the kindest, the most generous, the most loyal. It doesn't matter. That's not the point. Everyone's unique. Chusok was Chusok." He banged a fist against his chest, utterly heedless now of her contemptuous words. "There's a hole in me, and it will never be filled." That was the truth, even though he'd grow around it. He should have gone to the meal, it would have cost him nothing.

"You must be a real emotional Swiss cheese," observed Margit tartly.

Jamil came to his senses. "Why don't you f.u.c.k off to some other universe? No one wants you in Noether."

Margit was amused. "You are a bad loser." Jamil gazed at her, honestly confused for a moment; the game had slipped his mind completely. He gestured at the embers. "What are you doing here? Why did you follow the smoke, if it wasn't regret at not saying goodbye to him when you had the chance?" He wasn't sure how seriously to take Penina's lighthearted insinuation, but if Chusok had fallen for Margit, and it had not been reciprocated, that might even have been the reason he'd left.

She shook her head calmly. "He was nothing to me. I barely spoke to him."

"Well, that's your loss."

"From the look of things, I'd say the loss was all yours."

He had no reply. Margit turned and walked away.

Jamil crouched on the ground again, rocking back and forth, waiting for the pain to subside.

Jamil spent the next week preparing to resume his studies. The library had near-instantaneous contact with every artificial universe in the New Territories, and the additional lightspeed lag between Earth andthe point in s.p.a.ce from which the whole tree-structure blossomed was only a few hours. Jamil had been to Earth, but only as a tourist; land was scarce, they accepted no migrants. There were remote planets you could live on, in the home universe, but you had to be a certain kind of m.a.s.o.c.h.i.s.tic purist to want that. The precise reasons why his ancestors had entered the New Territories had been forgotten generations before-and it would have been presumptuous to track them down and ask them in person-but given a choice between the then even-more-crowded Earth, the horrifying reality of interstellar distances, and an endlessly extensible branching chain of worlds which could be traversed within a matter of weeks, the decision wasn't exactly baffling.

Jamil had devoted most of his time in Noether to studying the category of representations of Lie groups on complex vector s.p.a.ces-a fitting choice, since Emmy Noether had been a pioneer of group theory, and if she'd lived to see this field blossom she would probably have been in the thick of it herself.

Representations of Lie groups lay behind most of physics: each kind of subatomic particle was really nothing but a particular way of representing the universal symmetry group as a set of rotations of complex vectors. Organizing this kind of structure with category theory was ancient knowledge, but Jamil didn't care; he'd long ago reconciled himself to being a student, not a discoverer. The greatest gift of consciousness was the ability to take the patterns of the world inside you, and for all that he would have relished the thrill of being the first at anything, with ten-to-the-sixteenth people alive that was a futile ambition for most.

In the library, he spoke with fellow students of his chosen field on other worlds, or read their latest works. Though they were not researchers, they could still put a new pedagogical spin on old material, enriching the connections with other fields, finding ways to make the complex, subtle truth easier to a.s.similate without sacrificing the depth and detail that made it worth knowing in the first place. They would not advance the frontiers of knowledge. They would not discover new principles of nature, or invent new technologies. But to Jamil, understanding was an end in itself.

He rarely thought about the prospect of playing another match, and when he did the idea was not appealing. With Chusok gone, the same group could play ten-to-a-side without Jamil to skew the numbers. Margit might even choose to swap teams, if only for the sake of proving that her current team's monotonous string of victories really had been entirely down to her.

When the day arrived, though, he found himself unable to stay away. He turned up intending to remain a spectator, but Ryuichi had deserted Ezequiel's team, and everyone begged Jamil to join in.

As he took his place opposite Margit, there was nothing in her demeanour to acknowledge their previous encounter: no lingering contempt, but no hint of shame either. Jamil resolved to put it out of his mind; he owed it to his fellow players to concentrate on the game.

They lost, five nil.

Jamil forced himself to follow everyone to Eudore's house, to celebrate, commiserate, or as it turned out, to forget the whole thing. After they'd eaten, Jamil wandered from room to room, enjoying Eudore's choice of music but unable to settle into any conversation. No one mentioned Chusok in his hearing.

He left just after midnight. Laplace's near-full primary image and its eight brightest gibbous companions lit the streets so well that there was no need for anything more. Jamil thought: Chusok might have merely travelled to another city, one beneath his gaze right now. And wherever he'd gone, he might yet choose to stay in touch with his friends from Noether.

And his friends from the next town, and the next?

Century after century?

Margit was sitting on Jamil's doorstep, holding a bunch of white flowers in one hand.

Jamil was irritated. "What are you doing here?"

"I came to apologize."

He shrugged. "There's no need. We feel differently about certain things. That's fine. I can still face you on the playing field."

"I'm not apologizing for a difference of opinion. I wasn't honest with you. I was cruel." She shaded her eyes against the glare of the planet and looked up at him. "You were right: it was my loss. I wish I'd known your friend."He laughed curtly. "Well, it's too late for that."

She said simply, "I know."

Jamil relented. "Do you want to come in?" Margit nodded, and he instructed the door to open for her. As he followed her inside, he said, "How long have you been here? Have you eaten?"

"No."

"I'll cook something for you."

"You don't have to do that."

He called out to her from the kitchen, "Think of it as a peace offering. I don't have any flowers."

Margit replied, "They're not for you. They're for Chusok's house."

Jamil stopped rummaging through his vegetable bins, and walked back into the living room. "People don't usually do that in Noether."

Margit was sitting on the couch, staring at the floor. She said, "I'm so lonely here. I can't bear it any more."

He sat beside her. "Then why did you rebuff him? You could at least have been friends."

She shook her head. "Don't ask me to explain."

Jamil took her hand. She turned and embraced him, trembling miserably. He stroked her hair. "Sssh."

She said, "Just s.e.x. I don't want anything more."

He groaned softly. "There's no such thing as that."

"I just need someone to touch me again."

"I understand." He confessed, "So do I. But that won't be all. So don't ask me to promise there'll be nothing more."