Every evening, Ali joined Fahim in the common room to watch the news on TV. There was no doubt that the place they had come to was peaceful and prosperous; when war was mentioned, it was always in some distant land. The rulers here did not govern by force, they were chosen by the people, and even now this competition was in progress. The men who had sent the soldiers to block the bridge were asking the people to choose them again.
When the guard woke Ali at eight in the morning, he didn’t complain, though he’d had only three hours’ sleep. He showered quickly, then went to the compound’s south gate. It no longer seemed strange to him to move from place to place this way: to wait for guards to come and unlock a succession of doors and escort him through the fenced-off maze that separated the compound from the government offices.
James and Reza were waiting in the office. Ali greeted them, his mouth dry. James said, “Reza will read the decision for you. It’s about ten pages, so be patient. Then if you have any questions, let me know.”
Reza read from the papers without meeting Ali’s eyes. Fernandez, the man who’d interviewed Ali, had written that there were discrepancies between things Ali had said at different times, and gaps in his knowledge of the place and time he claimed to have come from. What’s more, an expert in the era of the Scholars had listened to the tape of Ali talking, and declared that his speech was not of that time. “Perhaps this man’s great-grandfather fled Khurosan in the time of the Scholars, and some sketchy information has been passed down the generations. The applicant himself, however, employs a number of words that were not in use until decades later.”
Ali waited for the litany of condemnation to come to an end, but it seemed to go on forever. “I have tried to give the applicant the benefit of the doubt,” Fernandez had written, “but the overwhelming weight of evidence supports the conclusion that he has lied about his origins, his background, and all of his claims.”
Ali sat with his head in his hands.
James said, “Do you understand what this means? You have seven days to lodge an appeal. If you don’t lodge an appeal, you will have to return to your country.”
Reza added, “You should call your lawyer. Have you got money for a phone card?”
Ali nodded. He’d taken a job cleaning the mess, he had thirty points in his account already.
Every time Ali called, his lawyer was busy. Fahim helped Ali fill out the appeal form, and they handed it to James two hours before the deadline. “Lucky Colonel Kurtz is gone,” Fahim told Ali. “Or that form would have sat in the fax tray for at least a week.”
Wild rumors swept the camp: the government was about to change, and everyone would be set free. Ali had seen the government’s rivals giving their blessing to the use of soldiers to block the bridge; he doubted that they’d show the prisoners in the desert much mercy if they won.
When the day of the election came, the government was returned, more powerful than ever.
That night, as they were preparing to sleep, Fahim saw Ali staring at the long white scars that criss-crossed his upper arms and chest. “I use a razor blade,” Fahim admitted. “It makes me feel better. The one power I’ve got left: to choose my own pain.”
“I’ll never do that,” Ali swore.
Fahim gave a hollow laugh. “It’s cheaper than cigarettes.”
Ali closed his eyes and tried to picture freedom, but all he saw was blackness. The past was gone, the future was gone, and the world had shrunk to this prison.
4
“Ali, wake up, come see!”
Daniel was shaking him. Ali swatted his hands away angrily. The African was one of his closest friends, and there’d been a time when he could still drag Ali along to English classes or the gym, but since the appeal tribunal had rejected him, Ali had no taste for anything. “Let me sleep.”
“There are people. Outside the fence.”
“Escaped?”
“No, no. From the city!”
Ali clambered off the bunk. He splashed water on his face, then followed his friend.
Dozens of prisoners had gathered at the south-west corner of the fence, blocking the view, but Ali could hear people on the outside, shouting and banging drums. Daniel tried to clear a path, but it was impossible. “Get on my shoulders.” He ducked down and motioned to Ali.
Ali laughed. “It’s not that important.”
Daniel raised a hand angrily, as if to slap him. “Get up, you have to see.” He was serious. Ali obeyed.
From his vantage, he could see that the mass of prisoners pressed against the inner fence was mirrored by another crowd struggling to reach the outer one. Police, some on horses, were trying to stop them. Ali peered into the scrum, amazed. Dozens of young people, men and women, were pushing against the cordon of policemen, and every now and then someone was slipping through and running forward. Some distance away across the desert stood a brightly colored bus. The word “freedom” was painted across it, in English, Persian, Arabic, and probably ten or twelve languages that Ali couldn’t read. The people were chanting, “Set them free! Set them free!” One young woman reached the fence and clung to it, shouting defiantly. Four policemen descended on her and tore her away.
A cloud of dust was moving along the desert road. More police cars were coming, reinforcements. A knife twisted in Ali’s heart. This gesture of friendship astonished him, but it would lead nowhere. In five or ten minutes, the protesters would all be rounded up and carried away.
A young man outside the fence met Ali’s gaze. “Hey! My name’s Ben.”
“I’m Ali.”
Ben looked around frantically. “What’s your number?”
“What?”
“We’ll write to you. Give us your number. They have to deliver the letters if we include the ID number.”
“Behind you!” Ali shouted, but the warning was too late. One policeman had him in a headlock, and another was helping wrestle him to the ground.
Ali felt Daniel stagger. The crowd on his own side was trying to fend off a wave of guards with batons and shields.
Ali dropped to his feet. “They want our ID numbers,” he told Daniel. Daniel looked around at the melee. “Got anything to write on?”
Ali checked his back pocket. The small notebook and pen it was his habit to carry were still there. He rested the notebook on Daniel’s back, and wrote “Ali 3739 Daniel 5420.” Who else? He quickly added Fahim and a few others.
He scrabbled on the ground for a stone, then wrapped the paper around it. Daniel lofted him up again.
The police were battling with the protesters, grabbing them by the hair, dragging them across the dirt. Ali couldn’t see anyone who didn’t have more pressing things to worry about than receiving his message. He lowered his arm, despondent.
Then he spotted someone standing by the bus. He couldn’t tell if it was a man or a woman. He, or she, raised a hand in greeting. Ali waved back, then let the stone fly. It fell short, but the distant figure ran forward and retrieved it from the sand.
Daniel collapsed beneath him, and the guards moved in with batons and tear gas. Ali covered his eyes with his forearm, weeping, alive again with hope.
DARK INTEGERS
“Good morning, Bruno. How is the weather there in Sparseland?”
The screen icon for my interlocutor was a three-holed torus tiled with triangles, endlessly turning itself inside out. The polished tones of the male synthetic voice I heard conveyed no specific origin, but gave a sense nonetheless that the speaker’s first language was something other than English.
I glanced out the window of my home office, taking in a patch of blue sky and the verdant gardens of a shady West Ryde cul-de-sac. Sam used “good morning” regardless of the hour, but it really was just after ten a.m., and the tranquil Sydney suburb was awash in sunshine and birdsong.
“Perfect,” I replied. “I wish I wasn’t chained to this desk.”
There was a long pause, and I wondered if the translator had mangled the idiom, creating the im
pression that I had been shackled by ruthless assailants, who had nonetheless left me with easy access to my instant messaging program. Then Sam said, “I’m glad you didn’t go for a run today. I’ve already tried Alison and Yuen, and they were both unavailable. If I hadn’t been able to get through to you, it might have been difficult to keep some of my colleagues in check.”
I felt a surge of anxiety, mixed with resentment. I refused to wear an iWatch, to make myself reachable twenty-four hours a day. I was a mathematician, not an obstetrician. Perhaps I was an amateur diplomat as well, but even if Alison, Yuen and I didn’t quite cover the time zones, it would never be more than a few hours before Sam could get hold of at least one of us.
“I didn’t realize you were surrounded by hot-heads,” I replied. “What’s the great emergency?” I hoped the translator would do justice to the sharpness in my voice. Sam’s colleagues were the ones with all the firepower, all the resources; they should not have been jumping at shadows. True, we had once tried to wipe them out, but that had been a perfectly innocent mistake, more than ten years before.
Sam said, “Someone from your side seems to have jumped the border.”
“Jumped it?”
“As far as we can see, there’s no trench cutting through it. But a few hours ago, a cluster of propositions on our side started obeying your axioms.”
I was stunned. “An isolated cluster? With no derivation leading back to us?”
“None that we could find.”
I thought for a while. “Maybe it was a natural event. A brief surge across the border from the background noise that left a kind of tidal pool behind.”
Sam was dismissive. “The cluster was too big for that. The probability would be vanishingly small.” Numbers came through on the data channel; he was right.
I rubbed my eyelids with my fingertips; I suddenly felt very tired. I’d thought our old nemesis, Industrial Algebra, had given up the chase long ago. They had stopped offering bribes and sending mercenaries to harass me, so I’d assumed they’d finally written off the defect as a hoax or a mirage, and gone back to their core business of helping the world’s military kill and maim people in ever more technologically sophisticated ways.
Maybe this wasn’t IA. Alison and I had first located the defect – a set of contradictory results in arithmetic that marked the border between our mathematics and the version underlying Sam’s world – by means of a vast set of calculations farmed out over the internet, with thousands of volunteers donating their computers’ processing power when the machines would otherwise have been idle. When we’d pulled the plug on that project – keeping our discovery secret, lest IA find a way to weaponize it – a few participants had been resentful, and had talked about continuing the search. It would have been easy enough for them to write their own software, adapting the same open source framework that Alison and I had used, but it was difficult to see how they could have gathered enough supporters without launching some kind of public appeal.
I said, “I can’t offer you an immediate explanation for this. All I can do is promise to investigate.”
“I understand,” Sam replied.
“You have no clues, yourself?” A decade before, in Shanghai, when Alison, Yuen and I had used the supercomputer called Luminous to mount a sustained attack on the defect, the mathematicians of the far side had grasped the details of our unwitting assault clearly enough to send a plume of alternative mathematics back across the border with pinpoint precision, striking at just the three of us.
Sam said, “If the cluster had been connected to something, we could have followed the trail. But in isolation it tells us nothing. That’s why my colleagues are so anxious.”
“Yeah.” I was still hoping that the whole thing might turn out to be a glitch – the mathematical equivalent of a flock of birds with a radar echo that just happened to look like something more sinister – but the full gravity of the situation was finally dawning on me.
The inhabitants of the far side were as peaceable as anyone might reasonably wish their neighbors to be, but if their mathematical infrastructure came under threat they faced the real prospect of annihilation. They had defended themselves from such a threat once before, but because they had been able to trace it to its source and understand its nature, they had shown great forbearance. They had not struck their assailants dead, or wiped out Shanghai, or pulled the ground out from under our universe.
This new assault had not been sustained, but nobody knew its origins, or what it might portend. I believed that our neighbors would do no more than they had to in order to ensure their survival, but if they were forced to strike back blindly, they might find themselves with no path to safety short of turning our world to dust.
#
Shanghai time was only two hours behind Sydney, but Yuen’s IM status was still “unavailable”. I emailed him, along with Alison, though it was the middle of the night in Zürich and she was unlikely to be awake for another four or five hours. All of us had programs that connected us to Sam by monitoring, and modifying, small portions of the defect: altering a handful of precariously balanced truths of arithmetic, wiggling the border between the two systems back and forth to encode each transmitted bit. The three of us on the near side might have communicated with each other in the same way, but on consideration we’d decided that conventional cryptography was a safer way to conceal our secret. The mere fact that communications data seemed to come from nowhere had the potential to attract suspicion, so we’d gone as far as to write software to send fake packets across the net to cover for our otherwise inexplicable conversations with Sam; anyone but the most diligent and resourceful of eavesdroppers would conclude that he was addressing us from an internet café in Lithuania.
While I was waiting for Yuen to reply, I scoured the logs where my knowledge miner deposited results of marginal relevance, wondering if some flaw in the criteria I’d given it might have left me with a blind spot. If anyone, anywhere had announced their intention to carry out some kind of calculation that might have led them to the defect, the news should have been plastered across my desktop in flashing red letters within seconds. Granted, most organizations with the necessary computing resources were secretive by nature, but they were also unlikely to be motivated to indulge in such a crazy stunt. Luminous itself had been decommissioned in 2012; in principle, various national security agencies, and even a few IT-centric businesses, now had enough silicon to hunt down the defect if they’d really set their sights on it, but as far as I knew Yuen, Alison and I were still the only three people in the world who were certain of its existence. The black budgets of even the most profligate governments, the deep pockets of even the richest tycoons, would not stretch far enough to take on the search as a long shot, or an act of whimsy.
An IM window popped up with Alison’s face. She looked ragged. “What time is it there?” I asked.
“Early. Laura’s got colic.”
“Ah. Are you OK to talk?”
“Yeah, she’s asleep now.”
My email had been brief, so I filled her in on the details. She pondered the matter in silence for a while, yawning unashamedly.
“The only thing I can think of is some gossip I heard at a conference in Rome a couple of months ago. It was a fourth-hand story about some guy in New Zealand who thinks he’s found a way to test fundamental laws of physics by doing computations in number theory.”
“Just random crackpot stuff, or ... what?”
Alison massaged her temples, as if trying to get more blood flowing to her brain. “I don’t know, what I heard was too vague to make a judgment. I gather he hasn’t tried to publish this anywhere, or even mentioned it in blogs. I guess he just confided in a few people directly, one of whom must have found it too amusing for them to keep their mouth shut.”
“Have you got a name?”
She went off camera and rummaged for a while. “Tim Campbell,” she announced. Her notes came through on the data channel. “He’s done res
pectable work in combinatorics, algorithmic complexity, optimization. I scoured the net, and there was no mention of this weird stuff. I was meaning to email him, but I never got around to it.”
I could understand why; that would have been about the time Laura was born. I said, “I’m glad you still go to so many conferences in the flesh. It’s easier in Europe, everything’s so close.”
“Ha! Don’t count on it continuing, Bruno. You might have to put your fat arse on a plane sometime yourself.”
“What about Yuen?”
Alison frowned. “Didn’t I tell you? He’s been in hospital for a couple of days. Pneumonia. I spoke to his daughter, he’s not in great shape.”
“I’m sorry.” Alison was much closer to him than I was; he’d been her doctoral supervisor, so she’d known him long before the events that had bound the three of us together.
Yuen was almost eighty. That wasn’t yet ancient for a middle-class Chinese man who could afford good medical care, but he would not be around forever.
I said, “Are we crazy, trying to do this ourselves?” She knew what I meant: liaising with Sam, managing the border, trying to keep the two worlds talking but the two sides separate, safe and intact.
Alison replied, “Which government would you trust not to screw this up? Not to try to exploit it?”
“None. But what’s the alternative? You pass the job on to Laura? Kate’s not interested in having kids. So do I pick some young mathematician at random to anoint as my successor?”
“Not at random, I’d hope.”
“You want me to advertise? ‘Must be proficient in number theory, familiar with Machiavelli, and own the complete boxed set of The West Wing?’”
She shrugged. “When the time comes, find someone competent you can trust. It’s a balance: the fewer people who know, the better, so long as there are always enough of us that the knowledge doesn’t risk getting lost completely.”