Dark Integers and Other Stories, page 15
I said, “We should trigger it manually. One counter-strike to start with, to give them something to think about.” I was still hoping that the downed jets were unintended, but we had no choice but to retaliate.
“Yeah.” Alison’s image was live now; I saw her reach down for her mouse. She said, “It’s not responding. The net’s too degraded.” All the fancy algorithms that the routers used, and that we’d leveraged so successfully for our imaging software, were turning them into paperweights.
The internet was robust against high levels of transmission noise and the loss of thousands of connections, but not against the decay of arithmetic itself.
My watch went dead. I looked to the laptop; it was still working. I reached over and hit a single hotkey, launching a program that would try to reach Alison and the others the same way we’d talked to Sam: by modulating part of the border. In theory, the hawks might have moved the whole border—in which case we were screwed—but the border was vast, and it made more sense for them to target their computing resources on the specific needs of the assault itself.
A small icon appeared on the laptop’s screen, a single letter A in reversed monochrome. I said, “Is this working?”
“Yes,” Alison replied. The icon blinked out, then came back again.
We were doing a Hedy Lamarr, hopping rapidly over a predetermined sequence of border points to minimize the chance of detection. Some of those points would be missing, but it looked as if enough of them remained intact.
The A was joined by a Y and a T. The whole cabal was online now, whatever that was worth. What we needed was S, but S was not answering.
Campbell said grimly, “I heard about the planes. I’ve started an attack.” The tactic we had agreed upon was to take turns running different variants of Campbell’s border-jumping algorithm from our scattered machines.
I said, “The miracle is that they’re not hitting us the same way we’re hitting them. They’re just pushing down part of the border with the old voting method, step by step. If we’d given them what they’d asked for, we’d all be dead by now.”
“Maybe not,” Yuen replied. “I’m only halfway through a proof, but I’m 90 percent sure that Tim’s method is asymmetrical. It only works in one direction. Even if we’d told them about it, they couldn’t have turned it against us.”
I opened my mouth to argue, but if Yuen was right that made perfect sense. The far side had probably been working on the same branch of mathematics for centuries; if there had been an equivalent weapon that could be used from their vantage point, they would have discovered it long ago.
My machine had synchronized with Campbell’s, and it took over the assault automatically. We had no real idea what we were hitting, except that the propositions were further from the border, describing far simpler arithmetic on the dark integers than anything of ours that the far side had yet touched. Were we crippling machines? Taking lives? I was torn between a triumphant vision of retribution, and a sense of shame that we’d allowed it to come to this.
Every hundred meters or so, I passed another car sitting motionless by the side of the highway. I was far from the only person still driving, but I had a feeling Kate wouldn’t have much luck getting a taxi. She had water in her backpack, and there was a small shelter at the spot where we’d parked.
There was little to be gained by reaching my office now; the laptop could do everything that mattered, and I could run it from the car battery if necessary.
If I turned around and went back for Kate, though, I’d have so much explaining to do that there’d be no time for anything else.
I switched on the car radio, but either its digital signal processor was too sophisticated for its own good, or all the local stations were out.
“Anyone still getting news?” I asked.
“I still have radio,” Campbell replied. “No TV, no internet. Landlines and mobiles here are dead.” It was the same for Alison and Yuen. There’d been no more reports of disasters on the radio, but the stations were probably as isolated now as their listeners. Ham operators would still be calling each other, but journalists and newsrooms would not be in the loop. I didn’t want to think about the contingency plans that might have been in place, given ten years’ preparation and an informed population.
By the time I reached Penrith there were so many abandoned cars that the remaining traffic was almost gridlocked. I decided not to even try to reach home. I didn’t know if Sam had literally scanned my brain in Shanghai and used that to target what he’d done to me then, and whether or not he could use the same neuroanatomical information against me now, wherever I was, but staying away from my usual haunts seemed like one more small advantage to cling to.
I found a gas station, and it was giving priority to customers with functioning cars over hoarders who’d appeared on foot with empty cans.
Their EFTPOS wasn’t working, but I had enough cash for the gas and some chocolate bars.
As dusk fell the streetlights came on; the traffic lights had never stopped working. All four laptops were holding up, hurling their grenades into the far side. The closer the attack front came to simple arithmetic, the more resistance it would face from natural processes voting at the border for near-side results. Our enemy had their supercomputers; we had every atom of the Earth, following its billion-year-old version of the truth.
We had modeled this scenario. The sheer arithmetical inertia of all that matter would buy us time, but in the long run a coherent, sustained, computational attack could still force its way through.
How would we die? Losing consciousness first, feeling no pain? Or was the brain more robust than that? Would all the cells of our bodies start committing apoptosis, once their biochemical errors mounted up beyond repair? Maybe it would be just like radiation sickness. We’d be burned by decaying arithmetic, just as if it was nuclear fire.
My laptop beeped. I swerved off the road and parked on a stretch of concrete beside a dark shopfront. A new icon had appeared on the screen: the letter S.
Sam said, “Bruno, this was not my decision.”
“I believe you,” I said. “But if you’re just a messenger now, what’s your message?”
“If you give us what we asked for, we’ll stop the attack.”
“We’re hurting you, aren’t we?”
“We know we’re hurting you,” Sam replied. Point taken: we were guessing, firing blind. He didn’t have to ask about the damage we’d suffered.
I steeled myself, and followed the script the cabal had agreed upon.
“We’ll give you the algorithm, but only if you retreat back to the old border, and then seal it.”
Sam was silent for four long heartbeats.
“Seal it?”
“I think you know what I mean.” In Shanghai, when we’d used Luminous to try to ensure that Industrial Algebra could not exploit the defect, we’d contemplated trying to seal the border rather than eliminating the defect altogether. The voting effect could only shift the border if it was crinkled in such a way that propositions on one side could be outnumbered by those on the other side. It was possible—given enough time and computing power—to smooth the border, to iron it flat. Once that was done, everywhere, the whole thing would become immovable. No force in the universe could shift it again.
Sam said, “You want to leave us with no weapon against you, while you still have the power to harm us.”
“We won’t have that power for long. Once you know exactly what we’re using, you’ll find a way to block it.”
There was a long pause. Then, “Stop your attacks on us, and we’ll consider your proposal.”
“We’ll stop our attacks when you pull the border back to the point where our lives are no longer at risk.”
“How would you even know that we’ve done that?” Sam replied. I wasn’t sure if the condescension was in his tone or just his words, but either way I welcomed it. The lower the far side’s opinion of our abilities, the more attractive the deal became for them.
I said, “Then you’d better back up far enough for all our communications systems to recover. When I can get news reports and see that there are no more planes going down, no power plants exploding, then we’ll start the ceasefire.”
Silence again, stretching out beyond mere hesitancy. His icon was still there, though, the S unblinking. I clutched at my shoulder, hoping that the burning pain was just tension in the muscle.
Finally: “All right. We agree. We’ll start shifting the border.”
I drove around looking for an all-night convenience store that might have had an old analog TV sitting in a corner to keep the cashier awake—that seemed like a good bet to start working long before the wireless connection to my laptop—but Campbell beat me to it. New Zealand radio and TV were reporting that the “digital blackout” appeared to be lifting, and ten minutes later Alison announced that she had internet access. A lot of the major servers were still down, or their sites weirdly garbled, but Reuters was starting to post updates on the crisis.
Sam had kept his word, so we halted the counter-strikes. Alison read from the Reuters site as the news came in. Seventeen planes had crashed, and four trains. There’d been fatalities at an oil refinery, and half a dozen manufacturing plants. One analyst put the global death toll at five thousand and rising.
I muted the microphone on my laptop and spent thirty seconds shouting obscenities and punching the dashboard. Then I rejoined the cabal.
Yuen said, “I’ve been reviewing my notes. If my instinct is worth anything, the theorem I mentioned before is correct: if the border is sealed, they’ll have no way to touch us.”
“What about the upside for them?” Alison asked. “Do you think they can protect themselves against Tim’s algorithm, once they understand it?”
Yuen hesitated. “Yes and no. Any cluster of near-side truth values it injects into the far side will have a non-smooth border, so they’ll be able to remove it with sheer computing power. In that sense, they’ll never be defenseless. But I don’t see how there’s anything they can do to prevent the attacks in the first place.”
“Short of wiping us out,” Campbell said.
I heard an infant sobbing. Alison said, “That’s Laura. I’m alone here.
Give me five minutes.”
I buried my head in my arms. I still had no idea what the right course would have been. If we’d handed over Campbell’s algorithm immediately, might the good will that bought us have averted the war? Or would the same attack merely have come sooner? What criminal vanity had ever made the three of us think we could shoulder this responsibility on our own? Five thousand people were dead. The hawks who had taken over on the far side would weigh up our offer, and decide that they had no choice but to fight on.
And if the reluctant cabal had passed its burden to Canberra, to Zurich, to Beijing? Would there really have been peace? Or was I just wishing that there had been more hands steeped in the same blood, to share the guilt around?
The idea came from nowhere, sweeping away every other thought. I said, “Is there any reason why the far side has to stay connected?”
“Connected to what?” Campbell asked.
“Connected to itself. Connected topologically. They should be able to send down a spike, then withdraw it, but leave behind a bubble of altered truth values: a kind of outpost, sitting within the near side, with a perfect, smooth border making it impregnable. Right?”
Yuen said, “Perhaps. With both sides collaborating on the construction, that might be possible.”
“Then the question is, can we find a place where we can do that so that it kills off the chance to use Tim’s method completely—without crippling any process that we need just to survive?”
“Fuck you, Bruno!” Campbell exclaimed happily. “We give them one small Achilles tendon to slice ... and then they’ve got nothing to fear from us!”
Yuen said, “A watertight proof of something like that is going to take weeks, months.”
“Then we’d better start work. And we’d better feed Sam the first plausible conjecture we get, so they can use their own resources to help us with the proof.”
Alison came back online and greeted the suggestion with cautious approval. I drove around until I found a quiet coffee shop. Electronic banking still wasn’t working, and I had no cash left, but the waiter agreed to take my credit card number and a signed authority for a deduction of one hundred dollars; whatever I didn’t eat and drink would be his tip.
I sat in the café, blanking out the world, steeping myself in the mathematics. Sometimes the four of us worked on separate tasks; sometimes we paired up, dragging each other out of dead ends and ruts.
There were an infinite number of variations that could be made to Campbell’s algorithm, but hour by hour we whittled away at the concept, finding the common ground that no version of the weapon could do without.
By four in the morning, we had a strong conjecture. I called Sam, and explained what we were hoping to achieve.
He said, “This is a good idea. We’ll consider it.”
The café closed. I sat in the car for a while, drained and numb, then I called Kate to find out where she was. A couple had given her a lift almost as far as Penrith, and when their car failed she’d walked the rest of the way home.
For close to four days, I spent most of my waking hours just sitting at my desk, watching as a wave of red inched its way across a map of the defect. The change of hue was not being rendered lightly; before each pixel turned red, twelve separate computers needed to confirm that the region of the border it represented was flat.
On the fifth day, Sam shut off his computers and allowed us to mount an attack from our side on the narrow corridor linking the bulk of the far side with the small enclave that now surrounded our Achilles’ Heel. We wouldn’t have suffered any real loss of essential arithmetic if this slender thread had remained, but keeping the corridor both small and impregnable had turned out to be impossible. The original plan was the only route to finality: to seal the border perfectly, the far side proper could not remain linked to its offshoot.
In the next stage, the two sides worked together to seal the enclave completely, polishing the scar where its umbilical had been sheared away.
When that task was complete, the map showed it as a single burnished ruby. No known process could reshape it now. Campbell’s method could have breached its border without touching it, reaching inside to reclaim it from within—but Campbell’s method was exactly what this jewel ruled out.
At the other end of the vanished umbilical, Sam’s machines set to work smoothing away the blemish. By early evening that, too, was done.
Only one tiny flaw in the border remained now: the handful of propositions that enabled communication between the two sides. The cabal had debated the fate of this for hours. So long as this small wrinkle persisted, in principle it could be used to unravel everything, to mobilize the entire border again. It was true that, compared to the border as a whole, it would be relatively easy to monitor and defend such a small site, but a sustained burst of brute-force computing from either side could still overpower any resistance and exploit it.
In the end, Sam’s political masters had made the decision for us.
What they had always aspired to was certainty, and even if their strength favored them, this wasn’t a gamble they were prepared to take.
I said, “Good luck with the future.”
“Good luck to Sparseland,” Sam replied. I believed he’d tried to hold out against the hawks, but I’d never been certain of his friendship. When his icon faded from my screen, I felt more relief than regret.
I’d learned the hard way not to assume that anything was permanent.
Perhaps in a thousand years, someone would discover that Campbell’s model was just an approximation to something deeper, and find a way to fracture these allegedly perfect walls. With any luck, by then both sides might also be better prepared to find a way to co-exist.
I found Kate sitting in the kitchen. I said, “I can answer your questions now, if that’s what you want.” On the morning after the disaster, I’d promised her this time would come—within weeks, not months—and she’d agreed to stay with me until it did.
She thought for a while.
“Did you have something to do with what happened last week?”
“Yes.”
“Are you saying you unleashed the virus? You’re the terrorist they’re looking for?” To my great relief, she asked this in roughly the tone she might have used if I’d claimed to be Genghis Khan.
“No, I’m not the cause of what happened. It was my job to try and stop it, and I failed. But it wasn’t any kind of computer virus.”
She searched my face. “What was it, then? Can you explain that to me?”
“It’s a long story.”
“I don’t care. We’ve got all night.”
I said, “It started in university. With an idea of Alison’s. One brilliant, beautiful, crazy idea.”
Kate looked away, her face flushing, as if I’d said something deliberately humiliating. She knew I was not a mass murderer. But there were other things about me of which she was less sure.
“The story starts with Alison,” I said. “But it ends here, with you.”
GLORY
1
An ingot of metallic hydrogen gleamed in the starlight, a narrow cylinder half a meter long with a mass of about a kilogram. To the naked eye it was a dense, solid object, but its lattice of tiny nuclei immersed in an insubstantial fog of electrons was one part matter to two hundred trillion parts empty space. A short distance away was a second ingot, apparently identical to the first, but composed of antihydrogen.
A sequence of finely tuned gamma rays flooded into both cylinders. The protons that absorbed them in the first ingot spat out positrons and were transformed into neutrons, breaking their bonds to the electron cloud that glued them in place. In the second ingot, antiprotons became antineutrons.
