Over the last three months, we’d worked out a way to augment our internet “telescope” software to launch a barrage of Campbell-style attacks on far-side propositions if it saw our own mathematics being encroached upon. The software couldn’t protect the whole border, but there were millions of individual trigger points, forming a randomly shifting minefield. The plan had been to buy ourselves some security, without ever reaching the point of actual retaliation. We’d been waiting to complete a final round of tests before unleashing this version live on the net, but it would only take a matter of minutes to get it up and running.
“Anything being hit besides financials?” I asked.
“Not that I’m picking up.”
If the far side was deliberately targeting the markets, that was infinitely preferable to the alternative: that financial systems had simply been the most fragile objects in the path of a much broader assault. Most modern engineering and aeronautical systems were more interested in resorting to fall-backs than agonizing over their failures. A bank’s computer might declare itself irretrievably compromised and shut down completely, the instant certain totals failed to reconcile; those in a chemical plant or an airliner would be designed to fail more gracefully, trying simpler alternatives and bringing all available humans into the loop.
I said, “Yuen and Tim—?”
“Both on board,” Alison confirmed. “Monitoring the deployment, ready to tweak the software if necessary.”
“Good. You really won’t need me at all, then, will you?”
Alison’s reply dissolved into digital noise, and the connection cut out. I refused to read anything sinister into that; given my location, I was lucky to have any coverage at all. I ran faster, trying not to think about the time in Shanghai when Sam had taken a mathematical scalpel to all of our brains. Luminous had been screaming out our position like a beacon; we would not be so easy to locate this time. Still, with a cruder approach, the hawks could take a hatchet to everyone’s head.
Would they go that far?
Only if this was meant as much more than a threat, much more than intimidation to make us hand over Campbell’s algorithm. Only if this was the end game: no warning, no negotiations, just Sparseland wiped off the map forever.
Fifteen minutes after Alison’s call, I reached the car. Apart from the entertainment console it didn’t contain a single microchip; I remembered the salesman laughing when I’d queried that twice. “What are you afraid of? Y3K?” The engine started immediately.
I had an ancient second-hand laptop in the trunk; I put it beside me on the passenger seat and started it booting up while I drove out on to the access road, heading for the highway. Alison and I had worked for a fortnight on a stripped-down operating system, as simple and robust as possible, to run on these old computers; if the far side kept reaching down from the arithmetic stratosphere, these would be like concrete bunkers compared to the glass skyscrapers of more modern machines. The four of us would also be running different versions of the OS, on CPUs with different instruction sets; our bunkers were scattered mathematically as well as geographically.
As I drove on to the highway, my watch stuttered back to life. Alison said, “Bruno? Can you hear me?”
“Go ahead.”
“Three passenger jets have crashed,” she said. “Poland, Indonesia, South Africa.”
I was dazed. Ten years before, when I’d tried to bulldoze his whole mathematical world into the sea, Sam had spared my life. Now the far side was slaughtering innocents.
“Is our minefield up?”
“It’s been up for ten minutes, but nothing’s tripped it yet.”
“You think they’re steering through it?”
Alison hesitated. “I don’t see how. There’s no way to predict a safe path.” We were using a quantum noise server to randomize the propositions we tested.
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 ninety 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 petrol 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 petrol 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 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.”