Greg Egan - SS - Dark Integers.pdf

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DARK INTEGERS
by Greg Egan
Our new story from Greg Egan is a stand-alone tale that follows on
the events of “Luminous” (September 1995). It’s also the first story
we’ve seen from Greg since “Oracle” appeared in our July 2000
issue. The author tells us, though, that “after spending a few years
away from writing, trying to assist some of the asylum seekers that
Australia imprisons in remote detention centers, I recently
completed my seventh SF novel, Incandescence, which is due to be
published by Gollancz in the UK in May 2008.” We hope that this
return to writing means we’ll soon be seeing more of his brilliant
fiction.
* * * *
“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 impression 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 hotheads,” 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 Zurich 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 so 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 okay 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
respectable 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.
 

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