Stephen Baxter - Starfall

The flitter slid briskly into the atmosphere, and descended towards the east coast of America. They were making for New York, a great city for three thousand years and now the capital of the Empire of Sol; the Shiras' world government had inherited some of the apparatus of the ancient United Nations.

They came down on a small landing pad near the centre of Central Park, close to a cluster of small buildings. Stillich and Pella emerged into the sunshine of a Manhattan spring. Flitters darted between the shoulders of ancient skyscrapers at the rim of the park. The sky above was laced by high, fluffy clouds. And beyond the clouds you could see crawling points of light: the habitats and factories of near-Earth space.

A hovering bot met them, done out in the imperial government's golden livery. They followed it to the nearest of the buildings. This, Stillich knew, was a portal to the complex of bunkers built into the granite keel of Manhattan, far beneath the green surface of the park; this was the gateway to the Empress's palace.

Pella was peering about curiously. "So this is the future."

Stillich asked, "So how are you feeling?"

"Not as disoriented as I expected. Twenty-seven years on, things look the same./I They watched a couple walking with their hands locked together, a young family playing with some kind of smart ball that evaded laughing children. Pella said, "Maybe the clothes are different. The trim on that flitter parked over there."

Stillich shrugged. "There's a kind of inertia about things. Much of this building stock is very ancient; that won't change short of a major calamity. Technology doesn't change much, on the surface; innovations in Virtual tech won't make much difference to the user interface, which optimised centuries ago. But fashions in clothes, vehicles, music and arts—they are mutable. The language shifts a little bit too; that might surprise you. But the fundamentals stay the same ... Of course AS helps with that."

AntiSenescence treatments had been available to everybody on the planet for millennia, but long lives hadn't led to social stasis. In practice you abandoned AS after a few centuries, if you were lucky enough to avoid misadventure that long. After seeing four or five or six generations grow up after you, you felt it was time to make room. So in among the smooth faces of the elderly there were always the true-young, with new thinking, new ideas, a balance between wisdom and innovation.

It was striking, though, that recruits to the armed services were always the very young. Only the young thought they were immortal, a necessary prerequisite to go to war; the old knew they were not. And for the young, twenty-seven years away was a long time.

"Have you spoken to your family yet?/I he asked Pella.

Pella grimaced. "My mother looks younger than I do. My father had the decency to age, but they divorced, and he has a whole new family I never met. I did answer the mails, but—you know."

"It's hard to make small talk."

"Yes, sir."

"You have the orientation packs from the ship. They should help. And the Navy has counsellors. The main thing to remember, and I know this is a bad time to say it, don't just hide away in work."

"As you do, sir."

Stillich grimaced. Well, that was true. But his excuse was he had no family, outside a son who he had never really got along with, and who had now actually lived more subjective years than he had. "I'm not necessarily a good role model, Number One."

"I'm sorry, sir. I'm sure I'll be able to adjust to the time slip just fine," Pella said dutifully.

"Glad to hear it, Commander," came a gruff voice from the shadow of the portal. "But the question is, are you up to meeting an admiral?"

They both snapped to attention.

Admiral Finmer Kale stepped forward. He was a robust man, AS-frozen at an imposing fifty—just as Stillich remembered him from twenty-seven years before. And the sunburst sigil on his uniform seemed to shine brighter than the sun itself. "At ease, both of you."

"Sir, it's an honour to meet you again."

"Well, it's been a quarter of a century for me, Captain Stillich, and you're still just as much a pain in the butt as you always were, or I wouldn't be here today. Come on, follow me."

They stepped out of the sunshine into a steel-walled elevator. The doors slid closed, and the cabin dropped smoothly.

"I have to tell you, Stillich, that I endorse none of the conclusions of your analysis. This nonsense about an imminent attack from Alpha."

"I defer to your wisdom, sir."

"Unfortunately you've got a fan at an even more elevated position than an Admiral of the Fleet. Which is why you've been summoned to the Palace, and not Navy HQ." He grinned at Pella. "Actually I asked you the wrong question, Commander. It's not an admiral you need to be ready to meet, but an Empress."

Pella's mouth dropped open.

The doors slid wide.

They stepped cautiously into a chamber, steel-walled like the elevator. It was centred on a glowing slab of light, metres wide, set into the floor, like a swimming pool. The room itself was bare of adornment, with no furniture save a handful of hard-backed chairs. There was nobody here.

"You're honoured," said the Admiral with a trace of envy. "Both of you. This is one of her inner sanctums. I've never been here before. I guess my advice was never crackpot enough to attract her attention. I'd keep away from the logic pool if I were you, Commander. The Empress shipped it all the way from what's left of Nereid, moon of Neptune, and she'd be most upset if you fell in."

"What," Pella asked, clearly fascinated, "is a logic pool?"

They all stepped forward to look. Within the glowing floor, light wriggled, wormlike.

The Admiral said, "The interior is a lattice of buckytubes—carbon—laced with iron nuclei. It's a kind of data store, constructed by the nanobots that excreted the lattice, patient little workers, billions of them. There is an immense amount of data here, waiting to be mined out."

Pella looked blank. "Data on what?"

"Metamathematics."

"Sir?"

Stillich had heard something of this obsession of the Empress's. "Number One, this pool was created by a rogue scientist called Highsmith Marsden. This was over a millennium ago. His data stores, when discovered on Nereid, contained a fragmented catalogue of mathematical variants. All founded on the postulates of arithmetic, but differing in their resolution of undecidable hypotheses."

"Undecidability. You're talking about the incompleteness theorems," Pella said.

"Right. No logical system rich enough to contain the axioms of simple arithmetic can ever be made complete. It is always possible to construct statements which can be neither disproved nor proved by deduction from the axioms. Instead your logical system must be enriched by incorporating the truth or falsehood of such statements as additional axioms ... "

Pella said, "So one can generate many versions of mathematics, by adding these true-false axioms."

"Yes. Because of incompleteness, there is an infinite number of such mathematical variants, spreading like the branches of a tree ... It seems that Marsden was compiling an immense catalogue of increasingly complete logical systems."

"Why?"

The Admiral grinned. "Why not? There is an immense mathematical universe to be explored in there, Commander."

"So what became of Marsden?"

"He was working illegally, under the sentience laws of his day."

"What's sentience got to do with it?"

"Everything." The new voice was faint.

There was a whir of servomotors. Empress Shira XXXII entered the room, a thin body wrapped in a sky-blue blanket, riding a golden wheelchair. They all bowed, but Shira shook her head, a minute gesture, irritated. "There is no need to prostrate yourself. We are here to work."