"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."
Stillich dared to look upon his Empress. Her features were delicate, her build thin to the point of scrawny under her blanket. Her scalp was clean-shaven, and Stillich found it hard not to stare at the clean lines of her skull. Her skin was sallow, her dark-rimmed eyes blue, huge and apparently lash less; her face, with prominent teeth and cheekbones, was skeletal.
The Empress said, "You, girl. You were curious."
Stillich admired Pella's cool as she replied. "Yes, ma'am. You said—sentience?"
"There is sentience in this logic pool." Shira rolled forward, her eyes reflecting the cold light of the pool. "I barely understand it myself. Those structures of light are intelligent. Living things—but artificial—inhabiting the buckytube lattice, living and dying in a metamathematical atmosphere, splitting off from one another like amoebae as they absorb undecidable postulates. It's a mathematical breeding tank, Commander."
"Yes, ma'am."
Stillich stared at the pool of light. He longed to know what Shira could be doing here, playing with this strange, ancient tank of once-illegal sentience, a pool of metamathematics. Especially since, Stillich knew, the inventor of this logic pool, Highsmith Marsden, had got himself killed by it. But an empress could do what she liked.
Shira turned to Stillich. "You have been sending back some very disturbing reports, Captain Stillich, from out among the stars. Despite the Admiral's best advice, I think we have much to discuss."
Stillich had not expected to be briefing the Empress. He glanced at the Admiral.
Kale spread his hands. "Go ahead, Captain, it's your show." He pulled up a chair and sat down.
Stillich licked his lips. "Very well, ma'am ... /I With the backup of text and Virtual graphics projected from Pella's desk, he summarised his gathering suspicions about the intent of the colonists at Alpha, seeded by his discovery of the reconstituted GUTships at Tau Ceti.
It had been hard to get firm data on the number of GUTships actually operating in Alpha system or elsewhere at this time. Ships supposedly cannibalised for colony building were formally decommissioned, and appeared on no imperial registers. Besides, it had been a number of years since a Navy ship had visited Alpha system. There were permanently based imperial agents, and the system was full of observation drones, but Pella had discovered that this surveillance had a number of blind spots—most noticeably in low orbit around Footprint, the principal colony world.
Admiral Kale said, "The existence of a blind spot doesn't prove there's a threat hiding in it, Captain."
"Of course not, sir. But still, we're blind there, we just don't know. Then there's the damage to Port Sol."
"An accident. Coincidence."
"Perhaps—but a convenient one." Stillich glanced at the Empress. "As for defence, we actually have few serviceable GUTships in Sol system, ma'am, aside from the interstellar cruisers like the Facula. Because of the wormhole network, there's no need for them; in fact we're still flying some antiques that date from the age of Poole a thousand years ago. And with Port Sol knocked out we don't have the facility to construct more, should we need them."
"'Should we need them'," she repeated.
Admiral Kale pulled his lip. "Ma'am, Captain Stillich is a conscientious young officer. But I have to say that Navy analysts don't concur with the case he is making here. He's stringing together coincidences to make a case for a coming rebellion for which we have no hard evidence. After all an interstellar war has always seemed inconceivable, at least with sublight technology. This is why we blew the interstellar wormholes decades back—a shell of empty space light years thick is our best defence against any uppity starborn. To imagine you could mount a campaign across light years, where a single transit takes years, and just as long even to return messages back to the home base—"
Shira's chair wheeled her back and forth, an oddly restless motion, though she sat as still as ever. "But Stillich has been out there. He has seen these 'rebellious' colonists with his own eyes. An invasion may be low risk. But given the disastrous consequences, it would be remiss of me not to listen, wouldn't it?" She turned to Stillich, servomotors purring. "So what must we do, Captain? Shall I dispatch my Navy?"
"Ma'am, it may already be too late for that. It may be the best course to keep the Navy in Sol system to meet any threat."
"A threat that may already be on its way."
"We must prepare for the worst case—yes."
"So what would you have me do?"
Stillich had Pella throw up some Virtual images - schematic maps of Sol system and its environs. "My strategy would be threefold, ma'am: detect, defend, dig in. We should watch for them coming. Send up or rededicate telescopes to hunt for GUTdrive emissions—gamma radiation, neutrinos. It's a distinctive spectrum. Use optical telescopes to look out for solar sail craft—try to spot them any way they might come."
"And if they do come, how do we defend ourselves?"
"Surely Earth will be the prime target. We need to consider a layered defence. Station ships and weapons stashes across the system. Use resource nodes like Titan, Jupiter's orbit, the Trojan asteroids—"
"Of course," Kale said, "if they do come from Alpha system it will be from out of the ecliptic, the plane of Sol system. That will make it harder still"
Stillich said, "Earth itself is obviously quite vulnerable. Earth has a massive population, yet almost all that sustains it—power, food—comes from space. Most of Earth's food is imported from Titan—a moon of Saturn. Even our communications links are space-based. If we were cut off from space resources—"
"And so we dig in," Shira said.
"Lay in reserves of food, clean water, medical supplies. Try to set up or restore power systems on the surface or underground. Communications—set up an emergency land-based network, using hardened optical fibre links."
Kale smiled. "We will be raiding the museums!"
"The point is to make the planet independent of space resources, at least for a period of a siege."
Shira said, "You are conjuring up apocalyptic images, Captain."
"That's not my intention," Stillich said firmly. "The invaders will be far from home, dependent on the resources they have brought with them across light years; they will be a few thousand facing a population of billions. They will be able to strike blows, for they will have the advantage of the high ground. But if we can deny them resupply, we can starve them out—it will be the Alphans under siege. We can win this war, ma'am, if it comes, but only if we prepare."