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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 have been dragged 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, however. 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 looked cautiously, without stepping closer. Within the glowing liquid, 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 that is 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. But he did not live to be charged.’

‘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 yourselves. We are here to work.’

Stillich dared to look upon his Empress. Her build was thin to the point of scrawny under her blanket. Her skin was sallow, her dark-rimmed eyes blue, huge and apparently lashless; her face, with prominent teeth and cheekbones, was skeletal. Her scalp was shaven, and Stillich found it hard not to stare at the clean lines of her skull.

The Empress said, ‘You, girl. You were curious about sentience.’

Stillich admired Pella’s cool as she replied. ‘Yes, ma’am.’

‘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 – in fact of logic – 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 breeding tank, Commander. And what it breeds are intelligences constructed of mathematical statements.’

‘Yes, ma’am.’

Stillich was proud of his subordinate’s dry, controlled response. He 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 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 herself. 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 . . .’ With the back-up of text and Virtual graphics projected from Pella’s data desk, he summarised his gathering suspicions about the intent of the colonists at Alpha, seeded by his suspicion 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. For one thing, ships supposedly cannibalised for colony buildings 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 just don’t know. And there are so many blind spots. My report on the Tau Ceti colony—’

‘Noted,’ Kale said briskly.

‘Then there’s the damage to Port Sol.’

‘An accident. Coincidence.’

‘Perhaps – but a convenient one.’ Stillich glanced at the Empress. ‘We actually have very few serviceable GUTships in the Solar System, ma’am, aside from interstellar cruisers like the Facula. Because of the in-System 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.’