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And when he added, ‘Welcome to GCHQ. Or rather, welcome back,’ his tone was only marginally warmer than neutral, mildly marking her re-entrance to the covert world.

FIFTY-SEVEN

MOLSIN 2603 AD

The maths was more painful than the fighting.

‘I can’t do this.’ Roger minimized the holo display. ‘Really, I can’t.’

They were sitting cross-legged on the quickglass floor, facing each other. Without the holo phase space and subsidiary equations glowing in mid-air, their mutual view was unobstructed.

‘It’s only a form of fear that holds you back,’ she said. ‘Are you open to a motivational technique?’

‘What kind of technique?’ he asked.

‘There are all sorts of mental states we can usefully distinguish.’ Reflected lights slid across Rhianna’s polished-jet eyes. ‘Being lost in a holodrama – very trance-like – or fascinated by abstract geometry or fearfully aware of physical danger. They’re all useful states in context, all worth triggering when appropriate. Agreed?’

‘Er, yes.’

Roger had grown wary of agreeing with her. It seemed to indicate a short path to a situation he was not going to like.

‘So here’s my psychological technique,’ said Rhianna, ‘for encouraging you to become fascinated with maths. All right?’

‘Um, OK.’

‘You’re ready for this technique?’

Saliva was doing odd things inside his throat.

‘I … Right.’

‘Brace yourself. Here it is.’

He held himself ready.

‘If you don’t solve the Lockwood equations,’ said Rhianna, ‘I will beat the fucking shit out of you.’

‘Er …’

Her knuckles cracked as she made fists.

‘Are we motivated yet?’

They were four days into the training. Roger checked through the inverse-power-law high-connection web that modelled the surveillance network Rhianna was tapped into – not just in Deltaville and Barbour, but in other sky-cities. It was a robust set-up, and he told her so.

‘But we haven’t caught sight of Helsen, have we?’ said Rhianna. ‘What do you think that means?’

‘That she’s not stupid. Specifically’ – he knew Rhianna would want an explanation – ‘she’s done the same kind of analysis, matching surveillance coverage to connectedness, and exploited the, er, dark areas. The places no one watches.’

He had come to another conclusion. Rhianna had helped ensure that no Zajinets or other Pilots remained on Molsin, thereby isolating Helsen and Ranulph, confining them to this world. It was better for the risk to be here, known and imminent, than on some other planet, unknown to those who lived there.

Roger did not want to die, but beyond that, he would have hesitated rather than risk Leeja’s life, even Tannier’s. Rhianna would have understood precisely what was going on; and he was sure that she would commit suicide before allowing darkness-controlled people to seize her ship … assuming she had one. Perhaps she was one of the Shipless (he dared not ask), requiring others to transport her. If anything, it might make her a better agent-in-place than Dad had been, always pining for his own ship.

Just as Roger missed his ship, child though she was, not big enough to fly for real.

‘We’ll make a true Pilot out of you,’ said Rhianna. ‘Back in Labyrinth, when this is over.’

He was getting used to her spooky manner of deducing thoughts. Then he processed the plural pronoun.

‘But you’re …’ Roger thought about it. ‘Dad was in place for decades. On Fulgor, I mean.’

‘I have to consider myself compromised.’ Rhianna popped open several holo-volumes. ‘Tannier is a good man, and I’m sure his superiors are good people. But someone will talk, even if the immediate group choose to protect me. Which I doubt.’

‘Not even if you move to another sky-city?’

‘Ah.’ Rhianna smiled. ‘I rather fancy living on Yukawa. But I think I’m done here.’

‘My fault.’

‘No, it’s the nature of the job. As you well know, and well done for keeping control of the conversation.’

‘What do you mean?’

‘I mean’ – Rhianna caused the holos to grow and brighten – ‘you’re trying to avoid more maths.’

Roger smiled. ‘Maybe.’

‘Yeah, well. Start by telling me what these pictures have in common. Keep it easy and conceptual, and we’ll get to the hairy equations shortly.’

That suited him. One by one he checked the holos: fireflies pulsing in a forest, wind-rays billowing and brightening above paramagnetic sands, the planet Mercury and Earth’s moon in their respective orbits, a swaying rope bridge as a party of tourists marched along it—

‘Resonance,’ he said, without examining the rest. ‘Synchronization caused by feedback.’

It was a universal property in so many contexts, from the quantum realm to entire worlds, like Mercury whose orbit and axial rotation were phase-locked, its year and day identical. Put two pendulum clocks together and they alter their swings until they are in opposite lock-step. Let the same effect occur in cardiac cells and you have a heart that knows how to beat in rhythm.

‘Give me some more examples of negative feedback adjusting towards resonance.’

‘Well, there’s—’

‘With equations now,’ said Rhianna. ‘Come on.’

‘Oh. Right.’

Later they stared at a holo depicting Fulgor.

‘Here be dragons,’ said Rhianna. ‘The place no ship dares to approach.’

‘Shouldn’t we be doing some modelling?’ asked Roger. ‘You know, maths? Those equations I love to formulate?’

‘Feeling more confident, are we? Well, good enough. Cheek your elders and betters, why don’t you.’

The more Roger grew used to her bullying, the less she seemed to do it.

‘We don’t know how far the Anomaly can reach through the hyperdimensions,’ he said. ‘Is that it? We haven’t got a critical parameter for the model.’

‘Maximum range is of the order of tens of kilometres in the main three dimensions.’ Rhianna enlarged the holo. ‘No doubt the Admiralty will have posted ships beyond that range. And other observers at successive distances further out, just in case we got it wrong.’

Cold-blooded but sensible.

‘So we’re safe,’ said Roger, ‘as long as we quarantine the planet.’

‘Molsin was under quarantine, but the bastard Zajinets still appeared.’

‘They hate the darkness more than we do.’

‘Maybe they’re not the problem, though I hate to say so.’

Alone and with time to think, Roger pondered while flexing his hand. The forearm felt intact, thanks to Rhianna’s ministrations after her armbar technique had snapped the bone through. Long-molecule arrays formed of smartatoms were aggregated into a lattice that held everything in place, promoting and directing the healing process. As the new cells formed, the smartatoms would pull away, dissolving themselves.

Resonance, global synchrony from local feedback, enabled the aggregated arrays to work as if collectively intelligent. Whether the Anomaly functioned like that, resonating from one component to another like pendulums in step, no one knew for sure. But reasoning from mathematical principles, it seemed likely.

Can you use maths that way?

The history of computation had been an odd subject, taught in Fulgidi schools at age twelve standard. Centuries ago, early software had been cobbled together more than mathematically designed, even though symbolic logic and set theory were well understood long before the mathematics of cohenstewart discontinuities and other forms of emergent phenomena. It was a wonder the old systems had ever worked at all.

And while AI had been a success for more than a century, it became subsumed in other technology – such as quickglass – and largely forgotten (while a part of Roger’s mind noted that Ai had been the forefather of the race of serfs, just as Fathir and Mothir had produced the noble-born). Nowadays system studies tended towards the descriptiveness of ecoscience as much as the prescriptiveness of engineering disciplines.

What the Fulgidi educational system did not address was the study of war.

Labyrinth must be different.