The Arrows of Time: Orthogonal Book Three (49 page)

She waited; the stars moved by serenely.

A dark speck interrupted the blaze of the colour trails. Agata didn’t wait to guess its nature; she pushed away and let herself fall. As she plummeted beside the rock face she hunted for
the occulter and found it again. It was almost level with her, hewing close to the rock just a saunter away. She started her jetpack and began arresting her fall, just in time – the thing was
above her now. She drew an arrow on her chest, angled in anticipation, and rose to meet the machine.

She collided with it, her arms outstretched, grabbed it and held it fast. They tumbled together and struck the rock; the mountain scraped at her shoulder, shredding fabric and skin. Agata
shouted from the pain and tried to form an arrow that would lift her clear, but nothing happened. Her jetpack was gone, smashed and torn away.

The half-circle of dawning stars wheeled around her. Agata looked directly at the thing in her embrace; she could feel its feeble puffs of air trying to get it back on course. All she could do
was apply whatever muscular force she had left and hope that would be enough to propel it out of range.

Her left arm was useless after the blow from the mountain, but she managed to bring her legs up and brace her feet against the stone box. She watched the stars spinning, and thought her way into
their cycle. Then she pushed her legs out and drove the occulter away.

The recoil slammed her against the rock. She closed her eyes as the mountain tore into her body.

A light appeared, penetrating her eyelids, filling her skull. Agata embraced the radiance and vanished.

‘One day there’ll be a whole set of synthetic influences that we can administer with a photonic device,’ Maddalena predicted. ‘There’ll be tools
for every occasion, but the best will be the one that forces the recipient to tell the truth.’

‘That’s your vision of the future, is it? That’s what you’ve taken away from all this?’ Ramiro stopped himself; whether she was goading him deliberately or not, he
was wasting his energy. ‘Just sign the release form and I’ll get out of your way.’

‘There’ll still be a trial,’ Maddalena insisted stubbornly. ‘You know we can implicate her in the sabotage.’

‘Whatever you say.’

Maddalena sprinkled dye on her palm and signed the form. Having released the longest-serving untried prisoners, the Council, even in its death throes, was still fighting every smaller
concession. Nobody in the mountain was quite sure what Tarquinia had or hadn’t done, but compared to four years without trial, four stints did not evoke quite so much passion. Ramiro had had
the money for a bond himself, but it had taken all his time to collect the requisite eight dozen signatures from disinterested travellers willing to attest that her ongoing imprisonment offended
their sense of justice.

He left Maddalena’s office and headed for the jail.

At the guard post there was more bureaucracy to deal with. Ramiro tried to stay calm as all the paperwork he’d lodged was scrutinised and complained about and the associated photonic
records summoned, peered at and misunderstood.

After half a bell of this idiocy, the guard told him, ‘Just wait now. We’re bringing her out.’

Ramiro watched her gait as she emerged. If she’d been shackled, she showed no sign of it now. He dragged himself forward and embraced her.

‘Are you all right?’

‘You know what they say,’ Tarquinia replied. ‘There’s no greater honour than following Yalda, mother of all prisoners.’

Ramiro wasn’t sure if she was being sarcastic.

‘What did you hear about the disruption?’ he asked, as they moved away down the corridor, side by side on the guide ropes.

‘Explosions at the base. People coming and going from the void. The confused version everyone got in the aftermath – that’s all, no details.’

Ramiro said, ‘Two of the tubes were breached at the base, but they were resealed in time. Giacomo’s group had their own occulters; they would have torn open the axis if they
could.’

Tarquinia had thought things over for too long to be surprised by the betrayal. ‘What stopped them?’

‘Agata,’ Ramiro replied. ‘With a couple of dozen friends. They went out onto the base and tossed the bombs into the sky. Only three light collectors were physically damaged. It
was the flash from the explosions that caused the disruption.’

Tarquinia absorbed that in silence.

‘They saved the
Peerless
,’ Ramiro said. His gratitude was sincere, but he still felt like a hypocrite.

‘Was anyone hurt?’

‘Agata lost a lot of flesh. For a couple of stints no one thought she’d survive, but she’s finally recovering.’

Tarquinia hummed softly. ‘Can we visit her?’

‘Of course.’

As they dragged themselves towards the nearest stairwell, Tarquinia recounted her own misadventure. ‘They let me have the observing time, and everything was looking perfect, but then the
most officious busybody among my colleagues decided to check in on me just when I was inspecting the jetpack from the emergency kit. She decided that was suspicious enough to execute a
citizen’s arrest; most of the other staff thought she was an idiot, but she had an ally. I was afraid that if I was released, the two of them would be disgruntled enough to make a real effort
to get the attention of someone with the power to mention the incident in an official message.’

‘And then the Council would have known from the start.’ The whole crew would have been under close surveillance from the moment the
Surveyor
arrived.

‘Exactly.’ Tarquinia buzzed. ‘So I ended up having to let myself be detained in a room at the observatory, with the idiots kept busy watching over me and arguing with my
colleagues who wanted me released. It was only after the disruption that they managed to get the security department involved.’

They’d reached the level of the hospital; it was just a short walk up-axis now. Ramiro said, ‘Before we see Agata, there’s something I need to tell you.’ He explained his
debunking of the hoax. ‘Don’t be angry with me,’ he pleaded. ‘The whole thing about the ancestors was making her crazy.’

Tarquinia said, ‘I’m not angry, but you shouldn’t have told her that.’

‘Why not?’

‘I didn’t make the inscription,’ Tarquinia declared. ‘I went out there to try, but nothing happened: no shards of stone rose from the ground to meet the chisel. I tried
different tools, different movements . . . but I couldn’t unwrite those symbols. If anything, when I left they were sharper than I’d found them – as if all I’d done was make
the message less clear for Agata and Azelio than if I’d stayed away completely. I wasn’t the author of those words. Someone else must be responsible for them.’

Ramiro didn’t know if she was telling the truth or just trying to hold on to the benefits of the hoax, but he wasn’t going to start questioning her version of events now. If this was
her story, there was nothing he’d seen with his own eyes that contradicted it.

When they entered the hospital ward, Agata caught sight of Tarquinia and called out excitedly, ‘Ah, you’re free! Congratulations! Come and hear some great
news!’

As they approached the sand bed, Ramiro could see that Agata had gained some flesh since his last visit, but she was still limbless. The doctors had told him that she would need every scrag of
tissue to support her recovering digestive tract.

‘What’s the news?’ Tarquinia asked her.

‘I just had a visit from Lila and her student Pelagia,’ Agata replied. ‘The innovation block is well and truly over!’

‘Yeah?’ Tarquinia had probably been expecting to spend the whole visit trying to put the record straight about the inscription, but Agata’s mind was on something else
entirely.

‘Pelagia’s settled the topology question,’ Agata proclaimed. ‘The cosmos is a four-dimensional sphere. It’s not a torus – it can’t be!’

‘This is from your work?’ Ramiro asked. ‘Pelagia found a way to complete the calculations?’

‘Not so much complete them as see into my blind spot,’ Agata explained. ‘Listen, it’s simple. A luxagen is described by a wave that changes sign when you rotate it by a
full turn. That has no effect on any probability you calculate – so long as you apply the same rotation to everything in sight – because the probability comes from squaring the value of
the wave. Minus one squared is one, so the change of sign makes no difference. It only shows up in more complicated experiments where you rotate some things and leave others unaltered.’

Tarquinia said, ‘I follow that much.’

‘Pelagia’s idea just replaces rotations with trips around the cosmos. Suppose the cosmos were a four-dimensional torus, and you carried a luxagen all the way around it in a giant
loop. What happens to the sign of its wave? Does it come back unchanged, or does it come back reversed?’

Ramiro frowned. ‘I can tell that you want us to say “reversed” by analogy, but I thought there had to be perfect agreement around a loop.’

Agata buzzed. ‘I didn’t want you to give either answer. There could be perfect agreement, or the sign could be reversed: nothing rules out either possibility. If the sign’s
reversed, that will be undetectable: everything you can measure locally will still be in perfect agreement.’

Tarquinia said, ‘Hang on, if the sign changes . . . where exactly does it change? What’s this special place on the torus where it flips over?’

‘There is no special place,’ Agata insisted. ‘It’s like cutting open a band and rejoining the ends with a twist: once you’ve glued them together, there’s
really nothing special going on at the join. The twist isn’t located there – or anywhere. It’s a property of the whole band.’

Agata began to form a sketch, but Ramiro saw that she was having trouble so he drew what she’d described on his own chest.

‘So you’re talking about the cosmos being some kind of . . . twisted torus?’ Tarquinia asked.

‘No, not the cosmos,’ Agata replied. ‘The two bands, twisted or not, both have identical circles as their midlines—’

Ramiro added the midlines to his diagram.

‘—and you should think of
those circles
as the cosmos. What happens with the bands is an additional structure that the topology of the cosmos doesn’t
fix, one way or the other. It’s all about the luxagens, not space itself.’

Tarquinia said, ‘All right. I think I’ve got it.’

‘Then the next step is to remember that we’re talking about a
four-dimensional
torus,’ Agata continued. ‘So there are four completely different ways you can
travel in a loop. There’s nothing that compels those four routes to have the same effect – it would be perfectly consistent to have a luxagen whose sign changed around some of those
loops but not the others. So there are sixteen possibilities altogether: for each loop, the sign might change or it might not.’

Ramiro understood the counting argument, but he couldn’t see where it was leading. ‘Aren’t these distinctions all invisible, though? They have no effect on any
probabilities.’

‘They have no effect on probabilities,’ Agata agreed. ‘But if there were sixteen times more choices for the state of every luxagen, that would multiply their contribution to
the vacuum energy by a factor of sixteen. Photons give a positive vacuum energy, but luxagens make the vacuum energy negative, and a factor of sixteen would be enough to guarantee that the total
energy density in the cosmos was negative,
absolutely everywhere
.’

Ramiro struggled to recall the implications of this, but Tarquinia beat him to it.

‘A negative energy density means positive curvature,’ she said tentatively. ‘But you can’t have a torus that’s positively curved everywhere.’

Agata chirped. ‘Exactly! You end up with a contradiction. So the cosmos can’t be a torus. But in a four-sphere, every route you might travel can be shrunk down gradually to a tiny
circle, and then to a point: a path that goes nowhere. The sign of the wave can’t change along a path that goes nowhere, so there are no extra modes for the luxagens. The vacuum energy stays
positive, which means the curvature will mostly be negative – but it also has to change from place to place, because you can’t have uniform negative curvature on a sphere. And because
the curvature depends on the entropy of matter, that has to change too. That’s why the cosmos isn’t in a state of equally high entropy everywhere. That’s why there’s a
gradient. That’s why we exist at all: with a history, with memories, with an arrow of time.’