The Arrows of Time: Orthogonal Book Three

by Egan, Greg

  More experienced now, she dared to let the rock below her blur a little, trading off perfect clarity for less costly centripetal force. Agata didn’t want to grow complacent, but the numbers were already better than she’d dared hope. While the majority of the team had barely been into the void before, five people had done maintenance work out on the hull. If those five alone had dealt with two bombs each, as she had, the job would already be completed.

  The amorphous blur below her was broken by a sharp edge spinning by. Agata went in pursuit, astonished by her luck. She was beginning to pity all the searchers who must have come just as far with no result; everyone would understand that that might happen to them, but three times now she’d seen the signs that their collective effort was heading for victory, while others would still be wondering if the whole endeavour had been misconceived.

  The third occulter came into view. The cargo was attached in exactly the same manner as it had been on the last one. Agata didn’t delay her assault; she grabbed one of the posts, shut off the jetpack and began applying her coherer. But as she worked, she sifted through the possibilities.

  Tarquinia had not repaired the lost occulter with stone and glue. This one and the last had not picked up their cargo in any manoeuvre out on the slopes; the bombs had been glued into place in a workshop somewhere. But how and why would Giacomo’s people have retrieved occulters from the slopes in order to do that? The answer was that they hadn’t. They’d built occulters for themselves, and affixed the bombs before sending them out.

  Agata moved her grip and began cutting through the second post. Three bombs diverted out of a dozen had seemed glorious. Three out of an unknown swarm could mean anything.

  Before she severed the second post completely, she stopped to think through her choices. If she spent air carrying the bomb onto the same kind of path as the others, that would be the end of her contribution; she’d have too little air left to intervene in any other way. But if there were already enough bombs waiting above the light collectors to cause the disruption, there was no need for this one to be carefully positioned. She could simply let it fall away into the void.

  Agata looked up across the rock face; she could see a glimmer from the transition circle reflected in the dome of one of the light collectors. How many other bombs had been grabbed and slowed and sent to play their part in the pyrotechnics? She should trust her fellow searchers to have caught at least half a dozen by now – all the more so, given how plentiful they’d turned out to be.

  She had one hand around the arm of the occulter, which remained firmly attached to the mountain. She snapped the second post and tossed the freed bomb over her shoulder, watching with her rear gaze as it tumbled down and disappeared.

  But how many remained, clinging to the rock, waiting to make a final dash towards the collectors? A dozen? A gross? Agata closed her eyes and thought of letting go, falling clear of everything and losing herself in the stars.

  She’d wanted a glimpse of the reunion before she died, but in the end the only thing that the future had ever promised her was the cosmos meeting up with itself: every particle, every field, every wrinkle in space matching perfectly as they came full circle. The geometry that achieved that had no need to please her; it was what it was, and she’d never been more than a tiny part of it. The miracle was that she’d lived to understand its nature as well as she had. But if a meteor struck or the bombs blew the axis open, she did not want to stay and witness the carnage.

  Agata opened her eyes. Her right arm was aching; she pulled herself up and managed to grab the occulter with her left hand as well, but it was too awkward maintaining both holds so she let her right arm rest completely. She checked the clock on her belt by touch; less than two chimes remained to the disruption. She wasn’t going to flee. She had no hope of finding another occulter on the rock face, but the time was approaching when the bombs could come to her.

  She stared down into the transition circle, but then she caught herself and turned her gaze to the side, trying to adjust for her own rotation and the arc that her adversary would need to follow as it fought to cancel its greater sideways velocity and spiral in on the target.

  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.

  33

  ‘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 b
e 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.’

  Watching her as she spoke, Ramiro couldn’t help sharing her joy. Perhaps the discovery changed nothing tangible, but it vindicated all her years of effort – and it proved that the Peerless was back on course. New ideas were possible again. The paralysis was over.

  ‘And that settles everything?’ he asked. ‘Cosmology is complete now?’

  ‘Not at all!’ Agata replied gleefully. ‘There are still dozens of open questions. People will be working on this until the reunion, and beyond.’

  Tarquinia said, ‘I have some news of my own that you should hear.’

  Ramiro had been afraid that the change of subject would go down badly, but Agata listened to the revised version of the last day on Esilio with no sign of hostility.

  When Tarquinia was finished, Agata said mildly, ‘I’m glad you weren’t lying to me, after all.’ She glanced over at Ramiro. ‘And I’m glad you weren’t either, even if you meant to.’ It was an infinitely gentler barb than he’d expected.

  A doctor approached and suggested that they let Agata rest. Agata glanced down at her shrivelled torso, as if she’d forgotten the state of it while they’d been talking. ‘Not one person has said that I look like I’ve shed twice,’ she complained. ‘I’ve been ready to tell them the names of the children, but the joke’s just not happening.’