The Arrows of Time: Orthogonal Book Three (10 page)

‘Well, there’ll never be a chance to repeat it,’ she said. The
Peerless
’s reversal had rendered every cousin of the Object into ordinary matter, and turned the
Hurtlers into nothing but slowly drifting sand. ‘We’re in for six generations of cosmic tranquillity.’

‘Good,’ Pio replied.

‘And you know there are no restrictions on the engines?’ Agata added.

‘I heard that at the time,’ he said. ‘They let us watch the news.’

A woman walked past them, looking twice when she recognised Pio, then hurrying on. Agata felt herself soften a little. She’d had visions of her brother emerging from prison ranting denials
against every unwelcome new fact. ‘If cooling air escapes from the mountain now,’ she said, ‘it will end up mingling with the orthogonal cluster, violating its arrow of time. And
yet—’ She stopped and spread her arms. ‘I don’t feel myself burning up.’

Pio buzzed. ‘I don’t think you blame me for the gnat; I think you’re still punishing me for my debate with Lila. There
might
have been a problem for us with the arrows
clashing. At the time nobody had proved that there wouldn’t be, and I was right to point that out.’

‘So you’d say we’ve been lucky,’ Agata pressed him, ‘but you’re satisfied now that there’s no reason not to forge ahead, all the way to the
reunion?’

‘That’s a weighty demand,’ Pio replied lightly. ‘If you’re asking me whether I’m going to advocate any kind of change in course in the immediate future, the
answer is no. There’s nothing we could do at this moment that would make the
Peerless
any safer, and no risk that we urgently need to avoid.’

He gestured towards the floor – towards the rim, out into the void. ‘But as Lila said in the debate, the orthogonal worlds are still out there, and they can’t annihilate us any
more. So don’t ask me to renounce the possibilities they offer. All I’m calling on people to do right now is to keep an open mind. Is that so terrible?’

Agata said, ‘You’ve forgotten your own slogan: “Let the ancestors burn.” Why should anyone open their mind to that?’

‘Let them burn
if necessary
,’ Pio replied. ‘If the alternative is even worse.’

Agata stopped walking. ‘You know, you almost sound convincing sometimes. But you were ready to give up on the home world before on much weaker grounds than
necessity
.’

Pio raised his hands contritely. ‘I got carried away in the debate. I know it offended you, and I’m sorry.’

They’d almost reached the turn-off to Lila’s office. Agata didn’t want to detour for a meal now in case Pio insisted on joining her.

‘I have to go,’ she said. ‘You can tell Cira that you tried your best, to no avail.’

‘What are you talking about?’ But Pio’s baffled demeanour was a bit too self-conscious to be believable.

‘You should find something useful to do,’ Agata suggested. ‘I’m sure they still need help re-bedding the medicinal gardens.’

‘And your work’s useful?’ he retorted. ‘Try some gardening yourself!’

‘Goodbye, Pio.’ Agata strode towards the intersection, glancing at her brother with her rear gaze in the hope that he’d set off back down the corridor so she could get to the
food hall after all. But he must have been hungry too, because he headed for the hall himself.

Agata muttered imprecations against her family and readied herself for a bell or two of higher mathematics through the eyes of a Starver.

‘Are you eating for four now?’ Medoro joked.

Agata looked up. ‘We can share if you want to. I might have ordered too much.’

Medoro sat on the floor, facing her, and helped himself to a loaf. The food hall was quiet, and Agata had been lost in thought.

‘How’s work?’ he asked.

‘I finished proving an interesting result today,’ she said. ‘Lila and I had been fairly sure that it was true, but it took a while to clear up all the
technicalities.’

‘Ah. Would I understand it?’

‘Maybe not the proof,’ Agata admitted, ‘but the result itself is simple.’

Medoro buzzed sceptically. ‘Try me, then. But be warned: if I can’t explain it properly afterwards you’ll be hearing from Gineto.’

‘Suppose the topology of the cosmos is that of a four-dimensional sphere,’ Agata began. ‘Not the shape, just the topology: the way it all connects up.’

‘I thought the cosmos was a torus,’ Medoro protested.

‘A torus was Yalda’s preferred model.‘ Agata had nothing but respect for Yalda, but she wished the schools would stop treating this favoured model as an established fact.
‘It makes for a nice, concrete example that’s simple to work with – but the truth is, we don’t know the real topology. It might be a torus, it might be a sphere, it might be
something else entirely. The only thing we know for sure is that it has to be finite in all four dimensions.’

Medoro said, ‘All right. So you hypothesise that the cosmos is a sphere. Then what?’

‘Then you ask what kind of curvature it might have.’

‘The curvature of a sphere?’ Medoro ventured.

‘Ha!’ To her amusement, Agata realised that her own intuition now filtered out this eminently sensible guess so rapidly that she hadn’t even thought of mentioning it.
‘Well, you might think so: why shouldn’t the cosmos have the curvature of a perfectly symmetrical four-dimensional sphere? The trouble is, a perfect sphere has equal positive curvature
in all dimensions: no direction is different from any other. But in Lila’s theory of gravity, if the disposition of matter is like that – with no direction favoured – what you get
is uniform
negative
curvature. You could only get uniform positive curvature if the energy density were negative, and we have no reason to believe that that’s the case.’

Medoro thought for a while, chewing on a second loaf. ‘So can you have something with the topology of a sphere, but with uniform
negative
curvature?’

‘You can’t,’ Agata said. ‘In fact that’s what we just proved. A four-sphere with positive curvature is possible geometrically but impossible physically, while a
four-sphere with negative curvature would make sense physically, but it’s impossible geometrically.’

‘Hmm.’ Medoro brushed crumbs from his tympanum. ‘Which leaves you with what? That the cosmos can’t really be a four-sphere at all?’

‘No, that doesn’t follow,’ Agata replied. ‘It just means that if the cosmos
is
a four-sphere, topologically, then it can’t be perfectly uniform: it must
differ from place to place.’

‘Aha!’ Medoro chirped appreciatively. ‘So it goes some way towards explaining the entropy gradient?’

‘Some way.’ Agata was pleased with the result, but she didn’t want to oversell it. ‘If we had a reason to believe that the topology
had to be
a four-sphere, then
we could say that the cosmos would need to contain some regions of lower entropy in order to meet the geometrical constraints.’

‘And do you have a reason?’

‘No,’ Agata admitted. ‘As far as anyone knows, the cosmos might just as easily be a torus, in which case our theorem can’t be applied and the entropy gradient is as
inexplicable as ever.’

‘Never mind,’ Medoro counselled consolingly. ‘I’m sure someone will work it all out eventually.’

Agata was about to retort that she had every intention of being that ‘someone’, but she caught herself; he was just goading her. ‘That’s enough cosmology,’ she
said. ‘How’s the camera business?’

‘Cosmological,’ Medoro replied. ‘Actually, that’s why I came looking for you. I’m starting a new project, and I wanted to hear your thoughts on it.’

Agata was intrigued. Medoro made cameras for the astronomers from time to time, but he’d never felt the need to consult with her before. ‘What are you building?’ she asked.

‘A new imaging chip,’ he said. ‘One that can visualise the orthogonal cluster.’

‘Visualise it?’ Agata scrutinised his face, half suspecting that she was being set up for a joke, but either way she couldn’t resist the bait. ‘How?’

Medoro said, ‘Instead of polling the array of pixels on the chip and counting how many photons have struck each of them, it will count how many photons each pixel has
emitted
.
Point the camera at the sky . . . and when it emits light towards the orthogonal stars, you can read off the details.’

Before the turnaround Agata would have been sceptical, but now she could see that the possibility of a camera like this had been implicit in the results of the very first engine tests after the
reversal. Just as the engines had happily given off light that the ultimate recipients would consider to be arriving from their future, the orthogonal stars were – presumably – still
shining down on the
Peerless
, despite being rendered invisible by the very same property. People’s eyes had not evolved to know when they were the joint authors of a beam of light,
as responsible for creating it as the distant star at the other end. But a camera could be made to catch its own strange radiance in the act.

‘Who commissioned this?’ she asked.

‘Do you know Greta?’

‘No.’ Agata knew all the astronomers, and there was no Greta among them.

‘She’s a technical adviser to the Council,’ Medoro explained. ‘She supervised the turnaround, but now that it’s over she’s been given this new
thing.’

‘Which is . . . ?’

Medoro leant forward as if to share some delicate confidence. ‘I was told that the camera would be part of a general upgrade of the navigation systems. The rationale being that the old
maps are fine for most purposes, but if we can find a way to keep getting real-time images of the orthogonal stars, so much the better.’

‘Except that this is better than real-time,’ Agata joked. ‘Instead of seeing where the star was, we’ll know where it will be.’

Medoro said, ‘That, and a great deal more.’

‘I’m sorry?’

He buzzed impatiently. ‘Come on, you’re the physicist! Do I have to spell it out?’

Agata stared at him, bemused. Knowing the future positions of the orthogonal stars would not be a momentous revelation: their trajectories were already predictable over a time-span of eons. And
in fact, these stars’ ‘future’ positions would be positions in which they’d already been observed, earlier in the
Peerless
’s own twisted history. Telescopes
had improved since then, but there were unlikely to be any spectacular, collision-avoiding surprises.

‘You’ve lost me,’ she confessed.

‘Suppose something occults an orthogonal star that I’ve been watching with this camera,’ Medoro said. ‘What happens then?’

‘The occulting object will take the place of the camera as the second source of the light.’

‘So we’ll know about the occultation?’ he pressed her.

Agata said, ‘Of course! If there’s no light passing between camera and star, the “image” of the star will disappear, just as an ordinary image would.’

‘And when will we know about it?’

‘When? The exact time will depend on the geometry: the location of the object that blocks the light, and the speed of light for the part of the star trail that’s obscured.’

Medoro said, ‘Now suppose that we
arrange
a sequence of occultations – of the slowest detectable light, with the blocking taking place as far from the telescope as
possible.’

Agata thought she knew where he was headed. ‘Then the image of the star will blink out before the blocking object is actually in place. But you know, even the slowest detectable infrared
is quite hard to outpace. So unless you build some massive engines, these flying shutters of yours would need to be launched long before you see their effect on the star.’

But Medoro wasn’t finished with his thought experiment. ‘Now add a pair of mirrors and fold up the light path, so we can achieve the same effect while manipulating an object
that’s much closer.’

Agata raised a quick sketch of the proposal.

‘Depending on the dimensions of the system and the number of bounces before the loss to the mirrors is too great,’ she said, ‘you’ll be able to make
observations that reveal the shutter’s position some time into the future. I’m no expert on practical optics, but I’d guess that a realistic time-span would be measured in
flickers at most.’

Medoro said, ‘Maybe. But suppose it’s more than twice the response time of an automated signal booster. You might only be able to receive the message from a short way into the
future, but so long as you can resend it to a time when the booster will be free to handle it “again” – without any overlap with the later boost – the process can go on
indefinitely.’