And the doors were definitely getting smaller.
It was an effort to squeeze through now, and while the suits were able to reshape themselves to some extent, there was a limit to how compact they could become.
It had taken us sixteen hours to reach this point. At this rate it would take many days to get anywhere near the summit.
But none of us had imagined that this would be over quickly.
‘Tricky,’ Celestine said, after studying the latest puzzle for many minutes. ‘I think I see what’s going on here, but…’
Childe looked at her. ‘You think, or you know?’
‘I mean what I said. It’s not easy, you know. Would you rather I let someone else take first crack at it?’
I put a hand on Celestine’s arm and spoke to her privately. ‘Easy. He’s just anxious, that’s all.’
She brushed my hand away. ‘I didn’t ask you to defend me, Richard.’
‘I’m sorry. I didn’t mean—’
‘Never mind.’ Celestine switched off private mode and addressed the group. ‘I think these markings are shadows. Look.’
By now we had all become reasonably adept at drawing figures using our suits’ visualisation systems. These sketchy hallucinations could be painted on any surface, apparently visible to all.
Celestine, who was the best at this, drew a short red hyphen on the wall.
‘See this? A one-dimensional line. Now watch.’ She made the line become a square; splitting into two parallel lines joined at their ends. Then she made the square rotate until it was edge-on again, and all we could see was the line.
‘We see it…’ Childe said.
‘You can think of a line as the one-dimensional shadow of a two-dimensional object, in this case a square. Understand?’
‘I think we get the gist,’ Trintigant said.
Celestine made the square freeze, and then slide diagonally, leaving a copy of itself to which it was joined at the corners. ‘Now. We’re looking at a two-dimensional figure this time; the shadow of a three-dimensional cube. See how it changes if I rotate the cube, how it elongates and contracts?’
‘Yes. Got that,’ Childe said, watching the two joined squares slide across each other with a hypnotically smooth motion, only one square visible as the imagined cube presented itself face-on to the wall.
‘Well, I think these figures…’ Celestine sketched a hand an inch over the intricate designs worked into the frame, ‘I think what these figures represent are two-dimensional shadows of four-dimensional objects.’
‘Fuck off,’ Hirz said.
‘Look, just concentrate, will you? This one’s easy. It’s a hypercube. That’s the four-dimensional analogue of a cube. You just take a cube and extend it outwards; just the same way that you make a cube from a square.’ Celestine paused, and for a moment I thought she was going to throw up her hands in despair. ‘Look. Look at this.’ And then she sketched something on the wall: a cube set inside a slightly larger one, to which it was joined by diagonal lines. ‘That’s what the three-dimensional shadow of a hypercube would look like. Now all you have to do is collapse that shadow by one more dimension, down to two, to get this—’ and she jabbed at the beguiling design marked on the door.
‘I think I see it,’ Childe said, without anything resembling confidence.
Maybe I did, too — though I felt the same lack of certainty. Childe and I had certainly taunted each other with higher-dimensional puzzles in our youth, but never had so much deended on an intuitive grasp of those mind-shattering mathematical realms. ‘All right,’ I said. ‘Supposing that is the shadow of a tesseract… what’s the puzzle?’
‘This,’ Celestine said, pointing to the other side of the door, to what seemed like an utterly different — though no less complex — design. ‘It’s the same object, after a rotation.’
‘The shadow changes that drastically?’
‘Start getting used to it, Richard.’
‘All right.’ I realised she was still annoyed with me for touching her. ‘What about the others?’
‘They’re all four-dimensional objects; relatively simple geometric forms. This one’s a 4-simplex; a hypertetrahedon. It’s a hyper-pyramid with five tetrahedral faces…’ Celestine trailed off, looking at us with an odd expression on her face. ‘Never mind. The point is, all the corresponding forms on the right should be the shadows of the same polytopes after a simple rotation through higher-dimensional space. But one isn’t.’
‘Which is?’
She pointed to one of the forms. ‘This one.’
‘And you’re certain of that?’ Hirz said. ‘Because I’m sure as fuck not.’
Celestine nodded. ‘Yes. I’m completely sure of it now.’
‘But you can’t make any of us see that this is the case?’
She shrugged. ‘I guess you either see it or you don’t.’
‘Yeah? Well maybe we should have all taken a trip to the Pattern Jugglers. Then maybe I wouldn’t be about to shit myself.’
Celestine said nothing, but merely reached out and touched the errant figure.
‘There’s good news and there’s bad news,’ Forqueray said after we had traversed another dozen or so rooms without injury.
‘Give us the bad news first,’ Celestine said.
Forqueray obliged, with what sounded like the tiniest degree of pleasure. ‘We won’t be able to get through more than two or three more doors. Not with these suits on.’
There had been no real need to tell us that. It had become crushingly obvious during the last three or four rooms that we were near the limit; that the Spire’s subtly shifting internal architecture would not permit further movement within the bulky suits. It had been an effort to squeeze through the last door; only Hirz was oblivious to these difficulties.
‘Then we might as well give up,’ I said.
‘Not exactly.’ Forqueray smiled his vampiric smile. ‘I said there was good news as well, didn’t I?’
‘Which is?’ Childe said.
‘You remember when we sent Hirz back to the beginning, to see if the Spire was going to allow us to leave at any point?’
‘Yes,’ Childe said. Hirz had not repeated the complete exercise since, but she had gone back a dozen rooms, and found that the Spire was just as co-operative as it had been before. There was no reason to think she would not have been able to make her way to the exit, had she wished.
‘Something bothered me,’ Forqueray said. ‘When she went back, the Spire opened and closed doors in sequence to allow her to pass. I couldn’t see the sense in that. Why not just open all the doors along her route?’
‘I confess it troubled me as well,’ Trintignant said.
‘So I thought about it, and decided there must be a reason not to have all the doors open at once.’
Childe sighed. ‘Which was?’
‘Air,’ Forqueray said.
‘You’re kidding, aren’t you?’
The Ultra shook his head. ‘When we began, we were moving in vacuum — or at least through air that was as thin as that on Golgotha’s surface. That continued to be the case for the next few rooms. Then it began to change. Very slowly, I’ll grant you — but my suit sensors picked up on it immediately.’
Childe pulled a face. ‘And it didn’t cross your mind to tell any of us about this?’
‘I thought it best to wait until a pattern became apparent.’ Forqueray glanced at Celestine, whose face was impassive.
‘He’s right,’ Trintignant said. ‘I too have become aware of the changing atmospheric conditions. Forqueray has also doubtless noticed that the temperature in each room has been a little warmer than the last. I have extrapolated these trends and arrived at a tentative conclusion. Within two — possibly three — rooms, we will be able to discard our suits and breathe normally.’
‘Discard our suits?’ Hirz looked at him as if he were insane. ‘You have got to be fucking kidding.’
Childe raised a hand. ‘Wait a minute. When you said air,
Doctor Trintignant, you didn’t say it was anything we’d be able to breathe.’
The Doctor’s answer was a melodious piped refrain. ‘Except it is. The ratios of the various gases are remarkably close to those we employ in our suits.’
‘Which isn’t possible. I don’t remember providing a sample.’
Trintignant dipped his head in a nod. ‘Nonetheless, it appears that one has been taken. The mix, incidentally, corresponds to precisely the atmospheric preferences of Ultras. Argyle’s expedition would surely have employed a slightly different mix, so it is not simply the case that the Spire has a long memory.’
I shivered.
The thought that the Spire — this vast breathing thing through which we were scurrying like rats — had somehow reached inside the hard armour of our suits to snatch a sample of air, without our knowing, made my guts turn cold. It not only knew of our presence, but it knew — intimately — what we were.
It understood our fragility.
As if wishing to reward Forqueray for his observation, the next room contained a substantially thicker atmosphere than any of its predecessors, and was also much warmer. It was not yet capable of supporting life, but one would not have died instantly without the protection of a suit.
The challenge that the room held was by far the hardest, even by Celestine’s reckoning. Once again the essence of the task lay in the figures marked on either side of the door, but now these figures were linked by various symbols and connecting loops, like the subway map of a foreign city. We had encountered some of these hieroglyphics before — they were akin to mathematical operators, like the addition and subtraction symbol — but we had never seen so many. And the problem itself was not simply a numerical exercise, but — as far as Celestine could say with any certainty — a problem about topological transformations in four dimensions.
‘Please tell me you see the answer immediately,’ Childe said.
‘I…’ Celestine trailed off. ‘I think I do. I’m just not absolutely certain. I need to think about this for a minute.’
‘Fine. Take all the time you want.’
Celestine fell into a reverie which lasted minutes, and then tens of minutes. Once or twice she would open her mouth and take a breath of air as if in readiness to speak, and on one or two other occasions she took a promising step closer to the door, but none of these things heralded the sudden, intuitive breakthrough we were all hoping for. She always returned to the same silent, standing posture. The time dragged on; first an hour and then the better part of two hours.
All this, I thought, before even Celestine had seen the answer.
It might take days if we were all expected to follow her reasoning.
Finally, however, she spoke. ‘Yes. I see it.’
Childe was the first to answer. ‘Is it the one you thought it was originally?’
‘No.’
‘Great,’ Hirz said.
‘Celestine…’ I said, trying to defuse the situation. ‘Do you understand why you made the wrong choice originally?’
‘Yes. I think so. It was a trick answer; an apparently correct solution which contained a subtle flaw. And what looked like the clearly wrong answer turned out to be the right one.’
‘Right. And you’re certain of that?’
‘I’m not certain of anything, Richard. I’m just saying this is what I believe the answer to be.’
I nodded. ‘I think that’s all any of us can honestly expect. Do you think there’s any chance of the rest of us following your line of argument?’
‘I don’t know. How much do you understand about Kaluza-Klein spaces?’
‘Not a vast amount, I have to admit.’
‘That’s what I feared. I could probably explain my reasoning to some of you, but there’d always be someone who didn’t get it—’ Celestine looked pointedly at Hirz. ‘We could be in this bloody room for weeks before any of us grasp the solution. And the Spire may not tolerate that kind of delay.’
‘We don’t know that,’ I cautioned.
‘No,’ Childe said. ‘On the other hand, we can’t afford to spend weeks solving every room. There’s going to have to come a point where we put our faith in Celestine’s judgement. I think that time may have come.’
I looked at him, remembering that his mathematical fluency had always been superior to mine. The puzzles I had set him had seldom defeated him, even if it had taken weeks for his intensely methodical mind to arrive at the solution. Conversely, he had often managed to beat me by setting a mathematical challenge of similar intricacy to the one now facing Celestine. They were not quite equals, I knew, but neither were their abilities radically different. It was just that, thanks to her experiences with the Pattern Jugglers, Celestine would always arrive at the answer with the superhuman speed of a savant.
‘Are you saying I should just press it, with no consultation?’ Celestine said.
Childe nodded. ‘Provided everyone else agrees with me…’
It was not an easy decision to make, especially after having navigated so many rooms via such a ruthlessly democratic process. But we all saw the sense, even Hirz coming around to our line of thinking in the end.
‘I’m telling you,’ she said. ‘We get through this door, I’m out of here, money or not.’
‘You’re giving up?’ Childe asked.
‘You saw what happened to those poor bastards outside. They must have thought they could keep on solving the next test.’
Childe looked sad, but said, ‘I understand perfectly. But I trust you’ll reassess your decision as soon as we’re through?’
‘Sorry, but my mind’s made up. I’ve had enough of this shit.’ Hirz turned to Celestine. ‘Put us all out of our misery, will you? Make the choice.’
Celestine looked at each of us in turn. ‘Are you ready for this?’
‘We are,’ Childe said, answering for the group. ‘Go ahead.’
Celestine pressed the symbol. There was the usual yawning moment of expectation; a moment that stretched agonisingly. We all stared at the door, willing it to begin sliding open.
This time nothing happened.
‘Oh God…’ Hirz began.
Something happened then, almost before she had finished speaking, but it was over almost before we had sensed any change in the room. It was only afterwards — playing back the visual record captured by our suits — that we were able to make any sense of events.
The walls of the chamber — like every room we had passed through, in fact — had looked totally seamless. But in a flash something emerged from the wall: a rigid, sharp-ended metal rod spearing out at waist-height. It flashed through the air from wall to wall, vanishing like a javelin thrown into water. None of us had time to notice it, let alone react bodily. Even the suits — programmed to move out of the way of obvious moving hazards — were too slow. By the time they began moving, the javelin had been and gone. And if there had been only that one javelin, we might almost have missed it happening at all.
But a second emerged, a fraction of a second after the first, spearing across the room at a slightly different angle.
Forqueray happened to be standing in the way.
The javelin passed through him as if he were made of smoke; its progress was unimpeded by his presence. But it dragged behind it a comet-tail of gore, exploding out of his suit where he had been speared, just below the elbow. The pressure in the room was still considerably less than atmospheric.
Forqueray’s suit reacted with impressive speed, but it was still sluggish compared to the javelin.
It assessed the damage that had been inflicted on the arm, aware of how quickly its self-repair systems could work to seal that inch-wide hole, and came to a rapid conclusion. The integrity could be restored, but not before unacceptable blood and pressure loss. Since its duty was always to keep its wearer alive, no matter what the costs, it opted to sever the arm above the wound; hyper-sharp irised blades snicked through flesh and bone in an instant.
All that took p
lace long before any pain signals had a chance to reach his brain. The first thing Forqueray knew of his misfortune was when his arm clanged to his feet.
‘I think—’ he started saying. Hirz dashed over to the Ultra and did her best to support him.
Forqueray’s truncated arm ended in a smooth silver iris.
‘Don’t talk,’ Childe said.
Forqueray, who was still standing, looked at his injury with something close to fascination. ‘I—’
‘I said don’t talk.’ Childe knelt down and picked up the amputated arm, showing the evidence to Forqueray. The hole went right through it, as cleanly bored as a rifle barrel.
‘I’ll live,’ Forqueray managed.
‘Yes, you will,’ Trintignant said. ‘And you may also count yourself fortunate. Had the projectile pierced your body, rather than one of its extremities, I do not believe we would be having this conversation.’
‘You call this fortunate?’
‘A wound such as yours can be made good with only trivial intervention. We have all the equipment we need aboard the shuttle.’
Hirz looked around uneasily. ‘You think the punishment’s over?’
‘I think we’d know if it wasn’t,’ I said. ‘That was our first mistake, after all. We can expect things to be a little worse in future, of course.’
‘Then we’d better not make any more screw-ups, had we?’ Hirz was directing her words at Celestine.
I had expected an angry rebuttal. Celestine would have been perfectly correct to remind Hirz that — had the rest of us been forced to make that choice — our chances of hitting the correct answer would have been a miserable one in six.
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