‘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?’