Diamond Dogs, Turquoise Days

by Alastair Reynolds

  But something she said upon her return disturbed us.

  “I’m not sure if it’s my imagination or not . . .”

  “What?” Childe snapped.

  “I think the doorways are getting narrower. And lower. There was definitely more headroom at the start than there is now. I guess we didn’t notice when we took so long to move from room to room.”

  “That doesn’t make much sense,” Celestine said.

  “As I said, maybe I imagined it.”

  But we all knew she had done no such thing. The last two times I had stepped across a door’s threshold my suit had bumped against the frame. I had thought nothing of it at the time—putting it down to carelessness—but that had evidently been wishful thinking.

  “I wondered about the doors already,” I said. “Doesn’t it seem a little convenient that the first one we met was just the right size for us? It could have come from a human building.”

  “Then why are they getting smaller?” Childe asked.

  “I don’t know. But I think Hirz is right. And it does worry me.”

  “Me too. But it’ll be a long time before it becomes a problem.” Childe turned to the Ultra. “Forqueray—do the honours, will you?”

  I turned and looked at the chamber ahead of us. The door was open now, but none of us had yet stepped across the threshold. As always, we waited for Forqueray to send his float-cam snooping ahead of us, establishing that the room contained no glaring pitfalls.

  Forqueray tossed the float-cam through the open door.

  We saw the usual red stutters as it swept the room in visible light. “No surprises,” Forqueray said, in the usual slightly absent tone he adopted when reporting the cam’s findings. “Empty metallic chamber . . . only slightly smaller than the one we’re standing in now. A door at the far end with a frame that extends half a metre out on either side. Complex inscriptions this time, Celestine.”

  “I’ll cope, don’t you worry.”

  Forqueray stepped a little closer to the door, one arm raised with his palm open. His expression remained calm as he waited for the drone to return to its master. We all watched, and then—as the moment elongated into seconds—began to suspect that something was wrong.

  The room beyond was utterly dark; no stammering flashes now.

  “The cam—” Forqueray said.

  Childe’s gaze snapped to the Ultra’s face. “Yes?” “It isn’t transmitting anymore. I can’t detect it.”

  “That isn’t possible.”

  “I’m telling you.” The Ultra looked at us, his fear not well concealed. “It’s gone.”

  Childe moved into the darkness, through the frame.

  Just as I was admiring his bravery I felt the floor shudder. Out of the corner of my eye I saw a flicker of rapid motion, like an eyelid closing.

  The rear door—the one that led out of the chamber in which we were standing—had just slammed shut.

  Celestine fell forward. She had been standing in the gap.

  “No . . .” she said, hitting the ground with a detectable thump.

  “Childe!” I shouted, unnecessarily. “Stay where you are—something just happened.”

  “What?”

  “The door behind us closed on Celestine. She’s been injured . . .”

  I was fearing the worst—that the door might have snipped off an arm or a leg as it closed—but it was, mercifully, not that serious. The door had damaged the thigh of her suit, grazing an inch of its armour away as it closed, but Celestine herself had not been injured. The damaged part was still airtight, and the suit’s mobility and critical systems remained unimpaired.

  Already, in fact, the self-healing mechanisms were coming into play, repairing the wound.

  She sat up on the ground. “I’m OK. The impact was hard, but I don’t think I’ve done any permanent damage.”

  “You sure?” I said, offering her a hand.

  “Perfectly sure,” she said, standing up without my assistance.

  “You were lucky,” Trintignant said. “You were only partly blocking the door. Had that not been the case, I suspect your injuries would have been more interesting.”

  “What happened?” Hirz asked.

  “Childe must have triggered it,” Forqueray said. “As soon as he stepped into the other room, it closed the rear door.” The Ultra stepped closer to the aperture. “What happened to my float-cam, Childe?”

  “I don’t know. It just isn’t here. There isn’t even a trace of debris, and there’s no sign of anything that could have destroyed it.”

  The silence that followed was broken by Trintignant’s piping tones. “I believe this makes a queer kind of sense.”

  “You do, do you?” I said.

  “Yes, my dear fellow. It is my suspicion that the Spire has been tolerating the drone until now—lulling us, if you will, into a false sense of security. Yet now the Spire has decreed that we must discard that particular mental crutch. It will no longer permit us to gain any knowledge of the contents of a room until one of us steps into it. And at that moment it will prevent any of us leaving until we have solved that problem.”

  “You mean it’s changing the rules as it goes along?” Hirz asked.

  The Doctor turned his exquisite silver mask towards her. “Which rules did you have in mind, Hirz?”

  “Don’t fuck with me, Doc. You know what I mean.”

  Trintignant touched a finger to the chin of his helmet. “I confess I do not. Unless it is your contention that the Spire has at some point agreed to bind by a set of strictures, which I would ardently suggest is far from the case.”

  “No,” I said. “Hirz is right, in one way. There have been rules. It’s clear that it won’t tolerate us inflicting physical harm against it. And it won’t allow us to enter a room until we’ve all stepped into the preceding one. I think those are pretty fundamental rules.”

  “Then what about the drone, and the door?” asked Childe.

  “It’s like Trintignant said. It tolerated us playing outside the rules until now, but we shouldn’t have assumed that was always going to be the case.”

  Hirz nodded. “Great. What else is it tolerating now?”

  “I don’t know.” I managed a thin smile. “I suppose the only way to find out is to keep going.”

  We passed through another eight rooms, taking between one and two hours to solve each.

  There had been a couple of occasions when we had debated whether to continue, with Hirz usually the least keen of us, but so far the problems had not been insurmountably difficult. And we were making a kind of progress. Mostly the rooms were blank, but every now and then there was a narrow, trellised window, panelled in stained sheets of what was obviously a substance very much more resilient than glass or even diamond. Sometimes these windows opened only into gloomy interior spaces, but on one occasion we were able to look outside, able to sense some of the height we had attained. Forqueray, who had been monitoring our journey with an inertial compass and gravitometer, confirmed that we had ascended at least fifteen vertical metres since the first chamber. That almost sounded impressive, until one considered the several hundred metres of Spire that undoubtedly lay above us. Another few hundred rooms, each posing a challenge more testing than the last?

  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—” 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 depended 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 cooperative 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 someh
ow 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.