The Inverted World

  “Yes it is.”

  “But you’ve been down past. What happened when you came back to the city?”

  “There was an attack on,” I said.

  “Yes…but how much time had elapsed?”

  “More than seventy miles.”

  “Was that more than you expected?”

  “Yes. I thought…I’d been gone only a few days, a mile or two in time.”

  “O.K.” Denton moved forward again, and I followed. “The opposite is true if you go north of optimum.”

  “What do you mean?”

  “Hasn’t anyone told you about the subjective time values?” My blank expression gave him the answer. “If you go anywhere south of optimum, subjective time is slowed. The further south you go, the more that occurs. In the city, the time scale is more or less normal while it is near the optimum, so that when you return from down past, it seems that the city has moved far further than possible.”

  “But we’ve been north.”

  “Yes, and the effect is opposite. While we ride north, our subjective time scale is speeded, so that the city appears not to have moved at all. From experience, I think you’ll find that about four days have elapsed in the city while we’ve been gone. It’s more difficult to estimate at the moment, as the city itself is further south of optimum than normal.”

  I said nothing for a few minutes, trying to understand the idea.

  Then: “So if the city itself could move north of optimum, it wouldn’t have so many miles to travel. It could stop.”

  “No. It always has to move.”

  “But if where we’ve been slows down time, the city would benefit from being there.”

  “No,” he said again. “The differential in subjective time is relative.”

  “I don’t understand,” I said honestly.

  We were now riding up the valley towards the pass. In a few minutes we would be able to see the city, if it was indeed where Denton had predicted.

  “There are two factors. One is the movement of the ground, the other is how one’s values of time are changed subjectively. Both are absolute, but not necessarily connected as far as we know.”

  “Then why—?”

  “Listen. The ground moves, physically. In the north it moves slowly—and the further north one travels the slower it moves—in the south it moves faster. If it was possible to reach the most northern point we believe the ground would not move at all. On the other hand, we believe that in the south the movement of the ground accelerates to an infinite speed at the furthest extremity of the world.”

  I said: “I’ve been there…to the furthest extremity.”

  “You went…what? Forty miles? Perhaps more by accident? That was far enough for you to feel the effects…but only the beginning. We’re talking in terms of millions of miles. Literally…millions. Much more, some would say. The city’s founder, Destaine, thought the world was of infinite size.”

  I said: “But the city has only to travel a few miles further, and it would be north of optimum.”

  “That’s right…and it would make life a lot easier. We would still have to move the city, and not so often and not so far. But the problem is that it’s as much as we can do to stay abreast of optimum.”

  “What is special about the optimum?”

  “It’s where conditions on this world are nearest to those on Earth planet. At the optimum point our subjective values for time are normal. In addition, a day lasts for twenty-four hours. Anywhere else on this world one’s subjective time produces slightly longer or shorter days. The velocity of the ground at optimum is about one mile in every ten days. The optimum is important because in a world like this, where there are so many variables, we need a standard. Don’t confuse miles-distance with miles-time. We say the city has moved so many miles when we really mean that ten times that number of twenty-four hour days have elapsed. So we would gain nothing in real terms by being north of optimum.”

  We had now ridden to the highest point of the pass. Cablestays had been erected, and the city was in the process of being winched. The militiamen were much in evidence, standing guard not only around the city itself but also at both sides of the tracks. We decided not to ride down to the city, but to wait by the stays until the winching was completed.

  Denton said suddenly: “Have you read Destaine’s Directive?”

  “No. I’ve heard of it. In the oath.”

  “That’s right. Clausewitz has a copy. You ought to read it if you’re a guildsman. Destaine laid down the rules for survival in this world, and no one’s ever seen any reason to change them. You’d understand the world a little better, I think.”

  “Did Destaine understand it?”

  “I think so.”

  It took another hour for the winching to be completed. There was no intervention by the tooks, and, in fact, there was no sign of them. I saw that several of the militiamen were now armed with rifles, presumably taken from the tooks killed in the last engagement.

  When we went inside the city I went straight to the central calendar, and discovered that while we had been north three and a half days had elapsed.

  There was a brief discussion with Clausewitz, then we were taken to see Navigator McMahon. In some detail, Denton and I described the terrain we had travelled through, pointing out the major physical features on our map. Denton outlined our suggestions for a route that the city could take, indicating the kinds of feature that might create a problem, and alternative routes around them. In fact, the terrain was in general suited to the city. The hills would mean several deviations from true north, but there were very few steep inclines, and overall the ground was some hundred feet lower at its northern point than the city’s present elevation.

  “We’ll have two more surveys immediately,” the Navigator said to Clausewitz. “One five degrees to east, and one five degrees to west. Do you have men available?”

  “Yes, sir.”

  “I’ll convene Council today, and we’ll set your provisional route for the time being. If better terrain appears from these two new surveys, we’ll reconsider later. How soon will you be able to conduct a normal surveying pattern?”

  “As soon as we can release men from Militia and Tracks,” said Clausewitz.

  “They’re priorities. For the moment, these surveys will have to suffice. If the situation eases, re-apply.”

  “Yes, sir.”

  The navigator took our map and my video tape, and we left the Navigation chambers.

  Outside, I said to Clausewitz: “Sir, I’d like to volunteer for one of the new surveys.”

  He shook his head. “No. You get three days’ leave, and then you go back to the Track guild.”

  “But—”

  “Guild rules.”

  Clausewitz turned away, and he and Denton walked towards the Futures’ room. Technically that area was mine too, but suddenly I felt excluded. Quite literally, I had nowhere to go. While I had been working outside the city I had been sleeping in one of the Militia dormitories; now, officially on leave, I wasn’t even sure where I lived. There were bunks in the Futures’ room, and I could sleep there for the moment, but I knew that I should see Victoria as soon as possible. I had been putting this off; being away from the city conveniently prevented it. I was still wondering how I could deal with the new situation with her, and the answer to that lay in meeting her. I changed my clothes, and had a shower.

  6

  Nothing much had changed inside the city while I’d been north, and the domestic and medical administrators were wholly preoccupied with looking after the wounded and reorganizing the sleeping accommodation. There was less sense of desperation in the faces of the people I saw, and some efforts had been made to keep the corridors clear, but even so I realized that this was probably a bad moment to try to settle a domestic issue.

  Victoria was difficult to trace. After enquiring of several of the domestic administrators I was sent to a makeshift dormitory on the lowest level, but she was not there. I spoke t
o the woman in charge.

  “You’re her ex-husband, aren’t you?”

  “That’s right. Where is she?”

  “She doesn’t want to see you. She’s very busy. She’ll contact you later.”

  “I want to see her,” I said.

  “You can’t. Now, if you’ll excuse me we’re very busy.”

  She turned her back on me and continued her work. I glanced around the crowded dormitory: off-shift workers slept at one end, and there were several wounded lying in rough beds at the other. Although there were a few people moving between the beds, Victoria was not among them.

  I walked back up to the Futures’ room. During the time I had been looking for Victoria I had made a decision. There was no point in my hanging around the city aimlessly; I might as well go back to work on the tracks. But first, I had decided to read Clausewitz’s copy of Destaine’s Directive.

  The Futures’ room was empty but for one guildsman. He introduced himself to me as Future Blayne.

  “You’re Mann’s son, aren’t you?”

  “Yes.”

  “Glad to see you. Have you been up future yet?”

  “Yes,” I said. I liked the look of Blayne. He was not much older than myself, and he had a fresh, open face. He seemed glad to have someone to talk to; he was, he said, due to go north on one of the surveys later in the day, and would be on his own for the next few miles.

  “Do we normally go north alone?” I said.

  “Normally, yes. We can work in pairs if Clausewitz gives his approval, but most Futures prefer to work alone. I like company myself, find it a bit lonely up there. How about you?”

  “I’ve only been up future once. That was with Future Denton.”

  “How did you get on with him?”

  And so we talked, amiably and without the usual guards that seemed to show up whenever I had talked to other guildsmen. I had unconsciously adopted this manner myself, and at first I suppose I might have seemed diffident in his company. Within a few minutes, though, I found his forthright manner relaxing, and soon I felt as if we were old friends.

  I told him I had made a video recording of the sun.

  “Did you wipe it?”

  “What do you mean?”

  “Erase it from the tape.”

  “No…should I have?”

  He laughed. “You’ll have the Navigators down on you if they see it. You’re not supposed to use the tapes for anything except cross-referenced images of the terrain.”

  “Will they see it?”

  “They might. If they’re satisfied with the map, they’ll probably check a few cross-references. They’re not likely to go through the whole tape. But if they do…”

  “What’s wrong with it?” I said.

  “Guild rules. Tape is valuable, and shouldn’t be wasted. But don’t worry about it. Why did you record the sun, anyway?”

  “An idea I had. I wanted to try and analyse it. It’s such an interesting shape.”

  He looked at me with new interest.

  “What do you make of it?” he said.

  “Inverse values.”

  “That’s right. How did you work it out? Did someone tell you?”

  “I remembered something from the crèche. A hyperbola.”

  “Have you thought it through yet? There’s more to it than that. Have you thought about the surface area?”

  “Future Denton was explaining. He said it was very large.”

  Blayne said: “Not very large…infinitely large. North of the city the surface curves up until it is almost, but never quite, vertical. South of the city it becomes almost but not quite horizontal. The world is spinning on its axis, and so with an infinite radius it is spinning at infinite speed.”

  He delivered this flatly and without expression.

  “You’re joking,” I said.

  “No I’m not. I’m perfectly serious. Where we are, near optimum, the effects of the spin are the same as they would be on Earth planet. Further south, although the angular velocity is identical, the speed increases. When you were down past, did you feel the centrifugal force?”

  “Yes.”

  “If you’d gone any further, you wouldn’t be here now to remember it. That force is bloody real.”

  “I was told,” I said, “that nothing could travel faster than the speed of light.”

  “That’s true. Nothing does. In theory the world’s circumference is infinitely long and moves at infinite speed. But there is, or there is considered to be, a point where matter ceases to exist, and serves as an effective circumference. That point is where the spinning of the world imparts a velocity on the matter equivalent to the speed of light.”

  “So it’s not infinite.”

  “Not quite. But bloody big. Look at the sun.”

  “I have,” I said. “Often.”

  “That’s the same. If it wasn’t spinning it would be, literally, infinitely large.”

  I said: “Even so, in theory it is that large. How can there be room for more than one object of infinite size?”

  “There’s an answer to that. You won’t like it.”

  “Try me.”

  “Go to the library, and find one of the astronomical books. It doesn’t matter which. They’re all Earth planet books, so they all have the same assumptions. If we were now on Earth planet we would be living in a universe of infinite size, which would be occupied by a number of large, but finite, bodies. Here the universe is the rule: we live in a large but finite universe, occupied by a number of bodies of infinite size.”

  “It doesn’t make sense.”

  “I know,” said Blayne. “I said you wouldn’t like it.”

  “Where are we?”

  “No one knows.”

  “Where is Earth planet?”

  “No one knows that either.”

  I said: “Down past something strange happened. I was with three girls. As we went south, their bodies changed. They—”

  “Did you see anyone up future?”

  “No, we…we kept away from the villages.”

  “North of optimum the local people change physically. They become very tall and thin. The further north we travel, the more the physical factors change.”

  “I’ve only been about fifteen miles north.”

  “Then you probably wouldn’t have noticed anything peculiar. Further than thirty-five miles north of optimum, it’s very strange.”

  Later, I said: “Why does the ground move?”

  “I’m not sure,” said Blayne.

  “Is anyone?”

  “No.”

  “Where is it moving to?”

  “More to the point,” said Blayne, “where is it moving from?”

  “Do you know?”

  “Destaine said that the movement of the ground was cyclic. He says in his Directive that the ground is actually stationary at the north pole. Further south, it is moving very slowly towards the equator. The nearer it approaches to the equator the faster it moves, both angularly, because of the rotation, and linearly. At the furthest extreme it is moving in two directions at once at infinite speed.”

  I stared at him. “But—”

  “Wait…it’s not finished. The world has a southern part too. If the world was a sphere it would be called a hemisphere, but Destaine adopted it for convenience. In the southern hemisphere, the opposite is true. That is, the ground moves from the equator towards the south pole, steadily decelerating. At the south pole it is stationary again.”

  “You still haven’t said where the ground moves from.”

  “Destaine suggested that north and south poles were identical. In other words, once any point on the ground reaches the south pole it reappears at the north pole.”

  “That’s impossible!”

  “Not according to Destaine. He says that the world is shaped like a solid hyperbola; that is, all limits are infinite. If you can imagine that, the limits adopt the characteristics of their opposite value. An infinite negative becomes an infinite positive,
and vice versa.”

  “Are you quoting him verbatim?”

  “I think so. But you should read the original.”

  “I intend to,” I said.

  Before Blayne left the city to go north, we agreed that when the crisis outside the city was settled we would ride together.

  Alone once more, I read through the copy of Destaine’s Directive that Blayne obtained for me from Clausewitz.

  It consisted of several pages of closely printed text, much of which would have been incomprehensible to me had I read it when I had first ventured outside the city. Now, with my own ideas and experiences, and with what Blayne had said, it served only to confirm. I saw some of the sense of the guild system: the experience had laid the way to understanding.

  There was a lot of theoretical mathematics, interspersed with profuse calculations, at which I glanced only briefly. Of more interest was what appeared to be a hurried journal, and some sections caught my eye:

  We are a long way from Earth. Our home planet is one I doubt we shall ever see again, but if we are to survive here we must maintain ourselves as a microcosm of Earth. We are in desolation and isolation. All around us is a hostile world that daily threatens our survival. As long as our buildings remain, so long shall man survive in this place. Protection and preservation of our home is paramount.

  Later he wrote:

  I have measured the rate of regression at one tenth of a statute mile in a period of twenty-three hours and forty-seven minutes. Although this southwards drift is slow it is relentless; the establishment shall therefore be moved at least one mile in every ten day period.

  Nothing must stand in the way. We have already encountered one river, and it was crossed at great hazard. Doubtless we shall encounter further obstacles in the days and miles ahead, and by then we must be ready. We must concentrate on finding some indigenous materials that can be stored permanently within the buildings for later use as construction materials. A bridge should not be too difficult to build if we have enough warning.

  Sturner has been forward and warns of a marshy region some miles ahead. Already we have sent other teams to north-east and north-west to determine the extent of this marsh. If it is not too wide we can deviate from the due north for a time, and make up the difference later.