Inverted World (23 page)

The journey northwards was slow and meandering. We did not take a route due north, but followed many diversions to east and west. Periodically Denton would measure our position against optimum, and never at any time were we further north than about fifteen miles.

I asked him if there were any reason why we should not strike even further north of optimum.

“Normally, we would go as far north as we can,” he said. “But the city’s in a special circumstance. As well as seeking the easiest northwards route, we need terrain that will allow us to defend ourselves best.”

The map we were compiling was becoming more complete and detailed every day. Denton allowed me to operate the equipment whenever I wished, and soon I was as adept as he. I learned how to triangulate the land with the surveying instrument, how to estimate the elevation of hills, and how to calculate the distance we were north or south of optimum. I was growing to like working the camera, in spite of the fact I was forced to curb my enthusiasm to conserve the energy in the batteries.

It was peaceful and agreeable away from the tensions of the city, and I discovered that Denton, in spite of his long silences, was an amiable and intelligent man.

I had lost track of the days we had been away, but it was certainly at least twenty. Denton showed no sign of wanting to return.

We encountered a small settlement, nestling in a shallow valley. We made no attempt to approach it. Denton merely marked it on the map, with a rough estimate of the population.

The countryside was greener and fresher than that to which I had grown accustomed, although the sun was no cooler. It rained more often here, usually during the night, and there were many different sizes of streams and rivers.

All the features of the region, natural or man-made, difficult for the city to pass through or suitable to its peculiar needs, Denton marked without comment on his map. It was not the job of the Future Surveyors to decide which route the city should take; we worked simply to establish the actual nature of future terrain.

The atmosphere was restful and soporific, the natural beauty of our surroundings seductive. I knew the city would travel through this region in the miles to come, and pass it without registering appreciation. For the city’s aesthetics, this verdant and gentle countryside might equally be a windswept desert.

During the hours when I was not actually engaged in any of our routine tasks, I was still lost in speculative thought. I could not get out of my mind that spectacle of the manifest appearance of the world on which we existed.

There must have been something, somewhere in those long years of tedious education that would, subconsciously, have prepared me for that sight. We live by our assumptions; if one took for granted that the world we travelled across was like any other, could any education ever prepare one for a total reversal of that assumption?

The preparation for that sight had begun the day Future Denton had taken me outside the city for the first time, to see for myself a sun that revealed itself to be any shape but that of a sphere.

But I still felt there must have been an earlier clue.

I waited for a few more days, still worrying at the problem when I found time, then had an idea. Denton and I had camped one evening in open country beside a broad, shallow river, and as sunset approached I took the video camera and recorder and walked alone up the side of a low hill about half a mile away. At the top there was a clear view towards the north-eastern horizon.

As the sun neared the horizon, the atmospheric haze dimmed its glare and its shape became visible: as ever, a broad disk spiked top and bottom. I switched on the camera, and took a long shot of it. Later I replayed the tape, checking that the picture was clear and steady.

I never tired of the spectacle. The sky was reddening, and after the main disk had passed beneath the horizon, the upright pinnacle of light slid quickly down. For a few minutes after its passing there was an impression of a bright focus of orangewhite at the centre of the red glow … but soon this passed and night came on quickly.

I played the tape again, watching the image of the sun on the recorder’s tiny monitor. I froze the picture, then adjusted the brightness control, dimming the image until only the white shape remained.

There in miniature was an image of the world. My world. I had seen that shape before … long before leaving the confines of the crèche. Those weird symmetrical curves made an overall pattern that someone had once shown me.

I stared at the monitor screen for a long time, then conscience struck me and I switched off to conserve the batteries. I did not return to Denton straight away: I was straining my memory for some key to that faint recollection of the time when someone had drawn four lines on a sheet of card, and held up for all to see the place where Earth city struggled to survive.

The map that Denton and I were compiling was taking on a definite shape.

Drawn on the long roll of stiff paper he had brought, the plan took the form of a long, narrow funnel, with its narrowest point at the patch of woodland a mile or so to the north of where the city had been when we left it.

Our travels had all been within the funnel, enabling us to make measurements of large features from all sides, to ensure that we compiled information as nearly accurate as possible.

Soon the work was finished, and Denton said that we would return at once to the city.

I had, in the video recorder, a complete and cross-referenced visual record of all the terrain we had covered. In the city, the Council of Navigators would examine as much as they felt necessary to plan the city’s next route. Denton told me that other Futures would go north soon, draw another funnel map of the terrain. Perhaps it too would start at the patch of woodland, and take a course five or ten degrees to east or west, or, if the Navigators felt that a safe route could be found in the terrain we had surveyed, the new map would start further up the known territory, and push forward again the frontier of the future we had surveyed.

We headed back towards the city. I had expected, in some melodramatic way, that now we had the information we had been despatched to obtain, we would ride through day and night with no regard to safety or comfort; instead, the leisurely ride through the countryside continued.

“Shouldn’t we hurry?” I said in the end, thinking that perhaps Denton was idling for some reason connected with me; I wished to show that I was willing to move with speed.

“There’s never any hurry up future,” he said.

I didn’t argue with him, but it had occurred to me that we had been away from the city for at least thirty days. In that time, the movement of the ground would have taken the city another three miles away from the optimum, and consequently the city would have had to travel at least that distance to stay within safety limits.

I knew that the unsurveyed territory began only a mile or so beyond the city’s last position.

In short, the city would need the information we had.

The return journey took three days. On the third day, as we loaded the horses and continued on south, the memory I had been seeking came to me. It came unbidden, as is often the case when trying for something buried in the subconscious.

I felt I had exhausted all my conscious memories of the lessons I’d had, and sorting through the memory of the long academic courses had been as fruitless as the sessions had been tedious at the time.

Then, from a subject I had not even considered, the answer came.

I remembered a period in my last few miles inside the crèche, when our teacher had taken us into the realms of calculus. All aspects of mathematics had induced the same response in me—I showed neither interest nor success—and this further development of abstract concepts had seemed no different.

The teaching had covered a kind of calculus known as functions, and we were taught how to draw graphs representing these functions. It was the graphs that had provided the memory key: I had always had a moderate talent for drawing, and for a few days my interest had flickered into life. It died almost immediately, for I discovered that the graphs were not an end in themselves but were drawn to provide a means of finding out more about the function … and I didn’t know what a function was.

One graph in particular had been discussed in great and onerous detail.

It showed the curve of an equation where one value was represented as a reciprocal—or an inverse—of the other. The graph for this was a hyperbola.

One part of the graph was drawn in the positive quadrant, one in the negative.

Each end of the curve had an infinite value, both positive and negative.

The teacher had discussed what would happen if that graph were to be rotated about one of its axes. I had neither understood why graphs should be drawn, nor that one might rotate them, and I’d suffered another attack of daydreaming. But I did notice that the teacher had drawn on a piece of large card what the solid body would look like should this rotation be performed.

The product was an impossible object: a solid with a disk of infinite radius, and two hyperbolic spires above and below the disk, each of which narrowed towards an infinitely distant point.

It was a mathematical abstraction, and held for me then as much interest as such an item should.

But that mathematical impossibility was not taught to us for no reason, and the teacher had not without reason attempted to draw it for us. In the indirect manner of all our education, that day I had seen the shape of the world on which I lived.

Denton and I rode through the woodland at the bottom of the range of hills… and there ahead of us was the pass.

Involuntarily, I drew back on the reins and halted the horse.

“The city!” I said. “Where is it?”

“Still by the river I should imagine.”

“Then it must have been destroyed!”

There could be no other explanation. Had the city not moved in all those thirty days, only another attack could have delayed it. By now the city should at least be in its new position in the pass.

Denton was watching me, an amused expression on his face.

“Is this the first time you’ve been so far north of optimum?” he said.

“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, but 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.