“Do you know?”

“Destaine said that the movement of the ground was cyclic. Fle 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 northwest to determine the extent of this marsh. If it is not too wide we can deviate from due north for a time, and make up the difference later.

Following this entry were two pages of the theory Blayne had tried to explain to me. I read it through twice, and each time it made slightly better sense. I left it and read on. Destaine wrote:

Chen has provided the inventory of fissionable materials I requested. All of it waste! With the translat generator, no more need! Said nothing to L. I enjoy the arguments with him… why curtail them now? Future generations will be warm!

Today’s outside temperature: — 23°C. Still we move north.

Later:

Trouble with one of the caterpillar tracks. T. has advised me to authorize stripping them. Says that Sturner reports from the north that he has found what appears to be the remains of a railway line. Some incredible scheme to run the establishment along the tracks somehow. T. says it would work O.K.

Later:

Decided to create a guild system. Pleasant archaism that everyone approves. A way of structuring the organization without drastically changing the way the place is run, but I think it might impose a form to the establishment that will survive us all.

Caterpillar-track stripping proceeding well. Has caused a long delay. Hope we can catch up.

Natasha gave birth today: boy.

Doctor S. gave me some more pills. Says I’m working too hard, and have to rest. Later, maybe.

Towards the end of the Directive, a more didactic tone emerged:

What I have written here shall be privy only to those who venture outside; no need for those inside the establishment to be reminded of our dreadful prospects. We are organized enough: we have sufficient mechanical power and human initiative to maintain us safely in this world for ever more. Those who follow must learn the hard way of what will happen if we fail to exploit either our power or our initiative, and this knowledge will suffice to keep both working to the maximum.

Someone from Earth must find us one day, God willing. Until then our maxim is survival, at any cost.

From now, it has been agreed and is hereby directed:

That the ultimate responsibility lies in the hands of the Council. These men shall navigate the establishment, and be known as Navigators. Their number, which shall at no time fall below twelve, shall be elected from the senior members of the following guilds:

Track Guild: who shall be responsible for the maintenance of the rail-way along which the establishment runs;

Traction Guild: who shall be responsible for the maintenance of the motive power of the establishment;

Future Guild: who shall be responsible for surveying the lands that lie in future time of our establishment;

Bridge-Builders Guild: who shall be responsible for safe conduit over physical obstacles, should no other way be available.

Further, should it be necessary to create other guilds in the future, no guild might be created except by unanimous vote of the Council.

(signed)

Francis Destaine

The major bulk of the Directive consisted of short entries, dated in a sequence that ran from 23 February 1987 to 19 August 2023. The final signed statement was dated 24 August 2023.

There were two further sheets. One was a codicil, marking the formation of the Barter Guild and the Militia Guild. These were undated. The other sheet was a graph drawn by hand. It showed the hyperbola produced by the equation y=1/x and beneath it were some mathematical signs which I could not understand.

Such was Destaine’s Directive.