The Pyramids had taken Earth out past Pluto's orbit with a simple shove, slow and massive. It had been enough merely to approximate the direction in which they would want to go. There would be plenty of time for refinements of course later.
But now the time for refinements had come, earlier than they might have expected. They had now time to travel, they knew where to—a star cluster reasonably sure to be rich in Componentiferous planets. It was inherent in the nature of Component mines that eventually they always played out.
There were always more mines, though. If that had not been so, it would have been necessary, perhaps, to stock-breed Components against future needs. But it was easier to work the vein out and move on.
Now the course had to be computed. There were such variables to be considered as: motion of the star cluster; acceleration of the binary-planet system; gravitational influence of every astronomical object in the island universe, without exception.
Precise computation on this basis was obviously not practical. That was not an answer to the problem, since the time required would approach eternity as one of its parameters.
It was possible to simplify the problem. Only the astronomical bodies which were relatively nearby need be treated as individuals. Farther away, the Pyramids began to group them in small bunches, still farther in large bunches, on to the point where the farthest—and the most numerous—bodies were lumped together as a vague gravitational "noise" whose average intensity alone it was required to know and to enter as a datum.
And still no single Component could handle even its own share of the problem, were the "computer" they formed to be kept within the range of permissible size.
It was for this that the Component which had once been Tropile was taken out of storage.
This was all old stuff to the Pyramids; they knew how to handle it. They broke the problem down to its essentials, separated even those into many parts. There was, for example, the subsection of one certain aspect of the logistical problem which involved locating and procuring additional Components to handle the load.
Even that tiny specialization was too much for a single Component, but fortunately the Pyramids had resources to bring to bear. The procedure in such cases was to hitch several Components together.