in what was left of the sky. He seemed to fluctuate between
bitter sureness of doom and a stupidly optimistic belief that something
could be done to avert that doom. But whatever his mood, he went on
working and scheming furiously. Maybe it was the desperate need to keep
himself occupied that drove him, or perhaps it was the pleading he saw
in the eyes around him. In the end, determination conquered his
pessimism.

Somewhere in the combination of the science he had learned in his own
world and the technique of magic that applied here there had to be an
answer--or a means to hold back the end of the world until an answer
could be found.

The biggest problem was the number of factors with which he had to deal.
There were seven planets and the sun, and three thousand fixed stars.
All had to be ordered in their courses, and the sky had to be complete
in his calculations.

He had learned his trade where the answer was always to add one more
circuit in increasing complexity. Now he had to think of the simplest
possible similarity computer. Electronics was out, obviously. He tried
to design a set of cams, like the tide machine, to make multiple
tracings on paper similar to a continuous horoscope, but finally gave
it up. They couldn't build the parts, even if there had been time.

He had to depend on what was available, since magic couldn't produce any
needed device and since the people here had depended on magic too long
to develop the other necessary skills. When only the broadest powers of
magic remained, they were hopeless. Names were still potent, resonance
worked within its limits, and the general principles of similarity still
applied; but those were not enough for them. They depended too heavily
on the second great principle of contagion, and that seemed to be
wrapped up with some kind of association through the signs and houses
and the courses of the planets.

He found himself thinking in circles of worry and pulled himself back to
his problem. Normally, a computer was designed for flexibility and to
handle varying conditions. This one could be designed to handle only one
set of factors. It had to duplicate the courses of the objects in their
sky and simulate the general behavior of the dome. It was not necessary
to allow for all theoretical courses, but only for the normal orbits.

And finally he realized that he was thinking of a model--the one thing
which is functionally the perfect analogue.

It brought hi