"We could do that, Wili. We could do that and more. But no longer."
"But why not?" It was as though the universe had suddenly been taken back from his grasp. His voice was almost a wail.
"In the beginning, it was the War. Fifty years ago there were men alive up there. They starved or they came back to Earth. After the War there were the plagues. Now... now we could do it again. It would be different from before, but we could do it... if it weren't for the Peace Authority." The last two words were in English. He paused and then said, "Mundopaz."
Wili looked into the sky. The Peace Authority. They had always seemed a part of the universe as far away and indifferent as the stars themselves. He saw their jets and occasionally their helicopters. The major highways passed two or three of their freighters every hour. They had their enclave in Los Angeles. The Ndelante Ali had never considered hitting it; better to burgle the feudal manors of Aztlán. And Wili remembered that even the lords of Aztlán, for all their arrogance, never spoke of the Peace Authority except in neutral tones. It was fitting in a way that something so nearly supernatural should have stolen the stars from mankind. Fitting, yet now he knew, intolerable.
"They brought us peace, Wili, but the price was very high." A meteor flashed across the sky, and Wili wondered if that had been a piece of man's work, too. Naismith's voice suddenly became businesslike, "I said we must talk, and this is the perfect time for it. I want you for my apprentice. But this is no good unless you want it also. Somehow, I don't think our goals are the same. I think you want wealth: I know what's in the bag yonder. I know what's in the tree behind the pond."
Naismith's voice was dry, cool. Wili's eyes hung on the point where the meteor had swept to nothingness. This was like a dream. In Los Angeles, he would be on his way to the headsman now, an adopted son caught in treachery. "But what will wealth get you, Wili? Minimal security, until someone takes it from you. Even if you could rule here, you would still be nothing more than a petty lord, insecure.
"Beyond wealth, Wili, there is power, and I think you have seen enough so that you can appreciate it, even if you never thought to have any"
Power. Yes. To control others the way he had been controlled. To make others fear as he had feared. Now he saw the power in Naismith. What else could really explain this man's castle? And Wili had thought the spirit a jealous lover. Hah! Spirit or projection, it was this man's servant. An hour ago, this insight alone would have made him stay and return all he had stolen. Somehow, he still couldn't take his eyes off the sky.
"And beyond power, Wili, there is knowledge — which some say is power." He had slipped into his native English, and Wili didn't bother to pretend ignorance. "Whether it is power or not depends on the will and the wisdom of its user. As my apprentice, Wili, I can offer you knowledge, for a surety; power, perhaps; wealth, only what you have already seen."
The crescent moon had cleared the pines now. It was one more thing that would never be the same for Wili.
Naismith looked at the boy and held out his hand. Wili offered his knife hilt first. The other accepted it with no show of surprise. They stood and walked back to the house.
SIX
Many things were the same after that night. They were the outward things: Wili worked in the gardens almost as much as before. Even with the gifts of food the visitors had brought, they still needed to work to feed themselves. (Wili's appetite was greater than the others'. It didn't seem to help; he remained as undernourished and stunted as ever.) But in the afternoons and evenings he worked with Naismith's machines.
It turned out the ghost was one of those machines. Jill, the old man called her, was actually an interface program run on a special processor system. She was good, almost like a person. With the projection equipment Naismith had built into the walls of the veranda, she could even appear in open space. Jill was the perfect tutor, infinitely patient but with enough "humanity" to make Wili want to please her. Hour after hour, she flashed language questions at him. It was like some verbal Celest. In a matter of weeks, Wili progressed from being barely literate to having a fair command of technical written English.
At the same time, Naismith began teaching him math. At first Wili was contemptuous of these problems. He could do arithmetic as fast as Naismith. But he discovered that there was more to math than the four basic arithmetic operations. There were roots and transcendental functions; there were the relationships that drove both Celest and the planets.
Naismith's machines showed him functions as graphs and related function operations to those pictures. As the days passed, the functions became very specialized and interesting. One night, Naismith sat at the controls and caused a string of rectangles of varying width to appear on the screen. They looked like irregular crenellations on some battlement. Below the first plot, the old man produced a second and then a third, each somewhat like the first but with more and narrower rectangles. The heights bounced back and forth between 1 and -1.
"Well," he said, turning from the display, "what is the pattern? Can you show me the next three plots in this series?" It was a game they had been playing for several days now. Of course, it was all a matter of opinion what really constituted a pattern, and sometimes there was more than one answer that would satisfy a person's taste, but it was amazing how often Wili felt a certain rightness in some answers and an unaesthetic blankness in others. He looked at the screen for several seconds. This was harder than Celest, where he merely cranked on deterministic relationships. Hmmm. The squares got smaller, the heights stayed the same, the minimum rectangle width decreased by a factor of two on every new line. He reached out and slid his finger across the screen, sketching the three graphs of his answer.
"Good," said Naismith. "And I think you see how you could make more plots, until the rectangles became so narrow that you couldn't finger-sketch or even display them properly.
"Now look at this." He drew another row of crenellations, one clearly not in the sequence: The heights were not restricted to 1 and -1 . "Write me that as the sum and differences of the functions we've already plotted. Decompose it into the other functions." Wili scowled at the display; worse than "guess the pattern," this was. Then he saw it: three of the first graph minus four copies of the third graph plus...
His answer was right, but Wili's pride was short-lived, since the old man followed this problem with similar decomposition questions that took Wili many minutes to solve... until Naismith showed him a little trick — something called orthogonal decomposition — that used a peculiar and wonderful property of these graphs, these "walsh waves" he called them. The insight brought a feeling of awe just a little like learning about the moving stars, to know that hidden away in the patterns were realities that might take him days to discover by himself.
Wili spent a week dreaming up other orthogonal families and was disappointed to discover that most of them were already famous — haar waves, trig waves — and that others were special cases of general families known for more than two hundred years. He was ready for Naismith's books now. He dived into them, rushed past the preliminary chapters, pushed himself toward the frontier where any new insights would be beyond the farthest reach of previous explorers.
In the outside world, in the fields and the forest that now were such a small part of his consciousness, summer moved into fall. They worked longer hours, to get what crops remained into storage before the frosts. Even Naismith did his best to help, though the others tried to prevent this. The old man was not weak, but there was an air of physical fragility about him.
From the high end of the bean patch, Wili could see over the pines. The leafy forests had changed color and were a band of orange-red beyond the evergreen. The land along the coast was clouded over, but Wili suspected that the jungle there was still wet and green. Vandenberg Dome seemed to hang in the clouds, as awesome as ever. Wili knew more about it now, and someday he would discover all its secrets. It was simply a matter of asking the right questions — of himself and of Paul Naismith.