by Vernor Vinge
“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.
6
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 Tightness in some answers and an unesthetic 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.
Indoors, in his greater universe, Wili had completed his first pass through functional analysis and now undertook a three-pronged expedition that Naismith had set for him: into finite Galois theory, stochastics, and electromagnetics. There was a goal in sight, though (Wili was pleased to see) there was no ultimate end to what could be learned. Naismith had a project, and it would be Wili’s if he was clever enough.
Wili saw why Naismith was valued and saw the peculiar service he provided to people all over the continent. Naismith solved problems. Almost every day the old man was on the phone, sometimes talking to people locally—like Miguel Rosas down in Santa Ynez—but just as often to people in Fremont, or in places so far away that it was night on the screen while still day here in Middle California. He talked to people in English and in Spanish, and in languages that Wili had never heard. He talked to people who were neither Jonques nor Anglos nor blacks.
Wili had learned enough now to see that these were not nearly as simple as making local calls. Communication between towns along the coast was trivial over the fiber, where almost any bandwidth c
ould be accommodated. For longer distances, such as from Naismith’s palace to the coast, it was still relatively easy to have video communication: The coherent radiators on the roof could put out microwave and infrared beams in any direction. On a clear day, when the IR radiator could be used, it was almost as good as a fiber (even with all the tricks Naismith used to disguise their location). But for talking around the curve of the Earth, across forests and rivers where no fiber had been strung and no line of sight existed, it was a different story: Naismith used what he called “short-waves” (which were really in the one- to ten-meter range). These were quite unsuitable for high-fidelity communication. To transmit video—even the wavery black-and-white flat pictures Naismith used in his transcontinental calls—took incredibly clever coding schemes and some real-time adaptation to changing conditions in the upper atmosphere.
The people at the other end brought Naismith problems, and he came back with answers. Not immediately, of course; it often took him weeks, but he eventually thought of something. At least the people at the other end seemed happy. Though it was still unclear to Wili how gratitude on the other side of the continent could help Naismith, he was beginning to understand what had paid for the palace and how Naismith could afford full-scale holo projectors. It was one of these problems that Naismith turned over to his apprentice. If he succeeded, they might actually be able to steal pictures off the Authority’s snooper satellites.
It wasn’t only people that appeared on the screens.
One evening shortly after the first snowfall of the season, Wili came in from the stable to find Naismith watching what appeared to be an empty patch of snow-covered ground. The picture jerked every few seconds, as if the camera were held by a drunkard. Wili sat down beside the old man. His stomach was more upset than usual and the swinging of the picture did nothing to help the situation—but his curiosity gave him no rest. The camera suddenly swung up to eye level and looked through the pine trees at a house, barely visible in the evening gloom. Wili gasped—it was the building they were sitting in.
Naismith turned from the screen and smiled. “It’s a deer, I think. South of the house. I’ve been following her for the last couple of nights.” It took Wili a second to realize he was referring to what was holding the camera. Wili tried to imagine how anyone could catch a deer and strap a camera on it. Naismith must have noticed his puzzlement. “Just a second.” He rummaged through a nearby drawer and handed Wili a tiny brown ball. “That’s a camera like the one on the critter. It’s wide enough so I have resolution about as good as the human eye. And I can shift the decoding parameters so it will ‘look’ in different directions without the deer’s having to move.
“Jill, move the look axis, will you?”
“Right, Paul.” The view slid upward till they were looking into overhanging branches and then down the other side. Wili and Naismith saw a scrawny back and part of a furry ear.
Wili looked at the object Paul had placed in his hand. The “camera” was only three or four millimeters across. It felt warm and almost sticky in Wili’s hand. It was a far cry from the lensed contraptions he had seen in Jonque villas. “So you just stick them to the fur, true?” said Wili.
Naismith shook his head. “Even easier than that. I can get these in hundred lots from the Greens in Norcross. I scatter them through the forest, on branches and such. All sorts of animals pick them up. It provides just a little extra security. The hills are safer than they were years ago, but there are still a few bandits.”
“Umm.” If Naismith had weapons to match his senses, the manor was better protected than any castle in Los Angeles. “This would be greater protection if you could have people watching all the views all the time.”
Naismith smiled, and Wili thought of Jill. He knew enough now to see that the program could be made to do just that.
Wili watched for more than an hour as Naismith showed him scenes from a number of cameras, including one from a bird. That gave the same sweeping view he imagined could be seen from Peace Authority aircraft.
When at last he went to his room, Wili sat for a long while looking out the garret window at the snow-covered trees, looking at what he had just seen with godlike clarity from dozens of other eyes. Finally he stood up, trying to ignore the cramp in his gut that had become so persistent these last few weeks. He removed his clothes from the closet and laid them on the bed, then inspected every square centimeter with his eyes and fingers. His favorite jacket and his usual work pants both had tiny brown balls stuck to cuffs or seams. Wili removed them; they looked so innocuous in the room’s pale lamplight.
He put them in a dresser drawer and returned his clothes to the closet.
He lay awake for many minutes, thinking about a place and time he had resolved never to dwell on again. What could a hovel in Glendora have in common with a palace in the mountains? Nothing. Everything. There had been safety there. There had been Uncle Sylvester. He had learned there, too—arithmetic and a little reading. Before the Jonques, before the Ndelante—it had been a child’s paradise, a time lost forever.
Wili quietly got up and slipped the cameras back into his clothing. Maybe not lost forever.
7
January passed, an almost uninterrupted snowstorm. The winds coming off Vandenberg brought ever-higher drifts that eventually reached the mansion’s second story and would have totally blocked the entrances if not for the heroic efforts of Bill and Irma. The pain in Wili’s middle became constant, intense. Winters had always been bad for him, but this one was worse than ever before, and the others eventually became aware of it. He could not suppress the occasional grimace, the faint groan. He was always hungry, always eating—and yet losing weight.
But there was great good, too. He was beyond the frontiers of Naismith’s books! Paul claimed that no previous human had insight on the coding problem that he had attacked! Wili didn’t need Naismith’s machines now; the images in his mind were so much more complete. He sat in the living room for hours—through most of his waking time—almost unaware of the outside world, almost unaware of his pain, dreaming of the problem and his schemes for its defeat. All existence was groups and graphs and endless combinatorical refinements on the decryption scheme he hoped would break the problem.
But when he ate and even when he slept, the pain levered itself back into his soul.
It was Irma, not Wili, who noticed that the paler skin on his palms had a yellow cast beneath the brown. She sat beside him at the dining table, holding his small hands in her large, calloused ones. Wili bristled at her touch. He was here to eat, not to be inspected. But Paul stood behind her.
“And the nails look discolored, too.” She reached across to one of Wili’s yellowed fingernails and gave it a gentle tug. Without sound or pain, the nail came away at its root. Wili stared stupidly for a second, then jerked his hand back with a shriek. Pain was one thing; this was the nightmare of a body slowly dismembering itself. For an instant terror blotted out his gut pain the way mathematics had done before.
They moved him to a basement room, where he could be warm all the time. Wili found himself in bed most of each day. His only view of the outside, of the cloudswept purity of Vandenberg, was via the holo. The mountain snows were too deep to pass travelers; there would be no doctors. But Naismith moved cameras and high-bandwidth equipment into the room, and once when Wili was not lost in dreaming, he saw that someone from far away was looking on, was being interrogated by Naismith. The old man seemed very angry.
Wili reached out to touch his sleeve. “It will be all right, Uncle Syl—Paul. This problem I have always had and worst in the winters. I will be okay in the spring.”
Naismith smiled and nodded, then turned away.
But Wili was not delirious in any normal sense. During the long hours an average patient would have lain staring at the ceiling or watching the holo and trying to ignore his pain, Wili dreamed on and on about the communications problem that had resisted his manifold efforts all these weeks. When the o
thers were absent, there was still Jill, taking notes, ready to call for help; she was more real than any of them. It was hard to imagine that her voice and pretty face had ever seemed threatening.
In a sense, he had already solved the problem, but his scheme was too slow; he needed n*log(n) time for this application. He was far beyond the tools provided by his brief, intense education. Something new, something clever was needed, and by the One True God he would find it!
And when the solution did come it was like a sun rising on a clear morning, which was appropriate since this was the first clear day in almost a month. Bill brought him up to ground level to sit in the sunlight before the newly cleared windows. The sky was not just clear, but an intense blue. The snow was piled deep, a blinding white. Icicles grew down from every edge and corner, dripping tiny diamonds in the warm light.
Wili had been dictating to Jill for nearly an hour when the old man came down for breakfast. He took one look over Wili’s shoulder and then grabbed his reader, saying not a word to Wili or anyone else. Naismith paused many times, his eyes half-closed in concentration. He was about a third of the way through when Wili finished. He looked up when Wili stopped talking. “You got it?”
Wili nodded, grinning. “Sure, and in n*log(n) time, too.” He glanced at Naismith’s reader. “You’re still looking at the filter setting up. The real trick isn’t for a hundred more lines.” He scanned forward. Naismith looked at it for a long time, finally nodded. “I, I think I see. I’ll have to study it, but I think…My little Ramanujan. How do you feel?”