"Did anyone ask you to do calculations?"
"Why, yes." His brow wrinkled. "When I was very young, it was my father. He encouraged me, gave me harder and harder problems."
According to every instrument, and backed by Lola's own experience, he was not lying.
"During our first session," Lola said gently, "you told me that you never knew your father."
"That's true." The instruments confirmed his confusion—and still insisted that he was telling the truth. "I didn't know him," he went on. "But this is weird. If I close my eyes, I can see him. He's bending down and asking me something. And I know he died, when I was still very little."
"Let's take a look. Concentrate on him. Listen to him."
Lola felt disappointment as the computer feed came in. This derived-reality scene lacked the sharpness of previous sequences. The visual information was minimal, and a gruff but soft voice was saying, "All right, here's another one. What's twelve thousand and sixteen times thirty-seven?" The human shape that came with the voice was blurred in outline, its features indistinct. Only the numbers seemed real, springing into existence before her, then rapidly reshaping themselves into a new form. She rattled off the result like a machine: "four hundred and forty-four thousand, five hundred and ninety-two."
"Right!"
After that word of praise came a sudden discontinuity. She felt overwhelming fear and sadness. Another form hovered over her, and a harsher voice was in her ears: "Forget that stuff, and forget them. They're both dead and they're not coming back. You do what I say now. Understand? Exactly what I say and when I say—or you'll pay."
The image faded. Lola waited, but nothing else happened.
Memory, or imagination?
"Bryce. I'm going to ask you questions. I want you to reply as quickly as you can, or tell me if you can't answer."
"Very well." There was no alarm or tension in him. He seemed almost bored.
"What is three hundred and sixty-four times nine hundred and seventy-six?" Lola had his interior body scans, as well as the evidence of the telemetry. He had no form of augmenting implant. His reply came almost before she had finished speaking: "Three hundred and fifty-five thousand, two hundred and sixty-four."
"What is the cube root of nineteen?" Lola did not bother to check his first answer. There would be time for that after the session.
"Two-point-six-six-eight-four-zero. How many more places do you want?"
"That will be enough." She would check that answer, too, but she had little doubt as to what she would find. No one would spit out answers with such confidence and precision unless they were correct. Bryce Sonnenberg was a born calculator. His "memory" of his father asking him questions was unreliable, since his own subconscious might be feeding him those answers.
However, there was a huge difference between arithmetic and mathematics. History was full of idiots savants, able to do prodigious feats of mental calculation while having no idea of the nature of mathematical proof. Was he truly a mathematician, as he had claimed?
"You specialize in number theory," she said. "Would you agree that theory is a long way from simple numbers and calculations?"
She expected agreement, but instead his whole face brightened and he laughed aloud. "Are you kidding? There couldn't be a closer connection. In classical number theory, everything starts and ends with the numbers." His words came bubbling out twice as fast as usual. He was more animated than he had ever been before. "You see, it's not like physics or biology, where you might do an experiment and then spend years trying to come up with a theory, or develop a theory and not be able to find a practical way to test it. All the great number theorists in history, Fermat and Euler and Gauss and Ramanujan and Deslisle, all the way back to Euclid—they found their theorems by playing with the numbers themselves. They still had to prove a result after they discovered it, and that can get fiendishly hard—like the Goldbach conjecture, or the infinite number of prime pairs, or the last Fermat theorem—but it helps a lot, when you're trying for a proof, if you are already convinced that the result is true. Quadratic reciprocity, the little Fermat theorem, the prime-number theorem—they all started from numerical examples. Of course, sometimes even the greatest theorists were wrong. Even Fermat was wrong about a particular sequence of numbers being primes. But then the numbers proved that, too. One ugly counterexample; it's enough to dispose of a beautiful conjecture. Did you ever hear of de Pulignac?"
Lola was surprised to find that he knew she was still there. "I don't think so. It's not a name that springs to mind."
"It ought to be." He grinned at her. "Poor old de Pulignac—he is an awful warning to number theorists. In 1848, he stated that every odd number can be written as a sum of a power of two and a prime number. For example, thirty-seven is thirty-two plus five, and eighty-seven is sixty-four plus twenty-three. De Pulignac said he had confirmed his theorem for every number up to three million."
"And?"
"Well, he was wrong. And in a very embarrassing way. His theorem doesn't work for one hundred and twenty-seven, and that's not what you'd call a big number. Try it for yourself and you'll see."
"I'll take your word for it." But she didn't need to. Anyone could improvise a lie. What a person could not do was display expert knowledge in a particular field where it was easy to expose a factual falsehood. "Have you ever had other memories in which you were doing mathematical calculations?"
"Not calculations, but writing numbers. I've had several sets of memories, all mixed up with each other."
"Let's take a look. This time I'd like to try for full synthesis."
"Sure." He was familiar with the protocol, and as his chair inclined backward, he was reaching for the sensor cups. Lola did the same. The other sensors were already in position. This morning the computer link was unusually slow to establish itself. She waited, wishing that her headache would go away.
The computer's difficulty in making linkage was not Bryce's fault; it was hers. Her stomach was churning, and the top of her head felt ready to blow off. Physician, heal thyself. She had had no sleep and no food, but who was to blame for that? She was. She had not been able to eat breakfast, could not get last night out of her mind. Who was Jinx Barker, what was he? Why had he taken on a false name? Had his move into an office close to hers been accidental, as he claimed? Or had he sought her out, stalked her, and moved effortlessly into her life and bed?
God, she had been so easy. A pushover. It hurt to think how easily she might have been deceived and used.
But her sense of logic came struggling back. Used how? He had given her great pleasure, and he had taken nothing from her. It was ridiculous to suggest she had been used or abused.
The computer's synthesis impatiently pulled her away from her introspection. It was almost a relief to be thrust into Bryce Sonnenberg's reality.
His hand moved in front of him, withered and marked by dark-brown spots. He was sitting in an easy chair, borne down by some crushing force. Not gravity, nor acceleration. It was the weight of years, a deadly fatigue that dragged him lower. He was painstakingly writing a long and meaningless series of numbers, in purple ink on creamy white paper: 3: 0.00463; 4: 0.01389; 5: 0.02778; 6: 0.04630; 7: 0.06944; 8: 0.09722 . . .
He ignored the numbers—they would all be recorded— and concentrated on the fingers that held the pen. He saw a strange double image. There was the skeletal hand, its joints swollen and reddened and its back marked with brown liver spots. At the same time it was a plumper, well-fleshed hand, trembling slightly, with pale digits and carefully trimmed nails.
And the field of view was also double. He was sitting at a desk, looking far out over the curved surface of a world with a pink sunset and a dusty, red landscape. And at the same time a younger version of himself was sitting in some kind of submersible, moving deep through clear water. The ports on either side showed long strands of dark-green weed, where little red-bellied silverfish were wriggling along through the trailing fronds. There was a sens
e of tension within him. He was waiting for something to happen, some long-planned accident that would not be an accident. And while he waited, simply to have something to do, he was writing. The same numbers were appearing, continuing the sequence: 7: 0.06944; 8: 0.09722; 9: 0.11574; 10: 0.12500 . . . As he watched, they began to vanish, fading into a faint set of isolated spectral digits.
Lola waited, staring at nothing, until the final ghostly number had gone completely. At last she removed the sensor cups. Bryce Sonnenberg was lying in the inclined chair, eyes covered.
"Well?" he said.
"I'll be honest with you." Lola gave the signal to swing Bryce back to an upright position. "I don't have the slightest idea what all that was about. But believe it or not, we are making progress. I hate to sound overoptimistic, but I think you are close to a breakthrough point. In another couple of sessions, you'll know what all this means—and it won't come from me, it will come from you. You are suddenly going to find that you can make sense of everything. Meanwhile, let me work on the numbers. I'll give the sequence to the computer, and it can look for correlations with every sequence that's ever been invented."
"Oh, you don't need to do that." Sonnenberg was removing the neural contacts. "I could have told you what the numbers were before we started, but I didn't think it would help. They are just probabilities for throwing dice. If you throw three dice, then your score must be some number between three and eighteen. Suppose you want to know your chances of scoring a particular total. Well, there's just one way you can score three. But there's ten different ways you can score six, and twenty-seven ways you can score ten. That gives odds of 1 in 216 for scoring three, 10 in 216 for scoring six, 27 in 216 for scoring ten, and so on, for all the others. Convert those to decimals, and you have the numbers that I—or whoever—was writing."
He was right. It did not help. But it was curious that he would have the answer so close at hand.
"Do you gamble much?"
"Never." The session was over, and he was standing up.
"So how do you know those odds so well?"
"I don't know." He shrugged. "I just do."
Was it something that any mathematician would know? He had said that in his own field, intimate familiarity with numbers was assumed. But it was not Lola's field. She needed help. For the rest, she was convinced that the real key did not lie in numbers. It lay in that swollen, arthritic hand, seen together with the overlain doppelganger of a younger version of its own self.
There, if anywhere, was the solution to Bryce Sonnenberg's problem.
16
The announcement had been placed in the fourth access level of the Electronic Daily. Only a reader who was interested in knowing everything about that specific subject would dig down so far in the files, and even then there would be little reward.
The obituary was quite short, not much more than a bald statement of facts: "The death was reported today of Jeffrey Cayuga, leader of the fifth, sixth, and seventh Saturn expeditions. Mr. Cayuga was a member of a well-known family of planetary explorers, and the great nephew of Jason Cayuga, who served as a junior officer on the first Saturn expedition. Mr. Cayuga's death, of natural causes, occurred aboard the vessel Weland. His heir is his nephew, Joss Cayuga, who is one of the few survivors of the Ceres final battle and recently arrived in the Jovian system from his home in the Belt."
Alicia Rios was watching Cayuga as he read the announcement. They were sitting facing each other across a low table in her forty-room apartment, deep in the lowest residential levels of Ganymede. She and Cayuga both sought the safest possible place to live, but they disagreed on how that could be achieved. He favored the isolated planetoid of Lysithea, a world that could not be approached from space without alerting his defense systems. Alicia preferred to live on a busy and populated world, in a large suite with a single guarded entrance—and a dozen hidden escape tunnels that she alone knew.
"Reasonable?" she said, as soon as he had finished.
"It would have been even better to have no announcement at all. And I don't like this part." Cayuga pointed to the last sentence, and the name, Joss Cayuga. He appeared to be a baby-faced nineteen-year-old, with glossy, jet-black hair and smooth, pale, and unlined skin. He had been nibbling constantly at the cold snacks on a great tray that Alicia had placed in front of him, and now he was playing with a sharp-edged serving knife.
Alicia sighed. "Be reasonable. The name's in there because I was specifically asked who inherited. It was a perfectly natural question. How could I avoid answering it?"
"I guess you couldn't. Anything else from the media?"
"Nothing significant. No one asked how you died; no one seemed to care what had happened to your body."
"How he died. What happened to his body. You know the rules, Rios. Jeffrey Cayuga must be a fading memory. Past tense only, please. And if you and I meet in public, remember that we hardly know each other."
"For God's sake, Cayuga." Alicia raised sculptured, pencil-thin eyebrows. "Are you getting even more paranoid? It's hardly as though you and I have never been through this before. As for what we say here, we're completely alone, and I check for bugs every day. No one gets in here whom I don't know personally."
"If I'm paranoid, then you are irresponsible." Joss Cayuga's voice resembled Jeffrey Cayuga's, but it was softer in tone and a little lower in pitch. "Have you forgotten how close we are to success on Helene? One more month, and it will be ready to proceed. How would you like the Club to label you as the one who risked the whole project?"
"Don't try to threaten me, Cayuga," Alicia snapped back. "And don't lecture me, either. I'm the one who said we should do this here, in person, rather than through some communication channel that might be tapped."
"Point taken." Cayuga turned from the display. "So let's get down to business. I don't want to stay on Ganymede one minute longer than I have to. What did Jinx Barker find out?"
"Exactly what we asked him to find out." Alicia summarized Jinx's activities over the past few weeks, and what he had learned about Lola Belman and Bryce Sonnenberg. "Her patient is a strange individual," she concluded, "but anyone who goes to a haldane is likely to be that. Jinx will stake his professional reputation on the fact that Sonnenberg has no relevance to our interests. So far as he is concerned, the investigation is over. He is lying low, asking me what he ought to do next. I think I know what he wants to do."
"Dispose of Lola Belman?"
"Exactly. But I don't see that as a necessity. Jinx can simply tell her that he has to return to the Belt, and break off the relationship."
"If it were anyone but Lola Belman, I would probably agree." Cayuga tested the knife's edge thoughtfully on his finger. "But Jinx has been dealing with a haldane. We know what he learned about her. I'm afraid of what she might have learned about him."
"He says, nothing—except what he wanted her to learn."
"That may reassure you, but it leaves me cold. Haldanes can't read minds, the way a lot of people think, but they are awfully good at reading everything else. I say, Why take the risk? Let Jinx do the rest of his work."
Alicia shrugged. "If you feel that way. Jinx will be delighted to oblige. Lola Belman?"
"Lola Belman, and while we're at it, Bryce Sonnenberg. That ends our worries, even if Jinx is wrong and she knows too much."
"What about the others? Jinx met Lola Belman's kid brother, and his fat friend Battachariya."
"I think so." Cayuga stabbed the knife he was holding deep into the serving tray. "Cut root and branch—that has been our philosophy. A clean sweep is safer."
"You don't have to get symbolic with me." She reached forward, plucked the knife free, and examined the gash it had made in the platter. "You just ruined my best tray. All right, I'll tell Jinx to go ahead at once."
"When you do, make something else clear to him." Cayuga gestured to the knife in her hand. "We don't want any physical evidence left behind. Tell him: no guns, no knives, nothing that might be traced back to him
or to us."
"Jinx won't mind that at all. In fact, he'll be delighted." Alicia smiled. "He always finds work more exciting when he's allowed to make it what you might call highly personal."
* * *
The haldane profession had its hidden dangers. Lola had heard of only two cases where a haldane had been attacked by patients, but she knew of scores where the haldane had been drawn deep into a patient's own psychoses.
It was a consequence of a natural empathy for others, reinforced by years of training. And perhaps it did not apply only to patients. Maybe it happened to lovers, too. Lola, with a dozen patients to worry about, found herself obsessed with Conner Preston.
She stared at her display screen, but she hardly knew what was showing there. After their last night together he had simply disappeared. His office was empty. His message center said that he was on special assignment and could not be reached. That sounded quite reasonable—he worked for the Belt, where secrecy and undercover work had been a way of life even before the war—but Lola's mind offered a dozen other explanations.
Suppose that Conner had been preconditioned to resist the sort of hooks that she had planted. Haldanes tended to assume that they were the keepers of the flame, guardians of a special set of secret techniques possessed by no one else. But that might not be true. There were rumors of Belt technologies, developed before the war, that affected the brain both physically and mentally. If anyone would find those techniques useful, it would surely be the media, with their obsession for scoops and exclusive stories.
Suppose Conner had been protected against her hooks and had responded with the "Jinx Barker" name as a red herring designed to keep her away from his real work. He had refused to talk about that, or reveal who he was working for, even when he appeared to be in the response state. According to conventional haldane theory, that meant either that the information was a closely guarded secret, or else the subject was protected against inquiry. Suppose Conner had been conditioned to say nothing if anyone tried to use haldane hooks and probes on him, and that, after it, he had been told to vanish without another word.
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