The twenty-first century had not been good to either of the two countries. In Venezuela it was politics, in Colombia drugs; in both countries there had been violence and frequent governmental crises, capped by the decision of the former narcotics lords to take over some of their neighbor’s now far more profitable oil business.
“Pax per Fidem took on North Korea first because it didn’t have a real friend in the world,” Ranjit told his wife. “This time they took on two countries at once because they had different friends—the U.S. has been propping Colombia up since the nineties, and Venezuela was close to both Russia and China.”
“But there’s a lot less killing going on now,” Mevrouw said thoughtfully. “I can’t feel unhappy about that.”
Myra sighed. “But do you think we’ll be better off when the whole world is run by Oceania, Eurasia, and Eastasia?” she asked.
30
BIG NEWS
When the seminar was over, no student had managed to produce a rigorous proof of the infinitude of twin primes, but then Ranjit hadn’t expected one would. Neither had Dr. Davoodbhoy. At their postseminar conference, though, he was visibly happier than before. He flourished the student comment slips at Ranjit with a grin. “Listen to these. ‘I had the feeling I wasn’t just learning how to do mathematics; I was learning what doing mathematics was all about.’ ‘Good stuff. Dr. Subramanian doesn’t treat us like children, more like we were new members of his research team.’ ‘Can I take his next seminar, too?’ And what would you say to”—he glanced again at the slip—“this young lady, Ramya Salgado?”
Ranjit looked uncomfortable. “I know who she is; she was very active in the seminar. Maybe if we needed another warm body to fill the class out.”
“Oh,” said Dr. Davoodbhoy, “I don’t think you need to worry about that. You do want to do another, don’t you? Have you thought of a subject? Maybe something like the Riemann conjecture?”
“There are proofs of that,” Ranjit reminded him.
“Some people don’t think they’re satisfactory. Anyway, there was a proof of Fermat, too—Wiles’s—and that didn’t keep you from finding a better one.”
Ranjit considered, then shook his head. “I’m afraid Riemann is too complicated for anybody but a professional mathematician to care about. How are you going to get the average college student to care about what way the zeros in the Riemann zeta function are distributed? There are better ones around. Euler’s reworking of the Goldbach conjecture, for instance. That’s pure gold. ‘All positive even integers greater than four can be expressed as the sum of two primes.’ Six is three plus three, eight is five plus three, ten is five plus five—or seven plus three, if you like that better. Anybody can understand that! Only nobody has ever proved it—yet.”
Davoodbhoy considered for one of the smaller fractions of a second, then nodded. “Go for it, Ranjit. I might even like to audit one of those sessions myself.”
As the years flowed from that point in time onward, Ranjit began to realize that he truly loved teaching. Each semester brought a new flock of eager students, and of course he had his monthly reviews of the ladder to tend to, and Natasha was growing from a young, promising girl to a slightly older girl of significant promise. If anyone in the world shared Myra’s concerns about the three Pax per Fidem sponsors’ dividing the world among them, there was little sign of it. Silent Thunder was as gentle a conquistador in South America as it had been on the Korean peninsula. The casualty list was not much longer. The problems of feeding and caring for the suddenly technology-less populations were as quickly met. The outside world observed, and discussed, and seemed to think that Pax per Fidem had done a reasonably good thing.
Part of the reason why the affair had gone so well, Ranjit knew, was that the advance planning had been meticulous. Weeks before the attack the two surviving old American aircraft carriers had been loaded up with everything needed for the job, the goods supplied mostly by Russia and China. Fully prepared, they were deployed to the Gulf of Mexico—on “training missions,” the routine Department of Defense announcement said—and in fact ready to start supplying emergency help almost before the echoes of Silent Thunder’s nuclear blasts had died away. Even Myra had to admit that the effects had not been bad.
They were dawdling over a leisurely Sunday breakfast in the garden, just the three of them. Ranjit was checking some lecture possibilities on one screen, Myra idly following the news on another, while Natasha, who was nearing her twelfth birthday, practiced her backstroke in the pool. Then Myra looked up, sighing. “It looks like they’re coming to an agreement,” she told her husband. “Kenya and Egypt, and the other countries that depend on the Nile River water.”
He gave her a comfortable smile. “I thought they would,” he said. He had, in fact, all but guaranteed they would, at a time, no more than six months past, when the two principals had mobilized their not inconsiderable military might and sent the armies to glare at each other. But then the UN Security Council had favored them with one of its strongly worded warnings. “I guess they take the Security Council more seriously now, with Silent Thunder always looming,” Myra ruminated.
Ranjit demonstrated what an intelligent husband he was by omitting any “I told you so.” All he said was, “I’m glad they’re working it out. Listen. What would you think if I said my next seminar would be on the Collatz conjecture?”
Myra looked puzzled. “I don’t think I’ve ever heard of that one.”
“Probably not,” Ranjit agreed. “Most people haven’t. Old Lothar Collatz never got the publicity he was entitled to. Here, I’ll show you.” He turned his screen so that they could both see it. “Take any number—something under three digits; it works with really big ones just as well, but it takes too long. Got the number?”
Myra essayed, “Well, how about, say, eight?”
“Good one. Now divide it by two, and keep on dividing by two until you can’t get a whole-number answer anymore.”
Obediently Myra said, “Eight, four, two, one. Is that what you mean?”
“That is exactly what I mean. Wait a minute while I put it on the screen…. All right. That is what we will call rule number one for Collatz: When it’s an even number, divide it by two and keep on doing that until you don’t have an even number anymore. Now take an odd number.”
“Um…five?”
Ranjit sighed. “All right, we’ll just do the easy ones. So now we apply rule number two. If the number is odd, you multiply it by three and add one.”
“Fifteen…sixteen,” Myra supplied.
“Good. Now you’ve got an even number again, so you go back to rule one. Let me put that on the screen.”
As Ranjit quickly typed eight, four, two, one next to his other numbers, Myra raised her eyebrows. “Huh,” she said. “They look the same.”
Ranjit gave her a large smile. “That’s the point. You take any number, even the largest number you can think of, and work on it with just those two rules. Divide by two if it’s even, multiply by three and add one if it’s odd, and you’ll come down to one as a result every time. Even if the numbers you start with are pretty big—wait, I’ll show you.”
He typed some programming instructions onto the screen and gave it the number twenty-seven to start with. Alternating rules one and two as directed, the screen displayed “81…82…41…123…124…62…31…93…94…47…141…142…71…213…214…107…” until Ranjit shut it off. “See how the number keeps bouncing up and down? It’s sort of pretty to watch, and sometimes the numbers get really large—there were some people at Carnegie Mellon who got it up to numbers with more than fifty thousand digits—but in the long run it always collapses to one.”
“Well,” Myra said comfortably, “sure it does. Why wouldn’t it?”
Ranjit gave her a hot look. “We mathematicians don’t deal in the intuitively obvious. We want proof! And back in 1937 old Collatz made his conjecture, which is that that will happen to any number at all, all the way up to infinity. B
ut it has never been proved.”
Myra nodded absently. “Sounds like a good possibility.” Then, shading her eyes as she looked toward the pool and raising her voice, she said, “Better take a break, Tashy! You don’t want to get overtired.”
Ranjit was quick to meet his daughter with a towel, but he was looking at his wife. Finally he said, “Myra? You sound a little bit distracted. Is anything wrong?”
She gave him a fond look, and then a real laugh. “Wrong? Not at all, Ranj. It’s just that—Well, I haven’t seen the doctor yet, but I’m pretty sure. I think I’m pregnant again.”
31
SKYHOOK DAYS
For Myra de Soyza Subramanian, caring for her second infant was even more of a breeze than caring for her first. Her husband, for example, did not now come home depressed from a job he thought irrelevant; his students liked him, he liked his students, and Dr. Davoodbhoy was unfailingly pleased. The outside world was easier to take now, too. Oh, a few nations could not seem to break the habit of making threatening noises at their neighbors. Hardly anyone was actually getting killed, though.
And, over Beatrix Vorhulst’s protest, they had finally moved into their own little house—“little” only by comparison with the Vorhulst mansion—just steps from one of the island’s beautiful broad beaches, where the water was as warm and welcoming as ever. By the time they were settled in their new house, the world outside no longer seemed as threatening. Little Robert splashed in the shallowest part of the pool, while Natasha found deeper water to demonstrate her considerable (and, Ranjit maintained, clearly inherited) skill at swimming—or any other way—when she wasn’t taking sailing lessons from a neighbor who owned a little Sunfish. What made being in their own home particularly pleasant was that Mevrouw Vorhulst had parted with her favorite cook and Natasha’s favorite maid to save Myra the trouble of housework.
Another way in which Myra’s second pregnancy was unlike the first went by the name of Natasha—well, more often it was Tashy. Tashy wasn’t a problem. When she wasn’t winning ribbons for swimming—only in children’s events so far, but she was seen to watch adult races with narrowed eyes and obvious intentions—she was busy at being her mother’s assistant, deputy, and sous-chef. Thus aided, Myra had a gratifying number of hours each day to spend catching up on what was going on in the field of artificial intelligence and autonomous prostheses.
That was quite a lot. By the time Myra had begun to evaluate each muscle twinge in the hope that it might be the beginnings of labor, she was pretty nearly up to speed again.
Of course, that wouldn’t last. By the time the new baby was birthed, weaned, toilet trained, and off to school, Myra would have slipped behind her cohort again. That was inevitable.
Was Myra angry at this tyrannical law of childbearing? It was clearly unjust. It dictated that any woman who wanted a baby had to accept Mother Nature’s inflexible decree that, for a period of time, the cognitive functions of her mind would have to take second place to mothering. It would have to be a fairly significant period, too. Ten years was the accepted minimum before a female AI nerd (or medical doctor or politician or, for that matter, pastry chef) could get back to her career.
Obviously that was unfair. But the world was chronically unfair in so many ways that Myra de Soyza Subramanian had no patience for wasting time in resentment. That was the unchangeable way the world was. What was the point in complaining? There would be a time when both her children were in college. Then she would be as free as any human could ever get, and then she would have twenty, thirty, maybe even fifty years of productive life in which to unravel the riddles of her chosen profession.
Deferred gratification was the name of that game. You didn’t have to like its rules to play by them. And, one way or another, you might even win.
Both Myra and Ranjit considered themselves big winners when Robert Ganesh Subramanian was born. His parents thought they had hit the jackpot with two fine offspring. Robert was a vociferously healthy newborn who gained weight and strength as rapidly as Ranjit and Myra could have hoped for. He tried to turn himself over in his crib even earlier than Natasha had, and was toilet trained almost as early. All of their friends declared that he was the handsomest child they had ever seen, and they weren’t really lying, either. Robert was the kind of infant for whose picture baby-food manufacturers would have paid handsomely to put on their labels.
Interestingly, if there was anyone who loved Baby Robert more than his parents did, that person was little Natasha, who wasn’t all that little anymore and was already beginning to demonstrate a considerable aptitude for athletics, education, and getting her parents to do just about everything she might require of them.
Which, in this case, was to let her take care of Baby Robert.
Well, not quite all of his care. Not the part that involved situations that smelled really bad. But dressing Robert, pushing Robert around in his stroller, playing with Robert—Natasha demanded the privilege of taking care of those things, and after some early worried hesitation, Myra gave her daughter what she asked.
Actually, Natasha was good at the job. When Robert screamed or roared, it was Natasha who could usually fit words to his outcries. And when his mother took him away, Natasha had her own life to live, school or her daily swim sessions or just spending time with her friends…or most likely combining her interests, with her friends joining her at the pool, or Robert slumbering beside her as she studied English verbs or the history of India and its satellite nations.
All this, of course, was a good thing for Myra. With Natasha relieving her of so much of the work of raising Robert, Myra was not falling behind as rapidly as she might have feared in AI nerding. And what was good for Myra was certainly good for Ranjit, for whom his wife was as dear—and as unpredictably exciting—as she had been on the day they were wed.
All in all, things were going well for Ranjit Subramanian. One seminar per semester was all he needed to do, Dr. Davoodbhoy had decreed, but as long as he was going to do the one, they might as well make it a big one. So Ranjit’s classroom had become the exact supersize theater in which he had thrilled to Joris Vorhulst’s stories of the worlds of the solar system. Ranjit didn’t have twenty students at a time anymore, either. Now he had a hundred. Which, Dr. Davoodbhoy assured him, entitled him to the luxury of a teaching assistant—that eager young woman, Ramya Salgado, now possessed of a master’s degree of her own, who had so enriched his second seminar—and freedom to do his own “research” for the rest of each semester. Davoodbhoy intimated that that was so he could get a head start on whatever proof he was going to assign his next class.
Or, Ranjit realized, it was a good time to do some of that exploration of his native country that he had been intending to get around to ever since Myra had first chided him as overparochial.
That was a more attractive idea than it might have been some years earlier, for even tourist travel was looking more attractive in this post–Silent Thunder world. They could, for example, cruise the Nile River, as Myra had longed to do since she was ten; both Egypt and Kenya had furloughed large fractions of their militaries while the ecologists for all the countries involved worked out water-saving ways of containing their thirsts for Nile water. The Subramanians could have taken the children to London—or to Paris, or New York, or Rome—to get an idea of what a great city was like. They could have settled for Norwegian fjords or Swiss mountains or the jungles of Amazonia; they could indeed have gone almost anywhere, but what in fact happened was that, while they were still studying travel brochures, they got a text from Joris Vorhulst. It said:
Mother tells me that you have some vacation time coming. I’ll be down at the terminal for at least a week, starting the first of next month. Why don’t you come see what we’re doing these days?
“Actually,” Myra said, “that would be fun.” And Natasha said, “You bet!” And even Robert, hanging on to Natasha’s chair and listening to every word, bellowed something that Natasha explained was a yes. And
so the family of four prepared for its first long trip together.
It wasn’t just Vorhulst’s invitation that made Ranjit look forward to visiting the Skyhook terminal. There were actually two reasons, and the first was the advisory board that Vorhulst had talked him into joining a number of years ago. It had been as undemanding as Vorhulst had promised—no meetings to go to, not even any voting on any issues, because if there were any issues troublesome enough to require a decision, that decision was made for them by the real controllers of the enterprise, the governments of China, Russia, and the United States. Ranjit had, however, been the recipient of a monthly progress report. There too the heavy hand of the big three was felt, because most of each report’s content was sternly secret, and even more of it was simply dismissed as what was cryptically called “development.” He had only been to the site a handful of times, and those visits had been quite cursory. Whether he would learn more by being at the scene Ranjit could not say, but he was anxious to find out.
The other reason was a surprise to Ranjit himself. The Subramanians didn’t have a car of their own—Ranjit and Myra biked to most places, sometimes with Natasha riding happily in front of them and Robert strapped into a child’s seat behind his father, and when they needed more in the way of transport, there were always cabs. But the university had promised the loan of a car for the trip, and Ranjit picked it up from the grinning Dr. Davoodbhoy. “It’s special for you,” he said. “Pax per Fidem sent it. It’s a new design from transparent Korea—with all those geniuses who used to build weapons now free for new civilian ideas, they’ve got a lot of stuff.” And when he’d explained what the perky little four-seater could do, it sent Ranjit back to Myra grinning with pleasure.