But N had a secret of its own. The way it was generated by cryptographers was by multiplying two large prime numbers together. Any decent computer could do that kind of multiplication in a fraction of a second, but once the two large primes were multiplied together, trying to discover what the primes themselves had been was a brutal job that, even with the best computers, could take many years. Hence the description “trapdoor cipher”—easy to get into, virtually impossible to get out of again. Still, public-key cryptography, as it was called, possessed one great virtue. Anybody could encrypt any message from the product of the primes—even, say, some harried member of the French Resistance in World War II, one step ahead of the Gestapo, with some crucial knowledge of where a bunch of panzer divisions were moving to. But only the people who knew what both those primes were could read the message.
Bledsoe took a sip of his rapidly cooling coffee. “The thing is, Subramanian,” he said, “we have some pretty important traffic going around the world right now—don’t ask me what it is. I have only a bare glimmering of a notion, and I can’t tell you even that much. But at this moment it is more important than ever that our code be unbreakable. Maybe there’s some way of decrypting that doesn’t involve all this factoring of prime numbers hocus-pocus. And if there is, we would like you to help us figure out what it is.”
Ranjit tried his best not to laugh. What he was being asked to do was what every code agency in the world had been working on ever since Diffie-Hellman had published their paper way back in 1975. “Why me?” he asked.
Bledsoe looked pleased with himself. “When I saw the news stories about your proof of Fermat’s Last Theorem, it rang a bell. All those mathematicians that work on this public-key stuff use what they call the Fermat test, right? So who would know more about that than the man who just proved his theorem? And there were others around who liked you, so we started the machinery going to recruit you for our team.”
When Ranjit considered all the ways in which Bledsoe’s notion was ridiculous, he was tempted to get up and walk away. Fermat’s test was certainly the basis for many more recent ways of identifying prime numbers. But to leap from that to the notion that the man who proved Fermat’s theorem would be any good at public-key code-cracking was, well, simply preposterous.
All the same, this was exactly the offer that Gamini had asked him to accept. Ranjit controlled the impulse to laugh in Bledsoe’s face and said only, “‘Recruit’ me. Does that mean you’re offering me a job?”
“Damn straight it does, Subramanian. You’ll be provided with all the resources you need—and the U.S. government has plenty of resources—and a generous salary. How about—?”
Ranjit could not help blinking at the figure mentioned. It would have supported several generations of Subramanians. “That seems adequate,” he commented drily. “When should I start?”
“Ah, well,” Bledsoe said moodily, “not right away, I’m afraid. It’s a matter of your security clearance. You did, after all, spend a couple of months in the slammer back home, under suspicion of being associated in terrorist activities.”
Then Ranjit did come close to blowing his top. “That’s ridiculous! I wasn’t involved in any—”
Bledsoe raised his hand. “I know. Do you think I’d be offering you this kind of a job if I didn’t know that? But the security clearance people get real antsy when there’s a connection with a certified terrorist bunch like your pirates. Don’t worry. It’s all just about straightened out. We had to go right to the top. It took actual White House intervention, but you’ll get your clearance. Only it will take a bit more time.”
Ranjit sighed and bit the bullet. “How long?”
“Three weeks, maybe. At most a month. So what I suggest is you go ahead and do all those speaking dates you’ve accepted, and when the word comes through, I’ll get in touch with you and arrange for your coming to California.”
There didn’t seem to be much help for it. “All right,” Ranjit said. “I’ll need an address for you so I can keep you posted on where to reach me.”
Bledsoe grinned. He showed a lot of teeth, a lot of sharklike teeth, when he smiled, Ranjit observed. “Don’t worry,” he said. “I’ll know where you are.”
Three weeks turned into six, and then into two months. Ranjit was beginning to wonder how long the generosity of the foundation that paid their hotel bills would last, and he still had not heard from Bledsoe again. “It’s just typical government red tape,” Myra said, consoling. “Gamini said to take the job. You took it. Now we just have to live by their timetable.”
“But where the hell is Gamini?” Ranjit said sulkily. He hadn’t appeared again, and when Ranjit e-mailed his father’s office to see if they could supply an address, they had simply replied, “He is in the field and can’t be reached.”
At least Myra had the visits to her old friends at MIT to amuse her. Ranjit didn’t have that much. When she came back to the hotel, puffing and—yes, you’d have to say it—waddling but full of news about the great new accomplishments of some of her old buddies, he greeted her with an unexpected question: “What would you think about catching the next plane back to Lanka?”
She eased herself and her great belly into a chair. “What’s the matter, dear?”
“This is going nowhere,” he announced, not adding that it was also very cold outside. “I’ve been thinking about what Dr. Bandara said. Being a full professor at the university wouldn’t be a bad life. I’d have a chance to do research, too, and you know there are plenty of other big problems that nobody has solved. If you wanted to be rich, I could see if I could work the bugs out of the Black-Scholes equation. Or, if I wanted a real challenge, there’s always P equals NP. If anybody could solve that, it would revolutionize mathematics.”
Myra shifted her weight around in the chair, trying to find a comfortable position. She decided there wasn’t one and leaned over to press her husband’s hand. “What’s P equals NP?” she asked. “Or that other equation?”
It was worse than she’d thought; Ranjit didn’t take the bait. “The thing is,” he said, “we’re just wasting our time here. We might as well give it up and go home.”
“You promised Gamini,” she reminded him. “Just give it a few more days.”
“A very few,” he said stubbornly. “A week at the most, and then we’re out of here.”
It didn’t come to that. It was the very next day that the teletext message came from ex–Lt. Col. T. Orion Bledsoe. “Clearance granted. Report to Pasadena ASAP.”
And they were certainly about ready to get out of Boston’s worst-yet climate. But when they were all packed up, and just waiting for the limo that was to take them to Logan Airport for the flight to LAX, Myra suddenly put her hand to her belly. “Oh, my,” she said. “I think that was a contraction.”
It was.
Once she made Ranjit understand what was happening, it was no problem to divert their limousine from the airport to Massachusetts General Hospital. Where, six hours later, little Natasha de Soyza Subramanian made her first appearance in the world.
23
FARMER “BILL”
And in another part of the galaxy, far, far away…
You couldn’t say that the Grand Galactics had forgotten about unruly Earth. That never happened. They were constitutionally incapable of forgetting anything. All the same, Earth had certainly slipped into the farther recesses of their collective mind, and their attention was concentrated on more important, or anyway more interesting, issues.
In the case of “Bill” himself, for example, there was the task of tending to their farm—or, perhaps it should be “farm” in quotation marks, since nothing organic grew there.
We wouldn’t usually think of the Grand Galactics as farmers of any kind. Nevertheless there were certain kinds of crops that they encouraged, and it is a curious fact that medieval human peasants had done something very similar with their own tiny plots.
The plot that interested Bill enough to cause
him to visit it was a volume of space several light-years on a side.
At first look, any astronomer might have thought it was nothing but empty space. As a matter of fact, that is exactly what human astronomers had thought when they’d first observed it. It wasn’t entirely empty, though. Better observations, achieved when humans had managed to acquire better telescopes, showed that there was something in that patch of space that bent light, refracting blue in one direction, red in the other.
That something, as the Grand Galactics had always known, was interstellar dust.
This trip was not, of course, Bill’s first visit to his farm. Not long before—oh, a matter of a few million years or so before—he had explored it in detail, making a careful census of the dust. What percentage of the dust particles (as humans might measure them) were less than a hundredth of a micron in size? What percentage, indeed, were in all the size ranges all the way up to the giants, which were as much as ten microns across, or even larger? He took note as well of the chemical composition of the dust particles, and of their neutron counts and ionization status.
All this was a simple and quite easy part of the self-imposed duties of a Grand Galactic. Bill however had always found it among what one could call the most enjoyable duties. After all, his census would ultimately contribute to one of the great goals the Grand Galactics possessed.
So, like some eleventh-century Norman baron, what Bill was doing was riding his fields. The dust patch was what the baron’s Saxon serfs would have called a fallow field, allowed to remain unplanted so that the soil could rest and regain its fertility.
Bill’s patch didn’t raise corn or oats. It raised only stars—big ones, little ones, all kinds; but the Grand Galactics preferred the big ones. Those giants—what humans would call the A’s and B’s and O’s—could be counted on to rapidly burn up their initial stocks of hydrogen in the nuclear furnaces at their cores. Then, when that was gone, they would do the same with their helium, carbon, neon, magnesium—each element heavier than the one that came before, until they came to iron, which was the end of the line.
When a star’s core has turned to iron, the nuclear furnace at its core weakens, until it can no longer fight off the terrible gravitational squeeze of the dead weight of its outer layers. The star collapses on itself….
And then it rebounds in a titanic explosion, pouring out new treasuries of heavier elements still, manufactured in the condign heat of that explosion, to turn into tiny particles that will enrich the next patch of interstellar gas.
That was what would inevitably happen, sooner or later, in the normal course of events, and it didn’t require any action on the part of Bill. It would be taken care of by those simple Newtonian-Einsteinian laws of gravitation that the Grand Galactics had never seen any reason to change.
As we say, “sooner or later,” but the Grand Galactics preferred sooner. Bill chose to speed things up. He scanned a considerable volume of adjacent space and was lucky enough to find a trickle of nearby dark matter…coaxed it to flow into his patch…and was pleased. One of the Grand Galactics’ main objectives was being helped along.
And what was that objective?
There is no way of expressing it in terms a human being could understand, but one step in its achievement was known to be an increase in the proportion of heavy elements to light—in this case “heavy” meaning those elements with at least twenty or so protons in their nuclei, along with crowds of neutrons. The kind of elements, that is, that the original creation of the universe had omitted entirely.
Changing all those light elements to heavy would take much work, and vast amounts of time…but time, after all, belonged to the Grand Galactics.
24
CALIFORNIA
The American East Coast might consider itself the center of power, of government, or of culture. (Of course, that would depend on which East Coast city you were talking about, New York, Washington, or Boston.) But in one very important way it was definitely inferior to the other edge of the North American continent. Oh, it wasn’t the palm trees and the flowers blooming everywhere that thrilled the Subramanians. After all, Myra and Ranjit were Lankans, and a riot of exotic vegetation was their natural ambience. No, the best thing about California was that it was warm! It never got painfully cold, especially around the Los Angeles area, where it wasn’t ever really cold at all.
So Pasadena, where Ranjit discovered he was based, was a great place to live. Well, it was if you didn’t count the possibility of earthquakes. Or wildfires that could flatten a whole subdivision of homes in a dry year. Or floods that could pull down some other subdivision, one that had been built on precipitous lots because all the flat lots had been built on already, floods that were always ready to do this in a year when some relatively minor fire had killed off enough of the brush to weaken the ground’s hold on the substrate.
Never mind. Those things might not happen. At least they might not before the Subramanian family had packed up and gone somewhere else. Meanwhile it was a splendid place to raise a child. Myra happily pushed Natasha’s carriage through the local supermarket, along with all the other mothers doing the same, and thought she had never been so lucky in her life.
Ranjit, on the other hand, had some doubts.
Oh, he loved the good parts of their life in Southern California as much as Myra did. Took pleasure in their excursions to the points of interest that were so unlike anything in Sri Lanka, the La Brea tar pits in the heart of the city, where millennia of ancient beasts had been trapped and preserved for humans to wonder over well into this twenty-first century. The movie studios, with their brilliantly engineered rides and exhibits. (Myra had been a little doubtful about taking Tashy to such a chancy place, but in the event, Natasha chortled and loved it.) Griffith Observatory with its seismographs and telescopes and its grand picnic area overlooking the city.
What he didn’t like was his job.
It gave him everything T. Orion Bledsoe had promised, that was true, and even a fair number of things Ranjit hadn’t expected at all. He had his own private office, which was spacious (three meters by more than five) if windowless (because, like all the rest of this installation, it was nearly twenty meters underground) and furnished with a large desk and a large leather armchair for his own use and several less pricey other chairs, at a clear oak table, for guests and meetings. And no fewer than three separate computer terminals, with unlimited access to almost everything. Now all it took was pushing a few keys for Ranjit to get his personal copies of just about every mathematical journal there was in the world. Not only did he get the journals themselves—hard copies when there were hard copies to begin with, electronic copies when that was all the original “publishers” had produced. He also received translations—horribly expensive, but paid for by the agency, out of their apparently limitless bank account—of at least the abstracts from those journals that happened to be in languages Ranjit had no hope of ever comprehending.
What was wrong was that he had nothing to do.
The first few days were busy enough, because Ranjit had to be walked through the places where red tape was generated so that they could generate Ranjit’s own contribution to the supply—identity badge to prepare, documents to sign, all the unavoidable flotsam of any large enterprise in the twenty-first century. Then nothing.
By the end of the first month, Ranjit, who was never grumpy, was waking up grumpy almost every workday morning. There was a cure. A prescribed dose of Natasha, along with one of Myra, usually cleared the symptoms up before he finished breakfast, but then by the time he came home for dinner, he was morose again. Apologetic about it, of course: “I don’t mean to take it out on Tashy and you, Myra, but I’m just wasting time here. No one will tell me what I’m supposed to be doing. When I find someone to ask, he just gets all mock-deferential and says, Well, that would be up to me, wouldn’t it?” But then, by the time he had finished dinner, and given Tashy her bath or changed her diaper or just dandled her on his knee, who co
uld stay morose? Not Ranjit, and he was then his usual cheery self until the next time he had to get up to go to his nonwork.
By the end of the second month the depression was deeper. It took longer to lift, because, as Ranjit told his wife—over and over!—“It’s worse than ever! I cornered Bledsoe today—not easy to do, because he’s hardly ever in his office—and asked him point-blank what kind of work I was supposed to be doing. He gave me a dirty look, and do you know what he said? He said, ‘If you ever find out, please tell me.’ It seems he had orders from high up to hire me, but nobody ever told him what my job was to be.”
“They wanted you because you’re famous and you add class to the operation,” his wife informed him.
“Good guess. I sort of had the same idea myself, but it can’t be right. That whole operation’s so secret nobody knows who’s working in the next office.”
“So do you want to quit?” Myra asked.
“Huh. Well, I don’t think so. Don’t know if I can, really, because I’m not sure what all I signed, but anyway I promised Gamini.”
“Then,” she said, “let’s just learn to love it. Why don’t you solve that P equals NP problem you talk about? And anyway, tomorrow’s Saturday, so why don’t we take Tashy to the zoo?”
The zoo, of course, was a delight, although in the rest of the world things were going as badly as ever. Recent developments? Well, Argentina’s vast herds of cattle were keeling over by the thousands with a new variety of the old disease called bluetongue. It had just been confirmed that the plague was a biowarfare strain. What wasn’t clear was who had spread it. Maybe Venezuela or Colombia, some people around the agency thought, because Argentina had contributed heavily to the international force that was trying to keep the Venezuelan and the Colombian armies apart. (They weren’t very successful at it, but the Venezuelans and the Colombians hated them for trying.) The rest of the world was as unquiet as ever. In Iraq nightly outbreaks of car-bombings and beheadings showed that the two kinds of Iraqi Muslims were again trying to ensure that there was only one true Islamic faith by exterminating each other. In Africa the number of officially recognized wars had grown to fourteen, not counting several dozen tribal skirmishes. In Asia the Adorable Leader’s North Koreans were issuing communiqué after communiqué charging most of the world’s other states with spreading lies about them.