Never before had Ranjit had occasion to visit the dean of students. He knew what the man looked like, though—the faculty file on the university’s home page supplied photos—and the elderly man reading a newspaper at the huge mahogany desk definitely was not him. But he put down his paper and rose, not exactly with a smile but certainly without the hanging-judge look Ranjit had expected. “Come in, Mr. Subramanian,” he called. “Sit down. I’m Dr. Denzel Davoodbhoy, chairman of the mathematics department, and as mathematical matters seem to play a significant role here, the dean asked me to conduct this interview for him.”
That hadn’t been a question, and Ranjit had no idea what response would have been appropriate. He simply went on gazing at the mathematician with an expression that, he hoped, conveyed attentive concern but no admission of guilt.
Dr. Davoodbhoy didn’t seem to mind. “First,” he said, “there are a couple of formal questions I must put to you. Did you use Dr. Dabare’s password to earn money you were not otherwise entitled to?”
“Certainly not, sir!”
“Or to alter your math grades?”
This time Ranjit was offended. “No! I mean, no, sir, I wouldn’t have done that!”
Dr. Davoodbhoy nodded as though he had expected both answers. “I think I can tell you that no evidence has been presented to suggest either charge. Finally, how, exactly, did you obtain his password?”
As far as Ranjit could see, there did not appear to be any reason to try to conceal anything. Hoping that this was so, he began with his discovery that the teacher would be out of the country for a prolonged visit and ended with that return to the library computer when he found the solution waiting on the screen.
When he finished, Davoodbhoy gazed at him in silence for a moment. Then he said, “You know, Subramanian, you might have a future in cryptography. It would be a better chance than continuing to spend your life trying to prove Fermat’s Last Theorem.”
He looked at Ranjit as though expecting a response. Ranjit didn’t choose to give him one, so Davoodbhoy added, “You’re not alone, you know. When I was your age, like every other math major in the world, I got interested in the final theorem myself. It is compelling, isn’t it? But then, when I was a little older, I gave up on it because—you know this, don’t you? Because the odds are pretty great that Fermat never did have the proof he was claiming.”
Unwilling to be baited, Ranjit kept his attention set at politely attentive and his mouth closed. “I mean,” Davoodbhoy added, “look at it this way. You do know, I suppose, that Fermat spent a lot of his time, right up to the day he died, trying to prove that his theorem held true for third-, fourth-, and fifth-power exponents. Well, think about it. Does doing that make any sense at all? I mean, if the man already did possess a general proof that the rule was true for all exponents greater than two, why would he bother trying to prove a few isolated examples?”
Ranjit gritted his teeth. It was a question that, on dark nights and disappointing days, he had asked himself often enough. Without ever finding a good answer, either. He gave Davoodbhoy the not wholly good answer he had usually tried to content himself with: “Who knows? How can someone like you or me try to guess why a mind like Fermat’s went in any direction it liked?”
The mathematician looked at him with an expression that somewhat resembled tolerance but also resembled, to some degree, respect. He sighed and spread his hands. “Let me offer you a different theory of what happened, Subramanian. Let’s suppose that in—what was it, 1637?—in 1637 Monsieur Fermat had just completed what he thought was a proof. Then later that night, while he was reading himself to sleep in his library, let’s suppose he just couldn’t help himself, and in a fit of exuberance he scribbled that note in his book.” He paused there for a moment, giving Ranjit what could only be described as a quizzical look. When he went on, however, his tone would have been appropriate for a respected colleague as much as for an undergraduate expecting to be disciplined. “Then let’s suppose that sometime later he went over his proof to double-check it, and found it possessed a fatal error. It wouldn’t have been the first time, would it? Because that had already happened with other ‘proofs’ of his that he later admitted were wrong, hadn’t it?” Mercifully he didn’t require an answer from Ranjit but kept right on going. “So he tried to repair his proof every way he could. Unfortunately, he failed. So, trying to salvage something from his mistake, he then tried the more limited task of proving the argument for an easier case like p equals three, and there he succeeded; and for p equals four, and succeeded again. He never did get a proof of the p equals five case, but he was still pretty sure that one existed. He was right, too, because somebody else proved it after Fermat died. And all that time his scribble in Diophantus was sitting on a shelf in his library. If he ever remembered he’d written it, he thought, well, he probably ought to go back and erase that bad guess. But, after all, what’s the chance that anyone would ever see it? And then he died, and somebody was riffling through his books and did see it…and didn’t know that the great man had changed his mind.”
Ranjit didn’t change expression. “That,” he said, “is a perfectly sensible theory. I just don’t happen to believe that it’s what happened.”
Davoodbhoy laughed. “All right, Subramanian. Let’s leave it at that. Just don’t do it again.” He thumbed through the papers before him, then nodded and closed the file. “Now you can go back to your classes.”
“All right, sir.” He tarried for a moment after picking up his backpack, then asked the question: “But am I going to be expelled?”
The mathematician looked surprised. “Expelled? Oh, no, nothing like that. It was only a first offense, you know. We don’t expel for that unless it’s something a lot worse than stealing a password, and anyway the dean received some extremely glowing letters of support for you.” He opened Ranjit’s folder again and thumbed through the papers. “Yes. Here we are. One is from your father. He is quite positive you are basically of good character. In itself, to be sure, a father’s opinion of his only son might not carry great weight, but then there is this other one. It is very nearly as commending as your father’s, but it comes from someone who is, I think, not very close to you but who is a person of considerable importance in the university. In fact, he’s the university’s attorney, Dhatusena Bandara.”
And now Ranjit had a new puzzle to mull over. Who would have suspected that Gamini’s father would have exerted himself to save his son’s friend?
7
GETTING THERE
The school year limped toward its end. It picked up speed remarkably in the all too brief periods when Ranjit was in his astronomy class, but the remainder of each week’s hours were in no hurry to move on at all.
For a little while Ranjit thought he had hopes of one bright—fairly bright—spot. Remembering the lecture on what they’d called the hydro-solar plan for Israel’s Dead Sea, he went back to the lecture series. But then what the lecturer was talking about was the increasing salinity of a lot of oceanfront wells, all over the world, and then about how some of the world’s great rivers no longer ran to the sea, any sea, because they were drained for farming and flushing city toilets and watering city folks’ front lawns first. Ranjit didn’t need more discouragement. After that he stayed away.
He even briefly considered trying to take, or at least pretend to take, his schooling seriously. Studying, for example, could be considered a game, and a fairly easy one to win. It did not at all resemble that insatiable thirst for learning that had marked his early consecration to the Fermat theorem. Now all he had to do was guess what questions each of his instructors would ask on each test and look up the answers. He didn’t always get it right, but then to attain a merely passing grade he didn’t have to.
None of this, of course, applied to Astronomy 101.
There Dr. Vorhulst managed to make every session a pleasure. Like what happened when they were talking about terraforming—that is, reworking planetary surfaces so tha
t human beings could live on them. And, if you were going to do that, how did you get there to do the terraforming?
Ranjit’s answer would have been “rocket ships.” His hand was already halfway toward the raised position so that he could offer that answer when the teacher froze it mid-motion. “You’re going to say ‘rocket ships,’ aren’t you?” Dr. Vorhulst asked, addressing the whole class and particularly the dozen or so who, like Ranjit, had been putting their hands up. “All right. Let’s think about that for a bit. Let’s suppose that we want to start terraforming Mars, but all we have to work with is an absolute minimum of heavy-duty earthmoving machinery. One very big backhoe, for instance. One bulldozer. A couple of medium-size dump trucks. Fuel enough to run them all for, let’s say, six months or so. Long enough to get the job started, anyway.” He paused, eyes on a hand from the second row that had just sprouted. “Yes, Janaka?”
The boy named Janaka eagerly shot to his feet. “But, Dr. Vorhulst, there’s a whole plan to make fuel from Martian resources that are already there!”
The professor beamed at him. “You’re absolutely right, Janaka. For instance, if there really is a large amount of methane under Mars’s permafrost, as many people think there is, then we could burn that for fuel, assuming we could find some oxygen to burn it with. Of course, to do that we’d really have to have a bunch more heavy machinery, which would need a bunch more fuel to run it until the extraction plants were working.” Vorhulst gave the boy a friendly smile. “So, Janaka,” he said, “I think that if you wanted to start any terraforming in the near future, probably you’d want to fly your fuel in after all. So let’s see.”
He turned to the whiteboard and began writing. “Say six or eight tons of fuel to start. The earthmoving machines themselves—what would you say, at least another twenty or thirty tons? Now to get those at least twenty-eight tons of cargo from low earth orbit, known as LEO, to Mars, we need to put them into some kind of spaceship. I don’t know what that would mass, but let’s say the ship itself would run fifty or sixty tons, plus the fuel to get it from LEO to Mars.” He stepped back to look at his figures on the board and frowned. “I’m afraid we have a problem,” he said to the class, addressing it over his shoulder. “All that stuff won’t start out in low earth orbit, will it? Before the ship can start heading for Mars, we have to get it into LEO. And I’m afraid that’s going to be expensive.”
He paused, looking with a sorrowful expression at his class. He was waiting for some student to rise to the occasion, and after a bit, one of the girls did. “That’s because it has to get out of the Earth’s gravity well, isn’t it, Dr. Vorhulst?”
He gave her a big smile. “Exactly right, Roshini,” he said, looking up at the class timer that had just turned amber. “So you see, it’s that first step that’s a killer. Is there anything we can do to make it easier? We’ll try to find out next time. But if any of you guys just can’t wait for the answer, hey, that’s what search engines are for.”
And then, as everybody began to rise, he said, “Oh, one more thing. You’re all invited to the end-of-term party at my house. Don’t dress any differently than you do for class, and don’t bring any house gifts but yourselves. But do come. You’ll hurt my mother’s feelings if you don’t.”
One of the things that Ranjit liked best about his astronomy teacher—apart from such unexpected surprising joys as end-of-term parties—was that Dr. Vorhulst didn’t actually spend a lot of time in the normal practice of teaching. When, at the end of each session, Dr. Vorhulst told the class what the next session was going to be about, Vorhulst knew perfectly well that his hundred eagerly motivated space-cadets would look all that material up long before the next session started. (The few who hadn’t started out all that motivated—the ones who had entertained the false hope of a snap course and an easy A—either soon dropped or were reformed by the enthusiasm of their fellows.) Thus, each time, Dr. Vorhulst had that next session to play.
This time, however, Ranjit couldn’t hit the search engines right away. He had other obligations. First there was the terminally tedious hour and fifty minutes of philosophy to get through. Then came the quick gulping of a detestable sandwich and a lukewarm bag of some anonymous variety of juice, which was lunch, all swallowed in a hurry so he could get to the two o’clock bus that would take him to the library.
But just outside the lunchroom his seatmate in Astronomy 101 was standing with a few of his fellows, and he had news for Ranjit. “You didn’t hear what Dr. Vorhulst had promised for our next session? I was just telling my friends the news about it. The Artsutanov project, you know. Vorhulst says we might get the project built right here! In Sri Lanka! Because the World Bank’s just announced that it has received a request for financing a study of a Sri Lankan terminal!”
Ranjit was just opening his mouth to ask what all that meant when one of the others said, “But you said it might not pass, Jude.”
Jude looked suddenly brought down. “Well, yes,” he admitted. “It’s the damn Americans and the damn Russians and the damn Chinese that have all the power—and all the money, too. They’re just as likely as not to hold it up, because once you’ve got an Artsutanov lifter going, any damn little pipsqueak country in the world can have a space program of its own. Even us! And there goes their monopoly! Don’t you think?”
Ranjit was saved the embarrassment of not having an answer for that—indeed, of not having any really good idea of what Jude was talking about in the first place—by the Sinhalese group’s growing hunger. And then in the library—search engines working—Ranjit was soaking up information at a high rate of knots. The more he learned, the more he shared Jude’s excitement. That tough first step of getting from Earth’s surface to LEO? With an Artsutanov skyhook it was no problem at all!
True, feasibility studies were a long way from an actual car that you could hop into and have drawn at high speed up to low earth orbit, no million-liter oceans of explosive liquid propellant required. But it might happen. Probably would happen, sooner or later, and then even Ranjit Subramanian might be one of those lucky ones who would circle the moon and cruise among Jupiter’s satellites and perhaps even walk across the hopelessly dry deserts of Mars.
According to what the search engines turned up for Ranjit, as far back as 1895 Russia’s first thinker on space travel, Konstantin Tsiolkovsky, got a look at Paris’s Eiffel Tower and then came up with his idea. A good way to get a spacecraft into orbit, he said, was to build a really tall tower with a built-in elevator and hike your ship up to the top before turning it loose to roam.
However, in 1960 a Leningrad engineer named Yuri Artsutanov read Tsiolkovsky’s book and quickly saw that the plan wouldn’t work. It was a lesson the ancient Egyptians had learned long ago—as had the Maya, a few thousand years later and on the other side of the world. The lesson was that there is a limit to how tall you can build a tower or a pyramid, and that limit is set by compression.
In a compression structure—which is to say, any structure that is built from the ground up—each level must support the weight of all the levels above it. That would be hundreds of kilometers of levels, to reach low earth orbit, and no imaginable structural material could support that weight without crumbling.
Artsutanov’s inspiration was to realize that compression was only one possible way to build a structure. Another equally viable way was tension.
A structure based on tension—one made up of cables attached to some orbiting body, for example—was a theoretically elegant but practically unattainable notion when considered from the point of view of an engineer who had only mid-twentieth-century materials to make the cables out of. But, Artsutanov contended, who was to say that the advanced cable materials that might be developed a few decades on wouldn’t be up to that challenge?
When at last Ranjit got himself to go to bed that night, he was smiling—and kept on smiling even in his sleep, because for the first time in quite a while he had found something that was really worth smiling about. r />
He was still smiling the next morning at breakfast, and was counting the hours (there would be almost a hundred and forty of them) until the next session of Astronomy 101. There was no doubt in Ranjit’s mind that his astronomy sessions were the brightest spots in his academic year….
That being so, why not change his major from math to astronomy?
He stopped chewing long enough to think that over, but not to any successful conclusion. There was something in his head that wouldn’t let him take the official step of giving up on math. Rightly or wrongly that felt too much like giving up on Fermat’s theorem.
On the other hand, it was pretty strange—as his guidance counselor had pointed out in the one session he had been willing to allow her—to be a math major who wasn’t taking any mathematics courses.
Ranjit knew what to do about that, and he had a whole free morning to do it in. As soon as the counselor was in her office, Ranjit was there to clear up his status with her, and by noon he was officially registered as a late entry into the course in basic statistics. Why statistics? Well, it was, after all, a kind of mathematics. But entering the class so late, how would that work? No problem, Ranjit assured the counselor; there was no undergraduate math course that he couldn’t pick up in no time at all. And so by lunchtime Ranjit had solved at least one of his problems, even though it was a problem he hadn’t really thought important enough to be worth solving. All in all, Ranjit attacked his boring lunch quite cheerfully.
Then things went bad.
Some fool had left the radio news on at high volume instead of the murmur of music the college students were willing to put up with at their meals. Nobody seemed to know how to turn it off, either.
Of course, it was inevitable that the principal news stories that day were exactly the sort of stories Ranjit didn’t want to hear, because that was pretty much all the world news there was.