The Last Theorem

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 that 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.

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.

Now that the news was on, however, Ranjit dutifully listened to it. Predictably the news was bad—all the little wars were still thriving, and new ones were being promised, just like always. And then the news turned to local Colombo stories. These were not of much interest to Ranjit, until one word caught his attention. The word was “Trincomalee.”

Then he gave the news his full attention. It seemed that a man from Trincomalee had been stopped because he had failed to give way in his old van to a police car with its siren going. (Actually the police in the car had been heading toward a place to eat lunch.) When they pulled him over, the police naturally looked around the van. That was when they caught him with a load of toasters, blenders, and other small domestic appliances, and no good explanation for how they came to be in his possession.

Ranjit had stopped with his spoonful of rice halfway to his mouth, just as the news reader mentioned the suspect’s name. Kirthis Kanakaratnam.

That left Ranjit worse off than before. He couldn’t place the name. It did sound vaguely familiar, but from where? School? His father’s temple? It could have been from almost anywhere, and try as he might, Ranjit could not fit a face to the name. A later news story, long after lunch, after Ranjit had nearly given up, said the suspect had left a wife and four small children behind him.

It really was not his business, Ranjit told himself. He wasn’t successful in convincing himself, though, because if he didn’t know for sure just who this Kirthis Kanakaratnam was, how could he know it wasn’t someone who had in some context been a friend?

That was why Ranjit called the police. He called their central headquarters number, and he did it from a phone in a part of the campus he rarely visited. The voice was a woman, not young, and not in the habit of giving information away. A prisoner named Kirthis Kanakaratnam? Yes, perhaps so. They had a good many persons held in one Colombo jail or another, and they didn’t always give their right names. Could the caller give more information about this person? The names of some of his associates, for example? And was the caller himself related to him? Or perhaps associated with him in some enterprise? Or—

Ranjit quietly hung the phone up and departed that area. He didn’t really think that a squad of Colombo police was likely to come racing down the hallway any minute. But he was also far from positive that they weren’t, and saw no reason to wait around to find out.

When Ranjit got back to his rooms that night, there was the next best thing to Gamini’s actual presence waiting for him, namely, an e-letter from London. (There was also a message that Ranjit’s father had called and wished to be called back—very good news, Ranjit thought, because at least the old man seemed willing to speak to him again…but, all the same, it was the e-letter from Gamini that he looked at first.)

Gamini was showing every sign of having a wonderful time in London. Just yesterday (he wrote) he had walked over to the campus of University College London because Madge had told him that there was something she wanted him to see. Well, it was interesting, all right, assuming you liked looking at dead—even long-dead—bodies, because what was there to see was the waxed and mummified corpse of the two-hundred-years-ago English utilitarian philosopher, Jeremy Bentham. He was always there, Gamini said, but usually locked away in the wooden cabinet he called his “Auto-Icon.” As a special favor to Madge it had been unlocked for her by a smitten junior faculty member. This Bentham, Gamini went on to explain, had been a really ahead-of-his-time early-nineteenth-century thinker, had even once written a carefully thought out argument for extending tolerance—well, some tolerance, anyway—to homosexuals. Bentham was revolutionary, Gamini added, but he was also somewhat cautious. He didn’t publish the argument. He locked it away, and so it stayed for a century and a half, until someone finally put it into print in 1978.

By then Ranjit was getting tired of Jeremy Bentham, and a little curious about why Gamini was telling him so much. Could it be because Bentham had been one of the first significant figures to write with some sympathy about homosexuals? And if so, what was it that Gamini wanted Ranjit to understand about that subject? It certainly wasn’t that either of the young men considered himself homosexual, because they certainly did not.

He found that subject uneasy to think about and went on. There wasn’t much more of the letter anyway. A bunch of Gamini’s fellow students—Gamini didn’t mention this Madge there, but Ranjit would have bet a large sum that she had been in the group—had gone up to Stratford-upon-Avon for a day. And then at the very end, in a brief afterthought, the big news: “Oh, listen, I’ve got some summer courses I need to take, but Dad wants me home for a few days this summer so I can see Gram one more time before she goes. He says she’s doing poorly. So I’ll be back in Lanka for a bit. Where will you be? I don’t know if I’ll have time to get to Trinco—but somewhere?”

Well, wasn’t that grand news? It was. And the only thing that slowed Ranjit’s quiet exultation was the fact that his father’s call needed to be returned.

The old man picked the phone up on its first ring. His voice was cheerful, too, as he said, “Ah, Ranjit”—affectionate, pleased—“why do you keep secrets from your father? You didn’t tell me that Gamini Bandara had gone to England!”

Though no one was there to see, Ranjit rolled his eyes. If he had failed to tell his father the news, it was almost entirely because he had been confident his father’s watchers would make sure it got to him. The only surprising thing was that it had taken so long. Ranjit considered for a moment whether or not to mention that Gamini would at least briefly be coming home, and decided not to do the dormitory staff’s work for them. He said guardedly, “Yes, he’s going to school there. London School of Economics. His father thinks it’s the best school in the world, I think.”

“And I’m sure it is,” his father agreed, “at least for certain kinds of studies. And I know you must miss him, Ranjit, but I have to say that it goes a long way toward solving a major problem for me. No one is going to be worrying about your closeness with a Sinhalese boy when there’s an ocean or two between you.”

Ranjit didn’t know what to say to that and sensibly said nothing. His father went on. “The thing is, I’ve missed you very much, Ranjit. Can you forgive me, Ranjit?”

Ranjit had no need to think over his answer to that. “I love you, Father,” he said at once, “and there is nothing to forgive. I understand why you had to do what you did.”

“Then,” his father said, “will you come and spend your summer holidays here in Trinco?”

Ranjit assured him he would like nothing better, but he was beginning to feel uneasy. The conversation was getting sticky. He was glad when he remembered the question his father might be able to answer. “Dad? There’s a man from Trinco who’s been arrested in Colombo, Kirthis Kanakaratnam, and I have a feeling I might have known him at some time. Do you know who he is?”

Ganesh Subramanian sighed deeply—whether because the question was troubling to him or because he, too, was grateful for the change of subject, Ranjit could not tell. “Yes, of course. Kirthis. Don’t you remember him, Ranjit? My tenant? The one with all those little children, and a wife in somewhat poor health? He usually worked as a coach driver for one of the hotels along the beach. His father used to do odd jobs around the temple until he died—”

“I remember now,” said Ranjit, and he did. The man they were talking about was short and as black as Ranjit himself. He had lived, family and all, in the tiny house at the edge of Ganesh Subramanian’s property: by the most optimistic count, three rooms all told, for two adults and four tiny kids, and no interior plumbing. Ranjit’s clearest memory was of the mother despondently washing children’s clothes in a huge tin tub…and the children whining around her feet as they assiduously dirtied more clothes, and themselves.

When Ranjit got off the phone, he readied himself for bed, feeling pretty good about the world. Things were going well. He had made up with his father. He was going to see Gamini, at least briefly. And that mystery concerning the identity of this Kirthis Kanakaratnam was solved, and he would never have to think of the man again, he thought.

Statistics wasn’t quite as boring as Ranjit had feared it might be. It wasn’t much fun, either. Long before Ranjit entered the class, he had a pretty good understanding of the differences between mean, median, and mode and knew what a standard deviation was, and it didn’t take him long to learn how to draw any kind of histogram the teacher wanted. But the teacher surprisingly turned out to have a sense of humor, and when she wasn’t teaching the class what stem-and-leaf and other statistical plots were, she was almost—well, sometimes she was almost—as entertaining to listen to as Joris Vorhulst himself.

But on second thought, Ranjit told himself, no. That was going too far. She was a nice enough person, but she just didn’t have the material of Astronomy 101 to work with. Such as the space elevator and its wondrous ways.

Even Artsutanov’s lift wasn’t the only game in town. What (asked one of the students one day in astronomy class) about something like the Lofstrom loop? For that you didn’t have to start by putting some humongous satellite into orbit because the thing just sat on Earth’s surface, from which it flung your space capsules into orbit.

But there Dr. Vorhulst began to rein in the class’s speculation. “Friction,” he said succinctly. “Don’t forget friction. Remember what reentry did to a lot of the early spacecraft. If you used a Lofstrom loop, you’d need to accelerate your capsule to that seven miles a second of escape velocity that I was talking about the other day before you let go of it, and then the air friction would burn it right up.”

He paused, eyes roving over his class, expression as good-natured as always but with a faint twinkle that made Ranjit expect some sort of surprise was coming. “So,” the teacher said sociably, “have any of you junior-grade astronauts figured out what kind of rocket drive your ship is going to have yet?”

Ranjit hadn’t thought of anything beyond the usual fuel-plus-oxidizer. He kept his mouth shut, though, because he knew, from the fact that the professor had raised the question in the first place, that Dr. Vorhulst had something else in mind.

So did his seatmate, but he responded in a different way. His hand went right up. “You’re not talking about a chemical rocket, are you, Dr. Vorhulst? So, then, what do you think? Maybe a nuclear-powered one?”

“Good guess,” the teacher said, “but, no, I don’t think a nuclear-powered rocket would be your best bet, at least not the kind of nuclear power you mean. Oh, there are designs around for rockets that were driven by exploding atom bombs, one after another. We can talk about them if you like, but for getting from LEO to Mars I think there are two much better possibilities. Both of them are tailor-made to be used with some kind of space elevator to boost them into low earth orbit because they’re both way too feeble to lift anything off Earth’s surface and into space. One is the solar sail. The other is the electric rocket.”

Ten minutes later Dr. Vorhulst had given short and convincing reasons for avoiding nuclear explosions as rocket propellants—the need for heavy shielding to protect astronauts from the deadly radiation, and anyway who wants to shoot a few hundred atomic bombs off into space? Solar sails had a lot to recommend them, he conceded, but they were dreadfully slow and not very maneuverable. However, the electric rocket, while also pretty slow to accelerate, required no fuel storage and produced no undesired byproducts. Where did the electricity come from? Perhaps from an onboard nuclear power plant, Vorhulst conceded, but just as easily from solar power—that is, from solar power in space, where there were no nights or cloudy weather, so that the sun always shone. “And what do you do with that electricity? You use it to ionize some working fluid—a gas like xenon, for instance—and the gas fires itself out of your rocket nozzles at very high velocity, and off you go.”

He paused for a breath. “All right,” he admitted, “an electric rocket would not accelerate very fast.” But it would keep right on accelerating as long as you liked, and the longer the acceleration, the greater its velocity would be. You could accelerate until you were halfway there. Then you could turn around and decelerate until you arrived. Did anyone see what that implied?

Vorhulst gave them a few moments to figure it out, but no one did. “It means,” he told them, “that the farther your trip, the faster the speed that you’ll attain. You wouldn’t want to use an electric rocket to go to the moon. Short trip; you don’t really have time to get going very fast. For Mars, though, it’s optimal. And for the outer planets, say Uranus or Neptune, why, that trip doesn’t take much longer than to Mars! And if you’re really going to go a far piece, say to the Oort cloud, you build up so much velocity with all that acceleration that that enormous journey in fact becomes feasible!”

Then he stopped and grinned. “Well,” he said, “I don’t want to oversell you on the electric rocket, because it has one serious fault. That is, we don’t have any.” He overrode the faint groans of disappointment. “Oh, it’s legitimate in principle, all right. But nobody has ever built one because if you have to start your flight from Earth’s surface, they won’t work. They need something to lift them into low earth orbit first, and then they can strut their stuff. Something like an Artsutanov space elevator, and, as you know, we just don’t have one of those around anywhere.”

He gave them a rueful smile. “Oh, one day we will,” he promised. “Then we’ll have electric rockets by the zillion, and I’d be willing to bet that more than one of you will be riding to all sorts of weird and wonderful places. But not yet, because at the present time they don’t exist.”

Which, when you stopped to think about it, was true enough, at least for the little volume of space near Earth, though it wouldn’t be for long.

Actually, somewhat farther away, there were 154 of those electric rockets that were already taking direct aim for Earth, and the individuals aboard them didn’t think they were unusual at all.

These individuals were the One Point Fives, and they (or their ancestors) had been traveling from star to star in spacecraft just like these for many, many generations. Always on much the same errand, too. The fact of the matter was that the One Point Fives had a unique place among the subordinate sapient species of the galaxy.

Basically they were the Grand Galactics’ hit men.

To a casual observer the One Point Fives might not have seemed to be good candidates for that sort of employment. Stripped of their shields and prostheses the average One Point Five wasn’t much bigger than a terrestrial cat. That casual observer would not be likely, however, to see a One Point Five in that stripped-down condition. A One Point Five’s indispensable protective devices massed just about half as much as his body itself (hence the name One Point Five), and every last bit of these devices was vitally necessary. Some of the devices guarded the fragile organic being inside against radiation—from the ionizing spillover from their nuclear power plants or from the residues of their many long-ago nuclear wars. Or even against the lethally high ultraviolet rays that came from their star and were no longer warded off by their planet’s ozone layer because their earlier activities had resulted in their planet’s no longer having one. Some of their chemical processors removed poisons from the air they breathed or the food and water they ingested. Some merely kept them from going insane from the unbearable din that suffused every part of their world (that took blanketing sound absorbers backed up with frequency nullifiers). Other processors toned down the maddening flashes and flares that accompanied their industry.

There were a few isolated spots on their planet where a One Point Five could strip naked and survive. Those places were the breeding rooms and the birthing rooms, as well as a scattering of spots where medical and surgical procedures were performed. There weren’t many of those. Because there was so much to guard against, neutralize, or prevent on that ravaged world, such places were not only scarce but expensive.

That being so, one might wonder why a species as technologically savvy as the One Point Fives didn’t just go ahead and build themselves a fleet of spaceships and proceed to start a new life on some unspoiled planet somewhere else in space.

Actually, the One Point Fives had done that… once.

The project had not been a success, however. Oh, the ships had got invented and built, all right, and a benign enough planet had been located. But the Grand Galactics had stepped in. After that happened, it had been so little of a success that, though many thousands of years had passed, the One Point Fives had never considered trying it again.