I switched my suit to internal propulsion and headed back for the Institute at top speed. McAndrew knew I was outside, and he met me at the lock waving a long printout sheet. His mop of sandy hair was straggling into his eyes, and a long streak of orange stickiness ran down the front of his shirt. I guessed he had been at dinner when the report came in.
“Did you see it?” he said.
“Heard it. I was on voice-only.”
“Well? What do you think?”
“Horrible. But I’m not surprised. I knew Tallboy hadn’t understood a thing.”
“Eh?” He stood goggling at me. “Are you trying to be funny? It’s the most exciting news in years. I knew she’d find out. What a lass!”
I may not be as smart as McAndrew but I’m no fool. I can recognize a breakdown in communications when I see one. When Mac concentrates, the world isn’t there any more. It seemed to me odds-on that he had been thinking of something else and hadn’t registered the Tallboy decision.
“Mac, stand still for a minute”—he was jiggling up and down with excitement—“and listen to me. The report from External Affairs is here, on the future of your programs.”
He grunted impatiently. “Aye, I know about it—I heard it come in.” He dismissed the subject with a wave of his hand. “Never mind that now, it’s not important. This is what counts.”
He shook the printout, stared at part of it, and went off into a trance. I finally reached out, removed it from his hand, and scanned the first few lines.
“It’s from Jan!”
“Of course it is. She’s on Triton Station. Do you realize what Wicklund’s done out there?”
With Mac in this kind of mood, I’d never get his mind on to Tallboy. “No. What has he done?”
“He’s solved it.” He grabbed the spacegram back from me. “See, it’s right here, can’t you read? Jan didn’t get the details, but she makes it clear enough. Wicklund has solved Vandell’s Fifth Problem.”
“Has he really?” I gently took the paper back from him. If it was news from Jan, I wanted to read it in full. “That’s wonderful. It only leaves one question.”
He frowned at me. “Many questions—we’ll have to wait for more details. But which one are you thinking of?”
“Nothing you can’t answer. But what in Heaven is Vandell’s Fifth Problem?”
He stared at me in disgust.
I got an answer—eventually. But before I had that answer we had been on a rambling tour of three hundred years of mathematics and physics. “In the year 1900—” he began.
“Mac!”
“No, listen to me. It’s the right place to begin.”
In the year 1900, at the second International Congress of Mathematicians in Paris, David Hilbert proposed a series of twenty-three problems to challenge the coming century. He was the greatest mathematician of his day, and his problems drew from a wide range of topics—topology, number theory, transfinite sets, and the foundations of mathematics itself. Each problem was important, and each was tough. Some were solved early in the century, others were shown to be undecidable, a few hung on for many decades; but by the year 2000 most of them had been wrapped up to everyone’s reasonable satisfaction.
In the year 2020, the South African astronomer and physicist Dirk Vandell had followed Hilbert’s precedent, and posed a series of twenty-one problems in astronomy and cosmology. Like Hilbert’s problems they covered a wide range of topics, theoretical and observational, and every one was a skull-cruncher.
McAndrew had solved Vandell’s Eleventh Problem when he was a very young man. From that work had emerged the whole theory for the existence and location of the kernel ring, the torus of Kerr-Newman black holes that circles the sun ten times as far out as Pluto. Nine years later, Wenig’s partial solution of the Fourteenth Problem had given McAndrew the clue that led him to the vacuum-energy drive. Now, assuming that Jan’s report was correct, the Fifth Problem had fallen to Wicklund’s analysis.
“But why is it so important?” I asked McAndrew. “The way you describe it, I don’t see practical uses. It’s just a way of amplifying an observed signal without amplifying background noise—and it only applies when the original signal is minute.”
He shook his head in vigorous disagreement. “It has a thousand applications. Vandell already proposed one when he first set the problem, and I’m sure Wicklund will tackle it as soon as his experimental equipment is working. He’ll use the technique to look for solitaries—rogue planets.”
Rogue planets.
With those last two words, McAndrew brought the explanation along to the point where it made sense to me. I could draw on my own formal training in classical celestial mechanics.
The possible existence of rogues went back a long way, farther than 1900. Probably all the way to Lagrange, who in his analysis of the three-body problem set up a mathematical framework to look at the motion of a planet moving in the gravitational fields of a binary star system. By 1880, that case was known to be “stable against ejection.” In other words, the planet could have close approaches to each of the stars, and might suffer extremes of temperature, but it would never be completely expelled from the stellar system.
But suppose you have a system with three or more stars in it? That’s not at all uncommon. Then the situation changes completely. A planet can pick up enough energy through a series of gravitational swing-bys past the stellar components to hurl it right out of the system. Once this happened it would become a sun-less world, travelling alone through the void. Even if it later encountered another star, the chance of capture was minute. The planet would be a solitary, a rogue world. Astronomers had speculated for centuries about the existence and possible numbers of such planets, but without a scrap of observational evidence.
Vandell had defined the problem: An Earth-sized planet shines only in reflected light. If it gives off radiation in the thermal infrared or microwave regions, the signal is swamped by the stellar background. Devise a technique that will permit the detection of a rogue planet as small as the Earth.
Now it seemed that Wicklund had done it, and McAndrew was happy as a pig, while everybody else at the Institute gloomed about in reaction to Tallboy’s effects on their work.
I sympathized with them. Rogue planets are fine, but I could see no way in which they could make any practical difference to me. Mac and Sven Wicklund could have my share of them. I spent a lot of time over on the Hoatzin wondering what to do next. I didn’t belong at the Penrose Institute, the only thing I offered there was the ability to pilot the long trips out. Once that was over, I might as well go back to the Titan run.
Jan’s next message back gave me mixed feelings, but at least it cheered me up.
“Not much to do out here,” she wrote—she was the only person I have ever met who could chat in a spacegram. “You were right, Jeanie. Wicklund’s as bad as McAndrew, totally wrapped up in the work he’s doing and won’t take much notice of me. And the rest of them hate company so much they run and hide when we meet in the corridors. I’ve been spending a lot of time over on Merganser. I got the impression from you that she’s an old hulk, but she’s not. She may be an antique, but everything’s still in good working shape. I’ve even been spinning-up the drive. If I can talk Wicklund into it maybe we can go off on a little bit of a trip together. He needs a rest (from physics!).”
That brought back some exciting memories. Merganser was one of the two original prototypes of the balanced drive, and McAndrew and I had ironed the bugs out of her personally. She was limited to a 50-gee acceleration, but still in good working order. I’d fly her anywhere. Mac seemed much less happy when he read the letter.
“I hope she knows what she’s doing,” he said. “That ship’s not a toy. Do you think it’s safe?”
“Safe as anything in the System. Jan won’t have any trouble. We used the Merganser for training before they mothballed her, don’t you remember?”
He didn’t, of course. He carries physics and mathematic
s in his head at an astonishing level of detail, but useful everyday information is another matter. He nodded at me vaguely, and wandered off to send more messages to Wicklund (who had to date provided no replies).
We heard from Jan again, just as the explicit order was coming in from Tallboy’s office to decommission Hoatzin and remove the supplies for the Alpha Centauri mission.
I screwed up Tallboy’s order into a tight ball and threw it across the room.
Then I sat down to read what Jan had to say.
No preamble this time: “Wicklund says it works! He’s already found three rogues, and expects a lot more. They must be a lot more common than anybody thought. Now sit back for the big news: there’s one only a light-year away! Isn’t it exciting?”
Well, maybe—less so to me than to Mac, I was sure of that. I assumed that solitary planets would be rather rare, so one closer than the nearest star was a bit surprising. But it was her next words that shot me bolt upright and sent a tingle through my spine.
“Merganser is working perfectly, all ready for a trip. I’ve persuaded Wicklund to take her out for a look at Vandell—that’s his name for the planet. I’m sure you don’t approve, so I won’t ask. Lots of love, and see you when we get back.”
Even as I screamed inside, I wasn’t completely surprised. She was McAndrew’s daughter all right—it was exactly the harebrained sort of thing he would have done.
Mac and I both played it very cool. That boneheaded pair, we said to each other. We might have guessed it, the follies of youth. They’ll be in trouble when they get back, even though the Merganser is an old ship that Triton Station can do what they like with.
But deep inside we both had other feelings. Wicklund had sent the coordinates of Vandell to us before they left, and as Jan said it was close, less than a light-year and a quarter away. Easily in Merganser’s range, and a lure that any scientist worth his salt would find hard to resist, even without Jan’s coaxing. Where had it come from, what was it made of, how long since it had been ejected from its parent star?—there were a hundred questions that could never be answered by remote observations, not even with the super-sensitive methods that Wicklund had developed.
But it was those same questions that made me so uneasy. If I’ve learned one thing wandering around inside and outside the Solar System, it’s this: Nature has more ways of killing you than you can imagine. When you think you’ve learned them all, another one pops up to teach you humility—if you’re lucky. If not, someone else will have to decide what did you in.
For a week after Jan’s message I monitored the messages closely that came in from the outer relay stations. And every day I would ride over to the Hoatzin and potter about there, sometimes with Mac, sometimes alone. I was supposed to be working on the decommissioning, but instead I would sit in the pilot’s chair, check all the status flags, and think my own thoughts. Until finally, ten days after Jan and Wicklund had left, I went over to visit the Hoatzin late one sleep period.
And found that the lock had been cycled since I left.
McAndrew was sitting in the pilot’s chair, staring at the controls. I came quietly up behind him, patted him on the shoulder, and slipped into the copilot’s seat. He turned toward me, straggly eyebrows raised.
“It’s now or never,” he said at last. “But what about Tallboy? What will he do to the Institute?”
I shrugged. “Nothing. Not if we make it clear that it’s our fault.”
I reached out and called for a destination reading. When I left, the coordinates had all been set to zero. Now they carried precise values.
“Do you think that anyone else suspects?” I said. “I checked the experimental logs in your lab today, and they were all current up to this afternoon—and you’re always months behind. If I noticed that, maybe one of the others will.”
He looked surprised. “Why should they? We’ve been careful not to talk about this when anyone else could hear.”
There was no point in telling Mac that he was probably the world’s worst person you’d want to keep a secret. I tapped him on the shoulder. “No point in worrying about it once we’re on our way. Come on, Mac, move over—you’re sitting in my chair. And think positively. We’ll have a nice, long trip, just the two of us.”
He stood up, rubbing at the back of his head the way he always did when he was embarrassed. “Och, Jeanie,” he said. But he was smiling to himself as we changed seats.
The calculations were elementary, and I could do them as well as he could. The Merganser would reach the rogue planet in about sixty days of shipboard time if they kept close to maximum acceleration all the way. We could be there in thirty-five days of shipboard time, but that would pick up only ten days of inertial time. We would reach Vandell a couple of days after them. For me, that was two days too late.
Our drive wake left an ionization track across the whole width of the Solar System. Mac checked that there were no ships directly behind for us to burn a hole through, and while he was doing it I had a new idea and sent a message back to External Affairs. I said that we were about to perform a brief high-gee test of the Hoatzin’s drive before we took her in and decommissioned her. With luck, Tallboy’s group would assume we had been the unhappy victims of a nasty accident, shooting out of the Solar System on a one-way journey when some control element of the drive unit had failed. Limperis and friends at the Institute wouldn’t believe that, not as soon as they checked our destination coordinates—but they would never tell their suspicions to Tallboy. Maybe they could even get some mileage from our disappearance, pointing out the need for more funds for reliability and system maintenance. Limperis could play that game with his eyes closed.
Perhaps everything would work out fine—until McAndrew and I came back. Then the truth would come out, and we’d be roasted for sure.
Neither of us could get too worried about that possibility. We had other things on our minds. As we raced out along the invisible scintillation of the Merganser’s drive, Mac dumped the data bank for information about Vandell’s rogueworld. He didn’t get much. We had coordinates relative to the Sun, and velocity components, but all they did was make sure we could find our way to the planet. Wicklund had been able to put an upper limit on its diameter using long base line interferometry, and estimated that we were dealing with a body no bigger than Earth. But we were missing the physical variables—no mass, internal structure, temperature, magnetic field, or physical composition, not even an estimate of rotation rate. Mac fumed, but at least I’d have a lot more information for him as soon as we got close. In the week before we left the Institute, I had put on board the Hoatzin every instrument that wasn’t nailed down, anything that might tell us something useful about Vandell without having to go down there and set foot on its surface.
At a hundred gees acceleration you head out of the Solar System on a trajectory that’s very close to a straight line. The gravitational accelerations produced by the Sun and planets are negligible by comparison, even in the Inner System. We were bee-lining for a point in the constellation Lupus, the Wolf, where Vandell lay close in apparent position to an ancient supernova fragment. That explosion had lit up the skies of Earth more than a millennium ago; an interesting object, but we wouldn’t be going even a thousandth of the way out to it. Wicklund was right; Vandell’s rogueworld sat in Sol’s backyard.
Without a complicated trajectory to worry about, I went round and round with a different problem. When the drives were on, both the Merganser and the Hoatzin were blind to incoming messages, and drowned out any of their own transmissions. Thus we had a chance to get a message to Sven Wicklund and Jan only when their drive was turned off, while they were coasting free to rubberneck or study the starscape scenery from a slightly different point of view. Even though they might not be listening for an incoming signal when the drive was off, their computer would, and should notify them of anything important.
But now see my problem: to send a message, we had to switch our drive off, and that would
delay our arrival a little bit every time we did it. Our signal would then take days or weeks to reach the Merganser—and to receive it, their ship had to have its drive off at just the right time. DON’T LAND was all I wanted to say. But how would I know when to switch off our drive and send an urgent message, so it would get to them just when their drive was not operating?
I wrestled with that until my brains began to boil, then handed it over to McAndrew. He pointed out that we had knowledge of the occasions when their drive had been switched off, from the gaps in their drive wake. So making a best prediction was a straightforward problem in stochastic optimization. He solved it, too, before we had been on our way for a week. But the solution predicted such a low probability of successful contact that I didn’t even try it—better to leave our drive on full blast, and try to make up some of their lead.
With the shields on to protect us from the sleet of particles and hard radiation induced by our light-chasing velocity, we had no sense of motion at all. But we were really moving. At turnover point we were within one part in ten thousand of light speed.
If I haven’t said it already, I’ll say it now: the 100-gee balanced drive is nice to have, but it’s a son of a bitch—you travel a light-year in just over a month of shipboard time. Two months, and you’ve gone fifty light-years. Four shipboard months, and you’re outside the Galaxy and well on your way to Andromeda.
I calculated that two hundred days would put you at the edge of the Universe, 18 billion light-years out. Of course, by the time you got there, the Universe would have had 18 billion more years to expand, so you wouldn’t be at the new edge. In fact, since the “edge” is defined as the place where the velocity of recession of the galaxies is light-speed, you’d still be 18 billion lightyears away from it—and that would remain true, no matter how long you journeyed. Worse still, if you arranged a trajectory that brought you to rest relative to the Earth, when you switched off the drive the Galaxies near you would be rushing away almost at light speed…
The Compleat McAndrew Page 25