I wasn’t worried about McAndrew. If they cut his research budget to zero, he would switch to straight theory and manage very well with just a pencil and paper. But everyone else would suffer.
And me? Tallboy wiped me out at the very end of the report, almost as an afterthought: experimental use of the Hoatzin was to be terminated completely, and the ship decommissioned. There would be no expedition to Alpha Centauri or anywhere else beyond the Halo. Worst of all, the report referred to “previous unauthorized use of the balanced drive, and high-risk treatment of official property” — a direct knock at me and McAndrew. We had enjoyed free use of the ship under the previous Administration, but apparently Woolford had never thought to put it in writing.
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!).”