And so matters stood as we went through our eighth and final point and emerged barely eight hundred thousand kilometers from the thriving colony world Taimyr … and found it deserted.
“Still nothing,” Alana said tightly, her voice reflecting both the remnants of cascade depression and the shock of our impossible discovery. “No response to our call; nothing on any frequency I can pick up. I can’t even find the comm satellites’ lock signal.”
I nodded, my eyes on the scope screen as the Dancer’s telescope slowly scanned Taimyr’s dark side. No lights showed anywhere. Shifting the aim, I began searching for the nine comm and nav satellites that should be circling the planet. “Alana, call up the astrogate again and find out what it’s giving as position uncertainty.”
“If you’re thinking we’re in the wrong system, forget it,” she said as she tapped keys.
“Just checking all possibilities,” I muttered. The satellites, too, were gone. I leaned back in my seat and bit at my lip.
“Yeah. Well, from eighteen positively identified stars we’ve got an error of no more than half a light-hour.” She swiveled to face me and I saw the fear starting to grow behind her eyes. “Pall, what is going on here? Two hundred million people can’t just disappear without a trace.”
I shrugged helplessly. “A nuclear war could do it, I suppose, and might account for the satellites being gone as well. But there’s no reason why anyone on Taimyr should have any nuclear weapons.” Leaning forward again, I activated the helm. “A better view might help. If there’s been some kind of war the major cities should now be big craters surrounded by rubble. I’m going to take us in and see what the day side looks like from high orbit.”
“Do you think that’s safe? I mean—” She hesitated. “Suppose the attack came from outside Taimyr?”
“What, you mean like an invasion?” I shook my head. “Even if there are alien intelligences somewhere who would want to invade us, we stand just as good a chance of getting away from orbit as we do from here.”
“All right,” she sighed. “But I’m setting up a cascade point maneuver, just in case. Do you think we should alert everybody yet?”
“Crewers, yes; passengers, no. I don’t want any silly questions until I’m ready to answer them.”
We took our time approaching Taimyr, but caution turned out to be unnecessary. No ships, human or otherwise, waited in orbit for us; no one hailed or shot at us; and as I turned the telescope planetward I saw no signs of warfare.
Nor did I see any cities, farmland, factories, or vehicles. It was as if Taimyr the colony had never existed.
“It doesn’t make any sense,” Matope said after I’d explained things over the crew intercom hookup. “How could a whole colony disappear?”
“I’ve looked up the records we’ve got on Taimyr,” Pascal spoke up. “Some of the tropical vegetation is pretty fierce in the growth department. If everyone down there was killed by a plague or something, it’s possible the plants have overgrown everything.”
“Except that most of the cities are in temperate regions,” I said shortly, “and two are smack in the middle of deserts. I can’t find any of those, either.”
“Hmm,” Pascal said and fell silent, probably already hard at work on a new theory.
“Captain, you don’t intend to land, do you?” Sarojis asked. “If launch facilities are gone and not merely covered over we’d be unable to lift again to orbit.”
“I’m aware of that, and I have no intention of landing,” I assured him. “But something’s happened down there, and I’d like to get back to Earth with at least some idea of what.”
“Maybe nothing’s happened to the colony,” Wilkinson said slowly. “Maybe something’s happened to us.”
“Such as?”
“Well … this may sound strange, but suppose we’ve somehow gone back in time, back to before the colony was started.”
“That’s crazy,” Sarojis scoffed before I could say anything. “How could we possibly do something like that?”
“Malfunction of the field generator, maybe?” Wilkinson suggested. “There’s a lot we don’t know about Colloton space.”
“It doesn’t send ships back in—”
“All right, ease up,” I told Sarojis. Beside me Alana snorted suddenly and reached for her keyboard. “I agree the idea sounds crazy, but whole cities don’t just walk off, either,” I continued. “It’s not like there’s a calendar we can look at out here, either. If we were a hundred years in the past, how would we know it?”
“Check the star positions,” Matope offered.
“No good; the astrogate program would have noticed if anything was too far out of place. But I expect that still leaves us a possible century or more to rattle around in.”
“No, it doesn’t.” Alana turned back to me with a grimly satisfied look on her face. “I’ve just taken signals from three pulsars. Compensating for our distance from Earth gives the proper rates for all three.”
“Any comments on that?” I asked, not expecting any. Pulsar signals occasionally break their normal pattern and suddenly increase their pulse frequency, but it was unlikely to have happened in three of the beasts simultaneously; and in the absence of such a glitch the steady decrease in frequency was as good a calendar as we could expect to find.
There was a short pause; then Tobbar spoke up. “Captain, I think maybe its time to bring the passengers in on this. We can’t hide the fact that we’re in Taimyr system, so they’re bound to figure out sooner or later that something’s wrong. And I think they’ll be more cooperative if we volunteer the information rather than making them demand it.”
“What do we need their cooperation for?” Sarojis snorted.
“If you bothered to listen as much as you talked,” Tobbar returned, a bit tartly, “you’d know that Chuck Raines is an advanced student in astrophysics and Dr. Chileogu has done a fair amount of work on Colloton field mathematics. I’d say chances are good that we’re going to need help from one or both of them before this is all over.”
I looked at Alana, raised my eyebrows questioningly. She hesitated, then nodded. “All right,” I said. “Matope, you’ll stay on duty down there; Alana will be in command here. Everyone else will assemble in the dining room. The meeting will begin in ten minutes.”
I waited for their acknowledgments and then flipped off the intercom. “I’d like to be there,” Alana said.
“I know,” I said, raising my palms helplessly. “But I have to be there, and someone’s got to keep an eye on things outside.”
“Pascal or Sarojis could do it.”
“True—and under normal circumstances I’d let them. But we’re facing an unknown and potentially dangerous situation, and I need someone here whose judgment I trust.”
She took a deep breath, exhaled loudly. “Yeah. Well … at least let me listen in by intercom, okay?”
“I’d planned to,” I nodded. Reaching over, I touched her shoulder. “Don’t worry; Bradley can handle the news.”
“I know,” she said, with a vehemence that told me she wasn’t anywhere near that certain.
Sighing, I flipped the PA switch and made the announcement.
They took the news considerably better than I’d expected them to—possibly, I suspected, because the emotional kick hadn’t hit them yet.
“But this is absolutely unbelievable, Captain Durriken,” Lissa Steadman said when I’d finished. She was a rising young business-administration type who I half-expected to call for a committee to study the problem. “How could a whole colony simply vanish?”
“My question exactly,” I told her. “We don’t know yet, but we’re going to try and find out before we head back to Earth.”
“We’re just going to leave?” Mr. Eklund asked timidly from the far end of the table. His hand, on top of the table, gripped his wife’s tightly, and
I belatedly remembered they’d been going to Taimyr to see a daughter who’d emigrated some thirty years earlier. Of all aboard, they had lost the most when the colony vanished.
“I’m sorry,” I told him, “but there’s no way we could land and take off again, not if we want to make Earth again on the fuel we have left.”
Eklund nodded silently. Beside them, Chuck Raines cleared his throat. “Has anybody considered the possibility that we’re the ones something has happened to? After all, it’s the Aura Dancer, not Taimyr, that’s been dipping in and out of normal space for the last six weeks. Maybe during all that activity something went wrong.”
“The floor is open for suggestions,” I said.
“Well … I presume you’ve confirmed we are in the Taimyr system. Could we be—oh—out of phase or something with the real universe?”
“Highly poetic,” Tobbar spoke up from his corner. “But what does out of phase physically mean in this case?”
“Something like a parallel universe, or maybe an alternate time line,” Raines suggested. “Some replica of our universe where humans never colonized Taimyr. After all, cascade images are supposed to be views of alternate universes, aren’t they? Maybe cascade points are somehow where all the possible paths intersect.”
“You’ve been reading too much science fiction,” I told him. “Cascade images are at least partly psychological, and they certainly have no visible substance. Besides, if you had to trace the proper path through a hundred universes every time you went through a cascade point, you’d lose ninety-nine ships out of every hundred that tried it.”
“Actually, Mr. Raines is not being all that far out,” Dr. Chileogu put in quietly. “It’s occasionally been speculated that the branch cuts and Riemann surfaces that show up in Colloton theory represent distinct universes. If so, it would be theoretically possible to cross between them.” He smiled slightly. “But it’s extremely unlikely that a responsible captain would put his ship through the sort of maneuver that would be necessary to do such a thing.”
“What sort of maneuver would it take?” I asked.
“Basically, a large-angle rotation within the cascade point. Say, eight degrees or more.”
I shook my head, feeling relieved and at the same time vaguely disappointed that a possible lead had evaporated. “Our largest angle was just under four point five degrees.”
He shrugged. “As I said.”
I glanced around the table, wondering what avenue to try next. But Wilkinson wasn’t ready to abandon this one yet. “I don’t understand what the ship’s rotation has to do with it, Dr. Chileogu,” he said. “I thought the farther you rotated, the farther you went in real space, and that was all.”
“Well … it would be easier if I could show you the curves involved. Basically, you’re right about the distance-angle relation as long as you stay below that eight degrees I mentioned. But above that point there’s a discontinuity, similar to what you get in the curve of the ordinary tangent function at ninety degrees; though unlike the tangent the next arm doesn’t start at minus infinity.” Chileogu glanced around the room, and I could see him revising the level of his explanation downward. “Anyway, the point is that the first arm of the curve—real rotations of zero to eight point six degrees—gives the complete range of translation distance from zero to infinity, and so that’s all a star ship ever uses. If the ship rotates past that discontinuity, mathematical theory would say it had gone off the edge of the universe and started over again on a different Riemann surface. What that means physically I don’t think anyone knows; but as Captain Durriken pointed out, all our real rotations have been well below the discontinuity.”
Wilkinson nodded, apparently satisfied; but the term “real rotation” had now set off a warning bell deep in my own mind. It was an expression I hadn’t heard—much less thought about—in years, but I vaguely remembered now that it had concealed a seven-liter can of worms. “Doctor, when you speak of a ‘real’ rotation, you’re referring to a mathematical entity, as opposed to an actual, physical one,” I said slowly. “Correct?”
He shrugged. “Correct, but with a ship such as this one the two are for all practical purposes identical. The Aura Dancer is a long, perfectly symmetrical craft, with both the Colloton-field generator and Ming-metal cargo shield along the center line. It’s only when you start working with the fancier liners, with their towers and blister lounges and all, that you get a serious divergence.”
I nodded carefully and looked around the room. Pascal had already gotten it, from the expression on his face; Wilkinson and Tobbar were starting to. “Could an extra piece of Ming metal, placed several meters off the ship’s center line, cause such a divergence?” I asked Chileogu.
“Possibly.” He frowned. “Very possibly.”
I shifted my gaze to Lanton. His face had gone white. “I think,” I said, “I’ve located the problem.”
Seated at the main terminal in Pascal’s cramped computer room, Chileogu turned the Ming-metal coil over in his hands and shook his head. “I’m sorry, Captain, but it simply can’t be done. A dual crossover winding is one of the most complex shapes in existence, and there’s no way I can calculate its effect with a computer this small.”
I glanced over his head at Pascal and Lanton, the latter having tagged along after I cut short the meeting and hustled the mathematician down here. “Can’t you even get us an estimate?” I asked.
“Certainly. But the estimate could be anywhere up to a factor of three off, which would be worse than useless to you.”
I nodded, pursing my lips tightly. “Well, then, how about going on from here? With that coil back in the shield, the real and physical rotations coincide again. Is there some way we can get back to our universe; say, by taking a long step out from Taimyr and two short ones back?”
Chileogu pondered that one for a long minute. “I would say that it depends on how many universes we’re actually dealing with,” he said at last. “If there are just two—ours and this one—then rotating past any one discontinuity should do it. But if there are more than two, you’d wind up just going one deeper into the stack if you crossed the wrong line.”
“Ouch,” Pascal murmured. “And if there are an infinite number, I presume, we’d never get back out?”
The mathematician shrugged uncomfortably. “Very likely.”
“But don’t the mathematics show how many universes there are?” Lanton spoke up.
“They show how many Riemann surfaces there are,” Chileogu corrected. “But physical reality is never obliged to correspond with our theories and constructs. Experimental checks are always required, and to the best of my knowledge no one has ever tried this one.”
I thought of all the ships that had simply disappeared, and shivered slightly. “In other words, trying to find the Taimyr colony is out. All right, then. What about the principle of reversibility? Will that let us go back the way we came?”
“Back to Earth?” Chileogu hesitated. “Ye-e-s, I think that would apply here. But to go back don’t you need to know … ?”
“The real rotations we used to get here,” I nodded heavily. “Yeah.” We looked at each other, and I saw that he, too, recognized the implications of that requirement.
Lanton, though, was still light-years behind us. “You act like there’s still a problem,” he said, looking back and forth between us. “Don’t you have records of the rotations we made at each point?”
I was suddenly tired of the psychiatrist. “Pascal, would you explain things to Dr. Lanton—on your way back to the passenger area?”
“Sure.” Pascal stepped to Lanton’s side and took his arm. “This way, Doctor.”
“But—” Lanton’s protests were cut off by the closing door.
I sat down carefully on a corner of the console, staring back at the Korusyn 630 that took up most of the room’s space. “I take it,” Chileogu said q
uietly, “that you can’t get the return-trip parameters?”
“We can get all but the last two points we’d need,” I told him. “The ship’s basic configuration was normal for all of those, and the Korusyn there can handle them.” I shook my head. “But even for those the parameters will be totally different—a two-degree rotation one way might become a one or three on the return trip. It depends on our relation to the galactic magnetic field and angular momentum vectors, closest-approach distance to large masses, and a half-dozen other parameters. Even if we had a mathematical expression for the influence Lanton’s damn coil had on our first two points, I wouldn’t know how to reprogram the machine to take that into account.”
Chileogu was silent for a moment. Then, straightening up in his seat, he flexed his fingers. “Well, I suppose we have to start somewhere. Can you clear me a section of memory?”
“Easily. What are you going to do?”
He picked up the coil again. “I can’t do a complete calculation, but there are several approximation methods that occasionally work pretty well; they’re scattered throughout my technical tapes if your library doesn’t have a list. If they give widely varying results—as they probably will, I’m afraid—then we’re back where we started. But if they happen to show a close agreement, we can probably use the result with reasonable confidence.” He smiled slightly. “Then we get to worry about programming it in.”
“Yeah. Well, first things first. Alana, have you been listening in?”
“Yes,” her voice came promptly through the intercom. “I’m clearing the computer now.”