by Mike Ashley
“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 starship 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 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 nod
ded 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 quietly, “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.”
Chileogu left a moment later to fetch his tapes. Pascal returned while he was gone, and I filled him in on what we were going to try. Together, he and Alana had the computer ready by the time Chileogu returned. I considered staying to watch, but common sense told me I would just be in the way, so instead I went up to the bridge and relieved Alana. It wasn’t really my shift, but I didn’t feel like mixing with the passengers, and I could think and brood as well on the bridge as I could in my cabin. Besides, I had a feeling Alana would like to check up on Bradley.
I’d been sitting there staring at Taimyr for about an hour when the intercom bleeped. “Captain,” Alana’s voice said, “can you come down to the dining room right away? Dr Lanton’s come up with an idea I think you’ll want to hear.”
I resisted my reflexive urge to tell her what Lanton could do with his ideas; her use of my title meant she wasn’t alone. “All right,” I sighed. “I’ll get Sarojis to take over here and be down in a few minutes.”
“I think Dr Chileogu and Pascal should be here, too.”
Something frosty went skittering down my back. Alana knew the importance of what those two were doing. Whatever Lanton’s brainstorm was, she must genuinely think it worth listening to. “All right. We’ll be there shortly.”
They were all waiting quietly around one of the tables when I arrived. Bradley, not surprisingly, was there too, seated next to Alana and across from Lanton. Only the six of us were present; the other passengers, I guessed, were keeping the autobar in the lounge busy. “Okay, let’s have it,” I said without preamble as I sat down.
“Yes, sir,” Lanton said, throwing a quick glance in Pascal’s direction. “If I understood Mr Pascal’s earlier explanation correctly, we’re basically stuck because there’s no way to calibrate the Aura Dancer’s instruments to take the, uh, extra Ming metal into account.”
“Close enough,” I grunted. “So?”
“So, it occurred to me that this ‘real’ rotation you were talking about ought to have some external manifestation, the same way a gyro needle shows the ship’s physical rotation.”
“You mean like something outside the viewports?” I frowned.
“No; something inside. I’m referring to the cascade images.”
I opened my mouth, closed it again. My first thought was that it was the world’s dumbest idea, but my second was why not? “You’re saying, what, that the image-shuffling that occurs while we rotate is tied to the real rotation, each shift being a hundredth of a radian or something?”
“Right,” he nodded, “although I don’t know whether that kind of calibration would be possible.”
I looked at Chileogu. “Doctor?”
The mathematician brought his gaze back from infinity. “I’m not sure what to say. The basic idea is actually not new – Colloton himself showed such a manifestation ought to be present, and several others have suggested the cascade images were it. But I’ve never heard of any actual test being made of the hypothesis; and from what I’ve heard of the images. I suspect there are grave practical problems, besides. The pattern doesn’t change in any mathematically predictable way, so I don’t know how you would keep track of the shifts.”
“I wouldn’t have to,” Lanton said. “I’ve been observing Rik’s cascade images throughout the trip. I remember what the pattern looked like at both the beginning and ending of each rotation.”
I looked at Bradley, suddenly understanding. His eyes met mine and he nodded fractionally.
“The only problem,” Lanton continued, “is that I’m not sure we could set up at either end to do the reverse rotation.”
“Chances are good we can,” I said absently, my eyes still on Bradley. His expression was strangely hard for someone who was supposedly seeing the way out of permanent exile. Alana, if possible, looked even less happy. “All rotations are supposed to begin at zero, and since we always go ‘forward’ we always rotate the same direction.”
I glanced back at Lanton to see his eyes go flat, as if he were watching a private movie. “You’re right; it is the same starting pattern each time. I hadn’t really noticed that before, with changes and all.”
“It should be easy enough to check, Captain,” Pascal spoke up. “We can compute the physical rotations for the first six points we’ll be going through. The real rotations should be the same as on the outbound leg, though, so if Dr Lanton’s right the images will wind up in the same pattern they did before.”
“But how – ?” Chileogu broke off suddenly. “Ah. You’ve had a mnemonic treatment?”
Lanton nodded and then looked at me. “I think Mr Pascal’s idea is a good one, Captain, and I don’t see any purpose in hanging around here any longer than necessary. Whenever you want to start back – ”
“I have a few questions to ask first,” I interrupted mildly. I glanced again at Bradley, decided to tackle the easier ones first. “Dr Chileogu, what’s the status of your project?”
“The approximations? We’ve just finished programming the first one; it’ll take another hour or so to collect enough data for a plot. I agree with Dr Lanton, though – we can do the calculations between cascade points as easily as we can do them in orbit here.”
“Thank you. Dr Lanton, you mentioned something about changes a minute ago. What exactly did you mean?”
Lanton’s eyes flicked to Bradley for an instant. “Well . . . as I told you several weeks ago, a person’s mind has a certain effect on the cascade image pattern. Some of the medicines Rik’s been taking have slightly altered the – oh, I guess you could call it the texture of the pattern.”
“Altered it how much
?”
“In some cases, fairly extensively.” He hesitated, just a bit too long. “But nothing I’ve done is absolutely irreversible. I should be able to recreate the original conditions before each cascade point.”
Deliberately, I leaned back in my chair. “All right. Now let’s hear what the problem is.”
“I beg your pardon?”
“You heard me.” I waved at Bradley and Alana. “Your patient and my first officer look like they’re about to leave for a funeral. I want to know why.”
Lanton’s cheek twitched. “I ddn’t think this is the time or the place to discuss – ”
“The problem, Captain,” Bradley interrupted quietly, “is that the reversing of the treatments may turn out to be permanent.”
It took a moment for that to sink in. When it did I turned my eyes back on Lanton. “Explain.”
The psychiatrist took a deep breath. “The day after the second point I used ultrasound to perform a type of minor neurosurgery called synapse fixing. It applies heat to selected regions of the brain to correct a tendency of the nerves to misfire. The effects can be reversed . . . but the procedure’s been done only rarely, and usually involves unavoidable peripheral damage.”
I felt my gaze hardening into an icy stare. “In other words,” I bit out, “not only will the progress he’s made lately be reversed, but he’ll likely wind up worse off than he started. Is that it?”
Lanton squirmed uncomfortably, avoiding my eyes. “I don’t know that he will. Now that I’ve found a treatment – ”
“You’re about to give him a brand-new disorder,” I snapped. “Damn it all, Lanton, you are the most cold-blooded – ”
“Captain.”
Bradley’s single word cut off my flow of invective faster than anything but hard vacuum could have. “What?” I said.
“Captain, I understand how you feel.” His voice was quiet but firm; and though the tightness remained in his expression, it had been joined by an odd sort of determination. “But Dr Lanton wasn’t really trying to maneuver you into supporting something unethical. For the record, I’ve already agreed to work with him on this; I’ll put that on tape if you’d like.” He smiled slightly. “And before you bring it up, I am recognized as legally responsible for my actions, so as long as Dr Lanton and I agree on a course of treatment your agreement is not required.”