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 manifestations, 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 the 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 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 re-create 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 don'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."