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Brain Ships - Anne McCaffrey [173]

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structure. Satyajohi's Conjecture." She quoted from her memory banks, "If h is a homeomorphism of E3 onto itself that is fixed on E3 – T, need one of h(J1), h(j2) contain an arc with four points of A+B such that no two of these points which are adjacent on the arc belong to the same one of A and B? If so, the decomposition space H does not yield E3. And in this application," she reminded Caleb, "E3 is equivalent to normal space."

Caleb blinked twice. "I didn't expect you to know Satyajohi's Conjecture, actually. Still—let me point out, XN, it's only a conjecture, not a theorem."

"In one hundred and twenty-five years of deep-space mathematics it's never been disproved," Nancia grumbled.

"So? Perhaps you'll be the first to find a counterexample."

Nancia didn't think there was much point in even trying, but she set an automatic string-development program to race through the display, illuminating various possible Singularity paths as lines of brilliant blue light, then letting them fade out as the impossibility of one after the other was proved. There was something else on which she very much wanted Caleb's advice, and now—with the Thrixtopple family intimidated into staying in their cabins, and Caleb in as good a mood as she'd ever seen him after his demonstration of Satyajohi's Conjecture—now was the best time she could have to bring it up.

"I haven't been commissioned very long, you know, Caleb," she began.

"No, but you're going to be one of the best," Caleb told her. "I can see it in the way you handle little things. I wouldn't have thought of finding a regulation to get the Thrixtopples out of our hair. And I don't think I'd have tested Satyajohi's Conjecture the way you're going about it right now, either." Two possible Singularity lines flashed bright blue and then vanished from the screen as he spoke, while a third snaked through A1 and into the B disk around the double torus.

"Some things," Nancia said carefully, "get more complicated than that. In mathematics a conjecture either is or isn't true."

"The same is true of Courier Service Regulations," Caleb pointed out.

"Yes, well . . . not everything. They don't tell you what to do if a brainship happens to hear her passengers making illegal plans."

"If you've been eavesdropping on Governor Thrixtopple in his cabin," Caleb said sternly, "that's a dishonorable action and I hereby formally request you to stop it immediately."

"Oh, I haven't," Nancia assured him. "But what if—if a brainship had some passengers who didn't know she was sentient, and they liked to sit in the central cabin and play SPACED OUT, and they just happened to discuss some possibly illegal plans while they were doing it?"

"Oh—a hypothetical case?" Caleb sounded relieved, and Nancia felt the same way. At least he hadn't guessed immediately, as Simeon had, that she was talking about her own previous experience. Everything Nancia had learned or seen of Caleb—the newsbeams of his heroic solo return to Vega, the dedication with which he put himself through a grueling exercise program, his respect for Courier Service regulations—made her think of him as a man of supreme integrity, one whose word she could trust under any circumstances. She would not have wanted to hear him laugh at her as Simeon had done, or suggest—as Simeon had done—that her own actions in this instance had been morally culpable.

"Well, in such a case—if it ever arises—you should remember that a sentient ship is morally obliged to identify herself as such to her passengers at the first opportunity."

"That's not in the regulations," Nancia defended herself against a charge Caleb didn't know he had made.

"No, but it's common sense. Anything else would be like—like me hiding in a closet to catch Governor Thrixtopple counting his ill-gotten gains from bribes while in public office." Caleb said this with so much disgust in his voice that Nancia shrank from pursuing the subject.

So, evidently, did Caleb. He looked up at the central display screen, where a network of dim gray lines showed Nancia's repeated attempts to compute a

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