Charles Sheffield - Proteus in the Underworld

“I’ll believe that. The closer you get to Sol, the more trouble you run into. But what about my other question. What do I tell Sondra?”

“Tell her—” Bey swore internally. “Tell her I am worried about her, but say you don’t know why.”

“You are worried about her. Fine. Very persuasive. Are you sure you’re not having it off with her? All right, all right.” Aybee pushed his hands, palm outward, toward Bey. “I’ll tell her. Is that it?”

“Yes,” Bey paused. Aybee’s finger was on the disconnect “No, wait a minute. One other question on the same subject What do you know about elliptic functions?”

“The same subject!” Aybee’s eyebrowless forehead wrinkled. “Wolfman, you could sure have fooled me.”

“I know. I felt the same way when I heard it. But if I understand anything at all about Robert Capman, it has to be relevant. Listen.”

As Bey summarized his conversation, Aybee sat totally still and silent. At the end he shook his head. “If Capman says it, you hafta take it seriously. He’s still wearing a Logian form?”

“He was when he talked to me.”

“Then you have to assume he’s a lot smarter than you. Hell, he’s even a lot smarter than me. Maybe he’s so smart, he thinks he’s helping you when he isn’t. Elliptic functions!”

“What do you know about them?”

“I know so much that I don’t know where to start. Wolfman, we’re talking here about a whole major branch of mathematics. There are scores of books and treatises and thousands of papers, all about elliptic functions. I can name a dozen great mathematicians who worked on the subject—Legendre, Abel, Jacobi, Weierstrass, Cayley, Riemann, Hermite, Poincarй—and that’s just the pure theory, without even getting into applications. Did I mention Kronecker—and Gauss, too, of course, though he didn’t publish what he had discovered—”

“Capman didn’t just say ‘elliptic functions.’ ”

Aybee had been in full stride. At Bey’s interruption he stopped and stared. “Then what did he say?”

“What he actually asked me was if I had ever looked at the early history of the theory of elliptic functions. Does that make a difference?”

“All the difference in the world. It means we don’t need to worry about work done after about 1830. And it means something else, too.” Aybee paused, and sat frowning at nothing. “You sure that Capman said elliptic functions, and not elliptic integrals’?”

“Quite sure. Though I hardly know the difference.”

“Well, shame on you. Let’s get you educated. The whole business started out by people trying to find the length of an arc of an ellipse. That gives you a certain sort of integral, and naturally it’s called an elliptic integral. A mathematician called Legendre spent a good chunk of his life writing down bunches of related sorts of integrals, and reduced them to three basic forms. He had done all that pretty much by about 1810.

“But he never saw to the bottom of the problem, or realized that he was studying it the wrong way round. Nor did anyone else at the time—except maybe Gauss, he had this horrible habit of discovering major stuff and putting it in his notebooks, then keeping quiet about it until somebody else came up with the same results. Then he’d say, look here, boys.”

“That sounds a bit like Apollo Belvedere Smith.”

“Could be. Easy to hate a guy like that, eh? Anyway, about 1820 along comes a younger mathematician called Abel. He dies of starvation and tuberculosis when he’s twenty-six years old—which isn’t as bad as it sounds, ’cause mathematicians usually do the good stuff in their early twenties and geeze along for the next century. Anyway, before Abel kicks it he finds the right way to handle elliptic integrals. He inverts the problem. Switches the roles of independent and dependent variables, if you want to get technical. That inversion of outlook starts the whole theory of elliptic functions off and running.”

Aybee paused to frown at Bey. “I may be wrong, but I get the feeling that you’re not overjoyed to hear all this. There’s lots more.”

“I’m sure there is. And I know you’re going to be disappointed and disgusted to hear that it all makes about as much sense to me as if you were singing folk songs in Cloudland Chinese. Let’s keep the rest of the inversion story until I’m feeling smarter.”

“I won’t hold my breath for that. Don’t you at least want to hear about elliptic modular functions, and how Hermite used them to solve the general quintic equation?”

“Naturally. There’s nothing in the whole universe I’d like better—after you get back from the Fugate Colony, and we know that Sondra is all right.”

“Some people got a one-track mind. Okay, I’ll go check her out. One more thing, Wolfman, then I’m on my way.” Aybee waited, his finger once more on the disconnect, until he had Bey’s full attention. Then: “Are you really hanging out close to home because you’re having it on with Trudy Melford?”

He grinned horribly. His finger stabbed down and he was gone, before Bey had time for even one cuss word.

Bey decided that he ought to talk with Aybee more often. The Cloudlander was rude and uppity, but a conversation with him was as good as a tonic. Also, it always clarified Bey’s own thoughts. Aybee had put his finger on a basic question: Why was Bey here, and not out in the Carcon and Fugate Colonies?

One part of the answer was his insistence that he was retired. He had his own interests, his private projects. Why should he become involved in Sondra’s problem?

That logic did not satisfy. After all, he had allowed himself to be drawn to Mars by Trudy Melford, when he had plenty of work to do back on Wolf Island. And he could not blame Trudy for everything. She had brought him here the first time, but he had only himself to thank for today’s meeting with the Old Mars council.

He knew what was happening, even if he did not want to admit it Maria Sun had warned him: Watch that bump of curiosity. I can see it swelling from here. Somewhere, deep inside, he knew that he was involved in the unfolding—or concealment—of a major mystery. People and events were being manipulated. If that included Bey himself, or even if it didn’t, he had to know how and why.

Bey placed a call to Trudy using the castle’s internal communicator. There was no reply—not even an invitation to leave a message. He went to the elevator, intending to ride it down to Trudy’s floor. The controller refused to obey him, sliding by the assigned destination as though that level did not exist Bey returned to the fifth floor. As before, it was deserted. He tried to walk down the flight of steps that had led him on his first visit to Trudy’s dressing- room. The stairwell was blocked by a Roguard, which gently and mutely refused him entry.

He returned to the elevator and rode it all the way up to the twelfth floor. That was accessible with no problem. So was the suite he had occupied on his last visit The decor still displayed the misguided attempt to match Bey’s personal tastes.

The good news, for the moment, was that it was empty. He would try to find out later what was going on with Trudy. For the moment he wanted a working data terminal and access to his own information sources.

He hesitated for a moment when the service asked him if he needed an encrypted line. Twelve hours earlier he would have thought it unnecessary within Melford Castle. Now he was not so sure. Finally he called for a scrambled signal that could be decoded only with his personal key.

Then the difficult part began. He had to convert thoughts, some of them vague and tentative, into queries specific enough for a semi-smart information system to be able to handle them.