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“I’ll tell you what I’ll do,” he said to Mandel’stahm. “Tomorrow, I’ll send a message to Titan, and initiate inquiries-very discreetly, of course. If

I learn something, I’ll let you know. But don’t expect too much or for

that matter, anything at all.” Mandel’stahm seemed quite, happy with this arrangement, and departed with rather fulsome protestations of gratitude. Duncan decided that it was also high time that he left the party. He had been on his feet for over two hours, and all his vertebrae were now starting to protest in unison. As he made his way toward the exit, he kept a lookout for George Washington, and managed to find him—despite his short stature—without falling back on the paging system.

“Everything going well?” asked George.

“Yes-I’ve had a very interesting time. And I’ve run into a curious character-he calls himself a gem expert—2’

“Ivor Mandel’stahm. What did the old fox want from you?”

“Oh-information. I was polite, but not very hellyful. Should I take him seriously, and can he be trusted?”

“Ivor is merely the world’s greatest expert on gems. And in that business, one can’t afford even the hint of a suspicion. You can trust him absolutely.”

“Thanks-that’s all I wanted to know.”

Half an hour later, back at the hotel, Duncan unlocked his case and laid out the set of pentominoes that Grandma had given him; he had not even touched it since arriving on Earth. Carefully, he lifted out the titanite cross and held it up to the light…. he first time he had ever seen the gem was at Grandma Ellen’s and he could date the event very accurately. Calindy had been with him, so he must have been sixteen years old. He could not remember how it had been arranged. In view of Grandma’s dislike of strangers (and even of relatives) the visit must have been a major diplomatic feat. He did recall that Calindy had been very anxious to meet the famous old lady, and had wanted to bring along her friends; that, however, had been firmly vetoed.

It was one of those days when Ellen Maken2ie’s co-ordinate system coincided with the external world’s, and she treated Calindy as if she were actually there. Doubtless the fact that she had a fascinating new

novelty to display had much to do with her unusual friendliness. This was not the first specimen of titanite that had been discovered, but the second or third-and the largest up to that time, with a mass of almost fifteen grams. It was irregularly shaped, and Duncan realized that the cross he was now holding must have been cut from it. In those days, no one thought of titanite as having any great value; it was merely a curiosity.

Grandma had polished a section a few millimeters on a side, and the specimen now lay on the stage of a binocular microscope, with a beam of pseudo white light from a tri chromatic laser shining into it. Most of the room illumination had been switched off, but refracted and reflected spots, many of them completely dispersed into their three component colors, glowed steadily from unexpected places on walls and ceiling. The room might have been some magician’s or alchemist’s cell-as, indeed, in a way it was. In earlier ages, Ellen Makenzie would probably have been regarded as a witch.

Calindy stared through the microscope for a long time, while Duncan waited more or less patiently. Then, with a whispered “It’s beautiful-I’ve never seen anything like it!” she had reluctantly stepped aside …. A hexagonal corridor of light, dwindling away to infinity, outlined by millions of sparkling points in a geometrically perfect array. By changing focus, Duncan could hurtle down that corridor, without ever coming to an end. How incredible that such a universe lay inside a piece of rock only a millimeter thick!

The slightest change of position, and the glittering hexagon vanished; it depended critically on the angle of illumination, as well as the orientation of the crystal. Once it was lost, even Grandma’s skilled hands took minutes to find it again.

“Quite unique,” she had said happily (Duncan had never seen her so cheerful), “and I’ve no explanations-merely half a dozen theories. I’m not even sure if we’re seeing a real structure-or some kind of moire pattern in three dimensions, if that’s possible….”

That had been fifteen years ago-and in that time, hundreds of theories had been proposed and demolished. It was widely agreed, however, that titanite’s extraordinarily perfect lattice structure must have been produced by a combination of extremely low temperatures and total absence of gravity. If this theory was correct, it could not have originated on any planet, or much nearer to the Sun than the orbit of Neptune. Some scientists had even built a whole elaborate theory of “interstellar crystallography” on this assumption.

There had been even wilder suggestions. Something as odd as titanite had, naturally, appealed to Karl’s speculative urges.