Mace rubbed his chin. "You want to talk to a Snowman?"

"Don't mock me," Kapur said patiently.

"What will you talk about?"

Kapur, feeling his way, thought quickly. "Godel's theorem."

Mace leaned forward, ready to scorn -- then hesitated. "Well, why not?" he said at last. "You could give it a human proof of the theorem. That might be kind of interesting."

Kapur waited, but Mace's laughter did not come. "You have to help me understand you, Mace. Are you serious?"

"Sure... I'll code up the proof in a form compatible with their storage templates; I'll dump it into your Eyes and you can download it into the sensors when we go over there again."

"No." Kapur held up a hand. "I want you to let me go alone."

Mace's Eyes glinted, steel globes embedded in the flesh of his lively, amused face. "Why?"

Kapur held his gaze. "Because you're waiting for me to fail. I don't need that; I don't consider this any kind of game, or contest between us. I don't want you around me."

Mace laughed, uncertainly. Then, as he perceived Kapur's seriousness, a look of bafflement and hurt spread across his broad face. This, Kapur realized, could be the first time any human being had rejected Mace in any way. He searched Mace's face for remorse, for shame; but he found only wounded pride.

"Do what you like," said Mace at last. "I'll code up the proof." There were two days left.

Kapur saw the Snowman as a dully-glowing globe of purple, miles wide, embedded beneath the planar skin of the 'Flake. Mach starbursts, Godel sunflowers and other characteristic formations littered the globe, as still as flowers under glass. 'Flake data streams chattered softly into the Snowman, and human sensor probes ringed the 'Man like patient puppies, blocks of metal silhouetted against lurid data.

Kapur, swaddled in his cold-suit, cowered. Here, confronting the reality of the 'Flake, his isolation scheme seemed vacuous. He had no idea, of course, if the arbitrary assemblage of data before him represented an individual -- or, indeed, if consciousness itself persisted at all in the 'Flake.

He was almost certain that it did not.

But he had to try, he reminded himself.

Enough. He focused his gaze on the nearest of the probes; tight laser light slid from his Eyes and into the probe's cold hide.

When the link was secure he downloaded the human proof of Godel to the probe.

The proof was a string of orange beads on a wire of light; the beads splashed against the target probe and rattled into the Snowman. Finally they settled into a cubical configuration: neat and precise, although dwarfed by the richness and profusion of other forms within the 'Man.

'Flake data slugs lanced through the human proof, copying, integrating -- but changing nothing.

Kapur opened a line to Mace, in the yacht. "I don't understand," he said. "Why don't they evaluate, interpret our proof?"