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Schild`s Ladder 9

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Cass said, "Of course it is, right now. But they"ve come from nothing, to this" - she gestured at the highway around them - "in just six hundred years. Give them another near-side month or two, and they"ll definitely be the ones leading the way."

They returned to the place Mariama had named Museum City. The tar pit would take time to stabilize, and until the Planck worms had either been trapped and killed, or failed to show up entirely, it would not be safe to try to drill through the mess and make contact with the border.

It had been less than a millisecond since the Sarumpaet had begun its flight. Tchicaya enjoyed imagining his own startled near-side version hearing the news that the Planck worms had been defeated, before he"d even had time to grow anxious about the fate of the mission. He"d made no firm plans for reversing his bifurcation, since he"d never really expected to return, but the less-traveled Tchicaya would probably be willing to be subsumed. If not, he only hoped that their continued separation would be justified, and they didn"t merely dog each other"s footsteps. If they both tried to meet up with Rasmah it would be awkward, though Tchicaya had little doubt which one of them she"d choose.

Cass gave Mariama xennobe language lessons. Tchicaya sat in on them, but he found them heavy going. Mariama made her own copy of the vendek-based communications software and began converting it into something a Mediator could work with, but filling in the gaps and formalizing the structures of the language was a huge task.

Tchicaya had expanded the Sarumpaet's scape, building rooms beyond the observation deck, giving all three passengers privacy. He began sleeping more, eight or ten hours in every ship-day.

Mostly, he dreamed that he was back on the Rindler. It was strange to feel pangs of nostalgia, not for solid ground and blue skies, but for stars and borderlight.

The Colonists were intensely curious about the aliens, and eager to explain their own world to them. They dragged the Sarumpaet from group to group, place to place; if Cass had let them, they probably would have taken her on a tour of every city in their realm, talking to her nonstop all the way. In near-side terms, their history only stretched back about a year, and they had only explored a few thousand cubic kilometers of the far side, but by any local measure their civilization was orders of magnitude vaster than all of inhabited space. And they were far from alone: they"d had direct contact with twelve other sentient species, and they had secondhand knowledge of hundreds more.

Tchicaya listened to Cass"s translations, and marveled at the things they were learning, but he could see how weary she was becoming, and he felt both a protective sympathy for her, and a lesser, parallel exhaustion of his own. He had dived into the far side unprepared, and whether or not he eventually made it his home, he needed to come up for air.

On their fifty-third night in the city, Mariama woke him, standing by his bed, shaking him by the arm. He squinted at her and willed the scape to grow brighter.

"It"s about Cass."

He nodded. "She has to get out soon. The minute the tar pit"s safe to traverse, we need to start drilling."

Mariama sat on the bed beside him. "She"s started talking to me about staying on. Seeing out her original project, in some form or other: freezing the border, pushing away the far side. Whatever can be done to stop the evacuations."

Tchicaya was horrified. "That could take centuries!" He only meant far-side time, though on reflection he wondered if that wasn"t optimistic.

Mariama said, "I don"t know what she"s thinking. That they"ll crucify her outside, if she dares to emerge without a solution? Or maybe it"s more personal. Either way, I don"t think she can hold out that long. It"s too open-ended, and she"s taking it all too personally. She"s already been through enough. Will you try to talk some sense into her?"


"Thanks." Mariama smiled. "It"ll come better from you. I"d sound too much like someone who"s simply angling for her job."

Tchicaya wondered for a moment if he"d misunderstood her, but she"d managed to be oblique without the slightest hint of ambiguity.

"Why do you want her job?" he said.

"I"m ready for this," Mariama declared. "It"s exactly what I came to the Rindler to do."

"You came to the Rindler to work with Tarek on Planck worms!"

"I came to the Rindler to give people a choice," she said. "There are limits to the way that can be achieved, complications that I never anticipated, but working with the Colonists to find the solution would be an entirely honorable compromise."

Tchicaya shook his head in mock admiration. "So you get to live exactly like a Yielder, while retaining your Preservationist credentials? Very slick." He made it sound like a joke, but he was angry. He could forgive her the almost tongue-in-cheek self-serving spin. What he hated was the fact that she"d set her sights so far beyond his own, again.

He wasn"t ready to stay. He couldn"t live among the Colonists with her, when the arrival of every other near-sider was an eternity away. He"d planned to meet Rasmah on the other side of the border. He needed to see the stars at least one more time.

"You"ll go mad," he said.

Mariama laughed. "That"s what my mother used to say, about travelers. Wandering from planet to planet, until they could no longer remember their own names."

"Sounds romantic, doesn"t it? No wonder you couldn"t resist." Tchicaya"s anger was fading, but the ache beneath it remained. He reached out and put his arms around her. There would never be an irrevocable parting, so long as they were both alive, but the gulf she was planning to create between them was the widest and the strangest he"d ever faced.

"What will I tell the version of you next to my kidney? She"ll think I made you walk the plank."

"She"ll understand. I"ll give you a messenger for her."

He pulled away, and held her at arm"s length. "What is it with you, that you always have to go further than anyone else?"

"What is it with you, that you always have to tag along?" Mariama ran her hand over his scalp, then she stood and walked to the doorway.

She stopped and turned back to face him. "Before I go, do you want to make love?"

Tchicaya was speechless. She had never once spoken of the possibility, since he"d willed an end to their first chance on Turaev.

"Now that I"m more your type," she said, spreading her arms wide, as if showing off some enhancement to her appearance.

"More my type?" he replied stupidly. He couldn"t detect any change in her.

Mariama smiled. "Acorporeal."

Tchicaya threw his pillow at her. She retreated, laughing.

He lay back on the bed, relieved. Nothing could have lived up to four thousand years of waiting. Except perhaps an original theorem.

Cass stood on the observation deck, listening patiently to Tchicaya"s appeal. Mariama had made herself scarce, and even the Colonists had finally noticed that their living legend began to emit incomprehensible streams of vendeks if they didn"t give her an occasional day off.

She"d done enough, he said. No sane person blamed her for her lack of omniscience. The Mimosans' plan to accelerate the far side had been ingenious, and she"d struggled valiantly to try to make it work, but the rules had changed, the prize she"d been reaching for had retreated into the distance. Other people could carry on in her place; the end result would be the same. And if she needed personal redemption, couldn"t that come from passing on her knowledge of the far side to someone rested, someone fully prepared for a second long haul?

Cass appeared calm, even slightly distracted. Tchicaya wondered if she"d taken in his words, if he should repeat himself from the beginning.

"I want to go swimming," she said suddenly.


Cass nodded earnestly.

"All right."

Tchicaya began to gesture at the scape, but she grabbed his arm. "In real water," she insisted fiercely. "Real molecules of water."

Tchicaya unclenched her grip on him, and held her by the shoulders. "Okay. As soon as we get out, you can do that."

"I swim in real water; that"s who I am." Her face contorted, and she emitted a long, anguished moan. "I didn"t want to be changed this much!"

"I"ll help you," he promised. "I"ll get you out of here."

On her last day in Museum City, Cass steered the Sarumpaet unescorted through the corridors and tunnels, searching for something. "I asked Hintikka, and she made some inspired guesses, but we never got around to investigating all the possibilities. The Colonists don"t really understand graphs, but they have a system for describing vendeks that maps quite well on to our picture, if you know how to make allowances for the parts that don"t match up."

They veered from wall to wall, scrutinizing various living gadgets: lamps, air conditioners, fragrance dispensers, parasprite telephones, humor replenishers - Mariama"s name for the sacs full of endogenous vendeks that the Colonists imbibed to keep themselves in peak condition.

They probed the gadgets, and the toolkit did its best to infer the fine structure of the vendeks they contained. Tchicaya had no idea what Cass was hunting for. She had bidden farewell to the Colonists earlier, formally handing her diplomatic role on to Mariama. He didn"t know how well that notion translated, but Mariama had begun conversing with the xennobes for herself weeks before, and she seemed satisfied that her newcomer status would not be a handicap. Her own new ship had been prepared; she"d named it in honor of Tarek, in spite of the fact that he was still very much alive. But as she"d pointed out, there were only so many dead people.

"Not quite," Cass muttered. She pulled the ship away from something whose most polite anthropomorphic equivalent was probably a spittoon.

Mariama glanced at Tchicaya inquiringly.

He said, "Don"t ask me. We"ll know when we find it."

The tar pit had stabilized, and the toolkit"s models suggested that the Planck worms would have drowned in its depths. Other, grimmer scenarios could not be ruled out entirely, but as the Sarumpaet made its way back to the border it would seal the tar pit behind it; even if the ship was lost, they would not be opening up an easy channel for the Planck worms.

The worms would certainly have destroyed the interface across the border, but he and Cass would build their own, as close as possible to the old one; it shouldn"t be hard to catch the attention of the equipment on the Left Hand.

From there, they would transmit themselves to Pfaff. It was on the route to Earth, and Tchicaya would accompany her at least that much of the way.

Cass said, "Here it is."

Tchicaya looked up at the toolkit"s display, a schematic of a graph, drawn node by node and edge by edge, superimposed over the larger scape portraying their busy surroundings.

It took him a moment to spot what she meant. Between two vendeks that resembled ornate ironwork, there was a plain, narrow, highly symmetrical layer.

It was the Diamond Graph. The state from which the whole near-side universe was believed to have arisen. Stable here, in this tiny sliver, cushioned between the right two vendeks.

The seed for a universe, lying in the gutter.

Cass gestured at the scape and summoned the image closer, placing it before them on the observation deck.

"That"s what I went looking for," she said. "A glimpse of that. Only I never expected I"d come this close. And I never thought there"d be so much else attached." She smiled uncertainly, then pushed the graph away.

"I think I"m ready to go home."


Quantum Graph Theory is fictitious, but the spin networks on which Sarumpaet"s work is based are part of a real theory, known as loop quantum gravity, discovered by Lee Smolin and Carlo Rovelli. There is a considerable literature on this subject; two comprehensive review papers are:

"An Introduction to Spin Foam Models of Quantum Gravity and BF Theory" by John C. Baez, in Geometry and Quantum Physics, edited by Helmut Gausterer and Harald Grosse, Springer, Berlin, 2000.


"The Future of Spin Networks" by Lee Smolin, in The Geometric Universe, edited by S. A. Huggett et al., Oxford University Press, Oxford, 1998.

I"m indebted to John Baez, who very kindly explained several points to me directly, as well as posting numerous articles on the news group sci.physics.research making these ideas more accessible to nonspecialists. Of course, any errors I"ve committed in describing the real theory, and any absurdities in the way I"ve imagined its future, are my fault entirely.

Decoherence is a real phenomenon, and it is widely accepted as playing a major role in the absence of detectable quantum effects in macroscopic objects. Its role in relation to the superselection rules that forbid superpositions of certain kinds of quantum states is more controversial. These ideas are discussed in:

Decoherence and the Appearance of a Classical World in Quantum Theory by D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Springer, Berlin, 1996.

I learned about the construction known as Schild"s ladder from:

Gravitation by C. W. Misner, K. S. Thorne and J. A. Wheeler, W. H. Freemann, New York, 1970.

who cite an unpublished lecture by Alfred Schild on January 19, 1970, at Princeton University.

Supplementary material for this novel can be found at

<p>About the Author</p>

Greg Egan is the author of several acclaimed SF novels and short stories. A winner of the Hugo Award and the John W. Campbell Memorial Award, he was voted the "Most Popular Science Fiction Author of the Decade" (1990s) by Interzone magazine. Mr. Egan lives in Australia.


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<p>Other Books by Greg Egan</p>


Permutation City






Cover design by Ervin Serrano

Cover illustration by John Lewis

This is a work of fiction. Names, characters, places, and incidents are products of the author"s imagination or are used fictitiously and are not to be construed as real. Any resemblance to actual events, locales, organizations, or persons, living or dead, is entirely coincidental.

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