The Gödel Sunflowers

A.D. 10515

It was one of the oldest stars in the Galaxy, a sphere of primordial matter hovering in the halo like a failed beacon. About five hundred of its contemporaries still sprinkled photons over the young-matter soup of the swirling main disc, defiant against the erosion of aeons.

But this star had failed, long since. Now it was choked with iron; carbon dusted its cooling surface.

The artifact humans called the Snowflake surrounded this dwarf star, a vast setting for an ancient, faded jewel.

Since the construction of the Snowflake, fourteen billion years had shivered across the swirling face of the Galaxy.

Now, at last, from out of the main disc, a ship was climbing up to the Snowflake.

Throughout his voyage from Earth aboard the Spline warship, Kapur remained alone. Endlessly he studied Virtuals on his destination, trying to comprehend the task that confronted him.

Kapur would be given five days to complete his task.

He was a policeman, seconded to this assignment. In the fleshy warmth of the Spline’s interior, the enormity of the crime he must prevent kept Kapur awake for long hours.

The Spline ship was a mile-wide ball of hardened flesh. Buried deep in pockmarks, sensors which had once been eyes turned slowly in response to the electronic prompting of humans.

The Spline sailed to within a hundred million miles of the Snowflake, slowed, stopped. For days it hovered. A swarm of passive, powerless probes were sprinkled cautiously over the Snowflake.

The disc of the Galaxy was smoke shot through with starlight, a carpet beneath this slow tableau.

At last the flesh of the Spline puckered, split, parted. A childcraft, a cylinder of silver, wriggled out of the revealed orifice. The child spread shining sails and shook them into a parasol shape; the sails seemed to glisten, as if damp from the womb.

Ruby-red laser light seared from the Spline, lanced into the sails. Slowly, slowly, the fine material billowed in response and filled out. Like thistledown, goaded by the laser-breath of the Spline, the child-yacht descended towards the Snowflake.

The interior of the yacht was a box twenty feet long and six wide. It was too small for two men and the equipment which kept them alive.

Kapur sat before the viewport which formed much of the nose of the yacht. Through the port he could see the dwindling fist of flesh that was the Spline freighter, the perpetually startling sight of the Galaxy in plain view. But even though the yacht was now mere hours away from its rendezvous, of the Snowflake he still saw nothing; not even a rusty smudge, he thought sourly.

Mace, the yacht’s other occupant, sat close to Kapur. He peered out with interest, his Eyes gleaming like an insect’s. Mace was a Navy man. Kapur, dark, slim, uncomfortable in his borrowed Navy uniform, shrank from Mace’s confident bulk.

Mace swiveled his turret of a head towards Kapur. “Well? What do you think of the ‘Flake?”

Kapur shrugged, in the small space he occupied. “What do you expect me to think?”

Mace peered at Kapur, then frowned. “Maybe if you Opened your Eyes you could form an opinion.”

Kapur, reluctant, complied.

His Eyes’ response spectrum broadened away from the narrow human band; his retinae stung under a sleet of photons of all wavelengths.

The Galaxy dazzled, its core shrieking X-rays. The Snowflake emerged from the darkness like frost crystallizing on a windowpane.

“Let’s get to work,” Mace said. “We’ll review the gross features first. OK?”

Kapur, his Eyes full of the infinite recesses of the Snowflake, did not reply.

“The ‘Flake is a regular tetrahedron,” Mace said. “It’s built around the remains of a black dwarf; the ancient star is at the tetrahedron’s centroid. The Snowflake measures over ten million miles along its edges. We don’t know how it maintains its structure in the gravity well of the star.” Mace’s voice was bright, clear, interested, and entirely lacking in awe. “The artifact has the mass of the Earth, approximately. But the Earth is eight thousand miles wide. This thing has been puffed out like candy-floss; it’s filled with struts, threads and whiskers of iron, like delicate scaffolding. The structure’s not a bad approximation to a space-filling curve. Strictly speaking it has a fractional dimension, somewhere between two and three… And it has a fractal architecture. Do you know what that means?”

“I don’t have a math background,” Kapur said.

Mace let his silence comment on that for a long second. “You’re going to do well with the Gödel theorem, then,” he said lightly.

“What?”

“Never mind. When we inspect the ‘Flake closely we’ll find the tetrahedron motif, repeated again and again, on all scales. That’s why we call it the Snowflake,” Mace said. “Not because of its shape, but because a snowflake is fractal too. Recursive structures at all scales. And it’s been there a long time.”

“How do you know that?”

Mace, his Eyes fixed on the ‘Flake, absently rubbed at his nostrils with his palm. “Because it’s so damn cold. In the aeons since its sun died, it’s cooled to close to the background temperature of the Universethree degrees above absolute zero… although,” he mused, “when the thing was built the sky still shone at about eighteen K.

“Do you understand what these numbers mean, Kapur? I know you’ve hardly been off Earth before this assignment.” Mace wasn’t bothering to conceal his relaxed, malice-free contempt. In fact this was Kapur’s second such mission. The first had been a requisition to the failed Assimilation of the Khorte Colony.

He said, “Why iron?”

“Because iron is the most stable element. The Snowmenthe builderswanted this to last a long time, Kapur.”

Kapur nodded. “Then was this a planet, once, before being spun out like a… fairy tale castle?”

“Maybe. Maybe not. When this was built, only a billion years after the Bang, there were scarcely any heavy elements to form planets. The Galaxy itself would have been no more than a disc of smoke, illuminated here and there by hot-spot protostars.” The gun-metal Eyes rotated to Kapur. “Kapur, you also need to understand that it’s not just the physical structure that’s important here. There are many levels beyond the material; even now that thing is an iron-wisp web of data, a cacophony of bits endlessly dancing against the depredations of entropy.”

Kapur smiled. “You use words well, Mace,” he said.

Mace seemed uninterested. He went on, “The Snowmen loaded everything they knew into this artifact. Eventually, they… went away.” He grinned at Kapur. “Maybe. Or maybe they’re still here.”

Kapur shivered; he grasped his own bony elbows. “And why, my friend? What do you think? Why did they build this marvelous sculpture of iron and data, slowly cooling?”

Mace still grinned. “It’s your job to find out, isn’t it?”

Kapur stared into the cold, waiting heart of the Snowflake.

He was not expected to succeed here.

Kapur had failed before.

He had watched the Khorte Colony, an ancient, hivelike accretion of crystalline carbondiamondfold in on itself, burn, die; perhaps one percent of the Colony’s stored knowledge had been saved amid the devastating beams.

Kapur’s mission was Assimilation. Humans would not let the Xeelee take anything they could not Assimilate.

Kapur wondered if this bright young Navy man had ever heard of the Khorte Colony.

The yacht tacked into the laser breeze, slowed, halted before one tetrahedral plane. Two men pushed through an air-curtain into space, bulbous and clumsy in cold-suits.

The faintest spurt of low-velocity helium pushed at Kapur’s back, propeling him towards the Snowflake. The fat, padded suit was snug and warm around him, like a blanket; he felt oddly safe, remote from the immensities around him. At the center of his visor Mace sailed ahead, arms and legs protruding comically from the bulk of his cold-suit.

They stopped a few thousand miles from the iron plane. The face swept to infinity all around Kapur like a vast geometrical diagram; the horizon was razor-sharp against the intergalactic darkness, the three vertices too distant to perceive as corners. His Eyes, set to human wavelengths, made out some detail in the ‘Flake; it was like a gigantic engraving, glowing dully in the smoky light of the Galaxy.

Kapur felt small and helpless. He had four days left.

Mace’s commentary came to him along a laser path, helmet to helmet. “All right,” Mace said. “Here we are in our patent cold-suits; inside, as snug as bugs; outside, radiating heat at barely a fraction more than the background three K.”

As Kapur stared the Snowflake seemed to open out like a flower; he saw layer on layer of recursive detail, sketches of nested tetrahedra dwindling into the soft brown heart of the artifact. “It’s wonderful, Mace.”

“Yeah. And as delicate as wishes. Hey, Kapur. Give me your Eyes. I’ll show you the data.”

Kapur hesitated, gathering his resolve.

He hated using the implants. Each time he Opened his Eyes he felt a little more of his humanity leach away.

Now he breathed deeply. The air inside the cold-suit was warm and scented, oddly, of cut grass. With an odd, semi-hypnotic relinquishing of will, he deferred to Mace.

His Eyes Opened wide.

The Snowflake changed, kaleidoscopically.

“You’re seeing a construct from our passive probes,” Mace whispered. “False-color graphics of the data streams.”

Terabits of ancient wisdom hissed on whiskers of iron, sparking like neurons in some splayed-out brain. It was beautiful, Kapur thought; beautiful and monstrous, like the mind of the antique gods of mankind.

His soul recoiled. He sought refuge in detail, the comparatively mundane.

Kapur knew that the mission profile had been designed with caution in mind. The Spline ship had parked over an AU away; he and Mace had approached in a yacht riding a tight laser beam, eschewing chemical flame. “Mace, what would happen if we let stray heat get at the ‘Flake? Would we disrupt the structure?”

“You mean the physical structure? Maybe, but that’s not the point, Kapur. It’s the data that’s the treasure here.”

“And would a little heat be so harmful?”

“It’s to do with thermodynamics. There’s a lower bound on how much energy it takes to store a bit. The limit is set by the three K background temperature of the Universe.”

“So the lower that global temperature is, the less energy a bit would take.”

“Right. And so if we raised the ‘Flake’s temperature, even locally, we would risk wiping out terabits. Also, it follows from the thermodynamic limit that there’s an upper bound on how much data you can store with a given amount of energyor, equivalently, mass. The upper limit for the Snowflake’s mass is around ten to power sixty-four bits. Kapur, we estimate that the ‘Flake actually holds around ten to power sixty.”

Kapur stared into the flowerlike heart of the Snowflake. “I should be impressed?”

“Damn right,” Mace growled, “For a start, the whole of human civilization would be characterized by only ten to power twenty bits. Even after hundreds of Assimilations. And, just in technological terms, to get within four orders of magnitude of the theoretical limit… it’s almost unimaginable.

“Now. Look.” Mace, silhouetted like a cartoon grotesque, pointed at a knot of color and activity. Kapur perceived something like a sunflower, a fist of spirals and tessellations surrounded by “petals,” great sheets of information which faded into the background chatter. Pellets of data streaked into and out of the corea little like insects, Kapur thought at first; but then he saw how the pellets embedded themselves in the sunflower, endlessly enriching and renewing it.

“What is it?”

“It seems to be the dominant data configuration,” Mace called. “The analogue of the tetrahedral motif on the physical level. It represents a theorem. See, the heart of the structure is the core statement, the petals corollaries, endlessly thrown off and lost…”

“What theorem?”

“Gödel’s Incompleteness. We think. We’re guessing, extrapolating on hints of structure we’ve picked up elsewhere… But it’s not really a theorem, here. It’s merely a statement of the result. Like an axiom; a given.”

“I don’t understand.”

Mace laughed, briefly and scornfully. Wriggling before the landscape of information he pointed again. Amid a meadow of data structures, Kapur picked out another sunflower, the characteristic Gödel shape. Mace jabbed both arms against the vast data diorama, again and again. “There, and there! What do you see, Kapur?”

Gödel, Kapur saw, repeated over and over; there was a fractal spiral of Gödel sunflowers here, embedded in this chill web of data.

“There’s more, of course,” Mace said. “We’ve recognized a lot of physical understanding in here, particularly representations of cosmic events. See that starburst?” A firework of red and yellow, endlessly dynamic, scattered a hundredfold through the ‘Flake. “That’s Mach’s principle: that the inertia of an object is induced by the net gravitational attraction of the rest of the Universe”

“Tell me about Gödel,” Kapur said patiently.

On the low-quality laser link, Mace’s voice was like a buzzing insect. “Gödel was a genius. An Austrian; a Mozart of his subject. In the middle of the twentieth century he produced a theorem on undecidability.

“Gödel studied mathematics in the abstract. Think about that, policeman: not just the mathematics you studied at high school; not the maths I studied in the Navy collegebut any sort of mathematics which it is possible to construct.”

“You have my attention,” Kapur said dryly. “Go on.”

“Gödel showed that within any mathematical scheme you can write down statements which it would be impossible to prove or disprove. They are undecidable, you see. And so mathematics can never be made complete. You could never deduce everything from a finite set of axioms; there would always be new statements to make… new facts to record, if you like.”

Kapur shook his head. “I cannot imagine how it is possible even to begin to frame such a theorem, let alone to prove it.”

“It isn’t that difficult,” Mace said lightly. “It’s rather like the standard proof that the real numbers are uncountable; you make a list of all possible statements within your general mathematical schemeand from that list generate another statement which isn’t in the list”

“Never mind.” Kapur let the terrifying implications sink in. How could there be a hole in mathematicsin the most fundamentally abstract of human inventions? He felt as if the floor had fallen away from his Universe.

What kind of people had these Snowmen become, to hold such an awesome, nihilistic theorem at the heart of their philosophy?

Kapur closed his Eyes againturned them off, in fact; the orchard of data frost-flowers melted to cold, inert iron.

Kapur and Mace made three more trips to the iron epidermis of the Snowflake. Mace pointed out more forests of rustling data, tentatively mapped by humans. There were tigers in those forests, though, Kapur came to realize; great beasts of wisdom and understanding whose nature humans could not even guess at.

Kapur spent several of his precious hours hanging immobile, his cold-suit barely warmer than the ancient, surrounding echo of the Big Bang. He felt old, inadequate. Assimilationbloodless Assimilationdepended on psychology, on the determination of goals. The goal of humanity was to rise up, to grow, and ultimately to confront the Xeelee. If Kapur could determine the goals of the Snowmen, then those objectives could be subvened to serve human purposes. If not, then the ‘Flake, the ‘Men, had no value.

But how could Kapur, inexpert as he was, touch the dreams of the ancient individuals frozen into this data sculpture?

He consoled himself with the thought that failure would be no disgrace, that he could return to his home, his job, without shame.

Kapur did not discuss his feelings openly with Mace; but, as his time wore away in the musty cage of the yacht, he sensed Mace’s swelling mood of triumph. The Navy man was intelligent and endlessly fascinated by his surroundings, Kapur came to see; but he clearly felt that Assimilation was a fool’s errand, a sop thrown to liberal instincts before the Navy was unleashed.

He was probably right, Kapur thought.

It was Mace’s faint gloating, as much as a sense of outrage at the damage the Spline gravity wave planet-breakers would do to the Snowflake, which determined him to keep trying to the end of his time. He could endure failure, he decided; but not failure in front of Mace.

He had a new idea.

“Tell me this,” he said to Mace. “How much data characterizes a human being?”

Mace opened his mouth, closed it again.

Kapur pressed politely, “If my thoughts were somehow transcribed, day and night for my entire lifehow many bits to capture that?”

Mace smiled and closed his Eyes. “All right, policeman; let’s play games. You produce, let’s say, a hundred thousand discrete thoughts per day. Each concept iswhat, a hundred bits?

“We’ll give you fifty years of active adulthood, between infancy and the onset of age. That gives, ah, two times ten to power eleven bits in all.” Mace pursed his lips, opened his Eyes and studied Kapur briefly. “Interesting. So there’s the equivalent of something like ten to power forty-nine human individuals in the ‘Flake”

Kapur nodded. “Isolate one of them, with your sensors. Can you do that? Pick out an island of bits. I don’t want to know what happens within it; arrange it so I only perceive the inputs and outputs.”

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. “Gödel’s theorem.”

Mace leaned forward, ready to scornthen 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, Gödel 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 individualor, 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 Gödel 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, integratingbut 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?”

“Are you surprised? Maybe the Snowmen aren’t interested in interpretation and evaluation.”

“What do you mean?”

“Gödel’s Incompleteness, remember? No matter how much you derive from a body of data, there will always be statements you could not have deduced. Always something else to store.”

“…Ah. And Gödel is at the heart of their ancient, world-weary, philosophy.”

Mace laughed briefly. “I think you’re working it out, policeman. Knowing the limitations of deduction, the Snowmen decided that to record eventsand only to recordwas the highest calling of life. And that’s all they want to do. They took apart their world, rebuilt it as a monstrous storage system… used all the material at their disposal to freeze as much data as they could. They won’t do anything with our proof; for fourteen billion years they have merely watched time unravel”

“There’s your streak of poetry again, Mace.”

“Your Assimilation must fail,” Mace said bluntly.

Kapur sighed. “Why?”

“Think about it. The Snowmen have no motivation we can connect with. Our actions will mean nothing to themwe, almost by definition within their Gödelian philosophy, dance meaninglessly before them. Even their own destruction would be no more than an event, a final act to be stored and noted.”

“That can’t be all, Mace. There must be more. Every species wants to grow, to develop.” Kapur reflected. “Even if all they wanted was a greater data storage capacity”

“Come in, Kapur. It’s over. I’ll call in the Spline.”

“No.” Kapur closed his eyes, tried to keep the trembling out of his voice. “I still have time.”

With slow insolence, Mace said, “It’s your mission, policeman.”

Without returning to the yacht Kapur had Mace download more human datasets and propositions; and he learned quickly how to input new materialhis own reflections and feelingsinto his Eye stores.

That took most of a day.

Kapur slept briefly, nestled within the meadow scents of his cold-suit.

When he turned to the ‘Flake once more, he had six hours left.

The Snowman had not changed. The human proof of Gödel remained lodged within its abstraction of a belly, a cold, primitive lump.

Kapur began to download data to the probes: more and more, as rapidly as he could. Mathematics first. He found data on an ancient, failed, experiment, a life form based on the Incompleteness theorem, a bizarre disaster which had resulted in the destruction of a moon, a loss of human life…

Then, on a whim, musiche watched as ancient compositions frosted into veils of blue ice within the ‘Man.

Human history. He told the ‘Man of the Xeelee, humanity’s vast, implacable foe; and of how mankind was seeking to mobilize the resources of a Galaxy in its war.

He told the ‘Man what the humans on board the Spline ship planned to do to the Snowflake.

He told of his own fears, doubtshis awe, here before the Snowflake, with the Galaxy a cloud beneath him; of his almost superstitious response to Gödel; of his fear of failure, and his petty relationship with Mace.

The ‘Man was like a mirror, one part of his mind told him, or like a Virtual psychoanalysis program. There was no one there to respond, he knew now, but he told it all anyway.

He told the ‘Man of his own, tenuous, qualifications for this Assimilation mission. That he was a policeman; that he specialized in the resolution of the cruel, the vicious, the most bizarre crimes. His job was to work through the sites of crimes, trying to see the smashed property, the bones and scattered flesh, through the eyes of the perpetrator.

Kapur was qualified enough to seek the motivation of the Snowmen, after twenty-five years striving to unravel the minds of aliens within his own species.

All of this shivered into the heart of the Snowman, without comment or reaction, without praise or disgust.

Kapur, his time spent, grew ashamed. He fell silent, arms akimbo, before the maw of the Snowflake.

The ‘Man watched steadily.

And, at last, Kapur understood.

Something like a ripple passed under Kapur; it was as if space were a lake on which his encased body floated, passive.

“Kapur.” Mace’s voice was strained. “The Spline.”

Kapur felt enormously tired. “What about it?”

“…It’s gone.”

Time had run out. The Spline had opened its laser-cannon orifices.

…The ship had been torn aside, dragged from its site like an eyeball from a socket, thrown a million miles across space; it had been left spinning, bruised and torn.

Kapur returned to the yacht.

“Were there injuries?”

Mace’s face was wide, blank, angry. “What do you think? But the automatics are functioning; the ship’s returning to pick us up. What did you do to the damn ‘Flake, Kapur?”

“It was not I who tried to open fire on it,” Kapur said softly. “What happened?”

“Gravity waves,” Mace said. “Like a tractor beam.” Suddenly fear broke to the surface of Mace’s hard features; his Eyes seemed even more incongruous, metal islands in a sea of human emotion. He pointed through the viewport, picking out a palm-sized patch of darkness. “From the direction of the Virgo supercluster; although that’s probably coincidence…”

“I caught an echo of the beam.”

“Kapur, I think I know how they did it.”

“The Snowmen?”

“Mach’s principle. I think they can manipulate Mach’s principle.”

Kapur shook his head.

With a kind of irritated patience, Mace said, “The Spline is embedded in a Universe of matter. That matter tugs at the Spline with gravity fieldsbut the fields surround the ship uniformly; they are equal in all directions, isotropic and timeless.”

Kapur frowned. “And you think the Snowmen have a way of making the fieldunequal?”

Mace laughed uneasily. “I guess you learn a lot in fourteen billion years.”

Kapur turned the concept over in his mind. The Mach beam was spectacular, he decided. But the Universe was filled with spectacular weapons and technologies.

Gödel’s theorem, though. That was something else. That was truly terrifying. Mace, young, unimaginative, had responded more to the blazing of a zap gun than to the fact of a Universe without bottom or top, without meaning, unknowable. Kapur almost envied him.

“I think I’ve figured it out,” he said to Mace.

“What? Their motivation?” Through his fear, Mace looked briefly interested. “Tell me, policeman. I knew there had to be something; every sentient species has goals.”

“We had the pieces of the puzzle, almost from the start,” Kapur said. “In their design of the ‘Flake, the Snowmen had already made near-optimal use of matter, by recording information right down to the thermodynamic limit… which is set by the background temperature of the Universe. But they knew from Gödel that there will always be more events to record.”

Mace’s face crumpled sourly. “Oh. Are you telling me that they are waiting for the Universe to cool down… just so they can store more data?”

Kapur smiled. “The idea is pleasing. In the aeons since the building of the Snowflake, they’ve already achieved a six-fold increase in capacity! And in another forty billion years the capacity will double again…

“Patience, Mace. That is the key.”

Mace stared into Kapur’s face, the lines around his Eyes betraying hostility. “Policeman, sometimes you frighten me.”

Kapur, obscurely pleased by this reaction, did not reply. Mace said, “Do you think there’ll be another attempt?”

“To Assimilate?” Kapur shook his head. “I doubt the ‘Flake would let us come so close again.”

He turned to face the emptiness of the viewport. With eyes no more than human he looked beyond the filmy sails of the laser yacht and saw the Spline coming to collect them. It moved cautiously, all weapons orifices open.

Over centuries and a million battles, mankind moved into a position of something like dominance over its peers. And it began to confront the Xeelee, who moved through space like ships over the surface of an ocean.

Gradually, slowly, humans probed the great projects of the Xeelee. A hundred epic quests were undertaken, a hundred names thrown up to resonate through the long afternoon of human history…

And over a hundred devastated human worlds, Xeelee fighters folded night-dark wings.

Vacuum Diagrams

A.D. 21124

Paul opened his eyes.

His body ached. He lay facedown on a surface that glowed with white light. Grass, or fine hair, washed over the surface.

What is this place? How did I get here? And…

What’s my name?

His face grew slick with sweat; his breath sawed through his mouth. He perceived the shape of answers, like figures seen through a fog. He writhed against the shining ground.

The answers floated away.

A meaningless jingle ran around his mind: “We’re here because we’re here because we’re here because we’re here…”

The grass vanished. He waited, hollow.

Three men walked slowly through Sugar Lump City. Paul trailed Taft and Green, their urgent talk washing past his awareness. The sights, sounds and smells of the new City poured into his empty memory.

The embryonic street was lined with blocky buildings of foamed meteorite ore. Most of the buildings were still dark, silent. Paul passed a construction site. Huge machines with ore spouts like mouths clawed aside meteorite debris and sprayed out floors and walls. The cold air was filled with dust, the stink of machine oiland an incongruous tang of fresh-cut wood. Four workmen stalked around the site, shouting at the huge devices which did their bidding.

Taft and Green had paused at the knee-high lip of a light well. Paul joined them and peered into the well. The exposed surface of the Sugar Lump, twenty feet down, was a shining disc. A beam of light thrust straight up from the well and splashed against curved mirrors above their heads, illuminating the surrounding streets.

Shadows passed beneath the exposed plane like fish in a light-filled pond.

The sky was blue-black. Above the City’s thin layer of air Spline warships prowled, visibly spherical.

Paul felt he was floating, suspended between mysteries above and below.

“Coexistence with the Xeelee,” Taft was saying. “That’s what the colony is about. The meteorite impact which smeared rock over this Face of the Lump was a miraculous break. By terraforming this region and colonizing it we can prove to the Xeelee we don’t have to go to war with them.” He was a tall, heavily-built man of about physical-forty; the well’s under-lighting gave his bearded face a demonic power, and when his metallic Eyes fixed on him, Paul felt a psychic shock.

“And isn’t your mysterious waif here going to endanger that?” Taft demanded.

…And one day, Paul realized, this man would try to kill him. He edged closer to Commander Green.

Green interposed his short, blocky frame between Taft and Paul. Well light glittered from his ornate Navy epaulets. “Your colonization project isn’t under question at present, Dr. Taft,” he said briskly.

“Isn’t it?” Taft raised bushy eyebrows. “Then call off your Spline war dogs. Spend your resources on my terraforming efforts down here.”

Green spread callused hands. “Let’s stick to the point, shall we? You know I don’t have the authority to call off the exclusion fleet. And those who do are unlikely to withdraw as long as there’s so much mystery, so much threat associated with the Sugar Lump.”

Taft snorted. “Threat? The government acts like a bunch of superstitious fools every time the Xeelee are mentioned. Look, Green, we’ve made a lot of progress. We’ve established that the Lump is an artifact, fabricated from Xeelee construction material”

“And that’s about all you have established,” Green said with a touch of steel. “Despite the money you’ve spent so far.”

“Commander, Xeelee construction plate isn’t tissue paper. You can’t just cut a hole in it.”

“I know that. So it seems to me that Paul herewith his proven non-local perception abilitiesis our best hope of getting some hard data.” He winked at Paul. “What I fail to see is what threat Paul represents to you.”

Taft stared at Paul. Well light glittered over his metal Eyes, and again Paul was flooded with a nameless fear. “I won’t discuss this in front of the boy,” Taft said.

Paul worked to keep his voice level. “I’d like to hear what you have to say. And I’m not a boy, Doctor. Physically I’m twenty years old.”

Green grinned, showing even teeth. “Good for you.”

“Damn it, Green, we don’t know anything about thisboyof yours. He’s found in a fouled, ill-fitting pressure suit on the exposed Face at the edge of the City. Nobody knows who he is, or how he got thereincluding Paul himself, so he says”

“His amnesia is genuine,” Green broke in. “And as to how he got to the LumpTaft, have you ever traveled on a Spline ship?”

Taft glared at him. “Do I look like a Navy goon?”

“A Spline warship,” Green said patiently, “is a living creature. A sphere miles across. Its human crew occupy chambers hollowed out of the stomach lining. A Spline ship is a big, complex, disorderly place. If Paul was a stowaway he won’t have been the first”

“He’s an unknown,” Taft insisted. “And by introducing him into this situation we incur an unknown risk.”

“But what’s beyond question is his bizarre, quantum-mechanical perceptive faculty. He represents an enormous opportunity.”

Taft folded his arms and stared into the light well. “Suppose I refuse to cooperate?”

“I have sufficient authority to force you, frankly,” Green said quietly. “Officially this is a war zone.”

“I’ll go over your head.”

“I could have you arrested. Requisition your staff. Doctor, you haven’t much choice.”

Slowly, Taft nodded. “You’re right, Commander. I don’t have any choice. For the present.” And he shot another savage metallic glance at Paul.

“I’m glad we agree,” Green said dryly. “Now, I believe you’ve a plan to have Paul taken to an Edge. That seems a good idea.”

Taft nodded reluctantly. “And if necessary we could go on to a Corner Mountain.”

“We?” Green asked suspiciously.

Taft indicated the construction site a few yards away. The four workmen had gathered around a machine which had shattered a nozzle against a stubborn lump of rock. “You can see how busy we are,” Taft said. “I’m not going to sacrifice my schedules for thisventure. I’ll accompany the boy myself.”

The four workers sang softly as they hauled at the broken nozzle. Paul strained to hear their words, struck by an unaccountable feeling of significance.

Green said carefully: “Of course I’ll escort you both.”

“As you wish.”

“Well, shall we start?”

The words of the work song drifted through the cold air: “We’re here because we’re here because we’re here because we’re here…”

Paul stood transfixed. The words echoed around his head.

Green touched his arm. “Paul? Are you okay?”

Paul turned with difficulty. Green’s lined face was reassuring. “That song,” Paul said. “What does it mean?”

Green listened for a few seconds, then chuckled. “Paul, soldiers and sailors have been singing that for centuries. Whenever they’re forced to do something they don’t particularly like. The tune’s called ‘Auld Lang Syne’. It’s thought to predate the Qax Occupation…” He searched Paul’s face. “Have you heard it before?”

“I… don’t know. Maybe.”

Green smiled sadly. “Come on. Let’s catch up with Taft before he has us thrown off the Lump.”

Taft escorted them to a car at the edge of the City.

The air here seemed colder and thinner. Raw meteorite material, scorched and fragmented, crunched under Paul’s feet. On the horizon the Face of the Sugar Lump lay naked, as still and flat as a sea of lighta sea which stretched thousands of miles until it plummeted over an Edge, as if over some huge waterfall of photons.

Twin cables ran over the debris and out over the Face. “We’ve laid cables across all the Lump’s Faces, and along the Edges,” Taft said with an ironic smile. “We’ve wrapped up this huge mystery like a birthday parcel, eh, Paul?” He opened up the car. It was a cylinder about forty feet long which clung like a glassy insect to its cables. Most of the hull was transparent, and it contained two rows of five large seats which were suspended from complex sets of gimbals. Taft helped Paul settle; straps were passed over his shoulders and around his waist, giving him a vicarious sense of security.

Taft took a seat near the front end of the car, before an instrument panel which centered on a small joystick. Taft pushed the stick forward and, with a jolt, the car began to pull itself along the cables.

They crawled out of the City’s dome of atmosphere. The sky’s deep blue faded, exposing hard stars. Spline ships drifted past the stars, diamond sharp.

The dark meteorite material grew sparse, and soon they were sailing smoothly over a glowing ocean. Occasional shadows, faint and miles across, washed from horizon to horizon.

Taft opaqued the hull, turning the car into a comfortable bubble of normality. Paul clung to his straps and settled into an uneasy sleep.

Light returned in a flood. Paul snapped awake… and screamed.

His chair had swiveled back on its gimbals. The nose of the car had tipped up through at least ten degrees. Outside, the Sugar Lump had tilted, too. He was falling backwards

Green stood before him. “Paul. Stop it. You’re perfectly safe.”

His throat was tight; he gulped for breath. “What’s happening?”

He heard Taft laugh. “I’ve told the damn kid what to expect on this trip.”

“Then tell him again,” Green snapped. He turned and, clinging to handholds, made his way to the car’s small galley area.

Taft reclined comfortably in the drive chair. He was eating a small peach; gobbets of orange flesh clung to his beard. “I didn’t realize your memory continues to fail, mystery boy”

“Skip it, Taft,” Green said casually.

Taft took another bite at his fruit. “Very well. Look, Paul, the surface on which the colony sits is utterly flat. The center of gravity of the Sugar Lump is somewhere beneath the center of the plane. The air we’ve been burning out of the meteorite material is attracted towards the center of gravity, so it clings to the middle of the plane as a kind of low dome. But now we’ve climbed away from the air and we’re being pulled back to the center of gravity. So your chair swivels until it points straight down to the centerbut that means it’s at an angle to the plane’s local vertical. We seem to be climbing up an incline. By the time we get to the Edge we’ll appear to be climbing at almost forty-five degrees. See?”

Paul twisted in his chair until he could look back the way the car had climbed. The twin cables were geometrically perfect lines laid over a shallow, glowing slope. Thousands of miles distant, covered by a blue dome of air, the brownish meteorite debris lay splashed over the unblemished plane.

It looked as if the whole arrangement should slide off into space.

Paul shuddered and turned away. Green stood awkwardly on the tilting floor, sipping a coffee. “How do you feel? Better?”

Paul shrugged. “How should I feel? Commander, the Sugar Lump has been strong enough to withstand a major meteorite impact. Without so much as a scratch. How am I going to get through it?”

Green ran a hand over his closely-cropped, graying hair. “Paul, the Xeelee always build big. And tough. I’ll tell you about Bolder’s Ring sometime… what I’m saying is that the awe you feel won’t go away. But you’ll get used to it.

“And remember, you’re not a meteorite. You’re not trying to blast your way through.” He lowered his voice. “And that’s been Taft’s mistake. He’s fired off lasers, projectiles, particle beamslike a stream of little meteorites, yeah? And the success he’s had is precisely zero.

“You’re different, Paul.” Green leaned forwards, his expression a crumpled mixture of compassion and fascination. “You’ve this extraordinary talent. You’re not unique; I don’t want you to think that.” He smiled. “None of us has any doubts about your humanity… and all of us share your faculty, your quantum-mechanical way of seeing things, to some extent. Did you know that the dark-adapted eye, even without augmentation, can pick up a single photon? So straightforward human senses can perceive events at the quantum level. And there’s speculation that consciousness itself is a quantum process… What’s different about you is the strength of thistalent. The rest of us live here in the macro world, this smoothed-over mock-up of the truth. But sometimes you can see beyond the approximations and shams; you seem to be able to see right down to the fundamental level of quantum wave functions.” Green’s voice grew intense. “You see, Paul, in Taft’s Universe the surface of the Lump is certain to keep out a meteorite. But in your Universe nothing is certain.”

Paul twisted away. “I don’t want to be uncertain, Commander. I’m frightened. I don’t even know my real name.”

Green grasped his shoulders. “Look, Paul, you are a puzzle to us. There’s no point pretending otherwise. But the parts of the puzzle have to be connected. Where you came from must be connected with the way you are. And by doing this thing, by extending your talent to its limits, I believe you’re going to discover more than what the Xeelee are up to inside the Sugar Lump. I believe you’ll discover yourself.”

Paul found himself shuddering. He tried to concentrate on the straps around his waist, the reassuring hands on his shoulders.

“Yeah,” Taft said slyly. “Or maybe you’ll discover you’re nothing more than a vacuum diagram. What about that, eh, Paul?”

“A what?”

“Shut up, Taft.”

“Come on, Commander. If this is a revision class, then let’s revise it all.” Taft stepped up to stand before Paul, grinning, brittle with bitterness. “You told me how you took Paul up to the Spline fleet, put him through a crash course on how to be a human. Well, what about your quantum physics, Paul? Remember Feynman diagrams? Those cute pictures which show particles interacting, living, dying?”

“Taft…” Green growled.

“Well, now, here’s a remarkable little interaction. From out of nowhere pop three particlesa pion, a proton, and an antineutron. Of course conservation is violated all over the placebut thanks to the Uncertainty Principle nothing is absolute in this Universe. I presume that’s the concept our naval friend was groping for just now. And then the diagram closes up. The three particles recombinethey disappear back into the vacuum again, and conservation is reasserted. What a relief!

“But what really happens is that the antineutron is created at that final impact and moves back through time to initiate the creation of the other particles! Bizarre enough for you? And so this particular Feynman picture is a closed loop. A vacuum diagram. The particles come from nothing and return to nothing.” He grinned. “We’re here because we’re here because”

Green raised one massive uniformed arm, pushed Taft away easily, muttered something Paul couldn’t hear.

Paul closed his eyes, hoping to make the incomprehensible Universe disappear into the vacuum from which it had sprung.

The approaching Edge was a knife-blade across the stars. The car climbed the one-in-one slope ever more slowly, finally stopping a hundred yards from the rim. “Come on, Paul,” Green said. “We walk from here.” Briskly he helped Paul seal himself into a light, one-piece pressure suit. “And go easy. Remember we’re that much further from the Lump’s center of mass; gravity is only about half what it is in the City.”

Paul climbed through the car’s membranelike airlock. A handrail had been bonded to the surface a few yards from the car. Paul stumbled towards it. The apparent forty-five-degree slope was without purchase, and his motions felt slow and dreamlike, as if he were underwater.

Clinging closely to the rail he turned and surveyed the Sugar Lump.

Beneath his feet was a hillside of glowing glass. Shadows bigger than cities moved through it. Paul knew the Face was a square six thousand miles to a side, and he had half-expected to see details of far Edges and Corners from this vantage point; but beyond a few hundred miles the surface collapsed in his vision into a single, shining line of light. Sugar Lump City was a low dome of blue, improbably clinging to the center of the line.

“Paul,” Green said softly. “Look up.”

Paul craned his neck. A Spline warship swooped overhead, no more than ten miles from the Edge. Paul could make out valley-sized wrinkles in the fleshy sphere, weapon emplacements twinkling in deep pocks. Finally the warship sailed over the Edge of the world, rolling grandly.

“They know we’re here,” Green said. “That was a salute roll.”

His voice seemed to come to Paul from far away. A sense of distance swept over him; it was as if he were shrinking, or as if the Universe were receding in all directions.

“Paul?… Are you okay?”

“What’s wrong with him? Damn it, the kid’s a liability.”

“Take it easy, Taft. Sometimes this state of semifaint is a prelude to his heightened awareness phases. Come on, help me get him to the Edge.”

The words swam by like fish. Green and Taft stood to either side of him, grasping his arms. They were figures of wood and paper, moving with dry rustles. The light of the Lump burned through them.

At last they stood in a line on the rim of the world. The Edge was an arrow-straight ridge, with the two identical Faces falling away on either side. It was like standing on the roof of some huge house. Cables had been laid along the Edge; a second car clung to them. Bundles of maintenance equipment had been fixed to the surface close to the car site.

“I hope this trip was worth it,” Green said, panting.

Taft barked laughter. The sound was like a dry leaf crumpling. “Well, you asked for my guidance and you got it. Obviously the stresses on the material are higher here than close to the center of a Face. So if your wonder boy is going to gain access he has as good a chance here as anywhere. Watch out for the Edge itself, though. It’s sharp as a knife, down to the finest limits we can perceive.”

“No,” Paul said.

Green and Taft stared at him, releasing his arms. With the loss of physical contact they became still more insubstantial, receding from his vision like ghosts.

He knelt awkwardly and ran a gloved finger along the Edge. The stuff was soft; it rippled. It was like running a hand through a fine, multicolored grass.

Words like “sharp” were meaningless, of course; wooden words used by macro-men.

Green had given him the language to understand what he was perceiving: that this was the fundamental level of reality, the grain of quantum-mechanical probability wave functions.

An event was like a stone thrown into a pond; probability functionsripples of what-might-bespread out through space and time. Macro-men might see the pale shadows where the waves were thickest.

And that was all.

Their hard language of “particles” and “waves” and “here” and “now” reflected their limited perception, stony words to describe shadows. But he, Paul, the boy with no past, could sometimes see the entire surface of the pondand even catch hints of the depths which lay below.

He watched wave functions ripple away from the Edge, diminishing softly into prismatic shades of improbability, and felt his consciousness drawn out like a sword from its scabbard. He looked down at his body, bent awkwardly in its ill-fitting pressure suit; at the two stick men standing over it, obviously blind to the kaleidoscopic probability sparkles all around them.

The Face of the Sugar Lump was a window. He drifted through it.

He floated like a snowflake, wafted by probability winds. The Sugar Lump was full of wonders.

Here was an array of crystals which would grow at a touch into a fleet of a thousand night fighters, unfurling glistening wings like dark butterflies. Twist this flowerlike artifact just so and a city would unfold in a storm of walls and ceilings. Point this other at a starand watch it collapse softly into nova.

And here, rank on rank of shadowy forms, were Xeelee themselves, features smoothed-over and indistinct, embryonic.

The Sugar Lump was a seed pod.

Something watched him. Paul twisted, scattered his being like diffusing mist…

Call it the antiXeelee.

It was as old as the Xeelee race, and as young. Inside the vessel men called the Sugar Lumpand, simultaneously, within a million similar vessels scattered through the galaxiesit waited out aeons, brooding.

The antiXeelee took Paul as if in the palm of a hand. Paul tried to relax. The gaze was all-knowing, full of strength… but not threatening.

Gently he was shepherded to the gleaming walls and released.

He opened his eyes. And moaned.

He was back in the world of the stick men.

Green’s face, lined with concern, hovered before him. “Take it easy,” he said. “We’ve brought you inside the Edge car.” He slid a hand behind Paul’s neck, tilted his head forward and helped him sip coffee. “How do you feel?”

Paul felt the softness of the seat beneath him, saw the warm brown light of the car interior. Beyond the windows the glow of the Sugar Lump seemed different. Harsher? Sharper? Shadows raced through the interior. “What’s happening, Commander? Where’s Taft?”

“At the controls of the car. He got a call from his team at the City site; some kind of problem.” Green leaned over him hungrily. “Paul. You were inside the Lump, weren’t you?”

“…Not really. It isn’t like that.” Paul reached for the coffee cup and took another mouthful. “You taught me what’s happening. I have a non-local perception. Like a quantum wave function I’m not limited to the here and now; I perceive events spacelike-separated from”

“Paul,” Green said urgently, “skip it. Tell me what you saw. I have to know. My career is hinging on this moment. Is it the Xeelee?”

“I… Yes. It’s the Xeelee.” He groped for analogies. “It’s like a huge hangar in there. There are Xeelee, waiting, whole populations of them. Thousands of ships, ready to beripened. Artifacts of all kinds.”

Green smiled. “Weapons?”

“Yes.” Over Green’s shoulder Paul could see Taft approach quietly.

“What are they doing?”

“I don’t know. But, Commander, I don’t think they mean us any harm. You see, there’s another presence which”

Taft’s bearded face was twisted with a kind of pain. He raised two clasped fists over Green’s head.

“Commander!” Paul jerked convulsively.

Green half-rose, turned his head. Two fists hit his skull with a sound like wood on wood. The reaction carried Taft perhaps a foot into the air. He cried out. His hands came away bloody.

Green tumbled into Paul’s lap; then he slid to the floor of the car.

Paul stared at the blood on Taft’s hands. Memories stirred impossibly. So it is coming to pass, as I knew/remembered. But how…?

“Paul, I” Taft spread his hands, palms upwards. Paul couldn’t read his face, the shining artificial Eyes. “I’m sorry. I have to do this.” With clumsy hands he fitted Green’s helmet into place and sealed the neck; then he began hauling the huge, limp body towards the airlock. “My team back in the City are being evacuated. Forcibly, by Green’s damnable Navy goons.”

“Why? What’s happened?”

“You’ve stirred up the Xeelee with your quantum jaunt,” Taft said acidly. “The glow of the surface is brighter. And it’s getting hotter. In some places the meteorite debris is already red hot. So we’re being evacuatedat the point of a gun.” Taft sealed up his own helmet. “So I’ve got to stop this, you see, Paul. I’m sorry. It’s for the good of the species. The Xeelee have to understand we’re not continually going to attack them. The colony has to be built.”

“What are you going to do?”

“I’m going to get Green back to the Face car. Then I’ll return here and”

Paul felt his breath grow shallow. “And what?”

Without replying Taft turned away and stepped through the airlock; the membrane closed behind Green’s booted feet.

Paul sat for long minutes. The humming of the car’s instruments was the only sound. Through the windows Taft and Green were silhouetted against a glowing Face, the pair of them looking like a single, struggling insect.

Paul imagined Taft’s return, those bloodied, space suited hands reaching for him, as they had for Green

There was a joystick at the front of the car.

He pushed himself out of his chair and stood swaying. He took cautious steps along the narrow aisle, looking neither to left nor right.

Nervously he pushed at the joystick. The car lurched a few yards; Paul stumbled back, grabbing the arm of the nearest chair. He felt a grin spread over his face. Had Taft expected him to sit patiently and wait to die? He pushed the stick once more. Motors whirred and the car slid along the Edge.

Taft dumped Green’s inert form and came floundering back up the slope, a toy figure gesturing in tiny frustration.

Paul settled into a seat and let the satisfaction of the small victory settle over him. There would be plenty of time to face the future later… when the car reached Corner Mountain, with nowhere else to go.

The car patiently climbed the Edge’s increasing slope. The brightness of the Faces continued to increase; at last the car’s lower windows opaqued automatically.

Paul could see Taft following, a silver-suited doll riding an open maintenance buggy up the dizzying slopes of the Edge. For the first few hours Paul let Taft speak to him. When the half-rational arguments turned to sobbed pleas for understanding Paul snapped the radio off.

The Corner Mountain became visible as a sharp angle against the stars. The car slowed to a halt, tipped up at about thirty-five degrees.

Paul closed his helmet and stepped through the airlock. His footsteps were light, airy; Green had told him how, this far from the mass center of the Lump, gravity would be down to a third that at the City. The brilliance of the surface hit him with a soft impact. Heat soaked through the soles of his boots. With an odd sense of calm he worked his way up the slope to the summit, his feet on the tilted surfaces to either side of the Edge.

At last he stood unsteadily at the summit itself, feet wrapped around the sharp-edged point, arms extended for balance. The vertical lurched around him as his inner ear sought the way to the center of mass of the Sugar Lump.

Taft had abandoned his vehicle and was scrambling up the dazzling ridge. Paul felt a huge peace, as if he were once more in the metaphorical palm of the antiXeelee. He turned slowly, feet working around the summit. Three square Faces as wide as Earth shared corners at the point where he stood; he saw Edges disappear into infinity, watched Faces collapse into glowing lines of abstraction.

Sugar Lump. Edge. Corner Mountain. He found himself laughing. Harmless words used to shield men from the astonishing truth of a world shaped like a cube, of a made thing whirling and sparkling in space.

Taft stood before him. The light showed him to be a machine of pulleys, cables and gears; quantum functions sparkled unnoticed around his eyes and fingers.

Paul smiled. And jumped backwards.

Taft stumbled forward, reaching. Then he was gone, eclipsed by an Edge.

Paul let his limbs dangle. Spline warships paddled across his view like agitated fish.

He was approaching a glowing Face. What next? Would he strike, bounce away, proceed skipping and sliding? Would the impacts crush his bones? Would the heat of the surface reach through the suit and boil his flesh?

The certainty of his death was unreal, intangible, un-threatening.

Now, why should that be? Was his death to be as great a mystery as his origin? Would he die ignorant of the answers of both the great questions of his existencewhere did I come from? and where am I going to?

Or perhaps the two answers were somehow linked…

He found he hoped Taft and Green would survive.

The Face rushed at him. Wave functions rippled like grass in a breeze.

Folded ships hung around him like moths.

There was a sense of motion, a thrumming of huge engines somewhere; as if the Sugar Lump and its contents were a great liner, forging through some huge sea.

The antiXeelee cradled him. It studied him dispassionately, huge and cold. Paul felt knowledge wash over him, and slowly understanding grew.

The cube planet had been created at that momentfar in the future of mankindwhen the Xeelee reached their full glory. And were ready to depart.

(Depart? Where to? Why? The answers wereawesome; beyond his comprehension.)

On its completion the cubewith its guardian, the antiXeelee, and with a million othershad been sent on an impossible voyage, forging back through the unfolding ages to the birth time of the Xeelee themselves. The Xeelee would erupt fully developed from the cubes, shaking out the wings of their beautiful spacecraft and ready for their huge projects. Paul sought human words to capture the vast concepts sailing around him. Vacuum diagrams! The cube worlds were antiparticles, moving back through time to initiate their own creation. The whole of Xeelee history was a single, vast vacuum diagram, closed and complete of itself.

But… what of me?

Now Paul sensed a monstrous amusement. He was cupped within gigantic palms for an unmeasurable period; the time engines surged steadily into the past

And then he was lifted up and released like a captive bird.

He looked down. He was outside the Sugar Lump, falling towards it. Spline ships converged. There was the City, still alive with the hopes of Taft and the rest, spreading over the meteorite debris. On the rim of the debris was a fallen figure, a young man in a soiled spacesuit lying facedown on the glowing surface.

Understanding came at last.

I have no beginning. I have no end. My lifeline is caught up in the vast Xeelee expedition into the past. I am a vacuum diagram, too, closed on myself. He remembered the absurd refrain: “We’re here because we’re here because we’re here…”

He tumbled into the head of the fallen man. Skull darkness hit him like a physical shock, and he felt the pieces of his understanding shatter like a dropped vessel, his memories seep away.

In the end he was left only with a vast amusement. Then even that fell away.

Paul opened his eyes.

His body ached. He lay facedown on a surface that glowed with white light. Grass, or fine hair, washed over the surface.

What is this place? How did I get here? And…

What’s my name?

His face grew slick with sweat; his breath sawed through his mouth. He perceived the shape of answers, like figures seen through a fog. He writhed against the shining ground.

The answers floated away.

A meaningless jingle ran around his mind: “We’re here because we’re here because we’re here because we’re here…”

The grass vanished. He waited, hollow.

A hundred heroes, a hundred fragmentsbut understanding did not come: What was the goal of the Xeelee? Why were they trying to rebuild their own history?

And what was the significance of Bolder’s Ring?why were the Xeelee trying to escape from the Universe itself?

Like leaves, the centuries fell away. Humanity’s growth in power and influence grew exponentially. But the legend of Xeelee achievementsthe manipulation of space and time, the Ring itselfgrew into a deep-rooted mythology.

At last, only the Xeelee themselves were more potent than mankind…

Humans railed against the Tyranny of Heaven.

More legends were written, as waves of human assaults pounded against the great Xeelee sites. It was a remote, inhuman time. I watched, repelled, terrified.

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