Vacuum Diagrams

by Stephen Baxter

  "Ambassador, what's happening?"

  "...I'm not certain."

  "Have you achieved Planck Zero?"

  "Yes. But the device should be signaling to us—"

  The walls of the sac contracted by a few hundred feet, trembling; it was as if the sac were a living creature, breathing in.

  My ship lurched away from the sac and towards the walls of the chamber. One crewman was left tumbling in space, like a drop of mercury in freefall. I clung grimly to my rope.

  The walls were still miles away.

  The sac's surface billowed out and overwhelmed us.

  I was utterly alone.

  Lonely.

  Darkness.

  ...Dark because photons could carry no energy, here at Planck Zero; nothing to excite my optic sensors...

  Cold. How could I be cold? I rubbed my hands together. I could feel my fingers break up like ancient, crumbled paper.

  Electron orbits in an atom are proportional to Planck's constant. At Planck Zero the orbits must collapse... right? So, no more chemistry. How long before the crumbling process reached my brain pan?

  How would it feel?

  And quantum wave functions, linking me to the rest of the Universe, had all turned to dust at Planck Zero.

  I could feel it. I was alone in this shattered space.

  What about the ship? Was it still heading for the wall?... Something else, in here with me. The Ghosts? No; something larger, more powerful.

  Infinite.

  The mind-device was without limit. It was stranded in this discontinuous space, and it was enraged.

  Enraged by a pain I recognized.

  Now I made out other minds. Ghosts. They were like tiny stars, shining out, falling away from each other.

  The Planck mind lashed out. Ghosts were overwhelmed, insects in fire.

  ...The ship burst out of the sac; quantum functions rushed over me (for a precious moment visible, like prismatic waves lapping around me) and I was bound into the Universe once more.

  The ship hurtled through a city-world passage, trailing ragged fragments. Ghosts lay dying all around me, their proud bodies deflated.

  I looked back down the passage. A silver half-dome peered after us like some vast eye.

  "...Sink Ambassador?"

  "I'm still here, Jack."

  We emerged from the city-world. Ghost paramedics floated onto our ship and tended the wounded.

  The city-world was changing.

  A light, clear and white, shone out of the hundreds of portals, illuminating the murky giant star material. The massive drive assemblies at the poles had been damaged; I saw sparks fizzing across the surface of the nearer. A flotilla of heavy Ghost ships approached the drive units.

  "Ambassador, what are they doing?"

  "We must endeavor to repair the drive units, or the moon will fall into the core... Jack, the growth of the Planck sac in that cavity was not controlled. We are afraid."

  "I bet you are."

  "We are going to try to move the moon out of the giant star."

  "And then what?"

  "We must find some way to restrain the sac."

  I stared down at the core of the giant. "Ambassador, it will overwhelm you. What are the limits to its growth?"

  "There are no limits. Perhaps the Xeelee will intervene."

  "The Xeelee aren't gods." I thought fast. "Sink Ambassador, listen to me. Do you have any influence over operations here?"

  "Why?"

  "Stop the efforts to repair the drives."

  "...I do not have the authority."

  "Then find someone who does. As acting human ambassador here, I formally request this. Sink Ambassador, have you recorded that?"

  "Yes, Jack. Why do you want this?"

  "Because I'm frightened, too. But I think there is a way out."

  The Ghosts cut the drive assemblies loose from the city-world. Within an hour the Planck sac had overwhelmed the battered moon; it hung in the giant star glow, perfectly silver. They got us out of there. I could see reflections in the sac's surface, chains of ropy Ghost ships heading for safety. It took about a day for the Planck sac to impact the star core. By that time it was ten thousand miles wide and still growing. Huge ripples crossed its monstrous surface. It slid inside the star core, fusing hydrogen closing smoothly over the shining ovoid, vacuoles flaring.

  An hour later the core started to implode.

  Disembodied, the Sink Ambassador and I floated over Virtual images of the collapsing core. I said, "I wish Eve could see this."

  "Yes."

  By now, of course, the Ghosts had figured it out for themselves; but I couldn't resist rubbing it in. "It was your chance comment about electron degeneracy pressure that gave me the key. Suppose Planck were reduced to zero in the star core. The higher quantum states would collapse — spin values, for instance, would fall from Planck multiples to zero."

  The Pauli Exclusion Principle could not work, and electron degeneracy pressure would fail. The star core must implode... all the way, past the neutron star compaction limit, on to become a black hole.

  "Actually," the Ambassador said smoothly, "there are technicalities you didn't consider. For example, no electron can have zero spin value. Nor can any fermion. Presumably the core fermions are collapsing to bosons, like photons... The physics must be interesting in there."

  "Whatever. It worked, didn't it?"

  "Yes. We have contained the Planck Zero sac expansion. Within an event horizon, for all time."

  "And we've locked away your Planck Zero AI."

  The Ghost thought that over. "That is important to you?"

  "What did you sense, inside the sac?"

  "Infinite power... and anger."

  "There was more, Ambassador. In discontinuous space, without the anchorage of quantum wave functions, it was utterly alone. And lonely. And it was furious. Do you see?"

  Quantum loneliness.

  I had recognized a fellow sufferer. In my loneliness I can only hurt myself, but the mind-device had an infinite capacity for destruction. Still, it was trapped now...

  Then I began to wonder, and I haven't been able to stop. Is there any way out of a black hole?

  The images conjured up by Eve had been like reflections in the glimmering walls of the Planck sac.

  I brooded, for a while unable to speak.

  Eve asked, "Are you all right?"

  "I don't know."

  I'd relived it all again. The rebuilding. The horror of that quantum loneliness.

  "Nobody should have to go through that twice," I said angrily.

  "I know, Jack. And I'm sorry. But it's important that—"

  "—I understand. I know. What next, Eve?"

  "Next," she said, "we'll look ahead..."

  "Ahead? Into the future? How is that possible?"

  "Watch," she said. "Just watch."

  ...Five thousand years in the future, and ten thousand years after its first eruption from Earth, humanity's colonization wavefront spread at lightspeed through the Galaxy.

  Its experiences, at the hands of the Qax and others, had changed humanity.

  Never again would humanity be made to serve at the behest of some alien power.

  As humans grew in power, the conquest of other species became an industry. A new era began.

  PART 4

  ERA: Assimilation

  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 ac
ross 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 Universe — three 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 Snowmen — the builders — wanted 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 carbon — diamond — fold 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, propelling 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 dwind
ling 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 energy — or, 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."