The Godel Sunflowers
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 Godel 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, 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
