by Greg Egan
It was hard to obtain a spectrum in the faint starlight, and after waiting passively for a megatau for any signs of life, and then as long again for a response to a wide spectrum of radio and infrared signals, they agreed to risk brushing the surface gently with a laser.
They were not incinerated in retaliation.
Apart from contamination with interstellar gas and dust, the surface was pure quartz, silicon dioxide. Silicon-30, oxygen-18, the heaviest stable isotopes of each. The artifact appeared to be in thermal equilibrium with its surroundings, but that didn’t prove that it was dead. Waste heat, entropy, could be poured into a hidden internal sink for a finite amount of time.
They landed microprobes on the artifact, and tomographed it with faint seismic waves. It was exactly the same density throughout, uniform solid quartz, but the technique only had a resolution of about a millimeter. Smaller structures would not show up.
Paolo suggested, “It might be a working polis. They could be getting energy in and out through a traversable wormhole.”
“If you’re right, are they deliberately ignoring us? Or are they oblivious to the outside world?” Even Ashton-Laval’s citizens would have known about it, immediately, if someone had stroked their polis hull with a laser. “And if they’re ignoring us now, what happens if we do something intrusive enough to get their attention?”
Paolo said, “We could wait a thousand years and see if they deign to make contact.”
They sent a small swarm of femtomachines burrowing below the surface. A few meters down, they found structure: a pattern of tiny defects in the quartz. Statistical analysis showed that the defects were not random; the probability of certain spatial correlations arising by chance was infinitesimal. But the whole crystal was static, completely unchanging.
It was not a polis. It was a store of data.
The sheer scale of it was overwhelming. The data was packed almost as densely as their own molecular storage, but the artifact was five hundred trillion times the volume of the polis. They ran pattern-analysis software, trying to make sense of slivers and fragments, but nothing emerged. They rushed for a century while the femtomachines went deeper, and software ground away at the problem.
They rushed for a millennium. The femtomachines found a copy of the old galactic map written in the defects, surrounded by undecipherable material. Taking heart at this, they rushed for another thousand years, but the software could not decode the storage protocol of any other data. And though they’d barely begun to sample it, Yatima suspected that they could read it all and still fail to understand anything more.
Out of the blue, Paolo said numbly, “Orlando will be dead. There’ll be nothing left of him but flesher great-great-grandchildren, living on some obscure planet in the second macrosphere.”
“Your other selves will have visited him. Met his children. Said goodbye.”
Paolo took ancestral form, and wept. Yatima said, “He was a bridger. He created you to touch other cultures. He wanted you to reach as far as you could.”
The surface of the artifact was full of long neutrons, bearing the same catalyst as always. And the core-burst map was encoded in the wormhole sequence, too — though the tiniest fluctuation of the vacuum, here, was an unimaginably greater event than any cataclysm devouring the Milky Way.
They took a sample of the neutrons, built a new polis in the seventh macrosphere, and moved through.
There was another artifact floating freely near the singularity, made out of the marker mineral they’d first seen on Poincaré.
It was cold and inert, and full of the same kind of microscopic defects as the first. It was impossible to say whether or not the data was identical; they could only compare tiny samples of each. The software found some matching sequences, bit strings that recurred relatively often in both crystals. The storage protocol remained opaque, but it was probably the same.
Yatima said, “We can turn back anytime.”
“Stop saying that! You know it’s not true.” Paolo laughed, more resigned than bitter. “We’ve burned six thousand years. We’ve turned our own people into strangers.”
“That’s a matter of degree. The sooner we return, the easier it will be to fit in again.”
Paolo was unswayed. “It’s past the point of going back empty-handed. If we cut our losses and give up now, it will mean the search was never worth it in the first place.”
There was a third artifact in the eighth macrosphere, and a fourth in the next. The shapes and sizes could be meaningfully compared between the same-dimensional pairs, and, random microcraters aside, the difference was barely measurable. When they sampled the artifacts at matching positions, lining up the femtomachines’ paths as best they could then hunting for correlations, they found large tracts of data the same. But not all of it.
The pattern continued in the tenth macrosphere, the eleventh, the twelfth. The artifacts changed shape, slightly. Ten or twenty percent of the bits in all the exabytes they sampled at corresponding positions were different.
Paolo said, “They’re like rows of tiles from the Orphean carpets. Only we don’t know the dynamics, we don’t know the rules to get from frame to frame.”
Yatima contemplated the prospect of trying to work it all out by inspection. “This is hopeless. We should stop poring over every artifact, trying to deduce the nature of the Transmuters from their technology.”
Paolo nodded soberly. “I agree. The quickest way to understand what these things are for will be to ask their makers.”
They automated the process, and had their exoselves rush, freeze, and clone them as necessary. They granted themselves eight-dimensional senses, and sat on the girders of an 8-scaped Satellite Pinatubo, watching perpendicular pairs of slender three- and five-dimensional artifacts rotate in and out of view. It was like whirling around a spiral staircase running from macrosphere to macrosphere, dimension to dimension.
As they reached the ninety-third level, contact was lost between the polis and the singularity on the twelfth.
On the two-hundred-and-seventh level, the twenty-sixth singularity slipped ten thousand years.
Yatima felt a surge of panic. “We’re fools. This will go on forever. They’re one step ahead of us, making these things as fast as we can jump.”
“You don’t believe that. Didn’t you tell me, back at Swift, that you were sure they weren’t malicious?”
“I’ve changed my mind.”
They agreed to silence the software that reported breaks in the chain; if they had no intention of turning back, there was no point being distracted by bad news.
The artifacts mutated, slowly.
Then, past the trillionth level, there were suddenly two in every universe. Locked rigid in relative position, despite being separated by hundreds of kilometers of vacuum.
Yatima asked Paolo, “Do you want to stop and find out how that’s done?”
“No.”
They couldn’t change the real time it took to complete each link, but they rushed ever faster, until they were perceiving only every tenth, every hundredth, every thousandth level.
A third artifact appeared, then a fourth.
Then they all drifted together, level by level, and merged.
One by one, three new artifacts appeared, all drawing closer to the large central one. Just as they began to fuse with it, a fourth budded off. The large artifact changed shape, becoming more spheroidal. It shrank, grew, shrank, vanished. The fourth of the second set of smaller artifacts — roughly the size of the very first, back in the sixth macrosphere — was all that remained.
It persisted for ten trillion more levels, changing only slightly, then abruptly shrank to a tenth, a hundredth its original size.
Then it vanished.
Their ascent halted.
The last singularity — 267,904,176,383,054 levels from the home universe — was in empty interstellar space.
They converted the scape and themselves back to three-dimensional versions, and looked a
round. They were in the plane of a spiral galaxy, and a band of stars wrapped the sky like the lost Milky Way. Paolo swayed on a girder, laughing.
Yatima checked with the observatory. There were no new Swifts in sight, no new long-neutron gateways leading upward. If the Transmuters were anywhere, they were here.
“What now? Where do we look for them?”
Paolo swung around the girder he was holding, then launched himself into space. He tumbled drunkenly away from the satellite, then violated the physics and came spinning back.
He said, “We look right in front of us.”
“There’s nothing in front of us.”
“Not now. Because it’s over. We’ve seen it all.”
“I don’t understand.”
Paolo closed his eyes and forced out the words. “The artifacts were polises. What else could they have been? But instead of changing the data in one fixed polis ... they kept building new ones, level after level.”
Yatima absorbed this. “Then why did they stop?”
“Because there was nothing more to do.” Paolo’s gestalt seemed to hover between comic agony over the failure of their search, and sheer exaltation at its completion. “They’d seen everything they wanted to see in the outside world — they’d risen through at least six universes — and then they’d spent two hundred trillion clock ticks thinking about it. Building abstract scapes, making art, reviewing their history. I don’t know. We’ll never decipher it; we’ll never know for sure what went on. But we don’t need to. Do you want to ransack the data, hunting for secrets? Do you want to rob their graves?”
Yatima shook vis head.
Paolo said, “I don’t understand the shapes, though. The changes in size, and number.”
“I think I do.”
Taken together, the artifacts comprised a giant sculpture, spanning more than a quadrillion dimensions. The Transmuters had built a structure that dwarfed universes, but touched each one only lightly. They hadn’t turned whole worlds to rubble, they hadn’t reshaped galaxies in their image. Having evolved on some distant, finite world, they’d inherited the most valuable survival trait of all.
Restraint.
Yatima played with a model of the sculpture until ve found the right way to assemble it. He converted the scape to five dimensions, then held the figure out to Paolo.
It was a four-legged, four-armed creature, with one arm stretched high above its head. No fingers; perhaps this was a stylized, post-Introdus version of the ancestral form. The tip of one foot was in the sixth macrosphere. The highest point of the Transmuters raised arm was in the level just beneath them, reaching up.
To the infinite number of levels above. To all the worlds it would never see, never touch, never understand.
They examined the record of communications failures. There’d been more than seven million broken links, and over ninety billion years of identified slippage in total. Statistically, by now it was beyond belief that at least one of the hundreds of trillions of singularities in the chain hadn’t been lost by the machinery. And even if they could return to the second macrosphere — or some level above, if that universe had been deserted as its stars ran out of fuel — there’d be nothing for them. The Earth culture they’d known would either have merged with others from the second macrosphere, or simply evolved beyond recognition.
Yatima shut off the flow of gestalt from the log book and looked around the star-filled scape. “What now?”
Paolo said, “The other versions of me would have done everything I’m capable of doing. And lived better lives than any I could make for myself, here.”
“We could keep traveling. Search for local civilizations.”
“That could be a long, lonely voyage.”
“If you want more company, we can always make some.”
Paolo laughed. “You do have a beautiful icon, Yatima, but I can’t see us making psychoblasts together.”
“No?” After a while Yatima said, “I’m not ready to stop. Not yet. Are you afraid to die alone?”
“It won’t be death.” Paolo seemed calm now, perfectly resolved. “The Transmuters didn’t die; they played out every possibility within themselves. And I believe I’ve done the same, back in U-double-star ... or maybe I’m still doing it, somewhere. But I’ve found what I came to find, here. There’s nothing more for me. That’s not death. It’s completion.”
“I understand.”
Paolo took ancestral form, and immediately started trembling and perspiring. “Ah. Flesher instincts. Bad idea.” He changed back, then laughed with relief. “That’s better.” He hesitated. “What will you do?”
“Go exploring, I think.”
He touched Yatima’s shoulder. “Good luck, then.”
Paolo closed his eyes, and followed the Transmuters.
Yatima felt a wave of grief wash over ver, but Paolo was right; other versions had lived for him, nothing had been lost.
And as the grief decayed into loneliness, Yatima was tempted to apply the same logic. Vis own clones must have done everything ve was contemplating, and more, long ago.
That wasn’t enough, though. There were still some discoveries ve needed to make for verself.
Yatima surveyed the sky of this universe one last time, then jumped to the copy of the Truth Mines ve’d carried all the way from Konishi.
To play out everything ve was, to be complete, ve had to find the invariants of consciousness: the parameters of vis mind that had remained unchanged all the way from orphan psychoblast to stranded explorer.
Yatima looked around the jewel-studded tunnel, and sensed the gestalt tags of axioms and definitions radiating from the walls. Everything else from vis life in the home universe had been diluted into insignificance by the scale of their journey, but this timeless world still made perfect sense. In the end, there was only mathematics.
Ve began to review the simple concepts nearby — open sets, connectedness, continuity — waking old memories, resurrecting ossified symbols. It would be a long, hard journey to the coal face, but this time there’d no distractions.
* * *
Glossary
« ^ »
address. A string of bits that specifies a source or destination for data, such as a file in a library, a camera on a satellite, or a location in a scape. Different addresses can be of different lengths, and the same data can have multiple addresses.
boson. All elementary particles can be classified as either bosons or fermions; the bosons include photons and gluons. The quantum wave function for two or more identical bosons is unchanged if any two particles are swapped, and the wave function for a single boson is unchanged if the particle is rotated by 360 degrees. Bosons have a spin which is an integer multiple of the fundamental unit of angular momentum. In Kozuch Theory, all these properties arise from the topology of the particle’s wormhole.
citizen. Conscious software which has been granted a set of inalienable rights in a particular polis. These rights vary from polis to polis, but always include inviolability, a pro rata share of processing power, and unimpeded access to public data.
Coalition of Polises. (1) The community of all polis citizens. (2) The physical computer network which comprises all polises.
CST. Coalition Standard Time. A system of specifying internal time used across the Coalition of Polises. CST is measured in “tau” elapsed since the system was adopted on 1 January 2065 UT; the equivalent in real time of 1 tau varies as polis hardware is improved.
cypherclerk. A structure within Konishi citizens which handles encryption and decryption tasks, including the authentication of claims of identity. See also signature.
delta. The base unit of all scape addresses. The usual height for a citizen’s icon is two delta. Multiples and fractions of a delta can be specified, and there is no universal smallest or largest distance. Plural: delta.
dream ape. A biological descendant of a group of exuberants who engineered-out their own language facilities.
embedding
. A way of fitting one manifold into another, larger one as an aid to visualizing its properties. For example, some 2-dimensional manifolds can be embedded as a surface in 3-dimensional Euclidean space (a sphere, a torus, a Mobius strip), while others (such as Klein’s bottle) can only be embedded in 4-dimensional space. The size and shape of the surface are properties of the embedding, not of the manifold itself — so a sphere and an ellipsoid are two different embeddings of exactly the same manifold — but a particular embedding in Euclidean space can be used to supplement a manifold with the geometrical concepts needed to make it into a Riemannian space.
Euclidean space. The Euclidean space of N dimensions is a natural generalization of the 2-dimensional Euclidean plane, where the square of the total distance between two points is the sum of the squares of their separation in each of the N dimensions. The Euclidean spaces are simple examples of the more general idea of a Riemannian space.
exoself. Non-conscious software that mediates between a citizen and the polis operating system.
exuberant. A flesher whose genes have been modified.
fermion. All elementary particles can be classified as either bosons or fermions; the fermions include electrons and quarks, and composites of three quarks like protons and neutrons. The quantum wave function for two or more identical fermions reverses phase if any two particles are swapped; this leads to the Pauli exclusion principle, which gives a zero probability for two fermions being in exactly the same state. The wave function of a single fermion reverses phase if the particle is rotated by 360 degrees, and is only restored exactly by two full rotations. Fermions have a spin which is an odd-integer multiple of half the fundamental unit of angular momentum. In Kozuch Theory, all these properties arise from the topology of the particle’s wormhole.