"Diaspora" - читать интересную книгу автора (Иган Грег)

2. Truth mining

Konishi polis, Earth

23 387 281 042 016 CST

18 May 2975, 10:10:39.170 UT

"What is it you’re having trouble with?"

Radiya’s icon was a fleshless skeleton made of twigs and branches, the skull carved from a knotted stump. Vis homescape was a forest of oak; they always met in the same clearing. Yatima wasn’t sure if Radiya spent much time here, or whether ve immersed verself completely in abstract mathematical spaces whenever ve was working, but the forest’s complex, arbitrary messiness made a curiously harmonious backdrop for the spartan objects they conjured up to explore.

"Spatial curvature. I still don’t understand where it comes from." Yatima created a translucent blob, floating between ver and Radiya at chest height, with half a dozen black triangles embedded in it. "If you start out with a manifold, shouldn’t you he able to impose any geometry you like on it?" A manifold was a space with nothing but dimension and topology; no angles, no distances, no parallel lines. As ve spoke, the blob stretched and bent, and the sides of the triangles swayed and undulated. "I thought curvature existed on a whole new level, a new set of rules you could write any way you liked. So you could choose zero curvature everywhere, if that' what you wanted." Ve straightened all the triangles into rigid, planar figures. "Now I’m not so sure. There are some simple two-dimensional manifolds, like a sphere, where I can’t see how to flatten the geometry. But I can’t prove that it’s impossible, either."

Radiya said, "What about a torus? Can you give a torus Euclidean geometry?"

"I couldn’t at first. But then I found a way."

"Show me."

Yatima banished the blob and created a torus, one delta wide and a quarter of a delta high, its white surface gridded with red meridians and blue circles of latitude. Ve’d found a standard tool in the library for treating the surface of any object as a scape; it re-scaled everything appropriately, forced notional light rays to follow the surface’s geodesics, and added a slight thickness so there was no need to become two-dimensional yourself. Politely offering the address so Radiya could follow, Yatima jumped into the torus’s scape.

They arrived standing on the outer rim—the torus’s "equator"—facing "south." With light rays clinging to the surface, the scape appeared boundless, though Yatima could clearly see the backs of both Radiya’s icon and vis own, one short revolution ahead, and ve could just make out a twice-distant Radiya through the gap between the two of them. The forest clearing was nowhere to be seen; above them was nothing but blackness.

Looking due south the perspective was very nearly linear, with the red meridians wrapping the torus appearing to converge toward a distant vanishing point. But to the east and west the blue lines of latitude—which seemed almost straight and parallel nearby—appeared to veer apart wildly as they approached a critical distance. Light rays circumnavigating the torus around the outer rim reconverged, as if focused by a magnifying lens, at the point directly opposite the place where they started out—so the vastly distended image of one tiny spot on the equator, exactly halfway around the torus, was hogging the view and pushing aside the image of everything north or south of it. Beyond the halfway mark the blue lines came together again and exhibited something like normal perspective for a while, before they came full circle and the effect was repeated. But this time the view beyond was blocked by a wide band of purple with a thin rim of black on top, stretching across the horizon: Yatima’s own icon, distorted by the curvature. A green and brown streak was also visible, partly obscuring the purple and black one, if Yatima looked directly away from Radiya.

"The geometry of this embedding is non-Euclidean, obviously." Yatima sketched a few triangles on the surface at their feet. "The sum of the angles of a triangle depends on where you put it: more than 180 degrees here, near the outer rim, but less than 180 near the inner rim. In between, it almost balances out."

Radiya nodded. "All right. So how do you balance it out everywhere without changing the topology?"

Yatima sent a stream of tags to the scape object, and the view around them began to he transformed. Their smeared icons on the horizon to the east and west began to shrink, and the blue lines of latitude began to straighten out. To the south, the narrow region of linear perspective was expanding rapidly. "If you bend a cylinder into a torus, the lines parallel to the cylinder’s axis get stretched into different-sized circles; that’s where the curvature really comes from. And if you tried to keep all those circles the same size, there’d be no way to keep them apart; you’d crush the cylinder flat in the process. But that’s only true in three dimensions."

The grid lines were all straight now, the perspective perfectly linear everywhere. They appeared to he standing on a boundless plane, with only the repeated images of their icons to reveal otherwise. The triangles had straightened out, too; Yatima made two identical copies of one of them, then maneuvered the three together into a fan that showed the angles summing to 180 degrees. "Topologically, nothing’s changed; I haven’t made any cuts or joins in the surface. The only difference is…"

Ve jumped back to the forest clearing. The torus appeared to have been transformed into a short cylindrical band; the large blue circles of latitude were all of equal size now-but the smaller red circles, the meridians, looked like they’d been flattened into straight lines. "I rotated each meridian 90 degrees, into a fourth spatial dimension. They only look flat because we’re seeing them edge-on." Yatima had rehearsed the trick with a lower-dimensional analogue: taking the band between a pair of concentric circles and twisting it 90 degrees out of the plane, standing it up on its edge; the extra dimension created room for the entire band to have a uniform radius. With a torus it was much the same; every circle of latitude could have the same radius, so long as they were given different "heights" in a fourth dimension to keep them apart. Yatima re-colored the whole torus in smoothly varying shades of green to reveal the hidden fourth coordinate. The inner and outer surfaces of the "cylinder" only matched colors at the top and bottom rims, "—here they met up in the fourth dimension; elsewhere, different hues on either side showed that they remained separated.

Radiya said, "Very nice. Now can you do the same for a sphere?"

Yatima grimaced with frustration. "I’ve tried! Intuitively, it just looks impossible… but I would have said the same thing about the torus, before I found the right trick." Ve created a sphere as ve spoke, then deformed it into a cube. No good, though—that was just sweeping all the curvature into the singularities of the corners, it didn’t make it go away.

"Okay. Here’s a hint." Radiya turned the cube back into a sphere, and drew three great circles on it in black: an equator, and two complete meridians 90 degrees apart.

"What have I divided the surface into?"

"Triangles. Right triangles." Four in the northern hemisphere, four in the south.

"And whatever you do to the surface—bend it, stretch it, twist it into a thousand other dimensions—you’ll always be able to divide it up the same way, won’t you? Eight triangles, drawn between six points?"

Yatima experimented, deforming the sphere into a succession of different shapes. "I think you’re right. But how does that help?"

Radiya remained silent. Yatima made the object transparent, so ve could see all the triangles at once. They formed a kind of coarse mesh, a six-pointed net, a closed bag of string. Ve straightened all twelve lines, which certainly flattened the triangles-but it transformed the sphere into an octahedral diamond, which was just as bad as a cube. Each face of the diamond was perfectly Euclidean, but the six sharp points were like infinitely concentrated repositories of curvature.

Ve tried smoothing and flattening the six points. That was easy—but it made the eight triangles as bowed and non-Euclidean as they’d been on the original sphere. It seemed "obvious" that the points and the triangles could never be made flat simultaneously… but Yatima still couldn’t pin down the reason why the two goals were irreconcilable. Ve measured the angles where four triangles met, around what had once been a point of the diamond: 90, 90, 90, 90. That much made perfect sense: to lie flat, and meet nicely without any gaps, they had to add up to 360 degrees. Ve reverted to the unblunted diamond, and measured the same angles again: 60, 60, 60, 60. A total of 240 was too small to lie flat; anything less than a full circle forced the surface to roll up like the point of a cone…

That was it! That was the heart of the contradiction! Every vertex needed angles totaling 360 degrees around it, in order to lie flat… while every flat, Euclidean triangle supplied just 180 degrees. Half as much. So if there’d been exactly twice as many triangles as vertices, everything would have added up perfectly-but with six vertices and only eight triangles, there wasn’t enough flatness to go round.

Yatima grinned triumphantly, and recounted vis chain of reasoning. Radiya said calmly, "Good. You’ve just discovered the Gauss-Bonnet Theorem, linking the Euler number and total curvature."

"Really?" Yatima felt a surge of pride; Euler and Gauss were legendary miners—long-dead fleshers, but their skills had rarely been equaled.

"Not quite." Radiya smiled slightly. "You should look up the precise statement of it, though; I think you’re ready for a formal treatment of Riemannian spaces. But if it all starts to seem too abstract, don’t be afraid to back off and play around with some more examples."

"Okay." Yatima didn’t need to be told that the lesson was over. Ve raised a hand in a gesture of thanks, then withdrew vis icon and viewpoint from the clearing.

For a moment Yatima was scapeless, input channels isolated, alone with vis thoughts. Ve knew ve still didn’t understand curvature fully—there were dozens of other ways to think about it—but at least ve’d grasped one more fragment of the whole picture.

Then ve jumped to the Truth Mines.

Ve arrived in a cavernous space with walls of dark rock, aggregates of gray igneous minerals, drab brown clays, streaks of rust red. Embedded in the floor of the cavern was a strange, luminous object: dozens of floating sparks of light, enclosed in an elaborate set of ethereal membranes. The membranes formed nested, concentric families, Daliesque onion layers—each series culminating in a bubble around a single spark, or occasionally a group of two or three. As the sparks drifted, the membranes flowed to accommodate them, in such a way that no spark ever escaped a single level of enclosure.

In one sense, the Truth Mines were just another indexscape. Hundreds of thousands of specialized selections of the library’s contents were accessible in similar ways—and Yatima had climbed the Evolutionary Tree, hopscotched the Periodic Table, walked the avenue-like Timelines for the histories of fleshers, gleisners, and citizens. Half a megatau before, ve’d swum through the Eukaryotic Cell; every protein, every nucleotide, even carbohydrate drifting through the cytoplasm had broadcast gestalt tags with references to everything the library had to say about the molecule in question.

In the Truth Mines, though, the tags weren’t just references; they included complete statements of the particular definitions, axioms, or theorems the objects represented. The Mines were self-contained: every mathematical result that fleshers and their descendants had ever proven was on display in its entirety. The library’s exegesis was helpful—but the truths themselves were all here.

The luminous object buried in the cavern floor broadcast the definition of a topological space: a set of points (the sparks), grouped into "open subsets" (the contents of one or more of the membranes) which specified how the points were connected to each other—without appealing to notions like "distance" or "dimension." Short of a raw set with no structure at all, this was about as basic as you could get: the common ancestor of virtually every entity worthy of the name "space," however exotic. A single tunnel led into the cavern, providing a link to the necessary prior concepts, and half a dozen tunnels led out, slanting gently "down" into the bedrock, pursuing various implications of the definition. Suppose T is a topological space… then what follows? These routes were paved with small gemstones, each one broadcasting an intermediate result on the way to a theorem. Every tunnel in the Mines was built from the steps of a watertight proof; every theorem, however deeply buried, could be traced back to every one of its assumptions. And to pin down exactly what was meant by a "proof," every field of mathematics used its own collection of formal systems: sets of axioms, definitions, and rules of deduction, along with the specialized vocabulary needed to state theorems and conjectures precisely.

When ve’d first met Radiya in the Mines, Yatima had asked ver why some non-sentient program couldn’t just take each formal system used by the miners and crank out all its theorems automatically sparing citizens the effort.

Radiya had replied, "Two is prime. Three is prime. Five is prime. Seven is prime. Eleven is prime. Thirteen is prime. Seventeen is-"

"Stop!"

"If I didn’t get bored, I could go on like that until the Big Crunch, and discover nothing else."

"But we could run a few billion programs at once, all mining in different directions. It wouldn’t matter if some of them never found anything interesting."

"Which different directions would you choose?"

"I don’t know. All of them?"

"A few billion blind moles won’t let you do that. Suppose you have just one axiom, taken as given, and ten valid logical steps you can use to generate new statements. After one step, you have ten truths to explore." Radiya had demonstrated, building a miniature, branching mine in the space in front of Yatima. "After ten steps, you have ten billion, ten to the tenth power." The fan of tunnels in the toy mine was already an unresolvable smear-but Radiya filled them with ten billion luminous moles, making the coal face glow strongly. "After twenty steps, you have ten to the twentieth. Too many to explore at once, by a factor of ten billion. How are you going to choose the right ones? Or would you time-share the moles between all of these paths—slowing them down to the point of uselessness?" The moles spread their light out proportionately-and the glow of activity became invisibly feeble. "Exponential growth is a curse in all its forms. You know it almost wiped out the fleshers? If we were insane enough, we could try turning the whole planet—or the whole galaxy—into some kind of machine able to exert the necessary brute computational force… but even then, I doubt we’d reach Fermat’s Last Theorem before the end of the universe."

Yatima had persisted. "You could make the programs more sophisticated. More discriminating. Let them generalize from examples, form conjectures… aim for proofs."

Radiya had conceded, "Perhaps it could be done. Some fleshers tried that approach before the Introdus—and if you’re short-lived, slow, and easily distracted, it almost makes sense to let unthinking software find the lodes you’d never hit before you died. For us, though… Why should we sacrifice the opportunity for pleasure?"

Now that ve’d experienced Truth Mining for verself, Yatima could only agree. There was nothing in any scape or library file, any satellite feed or drone image, more beautiful than mathematics. Ve sent the scape a query tag, and it lit the way to the Gauss-Bonnet Theorem with an azure glow for vis viewpoint only. Ve floated off slowly down one of the tunnels, reading all the tags from the jeweled path.

Learning was a strange business. Ve could have had vis exoself wire all this raw information straight into vis mind, in an instant—ve could have engulfed a complete copy of the Truth Mines, like an amoeba ingesting a planet—but the facts would have become barely more accessible than they already were, and it would have done nothing to increase vis understanding. The only way to grasp a mathematical concept was to see it in a multitude of different contexts, think through dozens of specific examples, and find at least two or three metaphors to power intuitive speculations. Curvature means the angles of a triangle might not add up to 180 degrees. Curvature means you have to stretch or shrink a plane non-uniformly to make it wrap a surface. Curvature means no room for parallel lines—or room for far more than Euclid ever dreamt of. Understanding an idea meant entangling it so thoroughly with all the other symbols in your mind that it changed the way you thought about everything.

Still, the library was full of the ways past miners had fleshed out the theorems, and Yatima could have had those details grafted in alongside the raw data, granting ver the archived understanding of thousands of Konishi citizens who’d traveled this route before. The right mind grafts would have enabled ver effortlessly to catch up with all the living miners who were pushing the coal face ever deeper in their own inspired directions… at the cost of making ver, mathematically speaking, little more than a patchwork clone of them, capable only of following in their shadows.

If ve ever wanted to be a miner in vis own right making and testing vis own conjectures at the coal face, like Gauss and Euler, Riemann and Levi-Civita, deRham and Cartan, Radiya and Blanca, then Yatima knew there were no shortcuts, no alternatives to exploring the Mines firsthand. Ve couldn’t hope to strike out in a fresh direction, a route no one had ever chosen before, without a new take on the old results. Only once ve’d constructed vis own map of the Mines—idiosyncratically crumpled and stained, adorned and annotated like one else’s—could ve begin to guess where the next rich vein of undiscovered truths lay buried.

Yatima was back in the savanna of vis homescape, playing with a torus crisscrossed with polygons, when Inoshiro sent a calling card; the tag entered the scape like a familiar scent on the wind. Yatima hesitated—ve was happy with what ve was doing, ve didn’t really want to be interrupted—but then ve relented, replying with a welcoming tag and granting Inoshiro access to the scape.

"What’s that ugly piece of crap?" Inoshiro gazed contemptuously at the minimalist torus. Ever since ve’d started visiting Ashton-Laval, ve seemed to have taken on the mantle of arbiter of scape aesthetics. Everything Yatima had seen in vis homescape wriggled ceaselessly, glowed across the spectrum, and had a fractal dimension of at least two point nine.

"A sketch of the proof that a torus has zero total curvature. I’m thinking of making it a permanent fixture."

Inoshiro groaned. "The establishment have really got their hooks into you. Orphan see, orphan do."

Yatima replied serenely, "I’ve decomposed the surface into polygons. The number of faces, minus the number of edges, plus the number of vertices—the Euler number—is zero."

"Not for long." Inoshiro scrawled a line across the object, defiantly bisecting one of the hexagons.

"You’ve just added one new face and one new edge. That cancels out exactly."

Inoshiro carved a square into four triangles.

"Three new faces, minus four new edges, plus one new vertex. Net change: zero."

"Mine fodder. Logic zombie." Inoshiro opened vis mouth and spewed out some random tags of propositional calculus.

Yatima laughed. "If you’ve got nothing better to do than insult me…" Ve began emitting the tag for imminent withdrawal of access.

"Come and see Hashim’s new piece."

"Maybe later." Hashim was one of Inoshiro’s Ashton-Laval artist friends. Yatima found most of their work bewildering, though whether it was the interpolis difference in mental architecture or just vis own personal taste, ve wasn’t sure. Certainly, Inoshiro insisted that it was all "sublime."

"It’s real time, ephemeral. Now or never."

"Not true: you could record it for me, or I could send a proxy—"

Inoshiro stretched vis pewter face into an exaggerated scowl. "Don’t be such a philistine. Once the artist decides the parameters, they’re sacrosanct—"

"Hashim’s parameters are just incomprehensible. Look, I know I won’t like it. You go."

Inoshiro hesitated, slowly letting vis features shrink back to normal size. "You could appreciate Hashim’s work, if you wanted to. If you ran the right outlook."

Yatima stared at ver. "Is that what you do?"

"Yes." Inoshiro stretched out vis hand, and a flower sprouted from the palm, a green-and-violet orchid which emitted an Ashton-Laval library address. "I didn’t call you before, because you might have told Blanca… and then it would have got back to one of my parents. And you know what they’re like."

Yatima shrugged. "You’re a citizen, it’s none of their business."

Inoshiro rolled vis eyes and gave ver vis best martyred look. Yatima doubted that ve’d ever understand families: there was nothing any of Inoshiro’s relatives could do to punish ver for using the outlook, let alone actually stop ver. All reproving messages could he filtered out; all family gatherings that turned into haranguing sessions could he instantly deserted. Yet Blanca’s parents—three of them Inoshiro’s—had badgered ver into breaking up with Gabriel (if only temporarily); the prospect of exogamy with Carter-Zimmerman was apparently beyond the pale. Now that they were together again, Blanca (for some reason) had to avoid Inoshiro as well as the rest of the family—and presumably Inoshiro no longer feared that vis part-sibling would blab.

Yatima was a little wounded. "I wouldn’t have told Blanca, if you’d asked me not to."

"Yeah, yeah. Do you think I don’t remember? Ve practically adopted you."

"Only when I was in the womb!" Yatima still liked Blanca very much, but they didn’t even see each other all that often, now.

Inoshiro sighed. "Okay: I’m sorry I didn’t tell you sooner. Now are you going to come see the piece?"

Yatima sniffed the flower again, warily. The Ashton-Laval address smelt distinctly foreign… but that was just unfamiliarity. Ve had vis exoself take a copy of the outlook and scrutinize it carefully. Yatima knew that Radiya, and most other miners, used outlooks to keep themselves focused on their work, gigatau after gigatau. Any citizen with a mind broadly modeled on a flesher’s was vulnerable to drift: the decay over time of even the most cherished goals and values. Flexibility was an essential part of the flesher legacy, but after a dozen computational equivalents of the pre-Introdus lifespan, even the most robust personality was liable to unwind into an entropic mess. None of the polises' founders had chosen to build predetermined stabilizing mechanisms into their basic designs, though, lest the entire species ossify into tribes of self-perpetuating monomaniacs, parasitized by a handful of memes. It was judged far safer for each citizen to he free to choose from a wide variety of outlooks: software that could run inside your exoself and reinforce the qualities you valued most, if and when you felt the need for such an anchor. The possibilities for short-term cross-cultural experimentation were almost incidental.

Each outlook offered a slightly different package of values and aesthetics, often built up from the ancestral reasons-to-be-cheerful that still lingered to some degree in most citizens' minds: Regularities and periodicities—rhythms like days and seasons. Harmonies and elaborations, in sounds and images, and in ideas. Novelty. Reminiscence and anticipation. Gossip, companionship, empathy, compassion. Solitude and silence. There was a continuum which stretched all the way from trivial aesthetic preferences to emotional associations to the cornerstones of morality and identity.

Yatima had vis exoself’s analysis of the outlook appear in the scape in front of ver as a pair of before-and-after maps of vis own most affected neural structures. 

The maps were like nets, with spheres at every junction to represent symbols; proportionate changes in the symbols' size showed how the outlook would tweak them.

"Death gets a tenfold boost? Spare me."

"Only because it’s so underdeveloped initially."

Yatima shot ver a poisonous look, then rendered the snaps private, and stood examining them with an air of intense concentration.

"Make up your mind; it’s starting soon."

"You mean make my mind Hashim’s?"

"Hashim doesn’t use an outlook."

"So it’s all down to raw artistic talent? Isn’t that what they all say?"

"Just… make a decision."

Vis exoself’s verdict on the potential for parasitism was fairly sanguine, though there could be no guarantees. If ve ran the outlook for a few kilotau, ve ought to be able to stop.

Yatima made a matching flower grow from vis own palm. "Why do you keep talking me into these crazy stunts?"

Inoshiro’s face formed the pure gestalt sign for unappreciated benefactor. "If I don’t save you from the Mines, who will?"

Yatima ran the outlook. At once, certain features of the scape seized vis attention: a thin streak of cloud in the blue sky, a cluster of distant trees, the wind rippling through the grass nearby. It was like switching from one gestalt color map to another, and seeing some objects leap out because they’d changed more than the rest. After a moment the effect died down, but Yatima still felt distinctly modified; the equilibrium had shifted in the tug-of-war between all the symbols in vis mind, and the ordinary buzz of consciousness had a slightly different tone to it.

"Are you okay?" Inoshiro actually looked concerned, and Yatima felt a rare, raw surge of affection for ver. Inoshiro always wanted to show ver what ve’d found in vis endless fossicking through the Coalition’s possibilities—because ve really did want ver to know what the choices were.

"I’m still myself. I think."

"Pity." Inoshiro sent the address, and they jumped into Hashim’s artwork together.

Their icons vanished; they were pure observers. Yatima found verself gazing at a red-tinged cluster of pulsing organic parts, a translucent confusion of fluids and tissue. Sections divided, dissolved, re-organized. It looked like a flesher embryo—though not quite a realist portrait. The imaging technique kept changing, revealing different structures: Yatima saw hints of delicate limbs and organs caught in slices of transmitted light; a stark silhouette of bones in an X-ray flash; the finely branched network of the nervous system bursting into view as a filigreed shadow, shrinking from myelin to lipids to a scatter of vesicled neurotransmitters against a radio-frequency MRI chirp.

There were two bodies, now. Twins? One was larger, though—sometimes much larger. The two kept changing places, twisting around each other, shrinking or growing in stroboscopic leaps while the wavelengths of the image stuttered across the spectrum.

One flesher child was turning into a creature of glass, nerves and blood vessels vitrifying into optical fibers. A sudden, startling white-light image showed living, breathing Siamese twins, impossibly transected to expose raw pink-and-gray muscles working side-by-side with shape-memory alloys and piezoelectric actuators, flesher and gleisner anatomies interpenetrating. The scene spun and morphed into a lone robot child in a flesher’s womb; spun again to show a luminous map of a citizen’s mind embedded in the same woman’s brain; zoomed out to place her, curled, in a cocoon of optical and electronic cables. Then a swarm of nanomachines burst through her skin, and everything scattered into a cloud of gray dust. Two flesher children walked side-by-side, hand-in-hand. Or father and son, gleisner and flesher, citizen and gleisner… Yatima gave up trying to pin them down, and let the impressions flow through ver. The two figures strode calmly along a city’s main street, while towers rose and crumbled around them, jungle and desert advanced and retreated.

The artwork, unbidden, sent Yatima’s viewpoint wheeling around the figures. Ve saw them exchanging glances, touches, kisses—and blows, awkwardly, their right arms fused at the wrists. Making peace and melting together. The smaller lifting the larger onto vis shoulders then the passenger’s height flowing down to the hearer like an hourglass’s sand.

They were parent and child, siblings, friends, lovers, species, and Yatima exulted in their companionship. Hashim’s piece was a distillation of the idea of friendship, within and across all borders. And whether it was all down to the outlook or not, Yatima was glad to he witnessing it, taking some part of it inside verself before every image dissolved into nothing but a flicker of entropy in Ashton-Laval’s coolant flow.

The scape began moving Yatima’s viewpoint away from the pair. For a few tau ve went along with this, but the whole city had decayed into a flat, fissured desert, so apart from the retreating figures there was nothing to be seen. Ve jumped hack to them-only to find that ve had to keep advancing vis coordinates just to stay in place. It was a strange experience: Yatima possessed no sense of touch, or balance, or proprioception—the Konishi design eschewed such delusions of corporeality-but the scape’s attempt to "push" ver away, and the need to accelerate against it, seemed so close to a physical struggle that ve could almost believe ve’d been embodied.

The figure facing Yatima aged suddenly, cheeks hollowing, eyes filming over. Yatima moved around to try to see the other’s face—and the scape sent ver flying across the desert, this time in the opposite direction, Ve fought vis way back to the… mother and daughter, then decaying robot and gleaming new one… and though the two remained locked together, hand-in-hand, Yatima could all but feel the force trying to tear them apart.

Ve watched flesh hand gripping skin-and-hones, metal gripping flesh, ceramic gripping metal. All of them slowly slipping. Yatima looked into the eyes of each figure; while everything else flowed and changed, their gazes remained locked together.

The scape split in two, the ground opened up, the sky divided. The figures were parted. Yatima was flung away from them, back into the desert with a force, now, that ve could not oppose. Ve saw them in the distance—twins again, of uncertain species, reaching out desperately across the empty space growing between them. Arms outstretched, fingertips almost brushing.

Then the halves of the world rushed apart. Someone bellowed with rage and grief.

The scape decayed into blackness before Yatima understood that the cry had been vis own.

The forum with the flying-pig fountain had been abandoned long ago, but Yatima had planted a copy from the archives in vis homescape, the cloistered square marooned in the middle of a vast expanse of parched scrubland. Empty, it looked at once too large and too small. A few hundred delta away, a copy (not to scale) of the asteroid ve’d watched being trimmed was buried in the ground. At one point Yatima had envisioned a vast trail of similar mementos stretching across the savanna, a map ve could fly over whenever ve wanted to review the turning points in vis life… but then the whole idea had begun to seem childish. If the things ve’d seen had changed ver, they’d changed ver; there was no need to re-create them as monuments. Ve’d kept the forum because ve genuinely liked to visit it—and the asteroid out of the sheer perverse pleasure of resisting the urge to tidy it away.

Yatima stood by the fountain for a while, watching its silver liquid effortlessly mock the physics it half-obeyed. Then ve re-created the octahedral diamond, the six-pointed net from vis lesson with Radiya, beside it. That physics meant nothing in the polises had always been clear to ver, as it was to most citizens; Gabriel disagreed, of course, but that was just Carter-Zimmerman doctrine talking. The fountain could ignore the laws of fluid dynamics just as easily as it could conform to them. Everything it did was simply arbitrary; even the perfect gravitational parabola of the start of each stream, before the piglets were formed, was nothing but an aesthetic choice and the aesthetic itself was nothing but the vestigial influence of flesher ancestry.

The diamond net was different, though. Yatima played with the object, deforming it wildly, stretching and twisting it beyond recognition. It was infinitely malleable… and yet a few tiny constraints on the changes ve could make to it rendered it, in a sense, unchangeable. However much ve distorted its shape, however many extra dimensions ve invoked, this net would never lie flat. Ve could replace it with something else entirely such as a net which wrapped a torus and then lay that new net flat… but that would have been as meaningless as creating a non-sentient, Inoshiro-shaped object, dragging it into the Truth Mines, and then claiming that ve’d succeeded in persuading vis real friend to come along.

Polis citizens, Yatima decided, were creatures of mathematics; it lay at the heart of everything they were, and everything they could become. However malleable their minds, in a sense they obeyed the same kind of deep constraints as the diamond net—short of suicide and de novo reinvention, short of obliterating themselves and constructing someone new. That meant that they had to possess their own immutable mathematical signatures—like the Euler number, only orders of magnitude more complex. Buried in the confusion of details of every mind, there had to be something untouched by time, unswayed by the shifting weight of memory and experience, unmodified by self-directed change.

Hashim’s artwork had been elegant and moving—and even without the outlook running, the powerful emotions it had evoked lingered—but Yatima was unswayed from vis choice of vocation. Art had its place, tweaking the remnants of all the instincts and drive, that the fleshers, in their innocence, had once mistaken for embodiments of immutable truth—but only in the Mines could ve hope to discover the real invariants of identity and consciousness.

Only in the Mines could ve begin to understand exactly who ve was.