Diaspora

'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—