Instantiation

by Greg Egan

  So whatever the game was, it would be a compromise. Sagreda’s hope had always been that the SludgeNet would turn out to have bitten off more than it could chew, exposing a multitude of new flaws in its GPUs and its world-building algorithms … without rendering the place so hostile to its inhabitants that they had no opportunity to exploit the bugs.

  She could hear a soft wind blowing, and she felt its touch upon her skin. She braced herself and opened her eyes.

  Her first impression was that she was standing in a desert landscape of bleached earthen colors, with what looked like a few low boulders nearby. The cloudless sky could not have been more perfect, short of turning to cobalt blue.

  But the ground bore a strange pattern of dark, concentric circles that spread out around her, dividing the landscape into narrow rings, while the “boulders” were two-dimensional, like cheap, painted stage scenery – only rescued from being literally flat by the fact that they conformed to the curves of the rings they belonged to. And as Sagreda looked past them toward more distant rings, the terrain grew crowded with detail at an alarming rate, packing in ever more variation in a manner that utterly defied her expectations about scale and perspective – as if kilometer-long strips plucked from an ordinary desert had been squeezed longitudinally and bent into circles just a few hundred meters across.

  All of which made a certain amount of sense. Distances in 3-adica couldn’t take on a continuous range of values: they only came in powers of three. By rights, every ring of solid ground she saw should have been followed by another ring exactly three times larger, with nothing in between. But perceiving her surroundings as mostly empty space would have been a waste of the act of perception, and whether this compressed version faithfully reflected the way 3-adica’s alien protagonists had seen things in the original book, or whether it was just a compromise the game had imposed, Sagreda didn’t find it unreasonable that she was aware of the gaps between the shells of possible distances, without having to squander ninety percent of the virtual neurons in her visual cortex on massive black moats that could literally never contain anything.

  She willed herself to start walking, and her body obliged, executing a gait that required no conscious effort, and worked so well that she was loathe to dissect it into a sequence of moves for each limb. She declined to peer down at her feet – or hooves – lest the strangeness of the sight paralyze her; it seemed wiser to try to grow into this body by using it for a while, purely by instinct.

  She decided to head for the nearest of the boulders, but after spending a few minutes supposedly ambling toward it, Sagreda realized that her target was just shifting from side to side within its original distance-ring. So were all the other discernible features in all the other rings. Nothing was getting closer.

  She stopped and looked down at the ground right in front of her, averting her gaze from the glimpse she caught of her forelimbs. Here, the rings were spaced so closely that she might as well have been staring at an unbroken surface – if not sand, maybe sandstone. She took a few steps to try to get a better sense of her own pace and recalibrate her expectations. As she walked, the texture beneath her drifted around in her field of view in a manner that seemed consonant with the rhythms of her body, but she never seemed to be leaving it behind and moving on to something new.

  “Okay,” she muttered out loud, amused that this world would allow her to utter and perceive the familiar syllables in a nasal voice that might have belonged to Mister Ed. Why wasn’t she getting anywhere? Because distances no longer added up the same way. From zero to one was a distance of one; from one to two was a distance of one. But from zero to two was a distance of one, again. In fact, however many steps you took, the distance you ended up from where you began could never be greater than the largest of those steps.

  One of the p-adic-savvy travelers Sagreda had met had called this “the non-Archimedean property,” and opined that the only way an object could move at all through a 3-adic space would be through some kind of quantum tunneling that bypassed the whole idea of a classical trajectory. So maybe at some level quantum effects were enabling her to move her legs, or maybe that was pure cheating, but whatever the mechanism, it did not seem able to propel her out across the landscape.

  Sagreda began walking again, with no expectations of any change in the result, but in the hope of gaining a better sense of what was happening. If each of her steps had had the effect of merely adding some fixed quantity to a 3-adic coordinate for her body, she would have mostly ended up at that distance from where she’d begun, switching abruptly to one-third, or one-ninth, or one-twenty-seventh and then back as her step count hit multiples of powers of three. But even allowing for her compressed perception of distances, she couldn’t discern any such pattern. So perhaps her steps, though of equal geometric size, involved adding a sequence of different numbers – whose numerators and denominators were all devoid of threes – to her location. With the right choice of fractions to maintain the lack of threes in their cumulative sums, all steps and all their successive totals could work out to have the same size. And just as her body knew instinctively which legs to raise and lower in which order, this arithmetic trick would be wired into it, sparing her the need to calculate anything.

  Which was all very nice if you wanted to trace out a circle in the desert. But how was she supposed to do anything else? The non-Archimedean law was clear: the total distance traveled could never be greater than the largest step. So how could she escape her invisible prison, if she couldn’t leap over the walls in one bound?

  Sagreda willed herself to run, and her body obliged with a gallop that made her newfound muscles sing. The texture of the ground ahead of her changed almost at once, and for a moment she was elated. But though her individual bounds were larger than her previous steps, they gained no more by force of repetition: she was just executing a slightly larger circle.

  She stopped to catch her breath, daring the world to play fair and suffocate her, since the stale air around her could hardly escape its starting position any more easily than she could. But if her body was largely a cheat to let her feel at home, a travesty of alien Euclidean nonsense spliced into the 3-adic terrain, there had to be some genuine, 3-adic way to go farther than a single bound, or the whole book would have been very short: A creature stood alone in the desert (please don’t ask how it got there). Soon it died from lack of food. The End.

  It was time to stop being squeamish: if she could survive waking up as the Captain, she could cope with this alien horsiness. She bent her neck as far as she could and looked down at herself as she took a few steps. Her legs were swinging back and forth, but beyond that, they were visibly expanding and contracting: swelling up beyond the wildest nightmare version of the Captain’s gout, then deflating just as rapidly. No accumulation of additions could carry an object farther than the largest distance traveled along the way – but her legs weren’t adding, they were multiplying.

  Sagreda kept walking, contemplating the meaning of this discovery. In the real world, when you inflated a balloon, the individual molecules in the rubber were moving in different directions depending on which side of the balloon they were on, but motion was motion; there was nothing special going on. Here, though, since ordinary motion couldn’t lead to dilation, dilation had to be an entirely separate thing. If the invented physics of 3-adica was symmetrical under a change of scale, then it might make sense for a system to possess “dilatational” momentum, as well as the usual kind. If your dilatational velocity was one tripling per second, you became three times larger, again and again, until something applied an opposing dilatational force that brought the process to a halt. And ditto for shrinking. That was how you got anywhere in this place.

  Out of habit, Sagreda looked around for Mathis to share her triumphant discovery with him. In his absence, a deadening numbness started creeping into her skull, but she stared it down: this wasn’t the time for grief, let alone anything darker. She’d stranded Sam in this bizarre place, an
d she owed it to him to keep going until she knew that he was safe. Love and reason had never been for the two of them alone; unless she had some fellow feeling for every last comp, she was no better than the mindless SludgeNet, and its worse-than-mindless creators.

  If her leg muscles possessed the power to expand and contract 3-adically, there was no reason why the rest of her body shouldn’t share it. It was just a matter of finding the cue. Sagreda closed her eyes and pictured herself growing larger; when she opened them nothing had changed. Then she tried tensing her shoulders, not just willing them to grow broader but actively forcing them apart. It made her feel ridiculous, as if she were posing like a vain equine body-builder, but to her astonishment and delight the landscape around her started to shrink.

  She watched the stage-scenery boulder she’d been trying to reach turn into a rock, then a pebble, then a grain of sand as it slipped between her feet. Curiouser and curiouser. She relaxed, and then discovered that she needed to apply a brief compression of her shoulder blades to bring the process to a halt.

  “What now?” she wondered. The desert was still a desert, self-similar enough under enlargement that only the details of the view had changed. Where exactly – and how big – were all the other characters? In what place, and at what scale, could she hope to find Sam?

  Given the potential disruption that a character’s dilation could cause, it would make sense for the game to wake new entrants at a very small scale, offering them a chance to find their feet, and shoulders, without bumping into anyone. And though the lesson was immensely hard to swallow, the fact remained that – colossus or not – she still couldn’t go striding out across the wilderness, exploring in any conventional way. Her choices were to reposition herself within her new, much larger, prison and then shrink down for a closer look in case she’d missed something, or to keep on inflating her body until her current surroundings in all their desolate grandeur revealed themselves to be nothing, on the scale that mattered, but a tiny patch of dirt.

  Sagreda spent a few minutes pacing in a circle, staring at the ground, but she saw no signs of any tiny cities hidden in the dust – and if the game’s greatest architectural features had been something she might easily have crushed beneath her feet from sheer inexperience, there’d have been a lot of rebooting going on.

  So she took a few deep breaths, steadied herself, then spread her shoulders wide.

  12

  “Make room, make room!” a male voice shouted irritably. Sagreda shrank out of the way as the passerby expanded to fill most of the square, deftly bloating and stepping then finally contracting, leaving him on the opposite side. For a moment or two, an afterimage of his blimp-pufferfish-horse-balloon body breaking up into distinct onion-layers lingered in Sagreda’s vision.

  She quickly expanded back to her previous scale before someone else muscled in; if you gave these people an inch, you ended up toy-sized. “Do you know a newcomer named Sam?” she asked a 3-adan who’d ended up beside her in the wake of the maneuver. There was no reply.

  She’d been standing at more or less the same spot in the corner of the square for hours, slowly increasing her size as the opportunities arose. Her fellow characters had been kind enough not to trample her as she ascended out of the “desert”, but actually traversing any significant distance here – by becoming as large as the journey you wished to make – seemed to require a combination of nerve, skill and luck that she had not yet attained. A few of her contributors were offering a collective flashback to their first attempts to cross an ice rink, but however conspicuous they might have felt as novices trying out their blades, Sagreda was fairly sure that they’d had nothing on this.

  She closed her eyes for a moment to escape from the headache-inducing perspective. Until now, she’d always been part of an ant-trail of travelers moving to and fro between the worlds, carrying intelligence of what lay ahead; this was the first time she’d arrived at her destination without a single contact. But she’d met at least a dozen people at different times who’d sworn they were heading for 3-adica, before she and Mathis had resolved to make the journey themselves. Even if no one had ever come back, she couldn’t be alone here.

  “Sam!” she bellowed, keeping her eyes closed; it was easier to feel uninhibited that way. Going on the barrage of noise striking her from all directions, she was fairly sure that sound had the means to propagate at least across the square. Whether there was anything beyond this place was another question; the only really practical way it could be part of a larger city was through a hierarchy of scales, with people having to bloat even more to move between them.

  “Sam!” If there was a customer nearby and she was violating the local mores, so be it: let them flag her for deletion. It was all she could do to move her body out of other people’s way here; she had no idea how she was going to find food or shelter. Did she really think she was going to be able to map this world’s flaws and exploit them, all on her own?

  “Captain!” a voice whinnied back. Sagreda had almost forgotten that she’d never given the boy her real name back in Midnight.

  She opened her eyes. “Sam! Where are you?”

  “Here! Over here!”

  Sagreda searched the crowd in the direction of his words, but how was she meant to recognize him?

  “Don’t worry! I’ll come to you!”

  The square’s mostly empty center was abruptly filled with a new parade-float pony, which shrank down beside her.

  “Can you see me now?” Sam joked.

  “Yes.” For a moment, Sagreda could find nothing more to say; her relief was too tainted with guilt. “I’m sorry you ended up here,” she said finally. “I never meant that to happen.”

  “It’s my own doing,” he replied. “I should have waited for you.”

  “How long have you been here?”

  “Ten days.”

  Sagreda bowed her head. If she’d been alone that long herself, she would have lost her mind.

  “It’s all right, Captain,” Sam said gently. “You’re here now. So at least I’ve got someone to talk to.”

  “You haven’t made any friends with the locals?”

  He snorted. “You know how some people back in London … you could tell there weren’t nobody home? Here, they’re all that way.”

  Making the two of them the only comps in a world of automata? He had to be exaggerating. If the SludgeNet had been willing to populate the place without resorting to comps at all, they would never have been plucked from the queue and embodied here.

  “Maybe the lifestyle has just ground them down,” she suggested. “Have you been able to learn the ropes at all?”

  “I seen how to get by,” Sam assured her. “If you want grub, you got to put in the work, tending one of them patches.”

  “Patches?”

  “They’re like … small farms,” he struggled. “You need to eat the weeds, not the shoots – if you take the shoots for yourself, you’ll get a flogging. But if you eat enough weeds, they can smell it on you, and they’ll feed you proper.” Sam must have read bemusement on her face, or perhaps just in her silence. He said, “Only way to learn it is by watching.”

  Sagreda found the courage to follow him across the square; once she’d done it, her previous timidity seemed absurd.

  The patches were small areas of walled-off ground in one corner of the square, full of agricultural workers who shrank down into them and did exactly as Sam had described: roaming across their circle of land, chomping red and yellow weeds that were competing with the tender green buds of some kind of crop that was sprouting from the dusty soil. The two of them watched for a while, peering down into the Lilliputian realm, until four of the workers grew tired and expanded back up to the scale of the square.

  “Now!” Sam urged her. Other 3-adans were jostling around them, eager for work. Sagreda followed Sam down into the patch, though her first attempt put her on land that had already been thoroughly weeded, and she had to re-bloat a little and move before
she found a suitable location.

  The weeds tasted foul, but no one else was spitting them out, and if the odor really was an essential meal-ticket Sagreda wasn’t going to risk defying convention. In some ways it was restful to have her gaze fixed on the ground, where the distance-rings were closely packed and the strange geometry was more hypnotic than emetic.

  She lost herself in the near-mindlessness of the task, trying not to think about how comfortable she could have been if she’d never left East at all. With everyone around her game-aware, and the water-wheels she’d built powering something close to civilization, it seemed like paradise now.

  “Captain!” Sam called to her. The sky above them was darkening, which was curious, because it contained no sun. “Time to eat!”

  She watched him grow, taking note of how he was able to shift his feet to avoid trampling either crops or workers, and followed him back to the square.

  “I don’t know what we should call this place,” Sam admitted cheerfully as he led her to a queue beside an opening in a wall. “‘Restaurant’ might be gilding the lily.” Sagreda waited for the gap in front of her to grow large enough for her to bloat into it and advance. She was starting to internalize the sequence of contortions needed to get from place to place, which was both helpful and a bit depressing.

  “We need to be on the look-out for things that appear wrong,” she told Sam.

  “By my count, that’s everything,” he retorted.

  “You know what I mean. Wrong by the rules of this place; standing out as different.” The possibility that everyone who’d come here before them had failed to identify a single new exploit was too grim to consider, even if it would explain why no traveler had ever emerged from 3-adica. The old cubical trigger wouldn’t work here; it relied too much on Euclidean geometry. But there had to be others. The whole eye-watering nightmare around them must have tested the GPU code to destruction at some point.