Instantiation

by Greg Egan

  Sagreda heard a rustle of clothing – maybe overcoats coming off – then a woman’s voice. “They were so rude to me! I can’t believe it! If I want to be called Lady Godwin, they should call me Lady Godwin!”

  A man replied, “It’s a historical fact: she took her husband’s name.”

  “Yes, but only because she had no choice! If she’d been vampire aristocracy, do you think she would have buckled to convention like that?”

  “Umm, given her politics, do you think she would have chosen to be an aristocrat of any kind?”

  “There are socialists in the British House of Lords, aren’t there?” the woman countered.

  The man was silent for a moment, then he said, “Can you smell that?”

  “Smell what?”

  “You really can’t smell it? Maybe your thing’s clogged.”

  “What are you talking about?”

  The man sighed impatiently. “You know … the little canister thing in the front of the helmet, under the goggles. There’s a mesh around it, but I think sometimes the stuff clogs up the holes. Just give it a flick with your finger.”

  The two customers went quiet. In the shadows of the drawing room, Lucy caught Sagreda’s eye and gestured to her to move behind a bookcase. Sagreda complied without hesitation, deferring to her accomplice’s experience.

  “Okay … yeah, I can smell it now,” the woman announced. “That’s foul! Do you think one of our experiments broke out of the basement?”

  “Maybe,” the man replied. “But it seems to be coming from down the hall.”

  Sagreda heard their footsteps approaching. She tensed, wishing she could see exactly where Mathis was. A couple of ordinary householders would not have posed much of a problem – least of all customers, whom Mathis would have no qualms about dispatching – but she did not like the phrase vampire aristocracy.

  “Wait!” the man said. The footsteps stopped, and then he groaned. “Yeah, yeah: sexy Russian babes are desperately seeking broad-minded couples to help fulfill their fantasies. How many times are they going to show me this crap before they realize we’re never going to follow the link?”

  “You could go ad-free, if you weren’t so stingy,” the woman chided him.

  “Stingy? Five dollars a month is a rip-off!”

  “Then stop complaining. It’s your choice.”

  “What costs do they actually have?” the man protested. “The books they start from are all public domain, or pirated. The world-building software comes from open-source projects. The brain maps they use for the comps are data from open-access journals. So, I’m meant to fork out five dollars a month just to pay rent on their servers?”

  “Well … enjoy smickering at your Russian babes, Lord Scrooge, I’m going to find out what’s stinking up the house.”

  The woman must have decided to approach on tip-toes, because Sagreda heard nothing but floorboards creaking. From her hiding place she could see neither Mathis nor Lucy, and she felt like a coward for not rushing out to block the doorway with the Captain’s ample girth. But the fact remained that the mild-mannered aficionado of kitsch creeping down the corridor, who would not have said boo to any fleshly equivalent of Sagreda if they’d sat next to each other on a bus, had been endowed by the game with the power to rip all of their throats out – and endowed by her own lack of empathy with the power to take off her goggles and sleep soundly afterward.

  The woman spoke, from just inside the doorway, calling back to her companion in a kind of stage whisper, “It’s definitely coming from in here!” Maybe her “experiments” were so brain-damaged that they would not have been alerted to her presence by these words. Or maybe she just didn’t give a damn. At five bucks a month, how invested would she be? If things turned out badly, she could still order a pizza.

  There was a sound of bodies colliding, and the woman crying out in shock, if not actual pain. Sagreda stepped out into the room to be greeted by the sight of Mathis holding Lady Godwin with her arms pinned from behind, his fangs plunging repeatedly deep into her carotid artery as he filled his mouth with blood then spat it out onto the floor. His victim was strong, and she was struggling hard, but he’d had the advantage of surprise, and whatever their relative age and vampiric prestige, his assault was progressively weakening her.

  Sagreda ran to the fireplace and picked up a long metal poker. As she approached, both vampires glared at her furiously, like a pair of brawling cats who’d rather scratch each other’s flesh off than brook any human intervention. But she wasn’t here to try to make peace between house-pets.

  She rammed the poker as hard as she could between Godwin’s ribs; the author-turned-unlikely-vivisector screeched and coughed black blood that dribbled down the front of her satin evening gown, then she went limp. Sagreda was sickened; even if her victim would barely feel a tickle in her VR harness, the imagery they were sharing debased them both.

  Mathis dropped his dead prey and snatched at Sagreda, as if he was so enraged to have been cheated of the animal pleasure of the fight that he was ready to turn on her as punishment. She stood her ground. “Don’t you fucking touch me!” she bellowed.

  “What’s going on?” asked Lord Shelley irritably. Mathis turned to confront him, but this time it was no ambush; the older man grabbed him by the shirtfront and thrust him aside with no concern for conservation of momentum, sending him crashing into a corner of the room without experiencing the least bit of recoil.

  As Shelley gazed down in horror at his murdered wife, Sagreda backed away slowly. Reminding this bozo that it was only a game would only get her deleted.

  The undead poet raised his eyes to the Captain, and spread his fanged jaws wide in a howl of grief.

  “‘Look on my works, ye Mighty, and despair?’” Sagreda offered sycophantically.

  Lucy chose this moment to make a run for the door. Shelley turned and grabbed her thin arm, then bent down and sank his fangs into it, apparently deterred by her garlic necklace from striking in the usual spot. Sagreda leaped forward and punched him in the side of the mouth with all of the Captain’s mortal strength; to her amazement, her blow dislodged his jaws from the girl’s flesh. Lucy was bawling with pain and terror; Sagreda kept striking the same spot above Shelley’s chin with her massive right paw, as fast and hard as she could, unsure if it was just her knuckles and finger bones that she could hear cracking and crumbling from the impacts.

  Mathis whispered calmly in her ear, “Step aside, my love.”

  She complied. Shelley looked up, but he had no time to react. Mathis drove the poker into his chest, all the way through to his spine.

  As Shelley slumped to the ground, Lucy fell beside him, looking every bit as lifeless. Mathis took his coat off, tore one sleeve free and wrapped it around the girl’s upper arm as a tourniquet.

  “What are you doing?” Sagreda asked. “That’s so tight, you’re…” She stifled a sob of revulsion. “Don’t cut it off!”

  “I’m not going to,” Mathis promised, “but we need to move fast to get the poison out. And I can’t do it, that would only make it worse.”

  Sagreda stared at him. “What?”

  “I’ll apply pressure; you have to suck the wound and spit.”

  “You’re sure that will work?”

  “Just do it, or she’s either going to lose her arm or be turned!”

  Sagreda quickly relit the lamp so she could see what she was doing, then she knelt on the floor and set to work. When every drop had been drained or spat onto the carpet, leaving Lucy’s arm corpse-white, Mathis loosened the tourniquet and the flesh became pink, bleeding freely from the puncture wounds above the wrist.

  “Let it bleed for a bit, just to flush it out some more,” Mathis insisted.

  “How do you know all this?”

  “I’m guessing,” he admitted. “I’ve heard things from the other vampires, but I don’t know if I ever got the whole story straight.”

  Sagreda sat on the bloody floor and cradled Lucy’s head in her
arms. There was no actual poison being traced through some elaborate, fluid-dynamical model of the circulatory system; the game would make a crude assessment of the efficacy of their actions under its fatuous rules and then throw its algorithmic dice.

  They had love, and they had reason, but the game could still do whatever it liked.

  8

  Shortly after sunset, Mathis emerged from the Captain’s bedroom, bleary-eyed and yawning. “Did you get any sleep?” he asked Sagreda.

  “A couple of hours, around noon,” she replied. “But it’s done.” She gestured toward the mosaic. “I just need you to check it.”

  “Okay.” Mathis slapped his own face a few times, trying to wake more fully. “How’s your hand?”

  “Still broken. But I don’t plan on having to use it much longer.”

  Mathis managed a hopeful nod. “And Lucy?”

  Sagreda said, “She seems stable; her pulse is steady, and she has no fever.”

  Mathis took a seat in the nearest armchair and turned to address Sagreda. “The game’s not going to accept that its biggest celebrity couple has been removed from the plot. But the SludgeNet’s not going to reboot everything while the city’s crawling with customers who want to maintain continuity. So, the way I see it there are only two options. They can pull a bit of necromantic fluff out from under the sofa cushions, and bring the Shelleys back in an explicit act of resurrection that would make Sigourney Weaver blush. Or, they can pretend that what happened last night never really happened, and just delete the witnesses.”

  “You and I can be out of here as soon as you’ve checked the mosaic,” Sagreda said. She glanced at the sofa, where Lucy still lay inert. “But I don’t know if she’ll agree to come with us.”

  “All we can do is be honest with her,” Mathis replied.

  “To be honest, we don’t even know if we’re ready for this ourselves.” Sagreda rubbed the good side of her smashed hand; it didn’t really affect the pain, but it helped distract her from it.

  “No. But what would you rather do? Go off on a tour of another twenty worlds, in the hope that we might pick up a few more tips?”

  “If 3-adica makes anything possible, why has no one ever come back?” she asked.

  “Because it’s so good there that no one wants to leave?”

  “Not even for a day or two, to spread the word?”

  “I don’t know,” Mathis confessed.

  “What’s 3-adica?” Lucy asked. Her eyes were open, and she looked remarkably lucid.

  Sagreda fetched a jug of water. “How long have you been awake?” she asked, handing the girl a glass.

  “A while.” Lucy downed the water in one long gulp, then went to use the chamber pot. When she returned, she said, “I helped you complete the mandala, didn’t I? So you owe it to me to divulge the nature of its powers.”

  Sagreda had been preparing for this question all day. “It’s taking us to a world where the distances between numbers aren’t the same as they are here.”

  Lucy frowned, but her expression was more intrigued than dismissive.

  “Here, you can put all the numbers on a line,” Sagreda said. “Like the house numbers on a street. And the distance between two houses is just the difference between their numbers: number twelve is two houses down from number ten … most of the time.” Whatever the historical truth, this version of Victorian London hadn’t made up its mind whether to number houses consecutively along each side of the street, or to adopt the even/odd rule that was more familiar to Sagreda’s contributors.

  “So you’re going to a world where the houses are higgledy-piggledy?” Lucy guessed.

  “Maybe, though that doesn’t quite cover it.” Sagreda walked over to the desk, took a sheet of writing paper and started scrawling ovals in ink. “In 3-adica, the numbers are like eggs in a sparrow’s nest. Zero, one and two are all in the same nest, and the distance between any pair of them is exactly one.”

  “From one to two is one,” Lucy said. “But from nothing to two is … also one?”

  “Exactly,” Sagreda confirmed. “The laws of arithmetic haven’t changed: two minus zero is still two, not one. But the laws of geometry aren’t the same, and the distance is no longer the difference.”

  “But where’s three?” Lucy demanded. “Where’s seventy-three?”

  “Each egg I’ve drawn,” Sagreda said, “is really a nest of its own. The zero-egg is a nest that contains zero, three and six. The one-egg is a nest that contains one, four and seven. The two-egg is a nest that contains two, five and eight.” She scribbled in the new numbers.

  “I can see what you’ve written clear enough,” Lucy acknowledged, “but I don’t know what it means.”

  “To be in a smaller nest with a number puts you closer to it,” Sagreda explained. “The distance between zero and one is one, because that’s the size of the smallest nest they’re both in, but the distance between zero and three is smaller, because they share a smaller nest. In fact, the distance between zero and three is one third, as is the distance between five and eight, or four and seven.”

  “And you keep on with that nonsense?” Lucy asked.

  Sagreda smiled. “Absolutely. However high you want to count, you just keep turning eggs into ever smaller nests of three.”

  Lucy sat pondering this for a while, but it was clear that something was bothering her. “You say the distance from nothing to three is one third,” she said finally. “But where does one third live in your nests? I can walk a third of the way between houses, and I know what that means on Baker Street, but what does it mean for these sparrow’s eggs?”

  “It means you need to look outside the first nest.” Sagreda added another two circles as large as the largest one she’d drawn previously, and then scratched an even bigger one around all three. “If you add one third to anything in the first nest, it goes in the second nest. If you add two thirds, it goes in the third one. And any two numbers that happen to be in a different pair of these new nests lie at a distance of three from each other, because that’s the size of the larger nest that encloses them all. And before you ask me where one ninth lives, the paper isn’t large enough for me to draw that, but I think you can guess how the pattern continues.”

  Lucy absorbed this, but she wasn’t done. “Where does one half live?”

  Sagreda was tired; she had to stop and think. “It’s somewhere inside the first nest I drew, at a distance of one from zero.”

  “But where?” Lucy pressed her. “Where is there room for it? I can see how your eggs there reach up to any number I could ever count to … but how are you going to squeeze yet another one in?”

  Mathis chuckled and stretched his arms above his head. “Good question!” he said. “And it took my friend here about a day to convince me of the answer.”

  Sagreda closed her eyes for a moment, and focused. “First, go to the number two. Then add three and go to five. Then add nine, which takes you to fourteen. Then add twenty-seven … and so on. Each time, you add thrice what you added before.”

  “And when do you stop?” Lucy asked, with a cunning look on her face, as if she was about to play cuckoo and toss the existing egg at the point of arrival out of its nest.

  “You don’t!” Mathis interjected. “You’re not allowed to stop! Which sounds nonsensical, but it’s no more absurd, in 3-adica, than it is in our world for Achilles to get halfway down a road, then another quarter, then another eighth … with always one more stage to go that’s shorter than the last. Because in 3-adica, adding thrice what you added before takes you a third less far. Five is actually fairly close to one half, but fourteen is closer, and forty-one is closer still. Because if you double each of these numbers, the result is always one … plus three multiplied by itself many times, which makes less and less of a difference the more times it’s been multiplied.”

  Lucy opened her mouth to protest, but then closed it again. Something was sinking in. Sagreda had never met a comp who, when given the chance to brush
away the learned helplessness of their character, turned out to know less about arithmetic than they would have picked up from a decent high school education in America at the height of the space race. And maybe one in a hundred had been remixed from the pool in such a way that they inherited enough recreational mathematics to have heard of the “p-adic numbers”: 2-adics, 3-adics, 5-adics … p-adics for any prime you cared to name.

  But the book, 3-adica, seemed to have been written after every contributor had died. And the only knowledge any comp had of the SludgeNet’s attempt to gamify it came from eavesdropping on customers, whose comments on the topic tended to be of the form “my migraine when I tried that shit was worse than x,” for various values of x.

  Lucy seemed to be anticipating a few headaches of her own. “I don’t know if the streets will be like bird’s nests where you’re going,” she said, “but it sounds like a place where I’d lose my way.”

  Sagreda said, “The beauty, though, is that it’s also a place where the forces that try to keep you down are even more likely to lose their own way.”

  Lucy shook her head. “No one keeps me down. I can dodge the muckety-mucks well enough, whether they’re carrying cut-throat razors or trying to take a drink from my neck. Last night was a tight spot I shouldn’t have gotten into, but I won’t make that mistake again.”

  Sagreda could see no alternative now to spelling out the whole truth. “This London is not the real London,” she said. “It’s a bad story that bad people have created to make money from very bad advertisements. The machines those people own brought you and me to life – using parts they might as well have obtained from grave-robbers, cut up and stitched together to form puppets to act in their very bad play.”

  Lucy laughed curtly, with a brashness that seemed forced. “You might have dispensed yourself a bit too much laudanum, Captain, to ease the pain from your fisticuffs.” But Sagreda suspected that the last traveler Lucy had encountered would have sketched a cosmology eerily similar to this opium dream.

  She said, “This world we’re in, and ten thousand others like it, were made by ten thousand clockwork monkeys chewing rotten fruit and spitting out the pulp. But what if a ball of polished marble slipped into the barrel of worm-ridden apples, and broke its monkey’s jaw? A clockwork monkey is too stupid to stop chewing when you feed it something unexpected, so there’s no end to the damage the marble might have caused. And once you tear open a hole in the clockwork, maybe you can crawl right into the innards and really start playing with all the springs and wheels. That’s why 3-adica could mean freedom: it’s tough enough to break the monkey’s jaw.”