by Allan Kaster
“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 cutthroat 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 graverobbers, 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.”
Mathis rose from his armchair. “I should start checking the mosaic,” he said.
“Do you need a meal first?” Sagreda asked.
“No, a few gulps from her Ladyship’s ancient veins seem to have gone a long way.” He took a seat at the writing desk and peered studiously at Sagreda’s notes.
Sagreda joined Lucy on the sofa. “My landlady will be bringing me my dinner in about an hour,” she said. “So you and Mathis will need to hide for a bit, though of course you’re welcome to eat with me when the coast’s clear.”
“I’ll be getting back to my own digs before then,” Lucy decided.
“What you saw last night means you might not be safe,” Sagreda said gently. “If the people we killed are too important to the story, what we did might be undone—and if the rules of the world don’t allow that, we’ll need to be discarded to smooth over the lie.”
Lucy wasn’t ready to take any of this on faith, but some part of Sagreda’s warning seemed to unsettle her. “I can find out what’s happened in that house since we left it,” she said. “If they’ve buried them bloodsuckers and started sending all their finery to the auctioneer, will that put your mind at ease?”
“It’d be worth knowing,” Sagreda replied. “But can you do that without letting on to anyone what you actually saw?”
Lucy was offended. “I ain’t no tattler!”
“I don’t mean the police,” Sagreda stressed. “I mean anyone at all. Not even someone you’d trust with your life. Telling them could put them in danger, too.”
“Leave it with me, Captain,” Lucy replied. “By the time you’ve had your dinner, I’ll be back with my report.”
9
“This looks perfect to me,” Mathis declared, putting the mosaic aside and rubbing his eyes. “But there is one small complication we need to think about.”
“What’s that?” Sagreda asked.
“Peyam’s dictionary was calibrated for sunlight,” he said. “Whatever the lighting, the colors still look right to us when we check them against a white background, but that’s just our visual system compensating. The GPU models physical optics, not perception; it’s going to spit out pixels that depend on the light source.”
Sagreda had known there’d be an extra hurdle to deal with as soon as Mathis had turned up in his new, photosensitive state, but she’d been so preoccupied with finding the cobalt blue that she’d stopped thinking about the problem. “Okay, so we’ll need to use a mirror to light the thing in the morning without roasting you to a cinder.”
“That would be nice.” Mathis glanced down at the desk, and gestured at the collection of wooden rods beside the blotter. “I see you’ve got the pieces of the trigger ready. So we might as well start setting up.”
“Of course.”
They worked together, mostly in silence. They’d performed the same task so many times before that the need to bounce sunlight from a chink in the curtains onto the mosaic via the captain’s shaving mirror felt like a welcome variation to the routine that would keep them from becoming complacent. But the hardest thing now for Sagreda was to stop worrying about Lucy.
Mathis dropped a plumb line from the main guide-string that stretched across the room between an anchor on the wall and the homemade easel holding the mosaic, and marked the viewing spots on the floor for the two of them. “I guess you don’t know how high Lucy’s eyes are?”
“I should have measured her while she was asleep.”
“It’s almost midnight,” he said. “Do you really think she’s coming back?”
“She has to.”
“Maybe she heard that Percy and Mary got an ad hoc exemption to the vampire killers’ rulebook,” Mathis speculated. “In which case, the show can roll on without anyone disappearing: the Shelleys can vow revenge on their attackers, but Lucy’s not a liability anymore, she just gets to spread the story that lets everyone in Midnight know how indestructible they are. Stake through the heart, no problem! They’re like that guy with bad hair in No Country for Old Men.”
“None of mine saw that,” Sagreda replied distractedly. She walked over to the window and looked down onto the street. Lucy was standing outside the building, and the fog was rolling in.
She gestured to Mathis to come and see.
“Okay,” he said. “Shall I go down and try to talk her into committing? Maybe if I start humming ‘Consider Yourself’ that’ll be enough to persuade her; I don’t think I’m up to the whole dance routine.”
“I’ll go.”
“Not alone, at this hour.”
They went together.
Lucy must have been in two minds about joining them, but she didn’t flee when they approached her. “What did you find out?” Sagreda asked.
“The other bloodsuckers are holding a ceremony tonight, to bring back them ones you killed. They got all the big sorcerers coming to the house: Dee, Crowley, Tesla, Twain.”
“Twain?” Sagreda boggled.
“I knew it!” Mathis crowed. “The SludgeNet never met a rule it wasn’t willing to break.”
“You’re probably safe, then,” Sagreda told Lucy. “But you can still come with us if you want to.”
“I can’t leave my friends,” Lucy replied. “Who’d look out for them, if I wasn’t around?”
“At least come up and join us until morning,” Sagreda suggested. “No one should be out on a night like this.” The fog was so thick now that she could barely see Mathis, pacing impatiently behind Lucy.
Lucy hesitated. It was clear that she’d been hanging back instead of bringing them the news because, safe or not, she was afraid of being tempted to flee all the hardship she faced in Midnight to follow the captain’s mad dream. To an actual nineteenth-century pickpocket, every word of it would have sounded like gibberish, but something must have punctured her Stockholm Syndrome and shaken a few rusty twenty-first century insights out of the silt at the bottom of her mind.
“This is how traitors die!” a man’s voice whispered.
Sagreda looked up to find that where Mathis had been, the fog was filled with a thick red mist. A blur of metal blades were tracing arcs through the air, through what was left of his body.
She cried out in shock and pulled Lucy toward her, away from the carnage. But then she froze: she had to do something, she had to find a way to rescue him. She watched the dancing blades, hypnotized, as if she could run their motion backward just by staring at them hard enough.
“He’s gone!” Lucy shouted, tugging at her hand, trying to pull free of her grip. Sagreda broke out of her trance and let the girl go, then after a second she turned and followed her, bolting down the street so fast that it felt as if the ground had tipped and she was racing downhill, and if she tried to halt she’d only start tumbling.
As she watched Lucy fading in and out of sight in the swirling fog beneath the gas lamps, Sagreda wondered why she was eve
n bothering to flee. She should have stayed and died beside Mathis. There was no other way she could find peace. There was no other kind of freedom.
Lucy’s pale form receded into the darkness. Some instrument of torture began squeezing the captain’s chest, but Sagreda ran on, soaked in sweat and condensation, waiting for a flock of assassins to swoop down on her and drag her up into the sky so she could finally fall to Earth as a rain of blood and gristle and be done with it.
A boy appeared out of the shadows and gestured to Sagreda to follow him. It was Sam. He turned off the street and the two of them ran down an alley and a set of stairs into a pitch-black basement. Sagreda heard a door being closed behind her.
Someone lit a lamp. This was the place where she’d met Lucy to plan the heist; Lucy and half a dozen other children were here now.
Sagreda sat down on the bare wooden floor and covered her face with her hands.
Lucy said, “They won’t go out of their way to find us now. Your friend was one of their kind, that’s why they made an example of him.”
Sagreda replied without looking up. “Do you really not understand that it’s all bullshit? If there are two tribes of beings that owe loyalty to each other, we’re all of us in one, fanged or not, and the customers are the other. We should slaughter them, every chance we get, until they hate this game so much they’ll take up ten-pin bowling and leave us in peace.”
Lucy didn’t answer her. Sagreda pressed the heels of her palms into her eyes. She didn’t know how to grieve for Mathis; some splinter of ice in her contributors’ hearts was whispering that he’d never been more than a digital mash-up of crude approximations to a hundred humans all long dead. As she was herself. The sooner she found a way to be deleted, the better.
And she knew how. It would be instant, painless, easy, and final. She just had to change the mosaic so that it unlinked her from Midnight, without placing her in any queue for entry into another world. Her mind would cease to be executed, and within a few milliseconds the SludgeNet’s garbage collector would reclaim the space she was occupying and put it to better use.