by Allan Kaster
Sagreda uncovered her face and wiped her tears away with the back of her hand. “Thanks for all you’ve done for me, but I need to go now.” She reached into her pocket, took out all the coins she had, and placed them on the floor beside her. Then she rose to her feet and started toward the door.
Lucy said, “Just stay until dawn, Captain. There’s nothing now can’t wait for morning.”
Sagreda stopped where she was, and Lucy came and led her—as she might guide a lumbering, docile animal—to a mattress in the corner of the room.
10
Sagreda was woken by a narrow shaft of sunlight that had entered the basement. The beam wasn’t even touching her skin, but the illumination it brought into the room was enough to penetrate her eyelids and drag her out of her broken sleep.
None of the pickpockets were awake yet. Someone had removed the captain’s shoes and left them by the mattress, so Sagreda picked them up and walked quietly to the door. It was better to have no goodbyes.
She was halfway back to the captain’s lodgings when Sam appeared beside her.
“What do you want?” she asked numbly.
He hesitated, as if gathering his courage. “I remember watching Neil Armstrong step onto the Moon,” he said.
“Congratulations,” Sagreda replied. She wasn’t being sarcastic, but she didn’t know what he expected her to do with this confession.
“Lucy told me all your stories, but she only half believes them,” Sam persisted. “I know they’re true.”
“So you know where you are, and what you are.” Sagreda shrugged. “Good for you. I wish you luck making something of it. I tried, but it came to nothing.”
“You can’t give up!” Sam said, alarmed at her indifference. “I need you to teach me what you know. I can’t keep living here, half-starving all the time, pretending all this supernatural gibberish is true. Pretending I’m a child, when I’m not. I need to learn how to escape.”
Sagreda strode on in silence, listening to the clomp of horseshoes on the road beside them, trying to find the words to brush him off without making herself feel like a monster. It had taken Peyam months to explain all the intricacies of the traveler’s art to his students. She wished the boy well—or the man, presumably—but she didn’t have it in her to stick around for that long.
They were almost at Mrs. Trotter’s house when the solution came to her. “If I offered you The Great Gatsby meets The Three Stooges, would that sound like a place you could live in for a while? Flappers, cocaine, Keystone Cops . . . what more could you want?”
“Will you be coming with me?”
“No,” Sagreda replied, “but I can give you the names of half a dozen people there who’d be willing to teach you everything. A lot of travelers reach that world and decide it’s good enough.” And since it was the last place she’d been, following the same linked list that led to 3-adica, it would only take a small change to the mosaic to send the viewer backward along the chain instead of forward.
Then she could scrub the whole forward/backward part and unlink herself from everything.
When they reached the house, she saw the dark stain on the sidewalk, but she kept it in her peripheral vision and refused to think about it. She led Sam up to the captain’s rooms and wrote down her list of contacts.
“‘Tire-Iron McGill’?” he read dubiously. “‘Cyanide Sally’?”
“Don’t worry,” Sagreda reassured him. “It’s not like meeting ‘Saw-Tooth Jim’ on a dark night in Whitechapel. All the violence is slapstick.”
“So why didn’t you stay?”
“Because everything else was slapstick too.”
Sagreda took Sam’s measurements. The sun was coming through the curtains, shining off the mirror and falling straight onto the mosaic; she pictured Mathis standing beside the easel, in the first body she’d ever seen him inhabiting. But she blinked away her tears and concentrated on the geometry, finding the optical center for Sam’s close-set eyes, dropping the plumb line, and outlining two footprints in chalk on the floor to make it easier for this novice to view the target squarely.
There was a knock on the door.
“Just wait here and keep quiet,” Sagreda told Sam.
When she opened the door, Mrs. Trotter was on the landing. “Captain, I’ve been forbearing,” she said, “but there are limits to my good nature.”
“I don’t follow your meaning, Mrs. Trotter.”
“Your gentleman caller who was killed last night! And the girl . . . and now some ragamuffin . . . !” Mrs. Trotter shook her head. “This is not a home for wayward children and unnatural dandies. I was expecting you to be a reputable tenant. Instead, you’ve made me the target of gossip from here to—”
“I’ll be gone by the end of the day,” Sagreda interjected bluntly. “Feel free to sell all of my possessions, or just throw them onto the street if you prefer.” She bit her lip and managed to say nothing about the bodies.
But even this announcement didn’t mollify Mrs. Trotter. “I never heard such a thing! Scarpering to the continent to escape your punishment for some wickedness, I’ll wager! Let me in, Captain. I want to see exactly what mischief you’ve been up to!”
“Just mind your own business, woman,” Sagreda replied flatly.
“This is my house!” Mrs. Trotter shrieked. “Whatever goes on within these walls is my concern!”
Sagreda slammed the door and bolted it. As she walked down the hall, she heard the sound of something falling to the floor in the sitting room, where she’d left Sam waiting. “Did you knock over the—?”
Sam was sprawled on the carpet. “No, no, no!” Sagreda checked his breathing and his pulse, but he was gone, irretrievably. “I told you to wait.” The commotion must have panicked him and made him think he might be losing his last chance to escape from Midnight. But Sagreda hadn’t got around to explaining that she’d need to change the mosaic before it would take him to the benign, almost familiar world she’d promised him.
His mind was now in the queue for 3-adica, and he had no idea what he’d be facing when he woke. Lucy might have told him some small smattering of what she’d learned, but even she had been in no condition to find her way around there on her own.
Mrs. Trotter was pounding on the door, and promising that seven kinds of constable would arrive at any minute. Sagreda wrapped her arms around the captain’s wide shoulders and rocked back and forth silently for a while. “I’m sorry,” she whispered, as if she owed Mathis an apology for doing what he’d almost certainly have wanted her to do.
She picked up Sam’s limp body and placed it on the sofa. Whatever kind of man she’d just dispatched to the afterlife, the fact remained that he’d be as unprepared to face it as any child. She tied a string around her waist, joined the other end to the easel so there’d be no more casualties once she’d fallen, and found her mark on the floor.
She looked up, and in the corner of her eye she saw the Escher-esque shape she’d built from the wooden rods: a cube that wasn’t actually impossible, merely unanticipated by some sloppily written graphics code. She shifted her gaze a fraction, bringing both the trigger and the mosaic into perfect alignment, and then she was gone.
11
Sagreda kept her eyes firmly closed, trying to get a sense of her new body from within before confronting the world around her. She felt sure that her spine was horizontal, with her chest facing down as if she were kneeling on all fours—but the task of bearing her weight seemed to be concentrated at the far ends of her limbs, not her elbows or knees. For most people, that would have felt awkward and strange, but all her joints and muscles were telling her that this posture was perfectly natural.
Apparently, she’d been reincarnated as a quadruped.
That probably ruled out the simplest version of 3-adica she and Mathis had contemplated: a kind of stylized mathematical fantasia, in which the participants (in fully human form) rode on a magic carpet over a fractal landscape of numbers that was ultimately just a prett
ified CGI version of the nested eggs she’d drawn for Lucy.
But those eggs didn’t really get the distances right; there was no way to choose points on a plane with all the right properties. The more radical, immersive approach would be to embed the characters in the 3-adic geometry itself, transforming them from spectators into participants. The problem, then, was that the human mind had evolved to work with its body and senses immersed in three-dimensional Euclidean space, and the SludgeNet wasn’t remotely smart enough to rewire a comp to perceive its environment on any other terms—let alone work the same magic on its flesh-bound customers.
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 loath 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, and 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 bodybuilder, 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?