The vehicle’s gentle sway lulled Sean to sleep only to rudely yank him awake whenever Mrs. Lambert slammed the brakes. Which was distressingly often. His phone beeped a text receipt.
Tiffany: Memorial Park 6 to 7pm, basketball court. If u wanna talk.
Sean straightened up banishing all thought of sleep, looking out the window to get his bearings. They were approaching the outskirts.
“Mrs. Lambert, could you please drop me off at, um... the exit after next? I’ll ask my mom to pick me up,” Sean reached into his backpack, pulling out the case containing SculptSight, “And please give this to Randall, I’ll collect it from him later.”
“If you’re sure?” she frowned, “it’s not the best part of town.”
Dusk painted the clouds pink when Mrs. Lambert dropped him off at the edge of Memorial Park. She drove away muttering about sketchy neighborhoods. The park was in disrepair with foot tall grass interrupted by crumbling sidewalks littered with hardened geese droppings and dead leaves of the fall. A swing set hung from rusted chains creaking in the breeze. Willow trees lined a large pond, its thermal mass resisting the coming freeze and reflecting the darkening sky. Shouts of laughter drifted from ahead. A basketball court next to a skateboard rink, lit by halogen lamps flickering ineffectively in the lingering twilight. Weeds poked through a broken expanse of concrete where silhouetted figures clustered, throwing long moving shadows as one of them threw a ball at the hoop.
Sean approached cautiously, ready to bolt if this was an ambush. He swore to himself that the Collection Agency would never get another crack at him. His breath caught when he spotted her. She lounged on one of the benches bordering the court, legs crossed. Her golden hair gleamed in the lamplight. Sean approached warily, his eye on the small group prancing around the court. They were a motely-looking lot, middle schoolers judging by their heights. Sean relaxed. They were no threat, even if they ganged up on him.
Tiffany might have stepped off the pages of Teen Vogue, with her pale Aeropostale jacket and skirt. Her red boots were a startling splash of color in a scene of browns and greys. Sean frowned. She didn't belong here. The east end of the city was a rough neighbourhood in contrast to the affluent west end. The gutted shell of a 70's housing project loomed beyond the edge of the park, underscoring the incongruity of an upper-middle class girl loitering in the armpit of Portsmouth. She noticed him, her smile faintly predatory.
"I won't bite," Tiffany patted a spot on the bench. A purse lay on her lap, its strap looping over her other arm that rested on a bulky duffel bag.
"Um, you want to go for a walk?" Sean gestured in the direction of the park entrance, "Maybe find a burger joint?"
"This place not good enough for you?" she gestured at the rundown ambience, smirking.
"No, it's... it's fine," Sean protested and sat down. He couldn't stop staring, now that he was inches from her perfect face. The lamplight seemed to halo her golden crown with unearthly beauty. Her slightly upturned nose took the sting out of her smile making it whimsical instead. Noise from the kids goofing about filled in the conversational lull.
"Gonna say something, dork, or just drool at me all evening?" Tiffany's smile faded.
"Why help me escape from Jason’s minions?" Sean blurted, "And the week before, you tipped me off that Jason had something nasty in store for me. The Collection Agency as it turned out. Trying to hedge your bets? Save your ass if Jason gets in legal trouble?"
"Legal trouble," she scoffed, "Half the county works for Jason's dad. Any idea how much clout his family has ?"
"I can guess," Sean grimaced, old bitter memories seeping through the cracks. The school administration certainly knew which way the bread was buttered.
"Because I know what Jason's tender loving care feels like," Tiffany pulled off her jacket and twisted around to face Sean, "And because you don't seem like a total loser anymore."
The jersey tank top left her arms bare. Dark blue bruises banded her left shoulder in stark contrast to pale skin, imprints like encircling lace. Faint bands of sickly green crisscrossed her other arm, fading memories of past trauma.
"Did... he hurt you?" Sean hissed, clenching his fist.
"Jason gets very possessive of his toys," Tiffany gave a twisted smile as she slipped back into her jacket, "especially when his toys don't want to play with him. But he never forgets to send me some foundation cream after he takes a belt to me. So the bruises don't show during cheerleading practice."
"Nice of him," Sean spat, feeling sick, "why the heck don't you report the bastard? Principal Stewart can't possibly let that slide. What's a smart girl like you doing with a dipshit like him anyway?"
"Rich dipshit," corrected Tiffany, "There was a time I needed his... resources. Now that I have a paying internship, I don't need Jason so much anymore. But he won't let me go. And if I report him, Jason's lawyers will find a way to pin this on my foster parents."
"Foster parents?" Sean stared blankly.
"Been shuttled between foster homes since I was twelve," Tiffany shrugged, "My birth mom was too drunk to care for me. Never knew my real dad. My life in a nutshell. Couldn't afford anything until Julia Thornton found me through a science talent search."
"But... but your clothes and stuff," Sean stammered in disbelief, "I thought..."
"Thought I was an upper class princess, didn't you," Tiffany bared her teeth, "I learnt to play the part after Jason got me into his social circle. The apartment where I'm fostered now is located as far east it can be within the Portsmouth school district and still be assigned to Cardiff High. So there's that."
"Wait... you live around here?" Sean gaped at the silhouttes of the low-income high-rises in the background.
"Dial down the snobbery, asshat," Tiffany scowled, "You aren't exactly rolling in cash yourself,"
"I... I didn't mean..." Sean flushed, "I meant... it must be tough being a foster kid..."
"Tough?" Tiffany snarled, her pretty face twisting, "You have no idea what it's like. At least you have parents you can call your own... who didn't discard you like so much..." She paused and sighed shakily, "Never mind. My turn to interrogate."
One of the kids in the court wandered up to them, holding a basketball, "This shmuck bothering you, Tiff?"
He was a pudgy boy in dreadlocks, wearing frayed jeans shorts and a sports tee shirt too big for him. He sounded like a squeaky middle-schooler trying hard to make his voice sound deep.
"Get lost kid," Sean waved dismissively.
The boy gave him a withering look, "Only Big Sis gets to tell me that."
"It's OK, Jaylen," Tiff smiled slightly, "Ready to calibrate your shots?"
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Jaylen nodded and Tiffany opened the duffel bag to reveal a one foot cube framed in wood and crammed with transparent plumbing in a miniature version of the analog solver Sean had seen earlier that day.
"Pick a spot for Jaylen, will you," Tiffany indicated one of the hoops for Sean who shrugged and lobbed a pebble through the gaggle of kids chasing each other around the court with loud yells.
Jaylen scowled as the pebble landed midcourt. The boy stared between the spot selected and at the hoop for a little longer as if mentally pacing out the distance. Then he crouched before the analog fluid device, quickly pouring water from a fresh bottle into an array of little glass funnels. As the water dripped through spigotted orifices, Jaylen cranked a bronze ratchet through a graduated dial that varied the flow metered through each spigot in a predetermined ramp.
Sean leaned closer for a better look at the gizmo, vividly aware of Tiffany's proximity. A stray strand from her hair tickled his cheek and it took all his self control not to be a creep. He gritted his teeth and thought of the promise of Sculptsight, of how much easier this would be if Tiffany wasn't so 'hot'. But then Sean wouldn't be so motivated to be here, he admitted to himself. Water was pooling into glass bulbs and then cascading through a second set of metered orifices. Second order differential equations being solved in parallel, Sean nodded thoughtfully. The weight of accumulating water opened up spring-loaded relief-valves to vent outside, diverting part of the flow from the primary path, probably to represent atmospheric drag on the basketball given the context.
Jaylen who had been staring at the water display with zen-like concentration got up suddenly and moved to midcourt. He hefted the ball and after a few trial feints threw it in an high arc that terminated perfectly through the basket hoop.
"You've got to be kidding me," Sean stared in disbelief, "Tell me he's been practicing for a while."
"He has," nodded Tiffany, "but his accuracy has really taken off since he's gotten the feel of all possible ballistic solutions by studying my analog integrator. Any basketball player is solving these equations subconsciously ofcourse, but I wanted to see if the learning curve could be consciously speed up."
"Couldn't he do the same thing on a computer screen?" Sean frowned skeptically.
"I don't think it's the same thing," Tiffany shrugged, "there's something... tactile about watching water flow that you don't get with a computer display. Anyway, just a trial run for what I want to do with low-tech computing."
"For your post-nuclear utopia?" Sean quirked a smile..
"Julia Thornton is crazy," Tiffany laughed, "she's been dealing with the dark side of international politics for so long, she sees doom everywhere. No, I want to make people smarter."
"How?" Sean stared mesmerized by her laughter.
"These analog cubes are so intuitive an elementary school kid could use it," Tiffany's eyes shone with passion, "Just think... a billion of these scattered across a continent. A new generation of children who can model their environment as intuitively as seeing or talking. Homo sapiens mathematicus. What problems can't they solve? Our world is messed up from our own stupidity. We are the stupidest species that can build a civilization. We need to do better, if we want to salvage the fucking planet..."
"You remind me of another girl," Sean whispered almost to himself.
"Oh?" Tiffany's tone was sarcastic, "You're saying the girls you hang out with look like me? Not subtle, are you?"
"I was talking about Judith Fuller..." Sean flushed, "Not saying she looks like you or anything... maybe just a little... it's just that she also wants to save the world so badly. She's been on my mind since she fell sick... "
"It's OK," Tiffany looked at her feet, "Judith's a nice girl. Not everyone in Jason's family is a skirt-chasing piece of shit. But, like I said, it’s my turn to ask questions. You were badmouthing my design on the phone. Tell me what you can do better, hotshot, or admit you're full of shit.”
From the duffel bag she pulled out and unfolded a large A1 size drawing print on her lap. It was an exploded view of the plumbing nightmare packed into the much larger analog solver that Sean had seen in Tiffany’s workspace at ZeroSum. The CAD blueprint was crammed with neat handwriting in the margins and blank spaces. Rows of differential equations, progressively crossed out and replaced with more complex ones. Sean studied it in silence under the lamplight, his face brightening with interest.
”Well?” she demanded.
”This mess... um, mass of plumbing isn’t doing much,” Sean traced an especially intricate cluster of lines with his finger, “in fact they aren’t representing anything as far as I can tell.”
”No, they are stablizing circuits, you chump,” Tiffany retorted.
”Stabilizing circuit?” Sean frowned, “for what?”
“The numerical solution of course,” Tiffany rolled her eyes, “These equations are way more complicated than modeling basketball trajectories. That variable is population... this one is grain production... that one is disease fraction... they are all interconnected. You get the picture. But the fucking solution won’t converge. Everytime I run it with the exact same input, the answer diverges after a while. I keep adding auxiliary lines, to damp out sensitivity, but they won’t help. I can’t forecast shit with this.”
Tiffany suddenly smacked the bluprint hard, startling Sean. She sounded frustrated to the verge of tears, as she got up from the bench.
“Oh, is that it?” Sean looked bemused at her outburst, “Obviously, for certain inputs the answer will always diverge.”
”What... obviously?” Tiffany turned on him, “Why would the same inputs ever end up with different answers? That doesn't make sense.”
”Look, you have three differential equations for three variables. Call them x, y and z,” Sean tapped the paper, “they are all non-linear because each of these variables is a function of the other two variables. There is a periodic disturbance to represent seasonal rains or whatever. More importantly the system is dissipative, there is some loss that depends on the values of the variables.”
”Tell me something I don't know, you pompous prick,” Tiffany snapped impatiently.
“Don’t you see,” Sean demanded, “it’s a chaotic system. With a classic Lorenz attractor.”
“A classic what?” Tiffany paused.
"Edward Lorenz was a meteorologist who tried to model weather on a computer using a set of non-linear equations much like these," Sean explained, "and he too found that when he tried to forecast weather more than a few weeks ahead, the answers would end up very different for reruns with the same inputs. Turns out that rounding off the last few decimal places in the inputs was enough for the system to end up in completely different states. Coupled dissipative systems are super-sensitive to initial conditions. You'd need infinite precision to get the same answer every time, which ofcourse isn't practical in the real world."
"You're saying my project won't work?" Tiffany glared at him, and Sean thought her eyes glistening so brightly were achingly beautiful, "that's its useless for predicting stuff like famine or epidemics?"
"No, I'm saying you should look at the structure of chaos," Sean smiled, "rather than the exact state of the variables. Think of a swinging pendulum. If you plot its position on one axis and velocity on another, you get a phase portrait. If there's no damping the pendulum will oscillate forever and its phase portait is a closed loop. If there's any damping the phase trajectory will spiral down to the origin as the pedulum comes to a stop. Right?"
Tiffany nodded.
"When Lorenz plotted the phase portrait of his weather model in three axis," Sean held up three fingers to mimic a Cartesian coordinate system, "he saw that the trajectory would randomly spiral around one part of the phase space and then suddenly cross over to another region then spiral there, tracing out something like a butterfly. The exact path the system traces is very sensitive to initial conditions, don't even think of predicting that. But you could predict which attractor - which part of the phase space the system will orbit around. And if you time the disturbance correctly, you can flip the system to a new attractor. Impose your own order on the chaos."
"Is that possible?" Tiffany stared, an unreadable expression on her face.
"Put a mosquito in a box without sunlight," Sean pointed to the insects fluttering around the light bulb on the post, "and it will revert to a 23 hour cycle, not twenty four. Sunlight resets its default internal clock to the 24 hour circadian rythm each day. But there's a singularity within its phase trajectory. A light pulse in the lab precisely timed to that singularity will knock out its circadian clock and give it jet lag. The human heart regulates itself with an electrical wavefront propagating in three dimensions. Shock it exactly during its singularity and it will go into fibrillation. George Mines figured that out in 1914. To test it, he built and attached a gizmo to his chest to zap his own heart. To send its phase trajectory into a new attractor. He didn't survive the experiment, but the ECG was still recording his glitching heartbeat when they found him."
"How the heck do you know this shit?" Tiffany demanded shrilly.
"The shape of the clouds tells us the world is non-linear," Sean pointed up, "We never see the same shape twice. But life oscillates around attractors in phase space. And that's how we'll beat Jason. Not through violence or threats or official complaints. He's too strong and well-connected. But by visualizing his phase space and giving his social life some well timed shocks."
"We?" Tiffany gestured between them.
"We both want the same thing," Sean got up to look Tiffany in the eye, "You want to be free of Jason and he won't have time to abuse you after I'm done with him."
"Revenge of the Nerds," Tiffany laughed shakily, "Who else would think of phase space in a revenge fantasy."
END OF CHAPTER