Chapter Text
Harvard – October 6, 2039
Angela strolled through the halls of the Maxwell Dworkin building, trying to find room 227. She held her smartphone in her hand, looking down at it every so often to reassure herself that she was, in fact, in the proper building. Angela had arrived in Cambridge a week ago, and hadn’t quite found time to properly explore the campus properly yet. She eventually came to a stop in front of room 227, giving her phone one last check before walking in. It was 11:23, and the class she was trying to sit in on didn’t start until 11:50. She’d grossly overestimated how lost she thought she’d get, but this gave her time to catch up on some readings that her advisor had assigned her.
Today was supposed to be the first day of the semester, though Dr. Harold Winston was the kind of man who didn’t believe in waiting to start, so he’d already sent her a few thousand pages worth of research on nanomachines and distributed computing. Still, his eagerness was probably because Angela had proudly told him that she intended to solve the Overhead problem during her interview for the PhD position. Winston replied with a grin and a promise to hold her to it.
Angela took a seat towards the back of the class, by the door, pulling up a thirty year old paper titled “Molecular Communication for Nanomachines Using Intercellular Calcium Signaling” on her phone. Winston said he intended for her to follow the history of nanomachines, so she would have a strong understanding of the foundations. He also told her to sign up for some Computer Science courses, recommending CS161, warning her that at least ninety percent of her work would be programming.
Angela glanced up from her phone, noticing that she wasn’t alone in the classroom. At the front a girl stood by the whiteboard, her fingers smudged with blue ink. She had wavy black hair, with purple tips, and wore a dark grey Harvard hoodie that was definitely a few sizes too big for her. The girl hadn’t seemed to notice Angela, though, since her attention was fixed on the whiteboard. At the top left she’d written down series of symbols and Angela started translating them in her head. “Given a variable m, which is any arbitrary integer, show that m squared modulo seven always equals 0, 1, 2 or 4.” Angela set her phone down on the desk in front of her, studying the girl’s work.
The girl heard the phone clatter against the desk and spun, looking around. She paused when she noticed Angela, “Oh, uhh, hi?”
Angela waved at the girl, “Hello there. Is this the right classroom for CS161?”
The girl nodded, “Yup, though it doesn’t start for err,” she checked the clock in the back of the room, “Another 25 minutes.”
“Yeah, I’m new to the campus, so I gave myself a bit too much time to find the classroom,” Angela looked down at herself, feeling slightly overdressed. She had worn a white blouse and trousers, with a heavy red coat and boots. Meanwhile the girl in front of the classroom was wearing a hoodie and flip flops, which made Angela wonder how her feet hadn’t frozen off yet. “Oh, I’m Angela by the way.“
Olivia,” the girl muttered, turning back to her problem. Olivia had written down the first twenty square numbers, along with their modulo 7. Sure enough, as the problem implied, there was a repeating pattern of 0, 1, 2 and 4, though from what Angela could see, Olivia hadn’t made much progress towards answering why exactly the pattern occurred.
Other students started to flock into the classroom, and Olivia erased her work from the board, taking a seat at the front of the class and pulling out her ThinkPad. At 11:50 the professor arrived and class began. Angela had always preferred to take notes by hand, finding that she was too easily distracted when she had access to the internet, though she found herself stealing glances over the other students’ shoulders, trying to catch a look at Olivia’s back. Eventually she decided that she didn’t really need to know what was on the syllabus, and she wrote down the problem that had been on the white board, along with the list of square numbers.
Angela had taken some proof based courses during her undergrad studies, even though she hadn’t been required to. Every single one of the great minds in history seemed to have a strong background in mathematics, and Angela had always intended to stand on their shoulders for the best view she could get. So following in their footsteps and taking math courses had seemed like a natural decision.
As the professor rambled on about how grades would be distributed, Angela found herself lost in the world of numbers. Seven was a prime, so she’d initially thought there might be some significance to that, but exploring the modulos of prime numbers had led her nowhere. She found herself staring at the square numbers. On a whim she changed the base of the numbers to seven and the pattern started to open up, revealing a tantalizing glimpse of the ever elusive why hidden behind the numbers.
By the time class ended Angela had written out a solution in her notebook. She tore the paper out, watching the other students flock out past her desk and out of the classroom, debating if she should approach Olivia. Eventually Olivia walked by and Angela stood up, getting a look at her face. Olivia had deep purple eyes, along with one of the worst cases of resting bitch face she had ever seen. Angela held out the piece of paper, “Olivia, right? Here.”
Olivia took the paper, narrowing her eyes at it, “I’m not interested.”
“Oh, uhh, it’s not my number. Though there are many other numbers on there!” Angela gave a goofy grin, holding her thumbs up. Olivia rolled her eyes, opening the paper and reading as she walked away. Angela headed out too, walking in the opposite direction of Olivia. She pulled her phone out, checking her schedule. Angela’s next appointment was a lab meeting with Dr. Winston in two hours; more than enough time for a quick jog. A hand suddenly tapped on Angela’s shoulder, and Angela turned, seeing Olivia standing behind her, out of breath.
“Did you just run across the hallway?” Angela said as Olivia took a second to compose herself.
“Y-yeah,” Olivia said, “Hey, uhh, sorry, what was your name again?”
“Angela. Angela Ziegler,” Angela said.
“Okay, any chance you didn’t remember my name?”
Angela shook her head, “It was Olivia. I just said it.”
“Ah crap, now I feel like an asshole,” Olivia flashed a sheepish smile, looking dangerously cute for an instant, “Can I buy you a coffee?”
Angela glanced down at Olivia’s hand, which was still holding onto her proof, “I think that depends.”
“On?”
“Did you understand my proof?”
Olivia held the piece of paper up, “Well yeah, but how the hell did you think to change the number base?”
Angela smiled warmly, “Now that’s a conversation I’d love to have over coffee.”
__________________________________
Olivia led Angela to the LISE building, which had a cafe in the entrance. On the walk over she’d gotten a better look at the tall stranger, deciding that she was worth impressing with a proper drink, “Go ahead and get whatever you’d like,” Olivia said when they stepped in, gesturing for Angela to step ahead of her in line.
Angela approached the counter, ordering a black coffee with a splash of milk. Olivia ordered a caramel mocha, paying for both their drinks and following Angela to a seat. Angela had clasped her hands together, glancing out into space. She had wild blonde hair that she’d forced back into a ponytail, and a thin pair of metal frames sat on her face over her bright blue eyes. Olivia plopped down in the seat across from her, setting their drinks down, “Hey, uhh, sorry again. I thought you were just some basic bitch trying to get in my pants.”
Angela laughed softly, and the sound was sweeter than any mocha Olivia had ever had. Angela cleared her throat, “Okay, so look at this. If we take the numbers 1 through 10 and square them we get 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. If we them modulo those with 10 we get 1, 4, 9, 6, 5, 6, 9, 4, 1 and 0. Now take 11 to 20 and square them. 121, 144, 169, and so on. If we take those and modulo them with 10 we get the exact same sequence of numbers.”
“Right that’s because the last digit of a product is only affected by the last digit of the two multipliers, and modulo 10 just gives the last digit of a number” Olivia leaned closer to Angela, smelling the coffee between them.
“You’re almost there, Olivia,” Angela grinned, “I think I’ll let you stumble around a bit.”
“Oh come on!” Olivia pouted before turning back to the paper. She blinked, looking at the sequence of base 7 numbers Angela had written. “Oh,” she flatly said. “Okay, yeah I’m an idiot. When you’re in base 7 the last digit of the square numbers can only end with 0, 1, 2 or 4 because only the last digit matters. And when we’re in base 7, the last digit is the solution to that number modulo 7.
“Exactly,” Angela drank some of her coffee.
Olivia rested her forehead in her hand, staring down at the paper, “That’s incredible. Don’t tell my number theory professor you gave me the answer, okay?” She looked across the table at Angela, who was quietly watching Olivia think, “You said you were new on campus?”
Angela nodded, “I arrived in Cambridge last week. I’m starting a PhD in Biomedical Engineering.”
“Wait, why are you sitting in on an undergrad CS course?”
“My advisor said he wanted me to get a stronger background in computer science, since it’s important for the work I’m trying to do,” Angela wrapped her hands around the cup of coffee, letting it warm her hands.
“Who’s your advisor?” Olivia folded up Angela’s proof, sliding it into her backpack.
“Dr. Harold Winston, I’m in his Nanomachine Research Lab.” Angela picked up her coffee, holding it to her lips.
“Woah! Whose dick do I have to suck to get in on that action?”
Angela spat out a bit of coffee back into her cup, coughing. Olivia grabbed her water bottle from her backpack and offered it to Angela. Angela took a drink of water, coughing again, then looked back at Olivia, “I’d say Winston’s, but he’s a bit too straight edge.” She handed Olivia her bottle back.
Olivia took the bottle, studying Angela, “Hmm, what is your thesis going to be about?”
Angela’s eyes lit up and she drained her coffee, “Have you heard of the Nanomachine Communication Overhead Problem?”
Olivia squinted, racking her brain, “I can’t say I have.”
Angela pushed her glasses back up her nose, “Okay, so right now nanomachines are capable of executing a preset sequence of commands, which is why we’re capable of those demonstrations where they form random shapes. However, all those demonstrations happen in extremely controlled environments, and there aren’t any decisions being made by the swarm of machines beyond where to go. The Overhead problem states that in order to have a swarm of nanomachines react dynamically to real life problems, we would have to use most of each individual nanomachine’s processing power to communicate with the other machines in the swarm; meaning that there’s no effective way to have a robust system of nanomachines that can react to unknown variables.” Angela placed both her arms against the table, supporting herself as she almost closed the space between the two, leaning in close enough for Olivia to faintly smell lilies.
Olivia found herself pulled in by Angela’s enthusiasm, losing herself in the PhD student’s blue eyes.
“IEEE has a 5 million dollar reward for anyone who can solve the problem, or prove that it’s impossible to solve,” Angela noticed how close she was to Olivia and pulled back suddenly, “Err, yeah. That’s what I’d like to do my research on.”
“Huh. Why’s that?”
Angela rubbed the back of her neck, “You know those healing beams that are in videogames?”
“Oh yeah! Like in TF2,” Olivia smiled.
“Exactly like in TF2,” Angela tilted her head, “Though that game is over 30 years old. Why do you know about it?”
“I could ask you the same question.”
“Would you believe me if I said that I tracked it down and played it to get inspiration for my research?”
Olivia raised an eyebrow, chuckling slightly, “Y’know, you had a window where you could’ve convinced me that you were this graceful aloof intellectual.”
“Ah, curses, I assume it’s long since passed,” Angela let out an exaggerated sigh, “Now you know the truth.”
“You’re an absolute dweeb. Don’t worry though, I prefer dweebs.”
Angela held her arms apart, “Guilty as charged. So, how about you? You’re in CS right?”
Olivia nodded, “I’m doing a double major: CS and math.”
“Hard to go wrong with those, why’d you decide to study them?”
“I don’t know if I’m quite ready for you to discover how much of a nerd I am,” Olivia finished her caramel mocha, wiping whipped cream from her lips.
“You’re the one that brought TF2 up in the first place,” Angela slyly grinned at Olivia, “And you’re the one that was doing math on the whiteboard before class began.”
“Oh right, damn,” Olivia rubbed her chin, “I, uhh. I really like computers,” she trailed off.
Angela let out a soft laugh, “It’s usually good to like the thing that you’re studying.”
“No, I,” Olivia sighed, “It’s just that computers are everywhere you look. They’re the most important thing humanity has ever invented, and when you get down to it, everything in a computer comes down to binary. We’ve taken the simplest possible thing: a 1 or a 0, a yes or a no; and turned it into systems so elaborate that we don’t even know how some of them work.”
Angela wordlessly gestured for Olivia to continue.
“And, well, math is just,” Olivia glanced at the ceiling, uncertain. After a minute she turned back to Angela, who was patiently waiting, “Math is our way of trying to express the rules of the universe, and every time someone opens a door it leads to a room with even more doors. It’s this endless journey of discovery that a small part of our species has decide to embark on. And, in a way, it’s as if there’s this small part of the universe reflecting back upon itself, trying to understand the very thing that it’s a part of.” Olivia looked back down, “One could argue that our attempts to understand the universe are just an extension of our desire to understand ourselves. And, uhh, y’know, why wouldn’t you want to be a part of that?”
“Perhaps I should learn more math,” Angela said.
“I could learn with you,” Olivia immediately replied.
“Are you sure you’re not just looking for someone to do your homework for you?” Angela flashed a knowing look to Olivia.
“As if I’d deprive myself of the thrill of discovery,” Olivia smiled, “How about meeting after the OS class? Are you usually free around now?”
“And what will we be learning?” Angela said.
Olivia leaned back, humming softly, “Let’s not constrain ourselves so early. We’ve got an infinite universe to explore.”
“Is this your way of saying you’ll figure it out later?” Angela hopped up, grabbing the empty cups and tossing them in a trashcan nearby.
“Miss Ziegler, however did you know?” Olivia stood up too, “I’ll make sure to bring a challenging problem for you to work on next time, okay?”
“Make sure it’s challenging for me, not just for you,” Angela teased.
“Oh, you’re going to regret that,” Olivia pulled out her phone, handing it to Angela, “Here, call yourself.”
Angela took the phone and called herself, verifying Olivia’s number once it popped up. They parted ways once they left the cafe, Olivia had another class and Angela had to make her way to her advisor’s office, both eager for the next session of CS161.