General Theory of Relatability

or solving the three-body problem

August 2021

Pop culture used to be about bad boys and sad girls. Now it's about sad boys and bad girls. Frankly, debating what's better is moot, and I'm not here to start a fight between Gen-Y and Gen-Z. I'll admit though that I do like both - I was born straddling the fence and often find myself jumping from side to side.

The following is an age-old story of boy meets girl - an homage to the 2000's rom-com. Heads up, each chapter [1-3] is also accompanied by a short lesson in control theory [i-iii]. These analyses contain no critical plot, and some readers may prefer to leave them to the end, or skip them altogether. Think of it as director's running commentary; optional yet insightful.

I'm also aware this might be a long read for some people. It's about the length of a TV episode or a lecture, so grab some popcorn and enjoy the show!

~1~
Ash met Blake in the summer before 9th grade. She was new to town, and had moved into the house next to his. An only child, her father had taken a job teaching freshman physics at the local university. Her mother had passed years earlier from cervical cancer, detected too late...

She had gotten used to raising herself. A little shy, a bit of a recluse, yet wise beyond her years. Perhaps it was puberty, or finding herself alone in an unfamiliar place, which made her yearn for companionship in ways she'd never felt before. Luckily for her Blake was nearby.

At a glance Blake was as typical a teen as he could be. Popular, sporty, and confident, yet with a kind of goofily adorable hometown charm. He welcomed Ash into his life without a moment of hesitation.

Such a seamless gesture by Blake meant the whole world to Ash. Every day they spent together that summer helped cleanse the misery of the years before. Soon they were inseparable, and Ash dreamed about what going to school with him would be like. Blake was her golden ticket to a normal life.

Yet as they rode the school bus on the first day back, sharing the music from her iPod, Ash couldn't help but notice the prying eyes pointing their way. "Maybe this is what it's like to be the new kid?" she thought to herself in denial. But the whispers only grew louder, and the rumours wilder as more kids got on the bus.

Boys are notoriously dumb at an early age - girls mature so much faster. Who knows what they might learn from observing young women instead of gawking and jeering?

Ash felt her anxiety slowly seeping in. She definitely wasn't used to the small-town stares. She leant into her single earpiece to try and drown out the noise, awkwardly resting her head on Blake's shoulder in the process. He was oblivious for a while, as though he were in a state of pre-game meditation. But soon Blake saw what was happening: how overwhelming the situation had become for her.

He sprang into action and waved over some of his friends who had just hopped on the bus. "Hey guys! This is my neighbour, Ash!" he introduced effortlessly, "She's new here and like SUPER smart - she'll fit right in!"

And just like that, her nerves vanished and the doubt was gone. She could not believe it. It was as if Blake's kind words had cast a spell on the entire room. They exchanged pleasantries - the mood swiftly switching to a comforting calm.

With a spring in her step that first day flew by. She dazzled the teachers with her wits, signed up for the science club and school band, and sat with the 'cool' kids at lunch. It was surreal. For the first time in Ash's life, SHE was part of the in-crowd.

The ride home was the polar opposite of that morning. No longer at the centre of attention, Ash beamed giddily with excitement in her seat. Adjacently, Blake was as cool and casual as always. In the blink of an eye, they arrived at their stop, and began their walk home up the hill.

They walked and talked on their way to the top. Or more accurately Blake listened politely whilst Ash eagerly recounted her day. Blake paused at the peak and turned to remind her, "Woah Ash, slow down. Breathe!"

She did. Processing for a moment before replying: "I just... had a really good day today." Honestly, this was an understatement. She had NEVER felt anything like this before in her life.

Then there in the heat of the moment she went in for the kiss...

And. It. Was. AWKWARD!

Between catching Blake off-guard mid-swerve, and the fact that she'd never kissed a boy before, it was really no surprise that her tongue ended up traversing from his top lip into his left nostril. Blake took a step back, visibly shook, as Ash looked into his eyes like a puppy who knows they've done something wrong - dreading what comes next.

Blake broke the standoff with a chuckle and a smile, his hand wiping the wetness off his face. Perfectly on-brand he joked: "I suppose you haven't read any books on kissing hey?"

"I'm sorry," she responded meekly, "I mean can you even call that a kiss?" knowing full well it was more of a vigorous lick.

"Hey, look, I'm not keeping score," Blake reassured her before adding: "but maybe we should keep this between ourselves? I mean you've been a really good friend to me this summer. We wouldn't want anyone getting the wrong idea you know?"

Ash's heart sank a little - she really had no other option but to agree. With her head screwed back on, her logical self began to bargain that hanging out with Blake as just friends would still be an overall positive experience.

Nonetheless a torrent of thoughts flooded her mind on the way down her street. Of course, she knew Blake was well within his right to rebut her. Sadly, that didn't stop the pain. There was a sticky sense of shame that Ash struggled to shake. She blamed herself for confusing friendship with love...

~i~
Let's take an intermission, and allow me to introduce you to the subject of Control Theory.

Contrary to what the name might suggest, control theory is not about propaganda or mind control. It's hardly Machiavellian - rather, it's the engineering principle of instigating and responding to change.

Given a thing that can be changed [Process Variable - PV], and a desired goal [Set Point - SP], control theory is primarily concerned with how you reach an end state [Stability]. Take the example of heating a room:

It's cold, and you want the temperature [PV] to be toasty warm [SP]. Maybe you could a) light a fire, or b) crank up the thermostat. For all practical purposes, both actions will respond to the desire for change, but in radically different ways.

Option a) is an example of Open-Loop control; set-and-forget, an approximate educated guess. Once a fire starts to burn it continues until it runs out of fuel. It doesn't really know or care about the room temperature, and will keep generating heat [assuming you don't put it out]. From experience or luck, you might get comfortably warm. But it also might not be enough. Or perhaps even burn your house down - this deviation is called the Error.

Option b) is an example of Closed-Loop control; taking feedback and altering your behaviour. Modern air-conditioning systems can sense the ambient temperature and adjust their outputs accordingly. As a result, the room will not deviate from the desired state by much; lower Error = more accurate Stability.

I've found that this analogy transcends engineering and applies to the real world in two ways. First is the importance of understanding that change is not instant [patience is a virtue], and second is that things respond far better when given feedback [communication is key].

Ash's strife was born out of naïvely applying a unilateral, open-loop approach to her feelings for Blake. A spiral in a vacuum, she is brought back to reality after expressing herself; thus closing the loop, and putting them stably on the same page.

~2~
Blake and Ash stayed good friends over the coming years. Their school had a reputation for being one of the best in the district, despite the lack of funding, and they both played their part in upholding it.

Athletically, Blake's swim team made state finals three years running. Academically, Ash's science team, debating team, chess team, and band consistently made the podium every time. Although Blake was a pretty lousy student, and Ash didn't know how to swim, it never stopped them from supporting each other at events religiously.

It's nice to have someone in your corner. Somebody to rely on. Especially when they have your back; rain or shine.

Romantically, Blake had dated a few girls from other schools. They were mostly swimmers too. You could say he had a 'type', but often that's where their similarities would end.

Ash was always low-key intimidated by the attractiveness of Blake's fit exes. She wasn't ugly by any standard, but remained convinced that she was under Blake's league. Blake had picked up on that vibe and had simply accepted that she probably still harboured a lingering crush.

Regardless, in the midst of 12th grade, there were so many more things to worry about besides dating. Studying for exams every weekday, extracurriculars every weeknight, and the quintessential high-school parties every weekend.

Well at least that's what they thought until THE NEW GIRL showed up...

Charlie was a mid-year transfer from the big city. The gossip train went into overdrive with theories about why she'd moved for final semester. Of course, kids are cruel and jumped straight to expulsion, seduction, corruption, or worse.

At first Blake and Ash sympathised with her, with flashbacks to the first day of 9th grade. This notion was immediately shattered when Charlie stormed into the cafeteria at recess:

"Listen up boys and girls! I've heard everything you've had to say about me and for the record not a single one of you are right!"

"No, I didn't get expelled!"

"No! I didn't f*ck a teacher!"

"And NO! my 'daddy' is not in jail!!!"

"Actually, it's quite the opposite. See, he's the new goddamn governor of this state. And do you know what that means? It means he needs to send his daughter to the BEST F*CKING STATE SCHOOL there is!"

"Yeah, that's right! You heard it right here, you're the best! So why don't we start acting like it? This is MY final semester and I sure as hell am not here to f*ck around! This year we're gonna take state champs for EVERYTHING you hear me!?"

"Who's with me?? Yeah. Yeah! YEAH!"

"THAT'S MORE LIKE IT! Let's show 'em what we've got! And all those preppy private school SH*TS can GO F*CK THEMSELVES!"

Such a brazen display of dominance was clearly a calculated Alpha move. Pure political diarrhoea but the audience sure lapped it up. Alas Charlie's pep talk managed to install the strangest mix of fear, motivation, and teen spirit in the air - right when everyone needed it the most.

Oh heck, did she have the bark AND the bite! Charlie made the swim team, the science team, and of course the debate team, amongst many others. Both hot AND smart, she was the whole package - the best parts of Blake and Ash combined.

Naturally, Blake and Ash ended up spending plenty of time with her. Interacting with Charlie was as easy as pie for Blake, and the way she flirted with him was a cherry on top. He could tell though that Ash didn't feel the same way.

Perhaps Ash was envious of her skills, or jealous of her getting close to him. Yet in Blake's mind he thought they were so similar. So Blake, being Blake, hatched a master plan: asking them both to tutor him... at the same time.

This was an absolutely terrible idea.

The three of them gathered in the library after school one Thursday; the topic: physics - theory of relativity. The mood was cold, and unusually quiet for Charlie. Light heartedly, Blake broke the ice, "You know I don't really get any of this stuff, but with two Einsteins helping me I know it'll be fine!"

The two tutors stared begrudgingly at Blake. After a moment Ash opened her textbook, "Okay. Let's see. What are we up to?"

"Time dilation." Charlie interjected.

"Right. Do you know the principle behind time dilation Blake?" Ash asked rhetorically, "Time passes slower for faster moving objects."

"It's like the saying: Time flies when you're having fun!" added Charlie, "an hour in the pool goes way faster than an hour of physics class yeah?"

"Um, yeah. Wait, no. I think... I get it?" mused Blake.

Ash [slightly irritated]: "Well it's not a simple as that. Time dilation only comes into play at astronomical speeds."

Charlie [inquisitively to Blake]: "Have you watched Interstellar?"

Ash [defensively]: "Yeah we saw it together last year."

Charlie [nonchalant]: "Cool, so time dilation is the reason why Matthew McConaughey's daughter is older than him after he leaves and comes back."

Blake [pondering]: "Ah yeah, makes sense."

Ash [grandstanding]: "But remember that velocity is relative. In an astronaut's frame of reference, the Earth could be leaving them as much they are leaving Earth. If you think about it this way then the astronaut could go away for years while time barely passes on Earth. But then how can you be older AND younger? This is what we call the Twin Paradox."

Charlie [going in for the kill]: "Although, it's not a 'real' paradox because there's a rational explanation. It's not just speed, forces like gravity affect time too."

Ash [scrambling]: "I'm getting there! So, it's the astronaut who experiences huge acceleration so they're the one who ages slower. Got it Blake?"

Blake [confused]: "Yeah. Nah. You lost me a while back. Please dumb it down for me?"

Charlie [flirtatiously]: "Fast, strong attraction keeps you young baby ;)"

This was the last straw for Ash. It was insufferable. She packed up her things and left without a word.

Blake didn't see Ash at the swim meet on Friday. She ghosted all his messages too. Looking out his window he could see she was just at home, ignoring him.

They spoke, albeit briefly, at a friend's party on Saturday night. Blake hadn't expected her to come. She said she needed to de-stress. Blake had brought Charlie along too and she was totally in her element. They played drinking games with the boys whilst Ash stuck to being a wallflower.

The night descended quickly from there. Blake lost the game of Kings Cup and had to drink a disgusting concoction of kitchen condiments. Like the blind leading the blind, Charlie accompanied him to sober up. At this point her advances ceased to be subtle, and next thing you know they were making out on the couch.

Mid-pash Blake pulled back, turned away, and vomited onto the carpet. Charlie wiped the spew off his face, then resumed making out as if nothing had happened. None of the witnesses seems to care except for Ash, who out of heartbreak and disgust went to find something stronger.

She laid her eyes on the liquor cabinet. She pulled down a bottle of whatever she could reach, and took a hefty swig. Her eyes welled up as she sat with her back against the wall - drinking to forget the kiss that was burning into her mind.

It seemed her cries were a call for others who also sought to drown their troubles. The floodgates were open and one-by-one sad, stressed-out teens toppled like dominoes around her. And that was last thing Ash remembered; a symphony of sadness singing her to sleep...

~ii~
Cue another cliff-hanger-copout-ad-break for my opportunity to shovel some more science down your throat.

The second tenet of control theory is Optimality a.k.a responding well to change. This is driven by the desire for fast, efficient, and accurate change; since fixing mistakes takes extra time and energy.

The term Transient refers to the behaviour of the Process Variable before it reaches a stable Steady-State. Consider another highly intricate thermodynamic problem that we face every day: setting the perfect shower temperature.

Say you begin by turning on the HOT water full blast. It scalds you, so you turn the HOT down and add some COLD water. Now it's disappointingly lukewarm, so you apply less COLD and up the HOT. Eventually via this cycle of feedback you'll get to have a relaxing shower.

This is the Goldilocks strategy [Under-Damped Behaviour]: lots of overshooting and undershooting before finally getting it just right. The opposite approach [Over-Damped] would be to slowly adjust the knobs, ramping up while you wait. Suppose that going slow and steady does win the race - but it comes at the cost of wasting excess time [and precious water].

The optimal control strategy is the one that gets it correct the fastest with the least amount of intervention [Critical Damping]. With enough knowledge and analysis of a system you can pick the perfect setting on the first try. Think about it, you probably already do this for your own shower!

Charlie's appearance disrupts Blake and Ash's stability. She raises the bar [SP] for Blake's affection [PV], prompting a transient shift in Blake's behaviour. Blake responds hastily, and ends up leaving Ash behind as she struggles to keep up.

~3~
Whilst the news of Charlie and Blake's hook-up spread like wildfire, other stories from the party didn't quite make the headlines. It took a few days for Charlie to find out what had apparently happened to Ash and she spread the news to Blake.

Blake dropped everything to support Ash, incessantly apologising for not being there sooner. Ash, withdrawn back into her shell, insisted that she was OK and didn't want his pity. Blake didn't know what to say. He had no cards to play. The hook-up was a catalyst for this whole ordeal but he couldn't turn back time.

"Charlie was the one that told me, you know?" Blake tried to console. "She's worried about you too."

"Do you honestly believe that? It's always theatrics with her," sobbed Ash.

"She really is quite a lot like you," replied Blake, as if that was meant to make her feel any better.

"WELL I'M LIKE ME! But you don't love ME at all!" she burst.

"I do! But... just in a different way?" Blake added before shutting up, conceding, and seeing himself out...

The rest of the school year dragged on slowly - time does not fly when you're not having fun. But true to her word as ever Charlie did manage to lead her teams to at least a few trophies.

For most of her high school career Charlie enjoyed playing puppeteer. She was never in the same place for long and so had perfected moving pawns to her delight. But behind the facade she knew this was simply a defence mechanism; to kill or be killed.

This time around it was different. Perhaps the pressure of being in the endgame got to her, or that she wanted to avoid a hollow pyrrhic victory. Whatever the reason, she seemed to feel remorse for her actions, prompting a shift in her strategy.

Despite Blake's eagerness she refrained from pursuing a serious relationship with him, stringing him along instead. The critics interpreted this as a power move. But in reality, it had more to do with the guilt of alienating Ash.

Slowly and surely, Charlie's plan had its intended effect; Blake, starved of attention, eventually made up with Ash. And enacting some sort of karma made Charlie feel better, like she'd given Blake a taste of his own medicine. Ash certainly noticed this, and so with a strange unsaid truce the three of them began to spend more time together.

By virtue, their love triangle became the centre of gossip and attention. Of course, Ash hated the limelight, and Charlie was used to it. But for the first time Blake felt torn between two worlds. Like the Moon, the Earth, and the Sun, they danced around one another - an endless cosmic soap opera.

Eventually the end of school arrived; a lacklustre affair. Graduation went by without a second thought, and at this point the wider audience abruptly lost interest. Now it was just their close friends following along; but these diehard fans sure as hell wanted to find out how this drama would end.

They didn't have to wait long either. As Charlie and Blake each drove a carload of teens down to her uncle's beach house, nobody knew that everything was about to reach the culmination.

It was a classic post-school party: drinking in the pool, fireworks on the beach, and the cheeky dose of skinny-dipping. A sight to behold, so young and free, as though a weight had been lifted off everyone's shoulders. Charlie finally let loose, unbound from the shackles of the reputation she had to uphold for her father. Inhibitions ran wild and countless combinations of pairings took place that night.

Yet as the champagne flowed free, neither Blake nor Ash felt particularly bubbly. Rather ironically, they felt empty inside. You could see a void of determination in their faces, faking smiles, nodding along, and pretending to be happy.

Then the time to play Seven Minutes in Heaven came around. Teens marched off two by two to do WHATEVER they wanted, the crowd waiting intently for the time to elapse, speculating about what was happening behind closed doors.

Perhaps by sheer luck, or by 'not-so-divine' intervention Ash and Blake were paired together. At first Ash was too shy to oblige, but as the peer pressure mounted and the liquid confidence kicked in, she thought to herself that this was what she had wanted all along. It wasn't at all the idyllic dream which she'd fabricated in her mind, but it would do.

Charlie egged them on, clearly drunk off her face by then. Blake took this as a sign, and perhaps out of a desperate desire to be able to feel SOMETHING, they entered the bedroom.

7 minutes turned to 8, then 10, 15, and 25 before the consensus ultimately agreed that they were banging. For everyone it looked like a deservingly happy finale to the ballad of Blake and Ash. A moment of celebration washed over them like rain... and in the next instant they were distracted by other things...

Later that night whilst everyone was asleep, Charlie was awoken by the sound of sobbing.

Intrigued, she followed the cries out into the balmy night air, catching the culprit stumbling down the street.

She made her way closer, taking care to conceal her presence.

In the light of the beachfront promenade, she could make out that the figure was Ash, hobbling barefoot in her underwear.

She called out to her from the shadows. Charlie quickly realising her mistake when this clearly spooked Ash into running down the boardwalk.

She hurried after her, identifying herself in an attempt to calm Ash down.

Finally, Charlie caught up to her at the end of the pier - where she was staring at the moon's reflection in the water.

"Why did YOU come?" Ash demanded, still crying in pain.

"I'm worried about you Ash, are you okay?" Charlie responded calmly.

"Obviously I'm doing great" Ash retorted sarcastically "Super F*cking Amazing!"

"Tell me about it? Please, I came all this way" prompted Charlie.

Ash held the thought in her mind for a moment before turning around and looking Charlie in the eye.

Ash [distraught]: "Why does it hurt SO much?"

Ash [frustrated]: "For YEARS this was what I wanted so why do I feel so sad?"

Ash [reeling]: "They say you never forget it, but if that's true I just want to f*cking die!"

Charlie, now noticing the streams of blood pouring down Ash's legs, started connecting the dots.

Charlie [sympathetic]: "You know, it hurt for me too."

Charlie [delicately]: "But Ash, I'm not sure if that's normal, I think we'd better find a doctor."

Ash, suddenly delirious from the blood loss and the booze, could only muster the slightest nod...

...before tumbling into the ocean.

.

.

.

.

.

The subsequent events went by in a blur. Charlie dived in after her, and the next thing she knew she was in the hospital waiting room.

It was daylight now, and Blake had arrived too. The mood was sombre as they waited and waited. Sleep deprived, hungry, and delusional, they couldn't help but feel they had hit rock bottom.

At last, the surgeon came out and spoke to Charlie.

"She's going to be alright, thanks to you. It's a miracle that you brought her in. A couple more tests then she's free to go."

But wherever could they go from here?

~iii~
In classical mechanics the three-body problem is concerned with the motion of three objects under mutual attraction. General closed-form solutions to the problem do not exist, and thus their motion is condemned to be chaotic [miniscule changes to initial conditions cause wildly unpredictable results].

A three-body system can only be 'solved' by observation or simulation.

When Charlie has a change of heart and becomes the third variable in the equation, the goalposts shift and everyone starts playing completely different games. She tries to stay in control but is doomed to fail despite her best efforts.

The allegory is blindingly obvious: in a love triangle, someone, if not everyone, will always end up getting hurt. However, the moral is open to interpretation. Perhaps in the words of a wise poet or scholar:

- "What doesn't kill you makes you stronger." - Nietzsche / Kelly Clarkson

I tried fitting many different endings to the story, but ultimately found it to be indescribable. Instead, I take solace in the beauty that the characters' destinies remain undefined; open-ended, yet forever intertwined.

~epilogue~
Now that we've reached the end you may be wondering what I mean by my General Theory of Relatability?

See, the plights of all three characters are based on feelings myself and others have faced. Despite stealing superficial character archetypes straight out of American TV Tropes, I find myself relating to aspects of Ash, Blake, and Charlie - and you might too? After all, life does have a habit of imitating art, far more than art imitates life.

And for those who noticed, it's no coincidence that I chose gender-neutral names...

Say what if you flip the script and read a story about a sadboi instead?

Is it strange, knowing that the structure stays the same? What changes? Is it more or less relatable? Or does it turn Ash into a simp?

How about LGBTQ girls or boys? All of a sudden, it's a story about coming out of your cage, feeling untouched, and grappling with one's sexuality.

What I'm trying to show is that the emotions we feel are universal. Although our stories may manifest differently on the surface, we are all human and capable of feeling the same way. So how about we start acting like it?

Hint: tap the underlined words or the number keys [1-4] to switch story modes