Work Text:
It starts with positive integers. Whole numbers. Counting numbers.
The first math humans ever did was counting. It started with one. And then one plus one. And then one plus one plus one. And then… you get the picture. Soon numbers became too big to count, and so they were counted in groups instead. Most early mathematics was unable to advance until the development of base systems. Modern time is counted on a base of sixty, the metric system on a base of ten, and many past societies utilized base twelve. It’s all different and yet it’s all the same. A comforting thought, Sheldon thinks, in the grand scheme of things.
-
One.
It starts with a new neighbor. A new, loud, peppy neighbor that quickly makes herself at home in Sheldon’s space. Penny situates herself in their lives like she’s been there all along. She shows up to movie nights and game nights, she sits in Sheldon’s seat, she talks back, it’s insufferable. Worst of all, his friends (he makes a mental note to find new ones) let her have her way, no questions, simply on virtue of her being new and loud and peppy and blonde.
One plus one.
“Everything can’t always be about you, Sheldon!”
“Well that’s rich, coming from someone who’s gotten her way ever since she got here!”
“You think I’m the only one who wanted things to change? The only one who’s happy with something new for once?”
“My apologies, Penny, but I don’t hear any of my friends complaining about our routine.”
“Probably because he doesn’t listen to us,” Howard mutters to Raj behind his hand, sending the both of them snickering.
Sheldon turns to glare at them both, silencing their laughter. “Besides, once the novelty of your arrival has worn off, things will be back to normal, I guarantee it.”
Penny lets out a noise that appears to be somewhere between a groan and a scream and whips her head around the room, “Someone back me up on this!”
One plus one plus one.
Penny and Leonard decide to enter into a relationship. A real relationship- something more solid than their previous failed attempts. The strangest part for Sheldon is the lack of any actual strangeness (besides the initial disbelief and mild disgust, less at the thought of Leonard coupling with someone as uneducated as Penny and more at the thought of Penny coupling with a physically inferior specimen like Leonard - really, Penny, he can’t even do a single pull up). She still tells Sheldon to “stuff it” when he complains about her speech patterns or her eating habits or her seating choices and she still comes over when Leonard isn’t there, borrowing milk or hogging their internet connection.
The only difference, or the only difference that Sheldon is aware of, is how she’ll sometimes be there in the mornings when Sheldon awakes. Or (giving her casual attitude regarding morning routines) more likely she will emerge, bleary-eyed and pajama-clad from Leonard’s bedroom when Sheldon is up and about.
The first time startled him. He wasn’t used to women in his apartment, certainly not ones asking him to reach the sugar for them in the mornings. He certainly wasn’t used to them calling him “sweetie” and squeezing his arm for far longer than is appropriate (exactly 1.6 seconds - 1.1 seconds longer than appropriate).
If he disrupts his detailed kitchen layout to put the sugar in a lower cabinet it’s obviously because he’s evolved enough (as Leonard likes to say in his snarky Leonard tone) to put someone else’s needs above his own. It certainly has nothing to do with her gentle and tired squeeze on his upper arm, her hair brushing against his ear.
* * *
Early math was practical. See a need and fill it. Man earned, and then man lost. Man received, and then man gave. Man incurred debt, and then man created the negative integers. Later, there would be talk of additive inverses and additive identities (just the one, really), but it was not this complex in the beginning.
-
It doesn’t surprise him when it finally happens. They had been fighting more than usual, so when Sheldon finds Leonard eating in his bed and listening to ballads, he knows before Leonard even vocalizes it that he and Penny have broken off their ill advised relationship.
What does surprise Sheldon, however, is the effect it has on him. He no longer has to vacuum up her long blonde hairs. There’s no one asking inane questions while he works, or singing loudly in the apartment’s communal spaces, or messing up his organizational system. All good things, his brain supplies. And, yet. He finds himself spending more and more time at her apartment. Watching her paint her nails when he should be working on his research, putting his headphones in to drown out her truly offensive singing and then never actually turning any music on, helping her read lines.
She says he misses her. He says he can’t stand Leonard’s moods since the breakup.
She laughs. He smiles at his feet.
* * *
It only makes sense that if numbers represent presence, they must also be able to represent absence. That’s where zero comes in. The invention of zero was resisted at the time, as were many, if not all, mathematical innovations. No one said innovation is easy.
-
Penny is mad. More specifically, Penny is mad at him. He’s used to the guys’ anger and he knows how to brush it off. He’s never had Penny mad at him before, though. Well, there’s actually no empirical evidence that she’s angry with him, but she’s been ignoring him for a week now, ever since she’d abruptly ended their conversation and told him she had to go to work, even though they both knew it was her day off. He’s not really sure what he said or did to make her upset which is unfortunate because, for the first time in his life, he actually wants to apologize to someone. He can’t handle the radio silence.
-
He doesn’t get the answers he wants but two days later, Penny asks him if he would like a ride to the grocery store and he says yes, thank you. The empty pit that had opened in his stomach starts to close back up.
He doesn’t ponder the significance.
* * *
Then came the rational numbers (a formalization of the practical concept of dividing) and multiplicative inverses and multiplicative identity. One-third (multiplicative inverse of three) will take three (multiplicative inverse of one-third) back to one (multiplicative identity). Zero caused quite a bit of trouble here. Zero naysayers likely rejoiced.
-
Sheldon is drunk. Penny tricked him into drinking and Sheldon is drunk and trying to explain to Penny why five to the negative first power is one-fifth. She asked (at least, he thinks she did) and now she isn’t even listening. He underlines the word “inverse” again and stabs the white board with his pen, “So??” (Morning After Sheldon will not remember why his favorite white board pen has been smushed. He will blame Wolowitz.)
“It’s really rather simple, Penny.” He tries to sound exasperated but he thinks he just sounds drunk.
She hmphs from the couch.
“It’s not something you can understand like a computation,” he tries again, “it’s just the notation. That’s it!”
She mhms from the couch.
“They’re inverses and the negative one is how we represent it.”
She is asleep on the couch.
“What aren’t you getting?”
* * *
After the rational numbers came the real numbers (a rather condescending title, Sheldon thinks): the rational numbers with the addition of the irrational ones. Sheldon has always thought that “irrational” is the perfect word to describe them. Imagine a square with sides of length one. Now imagine you’ve drawn a diagonal line from one corner to the other. Right there, that’s an irrational number. The square root of two, an irrational number, a never ending decimal. Pi (perhaps the most famous irrational number) is hidden in every single circle. The way these numbers hide their complexity in plain sight is a subject of fascination to Sheldon.
-
Sheldon notices things. He may have trouble reading social cues, or understanding someone else’s emotions (or his own, for that matter), but he isn’t oblivious. That’s what he says, anyway, when Raj accuses him.
Video game night has ended, Leonard has gone to bed, Howard and Penny have left, and Raj tells Sheldon that he’s oblivious.
Sheldon has no idea what that means. “I have no idea what that means.”
“Dude. Come on.”
“What?”
“Penny.”
This is not really an answer. “What about her?”
Raj sighs, pats Sheldon on the shoulder, and leaves.
This is even less of an answer.
* * *
Then, someone asks a new question: How can there be a quadratic equation without any roots? Even a mind less sophisticated than Sheldon’s own can see that a positive number (which any real number squared will indubitably be) added to another positive number will never be zero. However, mathematicians were not pleased with this, and the complex numbers were born. If we let i be equal to the square root of negative one, then every single quadratic will have a root, Sheldon imagines a petulant mathematician saying as he makes it so. Even the name is ridiculous. i, the imaginary number.
Sheldon doesn’t have any real issue with the complex numbers, after all they have a myriad of applications, even within his own field. Yet he can’t help but feel frustration that there was no real solution, and so one had to be made up out of thin air. Is it possible to just will things into existence when the going gets tough? Say something, and suddenly it’s real?
-
Perhaps it isn’t possible to will something into existence, but maybe, just maybe, that something was there all along.
That’s what Sheldon thinks when he watches Penny separating her laundry, when everything seems to fall into place in his brain, into slots he didn’t even know were there.
That’s what Sheldon hopes to be true when he dumps the rest of his clothes into the machine and asks Penny on a date.
And that’s what Sheldon knows to be true when she says yes, kisses him on the cheek, and punches him in the arm, took you long enough.
* * *
In algebra they teach you about variables. They tell you that a variable can be absolutely anything (that’s why they call it a variable!). Then they teach you how to solve for it. And sometimes it’s a function of another variable (x=y), sometimes two or three or more other variables (x=(y+z)/(c-10)). But sometimes, things fall into place and your variable turns out to be a simple constant (x=3). It’s a concept that has fascinated Sheldon, years after his first introduction and subsequent mastery of the topic.
Penny is a variable,
until she is a constant.