Fandom: Doctor Who
Characters/Pairings: Tenth Doctor
Date Written: 2007
Summary: f(x) = 1/x : The simplest of equations. The limit as x approaches infinity is zero. The limit as time approaches forever is nothing. Life is just math, in the end. Post-Doomsday.
Rating/Warnings: PG for one single possibly disturbing line.
Notes: If you're looking for a story where the Doctor is SO IN LOVE that he tears apart two universes trying to get back to Rose, this ain't it. Math is beautiful, and math teaches us to accept the trailing ends of infinity as the lost causes that they are.
Spoilers: Doomsday. Earthshock, sorta.
Humans have a funny way of doing math, of thinking about math. Limited, and elementary, with the occasional flash of epiphany slid in amongst the mundane. Calculus is not by any means the most advanced thing they’ve figured out, but it’s one of the most interesting to someone who spends a lot of time thinking in inverted figure-eights.
The idea of limits, for example – equations existing in a constant state of potentially equaling something or other, somehow, when some impossible set of circumstances are met or an impossible value plugged in. The mathematics of possibility, of may or may not. That’s more than most advanced cultures give humans credit for, this spending of an inordinate amount of time fixating on nothing and infinity. Not a good topic for apes, right? Hand them a banana to consider instead.
Give them a chance, he’s always telling them, give them half a chance, and they’ll surprise you.
In his experience, humans actually spend quite a lot of time thinking about infinity and nothing and forever and never and potentially and maybe, underlined with the same burning golden determination that strings him from moment to moment, maybe maybe maybe. It’s why he likes them so much.
The Doctor sits at a desk tucked away in some dark corner of the TARDIS, writing out and solving equations longhand as a way of mindless doodling, a distraction. f(x) = 1/x, f(x) = (x+1)/3x^3. Even the real equations, the laws that govern time and space and his ship and his own shifting, paradoxical life, the ones he cannot write out in the symbols they have on Earth and are too long for any single sheet of paper, approach zero if you carry them out to their extreme ends.
Rose said she would stay with him forever, and forever is just infinity, plugged into the equations of time. The numbers make sense as he scratches them across the paper, children’s math. Numbers don’t lie, and the longer people stay with him, the more likely it is that the numbers will swallow them up.
I got old, Sarah Jane says from the back of his mind.
Adric is back there too, and he screams like the Doctor imagines a person would scream as the skin is crisped from their bones.
As the input value approaches infinity, the output approaches zero. Nothing. The end. Forever isn’t real for them, a theoretical concept that would destroy the mathematics of life if it ever quite managed to exist. Rose wanders around in the back of his mind too, but she doesn’t have much to say, shuffling down one corridor and up another. There’s a specific equation that his life drops people into, and it plummets towards the x-axis faster than most. She’d been denied the chance to try to plug her impossible value into it, send it careening towards oblivion.
It’s better that way.
And forever isn’t real for him, either. He has a grander equation than they do, more graceful and elegant and convoluted, sweeping over the whole fabric of Everything and back again, but he’ll eventually reduce to zero too. As will the universe itself.
The numbers fill the paper, beautiful and honest. Sometimes, truth and beauty are all he needs.