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The TARDIS door opened, and Rose stepped in, tired after a few hours hard shopping. She peered under the console and grinned. Yep, the Doctor was still under there, where she'd expected him to be, right where she'd left him, and still just as intent on fixing the console. Except he was no longer fiddling with a spanner; instead, he was scribbling numbers on an enormous sheet of computer paper he was holding up against the underside of the grading.
"Hi, Rose. Where's Jack?"
"Oh, still looking at sonic blasters. He's one of those gadget men, I guess. Mickey was the same - show 'im a new computer with a load of RIM and RUM and he'd go all gooey-eyed and start strokin' the keyboard. What're you doing? Anywhere near finished?"
The Doctor ran his hand over his head as if expecting to find hair there, then settled for dragging his hand down his face and pinching the bridge of his nose in frustration. "No. It's not a massive problem - I mean, she still works - but I'm trying to make sure we don't end up in Cardiff instead of Naples again. Or a year ahead, which is even worse. Don't want that happening again." He winced, as if remembering a slap.
"So what're you fixing?"
"Oh, I'm just recalibrating some stuff, trying to see what's going on that could mean she works most of the time, but not all. Tightening up the coordinate precision. But she's acting funny - some of the numbers on the scanners just don't add up with what I know's right, and what's on her databanks - the old girl's going nuts trying to figure out what's going on, and so am I. So we're ignoring the readouts and just going on what we know, which is why," - he waved the sheet of paper in the air, causing several sheets of crumpled paper on the floor above his head to riffle about the floor - "I'm back to pen and paper."
Rose grinned. "Bit primitive for you, isn't it? Working with stupid ape methods?"
"I like stupid apes, remember? And I like maths. Haven't had an excuse to do it for ages."
"You like maths. I should have known." Rose rolled her eyes and groaned.
The Doctor returned fire instantly. "You hate maths. I should have known."
Rose made a face. "I don't get how you can like maths..."
"It's brilliantly simple. Everything is right or wrong, there's no dilemmas. Is this the right thing to do, will this hurt people, can I - should I - push this button. There's no choice, 'cos a number is what it is. Every simultaneous equation will always lead you to the right place, the right conclusion, and the numbers will always add up to the same thing. The whole's never more than the sum of its parts in maths. It's logical."
"So no surprises. Isn't that boring?" Rose sounded almost scornful, but behind her eyes there was a glimmer of interest, curious to see why the Doctor was so fired up.
"The surprises is how something so simple can add up to something so beautiful."
Rose was leaning over the console now, looking at him. Knowing he'd piqued her interest, he grinned to himself and went on.
"Ever seen fractals? Pictures, beautiful, but made by lists of numbers put into a program. Or flowers, the petals perfectly symmetrical and curved, the colours made by enzymes that are just the right shape to make them, the smell made by just the right mix of elements to make the right chemicals. 'Sall made with number webs, with algebra. Number patterns. Like curves. Sine and cosine - they're so simple, but you'd be surprised how many things can be represented with a sine graph. All the radiation in the world - x-rays, light, colours, radio waves, heat. And there's something beautiful in the way they go on for ever, repeating and repeating. And tangent graphs - they'll go both up and down forever, constantly striving for 90 degrees but never quite managing it, shooting off to infinity and getting so close - but not quite."
"Or music. Remember when I dragged you along to see Bach, and we ended up getting chased by the aliens who were trying to play subconscious frequencies into violin music to bend people to their will? Everything about music could be written with numbers. Dynamics and rhythms, chords are just sympathetic frequencies. The genius of Bach was just matching frequencies and rhythms at the right time, interweaving melodies. You respond to music because you respond to the maths at a subconscious level."
"Maths decides what we find beautiful; the symmetry of snowflakes, the curls a cloud of breath makes on a cold moring, the sun setting over sine-wave hills, the shape and warmth of smooth pebbles on a beach, the wind blowing over grass, the play of light through a cloud or through leaves. And you could describe them all with ten digits- less, in fact. You could do it with two, though it'd take longer."
The Doctor began to twist a line of wires around, putting the ends together, causing a line of lights above him to blink furiously. "That's what I like about maths. It's deceptively simple, but it can build up to something so complex. Heard of chaos theory? You can't understand the universe with just biology, or chemistry, or psychology, or even physics: you can't predict the future with any science. With maths, you can. In theory. There's always chaos everywhere, but with maths it can still be simple - ordered chaos, the world in two symbols, a line and a circle. When you look at the big picture, at skies and universes and burning suns, it's simple to understand them, knowing about gravity and forces, about maths. But inside those burning suns there's also simplicity; molecules pressed so tightly together that they become one and shine with enough energy for us to see them a million lightyears away. And that may be physics and chemistry, but you need maths to understand it - to understand why."
"The universe works on an equation. 'Scalled the Skasis Paradigm. It's long, and complicated, but all in all it's just numbers. If anyone understood it, they could control reality, all time and space at their command. Maths doesn't just help you know how much you've spent on tee-shirts or add up how much you have to pay for chips for four - it's simple, but it's the whole world."
He stopped. Rose was biting her lip.
"What about consciousness? I mean, how can we think and have memories? That's not just numbers, is it? What about emotions?"
The Doctor shrugged and twisted a small screw experimentally. "Nerve impulses firing. That's a flow of ions, a charge. Memories are when the nerves link up, a neural network. Emotions are just the result of external input. You sense a danger, you can feel heat, through sensory neurons or from information your brain takes in. Your brain responds in the right way. Like - if you were scared, adrenalin'd start pumping through your system, helping you to breathe faster, getting blood to your legs, getting ready to run. After a while, you just recognise the feeling of more of a certain cocktail of chemicals in your blood and the effect it has on your body as fear. Just a different concentration of chemicals."
Rose fiddled with something on the console that - she hoped - wouldn't do anything too spectacular if she twisted it. "What about - even love?" she said, her voice barely sounding, lost through the grating underneath her feet.
"Oh, love's just another emotion, like I said. Oh, it's a bit more complicated - apart from the chemicals that people give off to make people fancy them, there's a lot of subconscious thoughts about fertility and all that."
"What sort of thoughts?" Rose's voice seemed odd, but he supposed that was because he was hearing it through the grating. He went on.
"Well, through thousands of years of evolution, you lot get a lot of assumptions about who's the best person to carry on the human race with bred into you. A certain waist-to-hip ratio indicates how good a woman should be for childbearing - even though it doesn't matter because the only measurements that matter are on the inside - ". His voice trailed off. He was suddenly very aware of Rose above him.
"And - genetics," he continued hastily, trying to steer well clear of the subject of fertility. "Who's healthiest, who looks likely to stay and help you bring up the kids, be a good provider, all that. But it really just comes down to measurements of looks, and chemistry. So really, it all comes down to maths. Just maths."
He realised that he was sounding a lot less impressive than he had before, and that his lecture had ended weakly, so he stopped. There was a very long pause.
"You're wrong."
The words thudded through the air like a sonic boom, reverberated around the console room. There was silence.
"Maths might be beautiful and complex and simple and fantastic to you, Doctor, but that's not all there is out there. You can tell me that it's all nerves firing and chemical chance and pressure and friction and collisions in the air 'til you're blue in the face, but you can't convince me that's all there is to it, that we're just here because some numbers add up. Atoms can't think, can they? I could get pulled apart into a million bits and you could glue them back together 'til the end of time, but if I was dead at the end of it then I wouldn't be me."
"You can't just put down the numbers. Two arms, two legs, one head and one body equals one person and as long as you remember to carry the one then the sum'll come right in the end? 'Cos it's not how it works, and I'll not believe it is until you show me the equation for the soul. Maths is logical, right? Explain sacrifice, then! Explain why Jack went and saved us from that bomb! He didn't need to, he knew he was gonna die, and he did it anyway. Are you sayin' that's just a random variable?"
The silence swelled, like a breath from the TARDIS. Rose went on:
"And you were going on about love before. But you didn't mean love. Course you can explain people fancying each other with pheromones and genetics and how good they look for having children but that's just fancying. That's not the same as love. You can't explain away love, either.
There's no mathematical reason for the human race having all the things - the things you say you like us for - for sacrifice, or bravery despite the odds, or pure stubbornness until we get what we want, for us surviving for millions of years,in the stars, like you're always sayin'."
Rose paused, almost dizzy. She swallowed angrily.
"There's more out there than numbers, Doctor. Not everything adds up. Even if you don't believe it."
She spun around and left the room, closing the door rather more quickly than she had intended behind her.
The Doctor tried to sit up but hit his head on the underside of the console. Hard.
He frowned, and rubbed his head.
"Damn."