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.‘The horror must have had a very big floor,’ he concluded.‘But that’s beside the point.One of the horror’s victims was a girl.A teenage girl.The horror wanted to use her as a weapon against me.So it shaped her.Sculpted her.Fed her its own programme.’He tapped the floor.‘It didn’t work.Because I changed the temporal equation.Altered a few of the numbers myself.Subverted the mathematics of her destiny.’ The Doctor smiled to himself.‘Subverted the mathematics of her destiny.Yes.I rather like the sound of that.’Ahead of him, one of the equation’s branches cancelled itself out, but the other kept going, finally tailing off when it reached the far wall.He didn’t bother moving any further along the line.‘Ace didn’t end up quite the way I’d imagined, of course.I could have used the TARDIS to work out the equations properly, if I’d had a year or two to spare.I did it all instinctively.No visible mathematics.But I did it, didn’t I? I defeated the horror.I always do.’With that, he pulled himself upright, resting on both of his elbows.His broken arm still stung, but he could feel the bone twisting itself back into position, and a bit of pain would probably only help the process.‘I thought Sam was just like Ace, to begin with,’ said the Doctor.‘But she’s not.It took me a while to work out why she’s not, but she’s not.’He pressed his hand against his cheek, and pushed at the skin, forcing a few more drops of blood to the surface.Not much there, through.He considered using his gums.The guards had done some damage to his teeth, and he could feel his fillings moving around uneasily at the back of his mouth.He’d had them fitted during his second lifetime, and they’d never really settled in properly, even though he was sure they kept regenerating with the rest of his body.‘Back to work,’ he said.Ten minutes later, he’d scrawled another equation on the floor.Only a small one, short and linear.He stared at it for a while, then frowned.It all seemed much too simple.‘One human lifetime,’ he told his nonexistent audience.‘An overview, with all the interesting details left out.’Then he began to draw a second equation below it.The same sort of length as the first, but slightly more complex, a rather tricky sub‐equation stitched into the base algorithm.‘One human lifetime, plus one Time Lord’s interference,’ he said.‘That’s you, Liz.Or you, Tegan.Or you, Polly.Or you, Sarah.’Now, there was a thought.‘Sarah,’ he said.‘What was it I had to remember about Sarah? Oh yes.She’s looking into all of this as well.It was in the UN’s records.I wonder how she’s doing.Better than me, I hope.’He stared at the second equation for a while, but it didn’t give him any clues.Besides, there wasn’t a simple mathematical symbol for ‘tortured to death in a prison cell’ or ‘captured by alien arms dealers’.Then he remembered the dream.‘Not a dream,’ he said.‘The dream is part of the equation.The big equation.The one I haven’t started work on yet.Sending consequences backward in time.Good! That means I’ll succeed.Probably.Now, let’s see.’He smudged his finger with a little more blood, and began adjusting the second equation.‘Sam’s timeline was changed,’ he told himself, as he scribbled.‘By the Faction, I should think.Yes.That’s it.She was supposed to live her life in London.Never meet me at all.All that went out of the window, didn’t it?’Of course.The ‘real’ Sam didn’t exist any more.She’d been removed from history for good, as far as the Doctor had been able to tell.There was just ‘his’ Sam now, the one who’d been fated to end up on the TARDIS.The simple one.The clean one.Which meant that her timeline was tied to the Doctor’s timeline.Thanks to Faction Paradox, her sole purpose in life was to be part of the TARDIS crew.Now she was going to leave the TARDIS, so…So, the Doctor had no idea what was supposed to happen to her now.Perhaps she’d be a loose end, with no fixed destiny, existing outside the confines of history.Or perhaps she’d simply cease to exist altogether.‘I’m sorry, Sam,’ he told the equations.‘I didn’t want to have to interfere.Really I didn’t.But I can’t take the risk, can I? I have to give you a future.A life.Outside of mine.’He looked over his shoulder.‘We’ll have to be careful, though.We don’t want to become a horror ourselves, do we? A second Ace is the last thing the universe needs.’ He ran his hand over the equation, blurring the first few symbols in the sequence.‘Besides, I’m not the man I used to be.I doubt I could get away with it.So.One simple change.Not really a manipulation at all.The choice has to be Sam’s, not mine.She gets to choose the life she wants.’Then he turned, to face the rest of the cell, the parts of the floor he hadn’t even touched yet.The parts where Badar had lived.Never moving away from the wall, never going anywhere near the window.‘Beside the point,’ the Doctor told himself.‘The alteration isn’t going to be any use to me here.Concentrate.Think about Sam later.’With that, he crawled into the middle of the cell, and began the great work.One drop of blood at a time.* * *DuskThe guards hadn’t interrupted him all afternoon.That had been a mercy, anyway.The equation had turned out to be a lot more artistic than he’d expected.At least, he hoped it had just turned out that way
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