Elizabeth Shaw, five and a half years of why can't I's under her belt, crouches beside her neighbour George, half a year older than she, as he focusses the magnifying glass, angling it towards the sun. A thin white beam slices the pavement, following a rusty ant, tiny limbs trundling a wobbly path away from the beam.
"What are you doing, George?"
"Davy says this is how you set an ant on fire."
"That's mean. You shouldn't set ants on fire."
"It's just an ant."
"Stop it." Elizabeth reaches for the magnifying glass, and George lurches away from her, the beam wavering while the ant takes advantage of the confusion to chart a straighter path towards the grass.
"Get off! It's not yours!"
"You're hurting it!"
"Am not!" Refocussing the beam into a pinprick of heat wavering round the ant's path.
"Give it here! Stop it!" Elizabeth snatches for the glass, misses again; shoves George's shoulder, hard, toppling him like a beetle on its back, curled up and whimpering. The glass slips from George's fingers and clatters to the pavement, where Elizabeth grabs it, hurls it against the concrete, and watches it shatter.
"That was mine! You can't do that!"
"Don't kill ants," Elizabeth says. "You're nicer than that."
Later, she's sent to sweep the pavement and apologise to George, and is sent to bed without tea. But she's never sorry, not for a moment.
"Differential equations quantify change," says the professor. "Mass, velocity, fluid flow, particle density. Everything that winds or streams or slithers through the universe can be described with a differential equation. They are one of the most singularly beautiful areas of mathematics, and one of the most important."
Fifteen years old now, and Liz is still full of glorious whys she hopes university will teach her to answer. Both her parents and her secondary school had long since agreed they'd nothing more to teach her, at least not in matters scientific or mathematical, so here Liz sits, first day of class in a subject most new students wouldn't touch, but which whispers to her in the language of atoms and vibrations and the patterns of the universe.
There's a scattering of girls alongside her, a trace of signal amid the noise of an otherwise male-dominated classroom. The boys slump in their seats, arms crossed, notebooks closed; the girls, to a one, including Liz, are straight-spined, backup pencils lined up neatly on the desk or tucked into a tight bun behind their heads.
"Let's begin," says the professor. "Delta-y over delta-x equals the function of x and y. Who knows where to start?"
The boys rustle in their chairs. The girls tap their pencils against their desks.
And Liz raises her hand.
If she leaves, the Doctor will be fine without her. He's the most brilliant scientist she's ever known, and she's known the best of them.
If she stays, she might learn secrets her colleagues never will. Time travel. Transcendental dimensions. Cellular regeneration on a scale so far beyond geckos and salamanders it might as well be – well, it is, actually – alien.
If she leaves, the Doctor may grow even more rebellious when the Brigadier suggests explosives-based diplomacy. (And who could blame him, really? She dreams of Silurians sometimes; of wandering through dank tunnels and finding a people who offer her centuries of knowledge no human has ever seen. The dream always ends with dust and rock crashing down on her, and she wakes with sweating palms and a racing heartbeat.)
If she stays, they'll never know if he absolutely needs an assistant to cope. Whether no matter how well he plays the glad-handing aristocrat to get what he wants, he's terrified of living a normal life, and needs a human bridge to support him.
If she leaves, she leaves the Brigadier.
If she stays, she may have to explain the Brigadier and herself to the Doctor.
The Doctor's fountain pen scribbles across his notebook. "Pass me that flask of acetone, will you, Liz? There's a good girl."
If she leaves. If she stays.
The new lab assistant is generally competent, but must be broken of a habit of writing mus that look too much like nus. The new lab assistant is clever with sums and has a keen eye for the level of detail signal analysis requires, but cannot reliably remember that Liz prefers her tea with milk, no sugar, rather than sugar, no milk. The new lab assistant is persistent when she thinks she's right (which she often is) and occasionally wilful to the point of stubbornness; this has a certain ring of familiarity to Liz, though not enough that she won't put her foot down when the matter calls for it.
The new lab assistant is there, in fact, to assist, but not-so-secretly is also there to subtly persuade Liz to return to a life she left, which Liz knew was a risk when she admitted Kate Stewart to her lab. But there was something poetically and irresistibly satisfying about having a Stewart working for her rather than the other way round.
The new lab assistant is very fetching, which was also a problem with the last Stewart Liz worked with. Though with any luck, the current Stewart is unaware of previous Stewarts' relationship with their scientist, especially since the current Stewart has her hand halfway up Liz's thigh.
"This is very inappropriate," Liz says with some difficulty, because Kate is nibbling at her neck and it is frankly almost as distracting as the hand now two-thirds of the way up Liz's thigh. "I'm your supervisor, and I'm – ah – far too old for you."
"You know who my real supervisor is," Kate murmurs against Liz's collarbone, "and you're not old. You're ... well-seasoned."
"I'm not an experiment, Kate. If this is an attempt to get me back into UNIT, it's ..."
Kate's hand is now seven-eighths of the way up Liz's thigh. Possibly eight-ninths. Poor time to pull out the measuring tape, probably.
"... it's working," says Liz.
Liz is nearly through her obnoxiously mandatory three-month rota back on Earth – "it minimises calcium loss, which is no joke for someone your age," Kate had said when she imposed the requirement, and was promptly and tartly reminded that Liz's age had never been a problem for Kate before – when she's emailed instructions to visit Coal Hill School and discuss with a certain Miss Andrea Quill how it is, exactly, that an alien has come to look almost exactly like Liz herself did so many years ago. The haircut's sharper and more modern, and the clothing vastly less plaid, but sat across from Miss Quill, Liz has to admit the resemblance is unsettling.
"Ofsted, the Board of Governors, and now UNIT," says Miss Quill. "Should I be expecting the Shadow Proclamation next? Who's responsible for health inspection on this quaint little world? Perhaps they'd like a three-week observation of my cooking skills. I haven't got any, in case you're wondering. Shalimar practically brings tikka masala round the house before I place the order, though I'm learning to appreciate Matteusz's seventeen different variations on boiled potato."
"I'm not here to evaluate your cooking," Liz says. "I'm here to discuss why I'm looking at myself from forty years ago."
Miss Quill blinks slowly, gaze never shifting from Liz's face. It's not unlike a staring contest with a cat, which no matter how much smaller the size relative to a human is fired with utter certainty it can bring you down like the weakest antelope on the veldt. "Coincidence," says Miss Quill. "Nothing more."
"I doubt that very much. Where did you get the face?"
"You're not familiar with how I arrived on this backwater you call home?"
Liz sighs, rubs the bridge of her nose, pushes her glasses back into place. There is only one answer, of course.
"He saved me and Charlie. And when he told us we'd have to give up our native forms to live here, he let us choose. For some reason, he wouldn't let me pick any of the schoolteachers, but he said you knew more about physics than anyone other than him. Actually, he went on for quite some time comparing you to various physicists he'd known. I think I fell asleep somewhere in the middle. Anyway," Quill continues, "yours was not an unpleasing form. I made some minor modifications, but I must say, I admired your taste in boots."
"That's it? Physics and footwear?"
"Well, I started off with a random choice, but the Doctor seemed to think a giant penguin teaching quantum mechanics would be distracting."
"Tell me," Liz says, "tell me why he brought you here, to this place, this particular place."
Quill twitches. The cat is growing restless, in need of a new mouse to toy with. "I'm ... obligated to protect Charlie. And the Doctor has obligated me to protect the rest of the little whelps, too. I won't let them come to any harm," she says, her lips curling upwards, "while I'm obligated to do so."
"Did the Doctor tell you anything else about me?"
"Honestly, I don't recall. I'd just been saved from death by Shadowkin. Your biography wasn't foremost in my mind."
"Then I'll tell you," Liz says. She creaks out of her chair, her weight on her cane, stands as tall as she can in the gravity she's no longer accustomed to. The cat remains seated and complacent. "I am chief scientist on UNIT's Moonbase. I answer to no one other than Kate Stewart, and then only when it pleases me. I worked side-by-side with the Doctor, and sometimes he even treated me as an equal. I have saved this planet from destruction more times than there are hairs on your very familiar head."
She leans into Quill's space, looming in fast enough that the predator reels back. "You wear the face of someone who's spent her whole life protecting this world," Liz says. "Mind you live up to it, or you'll answer to me."
Quill's mouth opens slightly, as if she's about to speak, but Liz's gaze never wavers. At last, Quill nods, head lowered.
"Nice boots," Liz says on her way out the door.