It first happens shortly before Bernard's arrival and all the nonsense that ensued, in the small hours just before dawn. Slow, unproductive days lead to restless nights, and after some dedicated tossing and turning, Hannah is forced to give up the ghost. So she pulls on some trousers and goes out for what Lady Croom would term her "morning constitutional," although Hannah is employing a rather looser definition of morning than the Lady would consider standard.
Sidley Park is situated at the end of a long, winding country road several kilometers away from the nearest village. Hannah's not in a mood to slog through the muddy grounds at half four in the morning, so the road it is. It's a picturesque stroll by daylight, rendered Gothic by the blue-tinged predawn fog. She suspects Mr. Noakes deserves the blame for this as well.
She loses herself inside her own mind, sifting through facts and observations and hermitages and gardens, wondering if this book will ever come together properly on the page.
The road is empty, and then she's nearly run over by a horse-drawn carriage.
Afterward, she'll attribute it to distraction, to lack of sleep, to being too wrapped up in the world of Romanticism and the decline of English order and an unknown nineteenth-century hermit. Because that couldn't possibly have just happened.
But in the moment itself, there is a carriage, drawn by two grey horses; the sound of laughter; and a young woman's cheerfully exhausted voice, chattering on about a ball.
And then it's gone.
She feels a hand on her shoulder, and very nearly jumps out of her skin. But it's only Gus, looking at her with an eloquent query in his eyes.
"Yes, it's very late, isn't it?" Hannah says, heart still racing with adrenaline. The air is heavy and still. "Or early. Or both. What are you doing out here?"
Gus shrugs. He takes an awkward step back away from her.
"Yeah," Hannah sighs. "Me, too."
She keeps a wary watch as they walk back to the house, but there's no sign of the carriage. The only marks along the dirt road are tire tracks, days old, and her own faint footprints, vanishing into the mist.
In one of Thomasina Coverly's notebooks, Hannah finds a series of sketches of geometric shapes – a cone, a pyramid, a sphere – drawn with a decent eye and a deft hand. An sloppily shaded apple with an exquisitely rendered leaf at its stem lolls beside a staid textbook cube. The next few sheets descend into chaos, the cube repeating itself from several different angles and then becoming warped beyond recognition, as though seen through a kaleidoscope. In the margin of that page, a note is scrawled off-kilter in Thomasina's swirling cursive:
If a line may become transmuted into a square, and then further metamorphose into a cube, surely a fourth dimension might yet be extrapolated, if one could only find the correct perspective from which to sketch it.
Another hand – neater, though cramped – responds:
Are your current lessons so roundly unsatisfactory that you must utilize geometric figures to chart a course through Time itself? For you shall not yet escape tomorrow's Latin declensions.
To which Thomasina retorts:
Phooey to Time's relentless forward march, anyway.
The imperfectly imagined four-dimensional cube invades several later pages of Latin in fevered retaliation.
Then comes the night of the Regency party and Bernard's disgrace, and the final missing piece in the form of a student's drawing. Septimus with Plautus, Thomasina signed it triumphantly, and thus the victory of Romantic imagination over rationalism is laid bare.
The Genius of the Place, Hannah will call it, but she's no longer sure to whom she's referring. The grieving hermit whose mind turned inward upon itself, or the dead girl he'd once tutored – or both?
She can somehow imagine them, so clearly, as though they stand before her. The handsome young man from the sketch, as seen through the eyes of a girl on the cusp of womanhood, both together twirling around and around the room in a dance.
It's a waltz. She can hear the music, as though playing from the next room, that antique untouchable grand piano sounding fresh and new.
Her imagination could never be this vivid.
When Gus appears and proffers his hand to her, it's only natural to fall into step alongside them.
"You think you're being haunted by the ghost of a precocious mathematician," Valentine says flatly.
Hannah taps her pencil against the table. Her notepad lies blank in front of her, as it has for days. days. "Not the precise terminology I would employ. Not least because it assumes one believes in ghosts, which I really don't."
"And you're basing this on a statistical survey of… how many incidents?"
Hannah shoots him a glare. "It's happened twice. Thus far. That I'm aware of."
"Right. The invisible carriage—"
"Oh, it was fully visible. And corporeal. Nearly ran me off the road. It just didn't actually exist."
"And a Regency couple dancing. At our Regency-themed fancy dress party. At which just about everyone, myself certainly included but you as well, was utterly pissed."
"I never said it made sense," Hannah says crossly. "I'm inclined to disbelieve it myself, even though it happened to me."
"Oh, I believe you," Valentine says. Hannah blinks at him, and he lets out a short huff of laughter. "Well, it's you, isn't it? You're the last person on earth I'd expect to go on about ghostly visitations. Barring the possibility of sudden mental instability, it makes you a fairly credible witness."
Hannah sighs, setting the pencil down before she can snap its point off. She hasn't written a word since the party. "I've had an odd couple of days."
When she glances back up from the empty pages, she glimpses a strange, intent light in Valentine's eyes. He coughs and looks away. "So!" he says, too cheerfully. He tips his chair back, steepling his fingers. "Going by the literature – by which I of course mean Chloë's not-as-secret-as-she-thinks stash of penny dreadfuls – ghosts generally linger in the world of the living if they've got unfinished business to attend to. Something left undone."
"I sincerely hope Thomasina doesn't expect me to finish her iterated algorithms," Hannah says, dry as dust. "Because she's in for a bit of disappointment."
"Maybe she's not the one doing the haunting. Maybe it's the tutor, what's-his-name."
"Hodge. The hermit. No, I don't think so." Not that it's based on any sort of logical deduction, but she'd heard a young woman's voice in the carriage. And there was something in Thomasina's eyes as she waltzed, reflecting the candlelight—
Well, bollocks to going with one's gut, anyway.
Valentine shrugs. "Whichever. Look, if she turns up again, you might try asking her. Otherwise, I'm not sure it matters. Maybe she's always been here, and it's only that you've just noticed."
She's helping Gus out in the garden – he's enthusiastically yanking weeds, God only knows why, but it's a strangely soothing pastime – when she hears the voice.
It sounds like Chloë calling. "Augustus Coverly, you get over here this instant!"
Hannah glances over at Gus. He wears a vaguely hunted look. "What on earth could you possibly have done to her?"
Gus shakes his head and grabs another weed with determination.
That's when the girl dashes pell-mell through the garden, hair streaming down her back, pure fury in her eyes. Her feet leave no imprints across the flowers.
She looks to be about sixteen, and beautiful.
"If you breathe a word of this, I swear to God, I will tell Mama the truth about the incident with her silk stockings," Thomasina shouts, red-faced and gasping in a most unladylike fashion. She barrels on past them. Somewhere, Hannah can hear a boy's laughter, but she can't quite place it.
Thomasina rounds the hedge and is gone.
For a few long moments, there is silence, but for the buzzing of insects and the faint clink of Gus's trowel against the dirt.
"I'm not losing my mind, am I?" Hannah asks the air rhetorically. "That did just happen?"
Gus smiles briefly and goes back to his weeding.
"She was sleeping with the tutor, wasn't she?" Chloë remarks offhand, flicking through one of Thomasina's literary essays. She claims a newfound interest in Hannah's work. Hannah suspects she's rebelling against Bernard's conspicuous absence.
"It's hardly relevant," Hannah says.
Chloë gives her a look mingling pity with disbelief. "Sex is always relevant. Who would your Caroline Lamb have been, if she hadn't been sleeping with Lord Byron?"
"A better writer, probably."
Chloë snorts. "And society would have ignored her entirely – well, even more so than they did – and you'd probably never discovered her to write your book."
"I'd hardly say I discovered—"
"And if my precocious great-great-to-the-nth aunt hadn't been snogging her tutor, you'd have no mad hermit to draw you to Sidley Park in the first place," Chloë goes on. "So were they shagging or what? Because I've got to tell you, she was a sneaky little minx, if this bit on Marcus Antonius is anything to go by."
Hannah sighs, stroking Lightning's shell. "It doesn't matter if they were sleeping together. He loved her. That's the important bit."
An unfamiliar expression passes across Chloë's face – not quite pity anymore, but close enough to raise Hannah's hackles. "So that's why you won't shag Val."
"The fiancée thing is a joke!"
"Yes and no, but that's not the point. Here I thought you just weren't interested in sex—"
"Sex is perfectly lovely. It's people I'm not interested in."
"—but really, you're secretly a Romantic."
"I can hear the capitalization, Chloë, don't think I can't," Hannah says warningly. "You must be joking. Have you heard a single word I've said about my book?"
Chloë waves her hand dismissively. "The Romantic sham, the decline from thinking to feeling, et cetera et cetera, what a lot of rot. You're the sham, Hannah. Your pet genius didn't devote her little life to arcane maths just for the sake of being clever. She felt it, passionately, the same way your Caro felt about Byron, and that's what fascinates you so much. Because you're jealous of them both, to feel so strongly and allow that feeling to take over their whole lives, their whole beings. And you've never found anything like that for yourself."
Hannah doesn't quite throw the turtle at Chloë's face, but it's a near thing.
Hannah does her best work in the music room, in the late afternoon, when dying sunlight streams through the French windows and the usual clutter strewn about the table cuts odd shadows at steep angles across her notes. Lady Croom spends her afternoons gardening; her rarely-present husband is off doing whatever peers do without regular employment to occupy their hours. Valentine holes up in the library with his laptop, and Chloë visits with friends in town. Bernard threw off the harmony of the house; now that he's gone for good, God willing, their hard-won balance is restored.
One of these days, sooner rather than later, Hannah will finish up her research on the Coverlys and return to London. She doesn't dwell on it much. For all the distractions and aggravations, Valentine's awkward propositions and Chloë's headstrong interruptions, Hannah rather likes it here.
She sometimes wonders if the research doesn't mean more to her than the final product, really.
Hannah pores over Thomasina's notebooks with fresh eyes, reading new stories in between the theories and maths. She trips over the question of the fourth dimension anew, the strangely distorted cubes. "Time," she says aloud to herself. "Newtonian time, they called that the fourth dimension."
"I'm not trying to cheat," Thomasina protests, faintly outraged. "It's not like I'd skip ahead to the end of the book! But it is possible, don't you think?"
"What, time travel?" Hannah asks absently, still lost in her notes. "Didn't you predate Wells by a good fifty years, at least? Although I'm sure literary precedents could be found."
"We are all intrepid explorers through the fourth dimension, in our own way," a man says, voice rich with amusement.
At that, Hannah does look up.
Septimus Hodge is flipping idly through the same lesson book currently sitting open at Hannah's elbow, a smile playing at the corners of his lips. Thomasina, perched at the edge of her chair, lets out a heavy sigh and leans back, kicking her heels. "But that's an interminably long voyage, and with no return ticket," she sighs. "Yes, and we might turn our faces ever westward, and walk only in a perfect line towards the setting sun, but how dull! No explorer should survive obeying such an arbitrary law, when he might instead veer to the south, and warmer climes."
"But for the want of a compass," Hodge says, with such fondness that it makes Hannah want to look away.
Thomasina rolls her eyes, shoulders lifting in an inelegant shrug. "Well, clearly. But the possibility still exists. I merely haven't developed the neatest proof. Yet. But if all sides of a cube exist at once, although we can never see them all from one angle, then surely it is much the same for Time itself?"
"I'm not sure I understand, my lady," Hodge remarks.
"But it's the simplest thing in the world! All times are now. We simply can't see them all from our particular angle in Time and Space."
Hannah starts. She looks back down at the lesson book, at the four-dimensional not-cube sketched across page after page, and tries to see it from every angle at once. But her mind is not so agile as Thomasina's. She can't make this leap on her own.
There's a knock. Hannah and Thomasina both look up together, turning in unison to the door. Hodge is still lost in the drawing, brow creased with concentration, and doesn't so much as glance at Gus as he enters.
Gus gestures out, toward the dining room.
"Is it dinner already?" Thomasina asks.
The daylight has almost entirely faded, and the room feels very dark, all of a sudden. There are no lamps lit. Hannah rubs at her eyes, feeling an ache build between her temples. When she looks around, the room is empty, but for her and her papers and Gus still waiting patiently at the door.
"My goodness," Hannah says slowly. "I quite lost track of the time."
She corners Valentine in the library with Thomasina's notebook after dinner. "I have a geometry question."
Valentine wrinkles his nose. "You know I'm really more of—"
"I don't care what breed of mathematician you call yourself, I hardly got through isosceles triangles in school." She drops the open book on top of his laptop keyboard and ignores his wince. "What's this diagram?"
He glances down at it, frowns, and picks the book up to study it more closely. "I think it's meant to be a tesseract."
"A tesseract," he repeats, with studied patience. "That's what it's called. It's – okay, so one dimension, that's a line. Two dimensions, it's a square. Three dimensions, cube. Four dimensions, tesseract. But look, she as good as says that flat out, right here in the margins—"
"Yes, but I wanted to know the proper term, so thank you." Hannah rests her elbows on the back of his chair, propping her chin up on her hands. He starts at her sudden nearness, and tries to look as though he didn't. "The fourth dimension is time, isn't it?"
Valentine snorts. "In science fiction, sure. But that's neither here nor there. In formal math, a tesseract presupposes the existence of the fourth dimension without implying any theories on bending the structure of space. It's all very arcane and of no interest to anyone outside the field, really. But pretty."
"Well, your Thomasina seemed to have an eye for the beautiful maths. The Coverly Set. Tesseracts. Here, let me show you." He hands her back the book and brings up a window on his laptop. It takes a minute or so for him to render it. "This is what she was trying to draw."
"Oh," Hannah says. "That's... oddly mesmerizing."
"And yet, still not a TARDIS," Valentine remarks dryly. "How disappointing."
"My God, you really are hopeless," Valentine sighs, in fond exasperation. "Never mind. Is this the new ghost theory? She developed time travel and uses it to jump out in front of you at random moments to say boo? Mind, she's well in advance of the maths of her time on this as well. I can't recall quite when anyone coined the term tesseract, but it wasn't 1812, that's for sure."
"It's not about traveling through time," Hannah remarks absently, still watching the ever-shifting image on Valentine's screen. "It's about searching for the right angle."
If you could plot out the algorithm that shapes a sphere, Hannah writes, then why not an apple? If you run the numbers through over and over and over again, and it draws you a pyramid, then why not a leaf? Wherefore a blade of grass? A perfect summer evening? A bonfire?
Valentine once told her that scientists only understand the very large and very small – it's what's in the middle, the ordinary, that trips us up. That we don't understand at all.
Hannah doesn't want a cheat sheet for life's ordinary miracles, doesn't need to skip ahead to the end of the story and see how it all winds up. In that, she thinks she understands Thomasina. Poor grieving Septimus Hodge went mad trying to calculate the great heat death of the universe so that he could prevent it, so that he could reverse its course and bring the beautiful girl with the flowing hair back to him. After all, the equation must exist, if only one might attain it. But Thomasina simply loved the formulas for themselves, for the knowing. For the proving.
In a now-fading lesson book, she once tried to render the world in four dimensions, as only she was able to see it. Innumerable possibilities, unimaginable angles, the patterns repeating and shifting and echoing one another across history and geometric space, looping in endlessly upon themselves, infinite and beautiful.
There's a knock on the door to her guest bedroom at a quarter to midnight. Hannah pulls her dressing gown around her, rubbing at her eyes. She hadn't fallen asleep so early or easily in months. Of course it couldn't last.
"Sorry," Valentine says, pale-faced. He's still dressed in the jeans and jumper from earlier today, but they're rumpled. He'd probably fallen asleep at his laptop again. "Sorry, sorry, sorry. I woke you, didn't I? Christ, I'm sorry. It's just – Gus is asking for you."
"Bully for him," Hannah retorts, perhaps a bit snappishly. "Can it not wait until morning?"
"No, I don't think you understand," Valentine says. His voice sounds strained, odd. "Gus. Is asking. As in, verbally."
Hannah breathes in, and then out again.
"Oh," she says. "Oh, I see."
She makes her way downstairs, leaving Valentine muttering to himself in the corridor. Gus is waiting in the music room. He holds out a hand.
Hannah takes it.
He leads her out through the French windows and onto the grounds. The night is startlingly clear, and the moon shines brightly. It's only a night or two away from being full. There's a chill in the air, and the scent of wood smoke.
The house is burning.
Before Hannah has a chance to react properly, Gus catches her arm, holding her back. He shakes his head.
"Oh," Hannah says softly, willing her heart to stop racing. Cold sweat prickles her forehead. "That's not – it isn't happening now, is it?" But Thomasina's voice echoes in her ear: all times are now.
Gus's shoulders hitch in perfect mimicry of Thomasina's inelegant shrug. The family resemblance is striking, now that she knows to look for it.
His eyes have seen far too much for his teenaged face.
"You've seen it before, haven't you?" Hannah asks. It's a struggle to keep her voice steady, with the genius of the place dying above them nearly two hundred years ago. "The fire. When you were a child."
"I was five." Gus's voice is low and hoarse. It scratches in his throat like smoke. He won't meet her eyes, staring unblinkingly up at the burning garret. "It was my bedroom."
He doesn't speak again.
What do ghosts want? Valentine asked, not in so many words. But Thomasina had no unfinished business, whatever her tutor may have thought. Her work was never meant to have an ending. Iterated algorithms, infinite patterns, four-dimensional tesseracts revolving in an endless loop from every angle at once. Progress always marches forward, with or without her; the maths endure and evolve and refine themselves. The work is the point. She'd have been perfectly satisfied.
You've never found anything like that for yourself, Chloë told her. But she was wrong, too.
What do ghosts want? What does anyone want?
To be seen. To be remembered. To be known.
Hannah rests her hand on Gus's shoulder and together, they watch the tower burn.