The Life in Papers of Sofie K., page 1
THE LIFE IN PAPERS OF SOFIE K.
By Octavia Cade
Copyright 2014 Octavia Cade
Smashwords Edition
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Note on this edition: Cover design by Derek Murphy. Cover photograph by EricVega (istock).
Table of Contents
Introduction
On The Theory Of Partial Differential Equations
On The Refraction Of Light In Crystals
Supplementary Remarks And Observations On Laplace’s Research On The Form Of Saturn’s Rings
On The Problem Of The Rotation Of A Solid Body About A Fixed Point
On The Reduction Of A Certain Class Of Abelian Integrals Of The Third Rank To Elliptic Integrals
On The Theorem Of M. Bruns
Bibliography
About Octavia Cade
INTRODUCTION
I’ve always thought that there’s something in mathematics that is sympathetic to fantasy. Any discipline that traffics in imaginary numbers is bound to bump up against magical realism at some point. That’s my excuse, anyway.
This novella is as much biography as it is fantasy. Its subject is the Russian mathematician Sofia Kovalevskaya (1850-1891). Its structure is her papers: Kovalevskaya wrote and published half a dozen of them, although the number is often counted higher when different versions of these are included.
I have not presented these papers in the order that they were written. Instead, I have linked them thematically to aspects of Kovalevskaya’s life. Nor is the presentation entirely linear–in many ways this novella more closely resembles a collection of linked short stories. Events in one paper, or story, can occur before or after those in the following chapter. The third and fourth papers, especially, cover the same time period while focussing on different relationships.
That, too, is not an ordered approach. But then this is a story of monsters as well as mathematics, and there is nothing orderly about monsters...
ON THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS
I
A differential equation defines the relationship between a function and all the derivations of that function.
Sofie’s life begins in the nursery, listening to Nanny feed the monsters under the bed.
She doesn’t mean to feed them, but story-crumbs drop down from the coverlet, from the blankets, and disappear under the bed to growling. Nanny doesn’t hear the growling, or she pretends not to. “Who’s a silly thing, to have so many bad dreams,” she says when Sofie’s mother questions the screaming in the night, the tears and tantrums of waking moments, the pleas not to be sent to bed. “Don’t you know they’re not true here?”
Her stories are only true in other lands, in others times. “They were boarded up in their own little houses,” says Nanny of the plague victims, of the black death. “And burnt all alive to stop the infection.” But the black death and the burning wouldn’t happen to Sofie, oh no, and there weren’t any werewolves round here, nor were there snakes with so many heads that she’d lose count before she were bitten. There weren’t any witches in their chicken-houses, and there weren’t any sickly little children with ash around their feet and tooth marks in their throats.
Sofie thinks of those children so often that broken dolls send her into screaming fits. Unfit, imperfect, she wakes in the night to run to the mirror, her feet bare and cold on the floor and Sofie so afraid, lest she stare into the glass and see her own head opened up like porcelain and the stitching unravelled, her arms ragged and falling from her body. Then when she sees herself, her face and head in one piece still if slick with fear and night sweats, she has to turn around and face the bed again, the linens pale in moonlight and doing nothing to hide the dim movements under the bed, the shape of teeth, the growling and the hot breath that smells of pestilence and of fire.
Sofie watches the bed for a long time, her feet frozen beneath her and the nightdress thin around her. She waits until she can no longer feel her toes, and then runs for the bed before the numbness reaches her ankles and slows her running, weakens the final leap from the hard cold floor to the bed and the sudden silence beneath it. The silence that echoes in the bedroom after her body hits the blankets... that echoes still when those same blankets are pulled up over her head and kept there until Sofie’s breath turns the wool wet, as if it were breathing back.
And still Nanny tells her stories. Sofie is often the only one she has to tell them to. It’s not as if she is an only child. There are others–a sister, older, and a brother, younger, and both spend more time out of the nursery than Sofie does.
“Your sister’s with company,” says Nanny, of Aniuta. Aniuta is pretty and Aniuta is charming. The firstborn, the one trotted out for company and for pleasing, to be petted by the ladies and admired by the gentlemen guests with her golden hair all around her and smiles that please her parents. Aniuta never wakes screaming in the night; she scoffs at stories and scratchings and sleeps all through.
Sofie adores her. Everyone does. That’s the problem.
“They want to see your brother as well,” says Nanny. Five years younger than Sofie, Fedor is unextraordinary and therefore perfect. “Come, Fedia,” says Nanny, straightening little boy clothes and brushing little boy hair, hustling him out of the door, sending him off in his sister’s footsteps down into the parlour, into light and music. The pretty girl and the heir, and Sofie is left, dark and dark-haired and moping in a nursery that has no charms for her, too straight yet to dress for company and still too feminine in her straightness to be shown off before bedtime.
“Not you tonight, poppet,” her Nanny says when they’re alone again, and it is no comfort to Sofie to know that here at least she’s the favourite, even if only as an audience. “But don’t worry, my dove–stay with me and I’ll tell you all my stories. I know how much you love them.”
(She loves them enough to stay awake and think of them, to fall asleep and dream of them. To hear them under the beds and wait for them in every mirror.)
Pretty sister, pretty brother, and Sofie in the nursery learning nightmares: twelve-headed snakes, broken dolls and broken houses, witches and werewolves and the black death.
II
Ordinary differential equations depend on one independent variable–like time, or motion, or decay.
Sofie might not have been the first and she might not have been the favourite, but she is aware that she is spoiled, still. Indulged in her schooling, or in the lack of it, for what use is school to Sofie, who needs to be trained into dancing and music and French and that under Nanny’s care. But Nanny is slowing now, and was never too bright to begin with. Against Aniuta she has no defence, and the girls find themselves free with their days, mostly, and what little education they get filters through heads that are simultaneously critical and empty at once and is left to curl in corners like under-ripe fruit.
It’s the fruit that is their downfall, that ends innocence and gives freedom. Not that ideas are left to grow inside them, to spread seeds like apples. It’s the fruit in the garden, as always. Spoiled little monsters they are, and left to run wild in those gardens–which has the benefit at least of filling them up with something, anything, that isn’t stale repetitions and smothering. The fresh air and exercise makes Aniuta even prettier, lets her romp golden in the gardens and Sofie follows along behind, tripping and giggling and then they come across it, the poison fruit and tempting, and they are booted out of the garden in a sick and sudden haze of vomiting, left wretched and retching, broken in their beds.
“Serves you right for being so greedy,” Nanny says, mopping up, but she is not the only one with something to say and if Sofie and Aniuta are choking on their own gorges and griping about stomach aches then they are not the only ones with complaints.
“I hope you’ve learned your lesson?” says their mother, querulous, and Aniuta snaps back, sick as she is but backed by force of personality, by a tact undermined by illness and teetering over into aggression. It is her way, to go on offense.
“What lesson?” she says, and Nanny is exposed as a fraud, as a useless stop-gap of an educator and Aniuta is exonerated. “It’s not like I wanted her to get into trouble,” she says to Sofie later that night, the covers pulled tightly around them both as if to anchor them to their beds and darkness all around. “But I’m not actually sorry. I wanted to eat them, so I did.”
Sofie is too sick to do anything but agree, and that silently. Even nodding her head brings back the nausea, and for once she does not mind the growling under the bed. “Just come and eat me up already,” she says to the werewolf, to the snakes and the witch women and the dead scent of ashes. “Get it over with.”
She might poison them on the way down. That at least would be something. But she isn’t eaten up by anything but poison and the expectation, the accusation of guilt. For that, whatever it is that lives under her bed is sympathetic, and takes her for one of its own.
Their father is less sanguine. He sees them in their bedrooms, stands at safe distance so his clothes won’t be s poilt and neither will his expression, which is distant disapproval all the way. It gives Sofie a funny feeling in her tummy, and she doesn’t know if Aniuta truly isn’t bothered by the inspection or is just pretending, wearing a wolf skin over her own and with her teeth carefully covered over.
For it is an inspection, and one the girls have failed. It is a mark of reflection as well as failure, for supervision was lacking and all the adults know it. Their father inspects his fallen angels, pale in their beds with their hair spread all around. He’d like to think they ate in innocence, but a simple conversation teaches him the difference. The truth is his daughters are pig ignorant–like babies, they gobble whatever they can stuff in their mouths. Not proper young ladies at all.
He gets them better teachers, piles on books and lessons so they can learn to take little bland bites, and those delicately, like good girls should.
He thinks he has curbed their freedom, their ability to run amok and stuff themselves. He is very, very wrong.
III
Partial differential equations involve multiple independent variables and unknown functions.
These are not the only changes. The house changes around them, changes with the help. As the girls have their minds remade, their parents suppose, into something less greedy and hopefully a little less vacuous, the insides of the rooms are dressed with the same care as the inside of their skulls. It is a fresh start all round. Everything is to be tarted up, even the walls.
Paper comes from St. Petersburg in fat rolls. It is hugely expensive, and Sofie wants to touch, is fascinated by the fat and fibrous cylinders: the way that they feel under her fingers, the way that they look on the walls. Too often, she is hustled away from the hanging, from the workmen all on their step ladders and the way they smooth down the paper, covering up what she used to know with something different and far more exciting.
“Keep your sticky fingers away from it,” she is told, and Sofie scrubs until no smudges are left and goes to play with scraps, goes to draw on them and make paper dolls of the leavings. There aren’t many of these–the paper is too dear for that–but she takes what she can get and sneaks in to watch when the paper goes up, when her lessons are done.
The whole house smells of glue. Sometimes when she walks she can hear footsteps behind her, footsteps and breathing, small sneezes close to the ground and an uncertain growling. “I like the smell,” she declares, stubborn and setting forward, afraid to look behind her but angry in her fear. This much is new. But Sofie is learning, learning better from books than from fruit, and she has learned that what you don’t acknowledge is like the little piece of grit in oysters. It irritates, but she is girl instead of shellfish and irritation gives her scar tissue instead of pearls.
She tries to paper over her anger, but the cracks are shifting beneath and there is not enough paper to cover it, not enough of her to count the cost. She lacks the coin to pay for it, and is not yet grown enough to realise that sometimes there is more to be paid than coins. How could she? Coin is all she hears about.
“Stop pawing at that paper. Do you know how much it will cost to replace it if you ruin it? How much it will cost to bring it all the way from Petersburg?”
Sofie rolls her eyes and slinks away, hands tucked behind her back and locked around each other to counter temptation. There is more than enough, she thinks, with the wallpaper rolls laid out like logs before her, and enticing. They are big enough to sit on, almost. There seems to Sofie to be enough to paper the world, but if that were true the house would have to be bigger than the world for when rooms the size of continents are decorated there is not nearly enough remaining. The pretty rolls are spread up and smoothed out, and still one room is left unpapered. It’s the nursery, naturally. Not very important, no-one will see it–no-one but the children, and they won’t be there forever.
Still, it can’t be left bare–the nursery has to be covered with something. Even scrap paper will do. Her father has some, all done up in boxes, the remnants of his own school days when he studied more than Sofie. More and different, for even with new teachers to keep her out of the garden and her mouth shut against illicit fruit there is the question of suitability, and what is suitable for him is not for her. But there is nothing there that she can understand, though, nothing that will distract her from her studies in these her father’s notes. Might as well hang them up–it’s only wallpaper, only scraps. Better than nothing.
It’s not scrap. It’s calculus.
Lithographed lecture notes, strange symbols like hieroglyphs, formulas that might as well be magic and pasted at random.
Sofie stands solemn before them, stands for hours, then years, seeing doors not meant for her. If irritation produces scarring in little girls, then it’s curiosity makes the pearling. Sofie is enraptured, absorbed, and when the padding stops behind her, the heavy breaths and the stench of bone and pox, she lets her hands fall to her sides and does not catch them up again.
There is another step, a heavy one, and if Sofie does not look down and away from calculus there is fur under her fingers, and coarse.
IV
An obvious question, fundamental, important: can every differential equation–ordinary, partial–be integrated, or must they be solved piecemeal?
There is room for another child in the house. Not another son, or even a daughter, but Sofie is resentful nonetheless, and feels the same growl in her throat that she once heard under the bed. Cousin Mishel has come to take lessons with Sofie, come to sit in her schoolroom, to be surrounded by the symbols he knows nothing of.
Poor boy. He hates maths, would prefer art school where proofs and problems and parallels can be painted over and ignored. But his parents have other ideas, so he’s sent to Sofie to be embarrassed into effort. His presence in Sofie’s life, in her rooms, is not a reward for either of them. Their parents are not subtle in their punishments, for both children are unfit and should be brought to know it. They are children, after all, and there to be corrected.
Neither of them want the correction. Mishel has paints and pastels in his veins, and his blood is so thickened by them that he cannot sieve meaning from symbols, cannot solve suitably the suitable problems placed before him. Forcing him in front of blackboards is an exercise in bare success, for it is clear that he is lumpen in his mathematics and would sooner use the chalk for other things. But there are expectations, and preference is expected to slink before shame. This is where Sofie comes in–dragged in, as an article of embarrassment. “See?” says the family. “If a girl can do it, why can’t you? Aren’t you ashamed to be beaten by her?”
Shame thins his blood, enough to scrape passes and impress memory rather than understanding. Mishel learns to regurgitate what is fed to him, his own little pieces of poison fruit made from cut up paint brushes and disappointment. He has no Aniuta to talk to him in the night, to say So what? and go ahead anyway. He has no sister that is sorry for him, no sister to teach him to be not sorry. He only has Sofie, who could be that sister if she would, and will not. His presence makes her unsympathetic, because clearly their talents have been reversed somehow and it should be her chewing on her pencil, disconsolate, uncomprehending.
Stupid.
It should be her filled up with pastels, with paints, with dainty little sketches of flowers and animals and landscapes, inoffensive subjects all. It should be Mishel finding delight in calculus, making sense of secret languages and friendly with them. With her wallpaper, hers! But it isn’t, and so she is held up, ostensibly, as something to aspire to. A clever little girl with clever tricks and clever ways–but a little girl verging on too much clever and valued for her role as an exemplar of humiliation. Like a piglet able to do tricks in mud: isn’t it clever? Isn’t it strange? Look at the cunning little trotters, look at the shapes they make in the mud, the numbers and the slopes, the filthy inclinations of gradients.
