(You’d almost think it were human.)

  And Sofie, with her shameful female brain and footsteps that have more of the wolf in them than the pig, silent steps with the clicks of claws and rosary beads that the contaminated hold to themselves behind their boarded doors... Sofie is proud of her skill. Another girl, raised by other help might not have been but Sofie has around her bed, around her nursery, a miasma of the unnatural and the monstrous. It frightens her, but it is familiar and comes with its own rewards: there will be no trotting in her steps, no slow grunt behind her and no trace of mud on her skirts.

  There has been no mud since the garden. Her skirts are unstained, her monstrosity shown elsewhere: in Mishel’s gaze, resentful as her own, in the mixed pride and puppetry of her parents as she is dangled, bait in front of blood. An object. A lesson. It is why she is not friendly. She is aware, underneath, that if a pig could do mathematics Mishel would be sent out to the sty to sketch his geometry in mud.

  V

  A general solution for the analytic functions: a locally convergent power series.

  Sofie borrows a book from a neighbour, a primer in physics, and reads at night where her governess cannot see and disapprove. Bad enough that she is better than boys, but this is a betrayal beyond that. She does not enjoy being held up and held back for Mishel, but even so she has no desire to see him bruise further so she does not bring it with her to their classes, lest he see her with it while he struggles, still, with arithmetic. There is, too, the possibility that it would be taken off her. She is already too far outside the norm. It is one thing to be an example, another to court piggery and bring the sty into the parlour.

  But there is another reason, one buried deep beneath the surface, as if she had changed her skin and put another over the top: a surface layer of competence and of certainty with antonyms buried deep. The burial is not a success. She feels the bones of it knocking within her, the echoes that she hears in nightmares, barred behind bolted doors and nailed over, the contagion contained. For Sofie cannot understand the primer–or cannot understand all of it. She has no trigonometry, and the existence of sine is as apparent to her as algebra is to Mishel.

  This is her shame, as algebra and paintbrushes are Mishel’s. Strange symbols stagger down the page (stagger down the wall) and there is nothing in her that recognises them. This is something she can never tell. It would not be the sympathy that undermines her, for there would be no sympathy, not really. Instead, there would be relief. Relief, that her unnatural precocity, her strange and unfeminine brain had settled somewhat, that this quirk of childhood was a passing thing, and superficial. Her mother would smile, her father pat her head. “Too bad,” they would say, and the knowledge that they didn’t mean it would pierce her flesh, draw blood from deeper wells and leave her weeping behind.

  She wishes a deeper skin than that. One embossed with symbols, one with the fur turned inwards and the skin too thick to break. Sofie does not wish to be porcelain, for porcelain cracks and in those cracks are nightmares: broken dolls and the hiss of air escaping that sounds like snakes, their heads all entwined together and forcing through the china carcass. It is because she does not wish to be porcelain that she hides under the covers, keeps her primer in her pillow and does her best to puzzle out the parts that are a difficulty to her. She pulls the linens over and on her feet there is a weight, crawled out from under the bed and resting on her. She hears breathing in the dark, but if she looks she might see eyes and so she does not look. The breathing is slow, regular. Patient. If it has the hiss of snakes sometimes it does not sound hungry yet, so she learns to take comfort in the warmth it brings, the silent support of monsters as she turns pages and traces strangers.

  Slowly, slowly, as the blankets at her head come wet with her own breath, as the blankets at her feet dampen with the breath of another, sense comes to her with the silent slink of snakes. Little by little, she puzzles it out–how a chord, when very small, can substitute for the mysteriousness of sine. This strikes a tone within her, for Sofie knows what substitution is. She is a substitute herself: something to be used on Mishel in place of a birch rod, something to be shown off when Aniuta is out of the way and Fedia is not old or bright enough.

  It is as if she has invented trigonometry again; approached it in the same way it was invented before, except Sofie is a little girl and invention thought beyond her. Yet it is not beyond her, and under the blankets Sofie smiles–a wolf smile, a witch smile, for she has deciphered sine through the spell of substitution and the primer is laid open to her, spread out firm and flat as wallpaper, and this she can touch without scolding, for the weight on her feet she imagines to be many things, some of them frightening, but in that weight is nothing of expectation and nothing of proper behaviour.

  (In her success the symbols smile at her, the sine is dog-friendly and there are triumphant dimples on the nursery wall.)

  VI

  A counter-example: an equation for heat–not normal, and solved with a with divergent series.

  Sofie has more family members than Mishel, than her parents, than Aniuta. There is one that shares her interests, who looks at her mathematics without resentment or concern or disinterest. Sofie and her uncle converge on algae, on coral reefs and infusoria. His interest is biological where hers is mathematical, but the bridge between them is built of application and is a solid one. She settles close in fascination, sits on his lap for the stories of science. They are so much better and brighter than those of the nursery–he tells her of tiny marvellous creatures, almost magical in their appearance and their habits, but none of them have twelve heads and hiss over the best part of two octaves. There is no skin-changing in them, no locked doors, no disease and no fire.

  With her uncle footsteps fade, and there is no meat-breath on her face at night. Their time together is perfect, like a paradise, but Sofie has been in paradise before and the fruit was a poison to her. She does not realise that history is about to repeat, that the old apple cheek she presses against is also capable of a betrayal that will set her guts to twisting within her till her interest expels itself in sour tastes and cramping.

  (“I could have told you that,” says Nanny, but her duties have changed and no-one goes to her for classes now. Their education lies elsewhere.)

  It is an education that Sofie gets, the garden come to life in the parlour, come with treachery and teasing. There is a neighbourhood girl, one her own age, a suitable playmate. That Olya is none too bright herself is a negligible concern, for nobody asks Sofie what she wants in a playmate. She’d rather have her primer and the creature that walks behind, the creature come out of Nanny’s stories, but when Olya is present Sofie has an obligation as host and that means a series of idiotic games done over and over because Olya is fond of repetition.

  To save her sanity, Sofie drives a bargain. She’ll play nicely all day, all the silly boring games and she’ll do it smiling, with no single word of complaint if when evening comes Olya will leave her alone, let her have her uncle to herself. Olya promises, like butter wouldn’t melt and Sofie falls right for it, because how could such a girl out-cross her? But evening comes and Olya stays, her promise broken.

  Sofie’s uncle is faced with two little girls, and because he is a kind man who knows nothing of promises he tailors his tales to the guest, pinches Olya’s milk cheeks and makes much of her.

  It is too much to be borne. Olya primps, Sofie fumes–and bubbles with rage, and bites. Bites down, bites hard and deep as wolves do, draws blood until her mouth tastes of metal and Olya has paid for her broken promise with broken flesh: a little porcelain doll with her skin cracked open and the insides coming out.

  “Nasty little brat!” Uncle cries, but Sofie just smiles at him, red-mouthed. She knows she’s been a beast but doesn’t care. Her teeth have scuppered any relationship between them, and they are sharper now than they have ever been. She has turned away from him, and the bridge between them is washed away in betrayal. There is nothing of the coral about her now, no bright brittle formation with a pretty dress swirling about her like seaweed. Instead there is the rising heat inside her, a roaring rage of separation.

  She leaves the room, leaves Olya to her uncle and as she leaves him the footsteps return–not the heavy tread of parents or a quick hard trottery step, but the near-silent pad of wolves and witches. Whiskers tickle her palm, and a monster walks beside her.

  Nanny’s stories have won out after all.

  ON THE REFRACTION OF LIGHT IN CRYSTALS

  I

  When light travels through two different media, it refracts at the interface.

  Sofie’s uncle may have locked up his stories inside him, but she has a sister as well as an uncle–as well as a brother, as well as a cousin. And that sister does not scold her for biting, not when she hears of betrayal, and she does not resent Sofie for being better at mathematics than she is. Aniuta is not a mathematician. She prefers stories, prefers to string words together in ways that Sofie will always remember, and that gives them kinship of more than blood. Symbols bind them, for they have shared a garden.

  Sofie asks, when they are tucked up in bed, if Aniuta ever hears footsteps behind her in the day, ever hears breathing under her bed at night. Aniuta owns she hears of hissing, sometimes, the kind of susurration born of snakes, but that is all that she will say. She keeps her secrets well, Aniuta, and Sofie is never sure that she shares all she knows. She does share her stories though, reads them to Sofie at night with stained fingers, reads from pages she has written in her own heart-ink.

  Aniuta writes of what she knows, of crossroads and possibilities. She writes to understand her future life, to mark signposts on her way so that she may see what choices bring. She writes of a young girl, like herself. Like her sister. That girl is too scared to take chances; she always does the expected.

  “I don’t think I’m going to like this girl,” says Sofie, sceptical, her feet curling into blankets and her teeth sharp against her lips. “She sounds like she’d let herself be nailed in when the plague came.” Someone who’d hide under covers at the sound of the hammer at the door; someone who’d die and cry on her knees when the monsters came. Someone who was not a monster herself.

  “Maybe you’re not meant to like her,” says Aniuta. “Maybe she’s there to feel sorry for. Now hush, and let me read.”

  This girl, this young girl who lives in mirrors but darkly, who exists as a signpost on the road not taken, or the road that could be taken, has a dream. A dream, that old device–too old, and verging on cliché, but Aniuta is very young herself and clichés are fresh to her, exciting. They still retain meaning. The dreaming girl sees her life pass down a different path, shows the shadow of her own. In the dream she takes the simple choice, the dutiful one: a lover’s abnegation. She is left alone and suffering, and Sofie feels pity and embarrassment simultaneously, though that embarrassment is second hand and she shakes her head at simple choices, because for her who is so young and clever the simple choice is so often the stupid one, and stifling.

  Because it is a dream, Aniuta’s mirror-girl wakes, wakes from dream and into story and the reality of that story is not a happy one. Her determination to take another path is thwarted.

  “Serves her right,” says Sofie. “It shouldn’t take a dream to tell her what to do.”

  “Sometimes dreams are all we have,” says Aniuta, who is little enough older but that little is crucial, and she sees, if dimly perhaps, the lives that could be in store for her, for Sofie, better than her sister does.

  It’s too late for the dream girl, of course. When she wakes her chance is gone. The young man she loved and dreamed of, the man she left in that dream for duty, the key to her future, the beautiful boy, is dead.

  Typhoid.

  It’s not the black death. The dream girl’s too old for that, she and Aniuta both, and their shared idea of death is a prosaic one, and common. The black death is a children’s nightmare, something to be grown out of, and if Sofie is aware of the way that death stalks her in the night, sleeps under her bed in wolf skins and breathes pox into her rooms then she is the only one.

  Aniuta never worried about Nanny’s stories. She never took them seriously. She has always been more interested in the stories of herself, and there are other things that frighten her. Because of this the girl she has brought to paper and to dreaming dies of grief at her wasted life: she is only a character but she is Russian, after all; and from a land where unhappiness is suicide.

  (Sofie doesn’t complain that her sister’s story is an unhappy one. She never expected happiness, not really, and if witches are monsters come alive with foresight then her skin belongs to more than wolves.)

  II

  Calcite spar, the Icelandic crystal, shows double refraction. Each light ray passing through it splits in two–but only one of these beams is refractive.

  The house at Palibino has an underground post–has notes passed beneath and secret letters. It’s an informal thing; built for privacy and for freedom. The proper mail, brought properly, sits on salvers at table where the adults can see and disapprove. Aniuta finds this wearing, a limit on her correspondence. Instead, she bribes a servant. It is an easy thing, being beautiful and charming, and beauty and charm buy her latitude, buy her letters kept back and handed off in secret for sending and receiving both.

  It is a happy system if not a foolproof one, for there comes a night, on her mother’s birthday ball, where one letter slips through the netting she has set about herself. It is only a matter of time before she is found out: the latitude so cheaply bought is thin enough to last the night, perhaps, and Aniuta dances her slippers through in a state of sulky terror.

  She has always felt so grown-up at balls, passing into adulthood like a dream. Pretty dress, pretty slippers, and all the people who vie for her attention. Most of them are men, and balls are for Aniuta a place for practising power, but the little bits that she has scraped to herself are not enough to insulate her from what is to come, from the consequences of secrets kept and bargains made. Her fingers, scrubbed clean of ink, are perfect in their gloves, and it is all she can do to still the shaking.

  She has sold her story, the story she wrote to herself and read to Sofie, sold it for profit and for influence. Sold it to Dostoevsky, to that famous Russian writer, older and above her, for his magazine The Epoch. It will be printed in a neat fine Cyrillic more elegant than her own hand-writing and more permanent as well. “Why should I not?” she says to herself, angry at herself for shrinking, angry at the ball gown that is no armour.

  Aniuta knows what her father thinks of authoresses: “Any girl who sells her stories will sell herself!” he thunders. As if she were a whore to sell herself out for cash, to exercise her talents and be rewarded for them.

  She does not feel like a whore.

  She is proud of what she has done, and in that pride is strength. She bellows back, screams and cries and makes a fuss, does not give in, wraps her papers around her as a better shield than silk and will not, does not go quietly. She is determined to argue him round, and does. Beauty and charm are all to the good, but Aniuta has force of personality as well, has the charisma that never lets her sit out a dance, and when she is done with her father it is as if there are hammers in her hands and a wooden door between them.

  Sofie listens to them fight, listens to the shouts and screams and slammed doors, listens to sounds that reverberate not only through the beautifully wallpapered walls of the house, but into her future. She listens, and remembers–remembers so well and so vividly that one day she will later sell the story of that argument in her own autobiography.

  She wonders about the girl who sells her brains. The girl who sells her stories will sell herself, but Sofie’s stories are tied up in intelligence and in learning, in mathematics as well as monsters. If her stories rest on the contents of her skull, then is she not willing to sell herself as well? Her left hand rests on fur and she can feel growling vibrate through bone, a different type of reverberation, but that growl ends in silence. Ends with silence, and Aniuta closing the door on her father with her head held high and that is learning as well, something to be store away and considered.

  This is how it is, Sofie thinks. This is how it happens. Action, reaction, then being left to get on with it.

  III

  I thought it possible, said Fresnal, that the two resulting light waves did not interfere with each other.

  Dostoevsky is permitted to visit. It seems Aniuta’s correspondence with him has gone beyond dreams, beyond story. He is so very much older and she still so young, but he comes courting nonetheless, and if her parents are rocky about it they soon learn to leave well enough alone. They do not find it an especially savoury relationship, but supervision is better than scandal.

  Sofie’s heart beats like footsteps: quiet but heavy and with the weight of snow behind it, the weight of a large animal breaking through crust. She is charmed, enraptured, and for the first time she thinks that broken dolls might not send her screaming, because if Sofie is still a dark little creature in childish dresses then Aniuta is grown and golden and her skin is like porcelain.

  If you shatter, she thinks, he might not want you any longer. And then she is ashamed of the thought, ashamed of herself, and spends her nights on her knees. The floor is cold beneath her flesh but she brings her palms together against more than chill and prays, because if Sofie is made of monsters then she is part witch and wishing. She does not want her wishes to brings cracks and darkness to the face she loves beyond all others, because if there is one thing that Sofie has learned from the dreaming girl it is that her sister is herself.

 

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