The Arithmetic of Schoolgirls, Part I: Proofs
Posted on Sun May 10th, 2026 @ 10:36pm by Master Chief Petty Officer Vashti Rao
2,242 words; about a 11 minute read
Mission:
Character Backstories
Location: Ootacamund, India, Earth
Timeline: 2374
The mist seemed to move in the air as though the hills surrounding Ootacamund had breathed it out in a long and heavy exhale.
Vashti kept her head down as she crossed the path from the dormitory to the main academy building, her orange satchel bumping lightly against her hip with every step she took. The gravel was slightly damp beneath her shoes, and now and then it shifted treacherously, as if the ground might give way completely if she put too much trust into it. Of course, she didn't trust it. She didn't trust most things here yet.
The eucalyptus trees stood in long, pale rows, their bark peeling like old parchment paper. When the wind moved through them, it made a dry whispering sound--something like pages being turned in an old book she wasn't allowed to read just yet. To anyone not from Tamil Nadu, it would smell sharp and medicinal. It cleared the sinuses and lungs whether one wished it or not.
She had learned, in three months, the proper way for a student to arrive early to class without appearing overly eager. It was indeed a delicate balance. To be first was to invite notice; to be last was to invite harsh commentary. So she came as she did now--neither one nor the other--and slipped through the academy doors just as a small cannonade of girl gathered and dispersed around her.
Their voices rose and fell in different timbres and pitches like invisible wind instruments, some excited and sprightly--others moody and flat.
Saint Kateri Tekakwitha Academy was drawn back upon a long rise of land slightly north of Ootacamund proper, where the hills began to gently withdraw from the town and ceded themselves to the quieter countryside. The road that led to it wound upward through damp groves of eucalyptus and blue gum, past stone walls that were heavily fleeced with moss, until at last the school revealed itself.
Its oldest buildings had been constructed during another century entirely, when the Nilgiri air was still mentioned in colonial letters to family and British military officers as though simply breathing it might be a medical miracle for the sick. Grey stone was quarried from the hills, which formed the heart of the academy's main building. In the rains, those stones darkened almost to charcoal; in dry weather, they took on the tone of old ash. Ivy clung in bunches to certain walls despite the altitude while narrow Gothic windows stared outward over the slopes, patient and thoughtful.
To the west lay the famed botanical gardens--older even than the academy. Their terraces descended in green stages toward the valley, filled with trees imported from distant parts of Earth over centuries of unchecked ambition. On mist-heavy mornings, the gardens appeared less cultivated than enchanted. One could stand and stare for hours at the shapes which emerged and disappeared: monkey-puzzle trees like stalwart sentries, ancient cypresses that seem the dissolve beyond the vapour, flowerbeds glowing with vibrant colour through the fog as though they were painted glass. The older girls sometimes claimed you could see the gardens breathing like a pair of lungs at dawn. And there were days Vashti almost believed them.
Eastward, beyond the school's athletic fields and science buildings, the land rolled downward into tea country. The plantations striped the hills in symmetrical green curves that appeared so mathematically precise from a distance, one would be fooled into thinking agricultural machines deserved the credit and not human hands. When the wind shifted, particularly after a good downpour, the scent of sharp tea leaf reached the academy grounds, mixed with the scent of wet soil. It certainly wasn't an unpleasant smell. It carried something earthy and melancholy, like the memory of an old friend.
As Vashti found herself inside the main building, she remarked--not for the first time--how the corridors felt far colder than the exterior. But she kept her eyes forward and her hands occupied--always occupied--adjusting a strap, checking the clasp of her satchel, or even brushing a flyaway hair from her face. It was always easier to look busy than to appear alone.
Her classroom was at the end of a long corridor where the windows overlooked a drop of green that seemed to go on forever: the tea plantations. Rows upon rows and immaculately trimmed. She wondered, briefly, who had first taught them to grow like that.
She took her seat near the middle--not too near the front, and not so far to the rear--and laid out her student PADDs the same way she always did. She activated one PADD and the surface lit-up, greeting her with equations from the previous class.
Vashti hadn't bothered to look around or make eye-contact with any of the other girls. There was no need to. And she knew better than to invite scrutiny.
When Mr. Deshpande entered, the entire room shifted subtly. The conversations quieted while coiffed heads and burgundy-uniformed bodies faced forward while the sound of chairs adjusting against the hard floor echoed. A few girls exchanged glances that seemed to carry something Vashti didn't care to name, though she recognized it for what it was: admiration for a male instructor. Also something she didn't think belonged in classrooms.
He was a man of perhaps thirty-five years, possessing neither the sternness nor the faked elegance that some male teachers frequently commanded attention with, yet there existed about him a singular and quiet attractiveness which grew more apparent the longer one remained in his company. His hair was dark and thick, falling carelessly across his brow while he lectured. His attire was standard and respectable for the men who taught at the academy, though for Deshpande, it bore frequent signs of neglect: a loosened cuff here, an ink-mark near the wrist there, a collar partially twisted in the way it settled around his neck. His expression was often set in restrained amusement, almost as though both the folly of being human and the brilliance of being human intrigued him in equal measure. His deep-set brown eyes seemed to perceive more in a pupil than she had yet discovered in herself. Slow to anger, quick to forgive; he was one of the most liked teachers.
"Let us not waste the morning," he said, not unkindly, and without any preamble the lesson began.
They were speaking of motion. Of bodies in orbit, of forces that pulled and resisted, and the dance between mass and distance. He hadn't drawn or written anything on the board at first. He spoke, and the words seemed to align themselves into understandable diagrams for the girls.
"If a system appears stable," he said, pacing once along the front of the room, "we must ask whether it is truly so--or merely balanced upon conditions we have not yet disturbed."
A hand shot up before he had finished his point.
Then another.
It was always the same girls. Always. The confident, the certain.
The first as Catarina Desai--a peer of Vashti's who always seemed to be chasing approval. The girl from Goa was one of the most competitive in the class. She was quick, confident and assured of everything she did, whether it was field hockey or answering a question that might earn her a higher score.
"Yes, Miss Desai?"
"It destabilizes, sir," she replied, her voice clear and unequivocal. "The system compensates until it reaches a new equilibrium."
"Does it?" he asked mildly, almost smiling.
There was a ripple of uncertainty that passed through the room like the mist over the nearby tea fields.
Another girl offered a refinement. A third added to it. It was the same constellation of voices orbiting the question.
Mr. Deshpande listened, nodding now and again, his expression nonplussed.
"And the rest of you?" he said at last, turning from the board. "Are we to assume that the laws of physics apply only to those inclined to raise their hands?"
There were a few nervous laughs while he paused to run his eyes over the entirety of the classroom.
And then, without warning, he let his gaze drift somewhere past the front row and its familiar hands, only to settle somewhere nearer to the middle.
"Miss Rao."
Vashti nearly jumped out of her chair, looking up far too quickly. For just a second, she could have sworn he must be addressing someone else--some other Rao, maybe? Some other girl who didn't flinch or shake at the sound of her own name.
"Yes, sir," she said, only barely sounding normal.
"If the equilibrium of such a system is disturbed," he said, "what determines whether it returns to its prior state or collapses into a new one?"
It wasn't a simple question. There was nuance and numerous edges. Vashti felt them right away.
Her first instinct was to lower her eyes and let the silence stretch on and on until it snapped and someone else stepped in to fill it. That instinct had served her well in many classes up to this point. It wouldn't serve her here and she could feel the room waiting.
"The energy," she said, barely above a mumble. "The amount introduced--or removed. And the... the nature of the disturbance."
He tilted his head just a little--it was not disapproval but it also was not quite satisfaction either.
"Go on."
She swallowed once, feeling all eyes on her.
"It depends on whether the system can absorb the change without exceeding its limits," she said, the words coming out more steadily, though her hands had gone cold as if she'd just shoved them into a snowbank. "If the internal forces can compensate--if they redistribute--then it may return. Otherwise..." She hesitated, searching for the right word and finding nothing readily available to her which felt sufficient. "Otherwise it finds a different configuration."
There was a slight pause as if what she had constructed were being evaluated.
"And what," he asked, gently, "might determine those limits?"
Vashti didn't know if she was expected to know that. That was the trouble. Expectations in Mr. Deshpande's classroom didn't always call ahead.
"Structure," she said, after a long moment. "And... and the interactions within it. Some systems appear stable because they have not yet been tested."
There was a slight flicker that crossed his expression. It might have been approval, though it was quieter than she imagined it would be.
"Yes," he said. "Precisely."
He turned then, continuing the lesson as though nothing unusual had occurred. Though Vashti felt something had happened and it centered around her.
She didn't speak again nor did she lift her eyes back to the front of the room. The equations that followed the lesson seemed to fit into place nicely and she felt some satisfaction in completing the work.
When the bell rang, it was a mercy--it almost always was for Vashti. The room slowly dissolved with chairs scraping the floor and feminine voices rising in volume as attention shifted from learning to what she considered the weird world of socialization.
As she gathered her things carefully, she could still feel a slight numbness in her hands from earlier. She hoped no one would notice.
She nearly made her way to the door and the corridor without incident.
"Miss Rao."
Vashti turned, holding her books in front of her.
Mr. Deshpande stood a short distance away, one hand resting lightly on the edge of one of the front-most desks. Up close, he seemed less distant than he did at the front of the room. Younger, maybe. Or perhaps more approachable.
"Yes, sir?"
"I am, I confess, somewhat old-fashioned," he said, with the same trace of strangled amusement that never seemed to unfold into a smile. "I place a certain value on participation. It accounts for a portion of your final mark."
Vashti's stomach dipped.
"Yes, sir."
"You are not lacking in understanding," he continued. "On the contrary. But understanding, if kept to oneself, is of limited use in a place such as this."
She nodded, though she wasn't entirely certain she agreed with that. Understanding had always been something she held close. To expose it felt... dangerous.
"You think clearly," he said. "And you think quickly. There is no reason to hide that."
Oof. Hide. That word stung--even if it wasn't spoken cruelly.
"You're a first-rate student, Miss Rao. Your work speaks for itself. If you trust your work," he added, "you may find it speaks well enough for you--once you allow it to be heard."
She looked down at her hands again.
"I will try, sir," she said, and meant it in the same way someone promises something without any witnesses.
"I suspect you will do more than try," he replied, something behind his eyes seemed mirthful.
Mr. Deshpande didn't linger--he rarely did.
Vashti stepped out into the corridor a moment later, the noise of the academy reaching its usual levels once again. It felt no less foreign than it had an hour before. But there it was, perhaps, a small place within it now where she might stand without disappearing entirely.
Outside, the mist had thickened and it pressed against the windows like it might be trying to listen and gain a proper education.
Master Chief Petty Officer Vashti Rao
Chief of the Boat
USS Astrea
(NPC of JB Dorsainvil)
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