(DISCLAIMER: All characters and the whole Harry Potter franchise - except for Jeremiah Hallysworn, Mallory Evans, Alice Urie [plus a few other more characters I haven't decided to get into the story yet] - belong to none other than J. K. Rowling)

Zeno's dichotomy paradox -  a concept.

As recounted by the philosopher Aristotle himself, this is an idea of an object that which is in locomotion must arrive at the half-way stage before it arrives at the goal.

Suppose Homer wishes to walk to the end of a path. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The resulting sequence is as follows:

This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.

This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion. An alternative conclusion, proposed by Henri Bergson, is that motion (time and distance) is not actually divisible.

This argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. It contains some of the same elements as the Achilles and the Tortoise paradox, but with a more apparent conclusion of motionlessness. It is also known as the Race Course paradox. Some, like Aristotle, regard the Dichotomy as really just another version of Achilles and the Tortoise.

But how do we give a solution to Zeno's dichotomy para-

Alice's eyes had stoppped in the middle of reading a very interesting ancient if not for the feeling of her stomach slowly devouring itself. It produced a sound much like that of a Hungarian Hornback's roar when agitated. It wasn't a very pleasant sound to hear.

Have I really not eaten for a day? Why isn't my tea enough?

It irked her to some extent. Well, it was her fault that the person reminding her when to eat is not with her as of now.

The organ grumbled again and Alice groaned inwardly. She didn't want to get out of bed. She had her queerly designed socks on and a teacup on her bedside table half-finished that had gone cold.

Her hair was all over the place, she hadn't changed out of her nightgown from the night before, her face felt grimy and moist of tears and sweat, her eyes were puffy, her skin was paler than ever, although her voice was silky despite her horrid state.

She yawned loudly, not really caring if it could be heard in the common room because there weren't actually students around there at this time. She stretched, combed her fingers through her tangled locks in an attempt to tame her ratched bird's nest excuse of hair, stood up slowly and went into the bathroom.

In there she saw her sunken face. Her eyes had dark circles under them and her skin was a very sickly pale color, almost transparent.

"Could've been worse," she told herself. She got out of the bathroom, grabbed her towel and went back in. She set up her toiletries at the side of the bathtub and locked the bathroom door.

She started taking off her clothes as she hummed a solitary tune.

Turning on the faucet, she faced herself in the mirror once more without clothes and observed her ill-looking pale skin extending down her neck. When she inhaled, she saw her own ribcage.

She took a deep breath, noticing her chest cavity move, emphasizing her bones beneath the sickly color of her skin.

This is disturbing, I look like a skeleton prop with poorly put on make-believe flesh.

Shrugging her shoulders, Alice turned off the faucet, seeing that the water had filled nearly to the top. Again, she  took a deep breath and placed her right leg into the in-between-slightly-chilly-slightly-warm water.

She sighed as she put her other leg into the tub and carefully lay herself down. The water had only come up to just below her tiny chest when she heard sudden knocks on the bathroom door.

No, it wasn't just knocking. There was literal banging on the door.

"Emma!? Lauren!? Alice!? Anyone!? Is anyone in the bathroom!?" screamed a voice from the other side of the door.

"Whatever, whoever's in there, I'm just going to check. I'm going in!"

The voice casted an Alohamora and Alice could only do so much to cover most of her chest's 'chicken-like albino rubber integument' when the prefect Zeina had burst through her bathroom door.

Zeina stopped in her tracks when she saw Alice in an awkward stance inside the tub, with half her towel inside the water and her hair wet due to the panicky movements of trying to cover herself as much as possible had brought upon.

"Alice?" Zeina hesitantly asked.

"Top of the morning, Miss Zeina," Alice responded, resisting the urge to shiver.

"You don't suppose it's a bit chilly outside given the fact it's almost December?" Alice pointedly continued. She was slowly getting ahold of herself as the climax from the shock had passed.

Zeina blinked a few times before replying, "Um, yes! Did you know what? I'm just gonna stay outside your dorm room and wait 'til you get ready and all and-"

"No, tell me now. If you come close to breaking down a bathroom door just to check up on a naked sixteen-year-old trying to take a bath, it must have been pretty urgent."

Alice meant to come off irritated at this point but she took control of herself and instead came off exhausted. What she said almost sounded like she was joking. Almost.

She half expected Zeina to chuckle halfway through her remark, but immediately after about a second and no reaction was heard from Zeina, Alice knew something was up. She took a closer look Zeina's now very worrisome expression.

"Someone in our house was found petrified in the upstairs Tower," Zeina reported demeaningly.

Alice stared at her for a split second.

No.

Quickly acting, the exact oppisite of how fast she had been moving  these past few days, with the help of the  adrenaline coursing through her bloodstream, she wrapped the half-soaked towel around her, got out the bathtub and sprinted out the bathroom to her drawer to get decent.

++++

A group of teachers were huddled up around a bed in the Hospital Wing at 11 o'clock in the morning when Alice Urie burst through the doorway.

She came in panting and all eyes turned to her.

"Is she here? Is Mallory Evans here?" Alice voice came out breathy when she asked.

The matron came forward and gave her a look of concern. She placed a hand behind Alice's shaken figure and led her towards the bed where the teachers were huddled around. They gave way for Alice to see what was truly a mysteriously shocking sight.

Mallory's figure was cold, frozen, and laid on the bed. She looked as if she was about to scream and run. Her legs were crouched, ready to take into a sprint. Her arms were in front of her chest, as if she was trying to shield herself from something.

But what was definitely most worthy of notinf were her eyes. Her eyes that looked so terror-stricken that Alice could only wonder what she had seen before freezing.

"She's not dead, right, Professor?" Her head turned to the wizard with a long greying beard.

"Correct, Miss Urie. I commend you for your knowledge. She is merely petrified," he replied, looking at the girl frozen in place.

"But, if we won't be able to-"

"There's no need to worry, Miss Urie. Miss Evans is in good hands," Dumbledore reassured the girl gently. "The matron, along with Professor Beery shall prepare a potion derived from-"

"Mandrakes," Alice had continued for the Professor as realization dawned upon her. "Of course."

Professor Dumbledore eyed the girl with bright blue eyes looking sullenly at the girl glued to the thin hospital bed.

"Yes. Now, you need not to worry about anything anymore. With the supreme green thumb of Professor Beery," Professor Beery put a hand to his chest and bowed in response, "and the magnificent healing hand of our most dear matron," the matron had her cheeks red, Alice noticed, "I assure you, Miss Mallory shall be up and about in no time."

Alice could only chew on the inside of her cheek as she rubbed her sweater-covered arm. She had her eyebrows knitted together as she dwelled in deep thought.

"If anything else happens, we'll infor-"

"If it happens again?" Alice interrupted once more.

"Pardon?"

Alice looked at her Transfiguration teacher with a determined expression, "What if it happens again? What if another person gets petrified? Sir, you cannot simply ask me to go up to my dorm and tell me to not worry. Mallory is my friend. I do not think she would even entertain the thought of me doing nothing to make this problem any less of a problem than it already is."

Alice sighed and looked back at her friend again and she then faced her professor with tears nearly wanting to flow out of her eyes, "I will help. I shall offer my assistance in doing whatever is necessary for brewing the said potion for Mallory's recovery. I'll do anything. If it takes fighting a war for her to get better, then it will be worth it."

The teachers who had remained silent the entirety of the encounter had looked at one another in a silent discussion amongst themselves.

Dumbledore could only nod at her before the matron placed a hand on Alice's back before leading her out carefully.

Once she was gone, Dumbledore stared at the doorway she disappeared and in entered an almost dishevelled-looking Tom Riddle. Almost.

++++

Alice barely ate any food that night. Wanting to go right into business, she finished her plate of carrot soup and hurriedly went to stand up and exit the Great Hall. Right as she was just past the doorway, she bumped into a body that staggered down to the floor with her following suit.

Alice's eyes widened in shock and immediately stood up when she heard groaning beneath her.

"I- uh- I'm sorry!"

"It's alright, love," a friendly voice had struggled to mumble.

"Wait," Alice turned to the figure and helped them up, "Jeremiah? What in the world-"

She helped the bloke get up and help him dust off any dirt as he scratched the back of his neck.

"Yeah, sorry about that. I've been a bit clumsy these past few days."

Alice stood and stared at him. He had his sleeves rolled up, his hair was unkempt and his voice was coarse. He looked so different compared to the person she kissed that night in the Ravenclaw boys' dorm.

He stared back for a moment. Their eyes met and for a brief period in time, he saw Alice's piercing blue eyes convey much more than dominance, power, and strength. A frenzy of emotions had trickled down his spine before snapping back into reality. He was to ask permission to be excused. he looked way and lowered his right sleeve. Alice looked away as soon as he did.

"Well, it was nice seeing you, Alice." Just as he had turned on his heel, Alice spoke.

"You've been in a fight, haven't you?" she asked as she clenched her fists, knuckles turning white. Jem clenched his jaw. The skin in which the bunched up cloth of his right sleeve ached.

You know me so well, why can't you love me as much?

He didn't reply. When silence engulfed both of them, she grabbed his left arm and led him to the Ravenclaw dormitories.

They settled at Jeremiah's room. Tension floated densely in the air. Alice could almost taste it.

She had Jeremiah take off his robe and shirt, leaving the top half of his body only in a white undershirt with both his arms exposed. He was sat on his bed, standing so still at the command of his companion. Beside him was Alice with the little box of vials she had kept inside her room. On the floor was a clean bowl of warm water mixed with some ointments and at the edge of the bowl there was a clean white towel ready to be submerged in the said solution.

Alice took in the long wound along Jeremiah's elbow. It started just in the middle of his forearm and extended just a few centimeters below his elbow. It wasn't exactly a clean cut. There were several other scratches and rashes around the general area of the wound. The area around it hadn't become purple yet, so it was either the fight had just happened before their encounter or it happened less recently and Jeremiah had somehow managed to access something that kept his wound from bruising up. Alice thought the second option was quite unlikely, so she went with the first one.

Alice picked out a vial of dittany and placed the box of vials off of her lap and onto her side.

Opening the bottle and taking it's dropper already full of the liquid.

"This may hurt bit," she said, putting down her exposed vial of dittany.

She held out her unoccupied hand for the boy to hold. He took it shakily.

Alice wasted no time in pressing the dropper full of dittany onto the wound exposed. As the liquid came in contact with Jeremiah's skin, Alice felt his grip tighten around her fingers.

Once it was over, he let his fingers loosen around hers as she picked up the bowl of ointments. He hastily let her hand go so she could work more efficiently. She didn't tell him to do that, but he figured it would be best. It was strange of him to do so.

Alice massaged and folded the damp cloth in the solution for a but before squeezing it halfway, that way not all of the liquid it had absorbed was discarded back into the bowl.

Then, she held her hand out again. It took a few more seconds and Jeremiah was about to place his hand over hers when she grabbed it with suddenly, quickly working her way with the damp cloth into the rashy parts of his arm.

"You know, you could've-"

"Don't act like I don't know you would lie about wanting to go to the Hospital Wing. You've gone there a few times, always wanting to get out as soon as possible."

Alice just continued to gently rub the raw rashes despite the tone of her previous remark.

Jeremiah shut up at that. He swallowed the lump that was forming on his throat. He looked to the side opposite of Alice in embarassment and humiliation.

Way to ruin an intimate moment.

Alice didn't think quite the same.

It was only when Jeremiah felt the hand that held his shaking. His eyes widened and looked back at Alice. Her whole figure was shaking. Then there were tears and sniffing.

"Alice, love?"

At the sound of his sweet and caring voice tainted by the hoarse threat of a cough, she let out a small, barely audible sob. She had her arm raised up to her face in an attempt to wipe her tears with her sleeve.

"I'm not used to this," she started, her voice cracking at the end, "this whole friend thing."

Jeremiah could only stare at the fragile weeping mess of a friend he had beside him.

"I've never had friends before," she was looking down at her lap as she spoke. "It was always my brother," she choked back the urge to give out a loud sob, "sometimes my cousin, and I. Just us. No one else."

"And now, Mallory's petrified. She's been taken away just like that!"

Alice faced Jeremiah and tightened her grip around his hand.

"Don't go around getting into fights, Jem. I can't have you taken, too."

She broke into a sobbing fit and Jeremiah took her into his arms, letting the girl sob onto his chest with onky a thin cloth covering it. She clung onto him for dear life. Her hands had held onto his arms.

"Don't let them take you away, Jem. Don't ever leave me."

Jeremiah responded by hugging her and whispering words of reassurance into her ear as her body shook with sobs.

"I'm not going anywhere. I'm staying right here."

He said those words over and over again. He repeated them until she fell asleep on his chest, having no more worries, for now.

++++

A tall figure sat on a chair in what seemed to be a dark room. The floor was damp and wet. He waited silence.

It was a huge chamber, and an equally large porcelain carving of the mighting Salazar Slytherin himself was at the grand center of it all.

There was the sound of reptilian skin on the wet ground. Hissing can be heard and the tall figure's lips curved in what appeared to a be a slight smirk. Barely there, but you could se it if you looked hard enough.

The sound of an unspoken language rang in the air as the man opened his mouth, cold and slithering towards the ear of the listener, "Excellent, now, let's move on."

;-;-;-;-;-;-;-;-;-;

hiiiiiiiiiiiii :>

I don't exactly know whether it's been an actual year since I last updated or not, but hEY I UPDATED WHOOP WHOOP

Okay, but before anythung else, I just wanna thank you guys for holding out and waiting for these updates, and I, myself, am really surprised at how much attention this work is getting, like, DAYUM.

Nearly 40 thousand reads, and I last updated this work with an actual chapter like what, before it even reached 20k???? Holy mother of glory, I feel o l d.

Goddamn, I wish I had this much praise for the things I turn in for school HAHAHAHAHAHAHAHA. Okay, I've said too much.

SooooOOOOooo you've probably noticed how far the story's gone and the action is starting (DUN DUN DUUUUUUUN [ehe josh]). And Alice, my sweet, sour, sexy, Alice, has become quite a softie - and her FEELINGS SHOWED WOAH.

But that's all just going according to plan, sorta. Yeah, this isn't edited yet so excuse all the grammatical and typographical errors (cuz I basically just finished it).

I've said waaay too much, so byeeeeeee.

Hope you guys liked it!

All the love as always,

-tuffhufflepuff xx

P.S. source for the details on Zeno's dichotomy paradox is the Wikipedia page all about Zeno's paradoxes