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I was in the club room. I was working on the hailstone problem. Or you may know it as the Collatz conjecture. If a number is even, divide it by two. If a number is odd, multiply by three and add one. This created a sequence for all n \in \mathbb{Z}. The conjecture was that a given number always went to one. (This was only counting the positive reals \mathbb{Z}^{+}) I was studying several cycles. If a number started as negative one, it goes negative one, negative two, negative one. If a number started as one, it went one, four, two, one. If a number started as negative five it cycled through between negative fourteen, negative seven, negative twenty, negative ten, negative five. There was another sequence, one for negative seventeen but it was much longer.
Most mathematicians thought it was true and it had been shown to be true up to two to the sixty sixth. But that didn't make it a theorem. Schemes were demonstrated to be true heuristically all the time and then they turned out to be false.
I was working on the problem in the context of the Riemann sphere. I was assuming a number either went to one or blew up to infinity and if it blew up to infinity, the Riemann sphere was my best tool.
There came a knock at the door which did not sound like Hiratsuka-sensei.
Yukinoshita stopped turning a page of her book and decidedly inserted a bookmark inside.
I looked between her and the door. Nobody ever came here.
"Come in." She called, facing the door.
"E-excuse me," came a voice that was a little excited and may have indicated some nervousness. The door was then slid open only a little so that a small gap was apparent. The girl slipped her body in through the gap and entered the room. An action that could only mean she really didn't want anyone seeing her come in.
Her shoulder length brown hair was curled in loose waves that swayed as she walked. Her eyes moved around the room anxiously until they met mine. She let out a small shriek.
Boo. I spooked in my head. I mean, I literally never did anything to anybody! Come on man.
"W-why is Hikki here?!"
"…..I'm actually a member of this club," I murmured by the chalkboard.
Or should I say are you calling me 'Hikki?' More importantly, who the hell is this chick anyway?
Frankly, I have no idea. But despite that, she looked exactly like your typical high school girl. I've seen her type around a lot – a flamboyant girl revelling in her youth. Short skirt, three buttons of her blouse popped, hair dyed light brown, and a quick glance at her chest revealed a heart charm on a gleaming necklace. It was an outfit that completely defied the school code. I've no business with such girls.
In fact, I have no business with any girls. Bangarang!
Also, I noticed that the color of the ribbon pinned to her chest was red. In our school, each grade is distinguishable by a particularly coloured ribbon. A red ribbon meant she was in grade eleven like me.
"Well just sit down for the time being." I said and casually pulled up a chair, motioning for her to sit. I didn't know her but it probably wouldn't go well to ask. "And what was your name?" I asked anyway.
"Yuigahama Yui. You don't know me?"
"I do," Yukinoshita spared me with a glance.
"Y-you know who I am?" Yuigahama stuttered off.
Her face, Yuigahama Yui's, suddenly lit up when her name was called. It was like being known by Yukinoshita gave you some kind of status.
"You certainly know a lot…Do you remember everybody's name in this school?" I asked.
"Not at all. I didn't know you existed," she counter pointed. If only I could find a counterexample for the Collatz conjecture.
I laughed at Yukinoshita's words. "Is that so…"
"It's not really something to get excited over. In fact, it was my mistake. I didn't notice your diminutive presence and above all I unintentionally wished to avert my eyes from your existence. The blame lies with the weakness of my mind."
"Is that supposed some form of consolation? That's a really lousy way to console someone. In the end, you pretty much concluded that it's my fault."
"I wasn't trying to console you. I was just being sarcastic." Yukinoshita said, disregarding me as she flipped her hair over her shoulder.
"This sorta….seems like a really fun club." Yuigahama said as she looked at Yukinoshita and me with twinkling eyes. ….This girl – Is her mind just full of sunshine and daisies? How the fuck did she reach that conclusion? I laughed again, a low chuckle.
"That remark isn't particularly pleasing in any way…on the other hand, your misunderstanding is terribly displeasing." Yukinoshita shot her a cold glare. As Yuigahama registered her words, she became flustered and frantically waved her hands in denial.
"Uh, no, how do I put it? I was just thinking that you guys seem to be acting really natural! Like I mean, Hikki is like totally different from how he's like in class. He's like actually talking and stuff."
"I…" I trailed off. "I agree?"
"Oh that's right. Yuigahama-san is also in class F."
"What? Really?" I asked.
"Don't tell me you really didn't know that?" Yukinoshita asked in return.
Yuigahama appeared startled by Yukinoshita's words.
Oh hell.
"Ya caught me. I don't really pay attention," I murmured.
"It's true. You always have a far away look in your eyes," Yuigahama coupled. "Isn't that why you don't have any friends in class? I mean you act weird and it's creepy."
"Granted," I decided. I was a creep. She said that all I'll ever be was a creep. Little creepy. So, yeah. This was all fair cop. I couldn't really even be mad.
Oh that's right, I remember this girl's scornful eyes. Of course, the other girls in my class have also occasionally looked at me like I was piece of shit. She must be part of that clique that hangs around the soccer club a lot.
What the hell. Isn't she one of my enemies then? I just wasted my time trying to be nice.
"Sorry Hikki, it's just what with the way you act and all…" Yuigahama pressed. She sounded too sweet. Like she was being nice to a hurt dog.
"Don't worry about it. Are you calling me a hikikomori? You bitch." I laughed.
Oh, she must've meant it as an insult in that way. That must be some kind of derogatory nickname people in my class have for me. Well. Put it on my tombstone and call it good.
"What? Who are you calling a bitch?!" Yuigahama lashed out in response. "I'm still a vir-….. w-woah! Never mind!" She blushed furiously and waved her hands back and forth in an attempt to take back her words. What an airhead.
Yukinoshita began to say something as if to save Yuigahama from her panic. "It's not really something to be embarrassed about. At this age being a virg-"
"W-woah hold up! What are you saying?! It's embarrassing still being one in grade eleven! Yukinoshita-san, where's your sense of femininity?!" Eleven…
Eleven, thirty-four, seventeen, fifty-two, twenty-six, thirteen, forty, twenty, ten, five, sixteen, eight, four, two, one. Collatz confirmed.
"…..A pointless thing to value."
Woah there, I don't know how but Yukinoshita just increased her coldness a hundred fold.
One-hundred, fifty, twenty-five, seventy-six, thirty-eight, nineteen, fifty-eight, twenty-nine, eighty-eight, forty-four, twenty-two, eleven, thirty-four, seventeen, fifty-two, twenty-six, thirteen, forty, twenty, ten, five, sixteen, eight, four, two, one. Collatz confirmed.
"Even if you say that, the word 'femininity' just screams 'bitch' to me." I added in.
"You said it again! Calling someone a bitch is way out of line! Hikki, you're so gross!" Yuigahama made a small derisive growl and looked at me with teary eyes.
"Me calling you a bitch has nothing to do with being gross. And don't call me 'Hikki.' Bitch." I added.
"Y-you! You're so annoying! Like seriously gross! Can't you just go fucking die?!" Yuigahama demanded.
Yukinoshita flinched and I laughed.
"You shouldn't say things like 'go die' or 'I'll kill you' so lightly," I grinned.
"…Uh… s-sorry. I didn't mean to…"
"It's not a big deal to me but you might hurt somebody else," I shrugged.
She might've noticed but Yuigahama is really just an airhead. But what was surprising was that she seemed like the kind of girl who could actually apologize properly.
She seemed a little different from what I'd envisioned judging by her appearance. I was certain she would be the same as the girls in her group and not to mention those guys in the soccer club and the people around them. I thought her head would always be filled with thoughts of sex, drugs and fooling around.
Yuigahama let out a small sigh as though being hyper made her tired.
"…..Hey um I heard this from Hiratsuka sensei but this club fulfils students' desires right?" Yuigahama broke the short moment of silence.
"For real?" I put in. I was sure that this was a club for reading books to no end.
"You didn't know?" Yuigahama asked.
"I never asked," I sighed and confessed.
Yukinoshita completed ignored my question and answered Yuigahama's.
"I believe it differs a little. Ultimately, the aim of this club only lies in lending people a hand. Whether or not that fulfils your desires depends upon you."
Yukinoshita's blunt denial seemed somewhat cold.
"How is it different?" Yuigahama asked with a dubious expression. That was exactly what I was wondering.
"Would you give a hungry man a fish or would you teach him how to fish? That is where the difference lies. Essentially, a volunteer does not provide results but a methodology. I suppose ' to encourage independence' would be the most accurate answer." Her speech seemed like something pulled straight out of a textbook on morals. An empty principle any goddamn school would preach - 'club activities that allow students to demonstrate their ability to act independently as well as with others'.
I'm sure my general understanding of the club's activities as that would be correct. And well, Sensei also said something or rather about labor so it must be a club that works for the sake of the student body.
"That's kinda really awesome!" Yuigahama exclaimed with a look that said 'You opened my eyes so I totally get it now!' I was a little worried that she might get brainwashed by some satanic religion in the future.
"Although I cannot say for sure that I will fulfil your wishes, I will help you as much as I can."
Upon hearing those words, Yuigahama spoke up as though she'd suddenly remembered what she had come here for.
"Hey! Um I was kind of thinking about making some cookies…." Yuigahama said and glanced at me.
"Hikigaya-kun." Yukinoshita said and motioned toward the hallway with a quick jerk of her chin – a gesture that told me to get lost. I nodded in agreement. I could Collatz out in the hallway. I needed a really big number. Probably a really big Prime number. Fuck me sideways it always came back to the Prime numbers.
I could hear Euler laugh and say, "I know, right! If only there was a way to get all the Prime numbers and put them in a box." He laughed in my ears again. Fucking asshole.
"…I'll just go buy some 'Sportop.'"
As I put my hand on the door to leave, Yukinoshita called out to me. Maybe even Yukinoshita had some feelings to express.
"I'll have a 'Yasai seikatsu 100 Strawberry Mix.'"
To think that she can just naturally command people to do errands for her. Yukinoshita-san, you're fucking unbelievable. "You're lucky that you're cute." I fired back like a missile. She glowered. But she was going to get some juice so who was she to complain?
It wouldn't take more than ten minutes to get from the third floor to the first floor of the special building and back again. If I took my time and walked at a leisurely pace, their conversation would probably be finished by the time I got there.
Well, no matter what kind of person she was, Yuigahama was our first client. In other words, her appearance marked the beginning of the so-called battle between Yukinoshita and me.
Well, it's not like I'm going to win so if I just concerned myself with figuring out how to minimise as much damage as possible, all would be good. That fancy first derivative test.
In front of the school canteen there was a suspicious vending machine. It sold some peculiar kinds of soda in juice boxes that you can't find at regular convenience stores. They seem to be pretty good at replicating flavors so they've caught my interest.
I was particularly interested in a soda called 'Sportop,' which goes against the norm. It has a flavor like that of cheap candy and challenges the latest 'zero calories' and 'sugar-free' trends. It tastes pretty good.
As I inserted two hundred yen coins into the vending machine, it groaned loudly like it some sky fortress about to let drop the 'Yasai Seikatsu' and 'Sportop' I purchased. Then, I inserted another hundred yen coin in and pressed the 'Otoko no Café au Lait' button.
It would be weird if only two out of three people were drinking something. So I'd decided to buy something for Yuigahama too.
The drinks were 300 yen in total meaning I had lost fifty percent of the money I had on me. I was way too broke. You know what would solve that? If my dumb ass could figure out the Prime numbers!
"You're late," Yukinoshita said, snatching the 'Yasai Seikatsu' from my hands. She poked a straw in it and started drinking. All that was left was the 'Sportop' and 'Otoko no Café au Lait.' It seemed like Yuigahama realized who the 'Otoko no Café au Lait' was for.
"... Oh right," Yuigahama said, pulling a hundred yen coin out of a pocket-like coin purse.
"Ah, don't worry about it." I mean, Yukinoshita didn't pay me back, and above all, I bought them of my own volition. Even though it might have been reasonable to accept money from Yukinoshita, I was not obliged to accept money from Yuigahama. So instead of taking the hundred yen coin she held out, I placed the Café au Lait in her hand.
"B-But I haven't paid you back!" Yuigahama adamantly attempted to hand me the coin. It would have been annoying to argue back and forth about her paying me back so I just walked over to my seat closer to Yukinoshita.
Yuigahama appeared slightly miffed as she reluctantly put away her change.
"... Thanks." She expressed her gratitude in a small voice, laughing a little happily as she shyly held the Café au Lait in both hands.
That was most certainly the most gratitude I'd ever received in my entire life. She had probably overpaid me with that smiling face for what was worth only a hundred yen.
"Have you finished your chat?" I inclined. Satisfied, I attempted to get Yukinoshita to show me some appreciation as well.
"Yes. As a result of your absence, our conversation went along swimmingly. Thanks."
That was most certainly the least gratitude I've ever received in my entire life. I chuckled.
"…Well, that's good. So, what are you going to do now?"
"We're going to the home economics room. You're coming with us."
"The home economics room?" I wondered.
It was an iron maiden-like classroom for the torture of cooking training conducted in groups of your own choosing.
They have kitchen knives and gas ranges, which are dangerous and should have restricted use!
"And what are we going to do there?"
Along with gym class and field trips, cooking training was one of the top three school activities known for trauma infliction. There probably wasn't a single person who actually enjoyed any one of them. I mean, imagine a group that is happily chatting among themselves and getting along well…then imagine the immediate silence that fell over them the moment I had joined…yeah, it was beyond unbearable.
"Cookies… I want to bake some cookies," Yuigahama murmured.
"Huh? Cookies?" It was the only response I could give her, having had no idea what she was talking about.
"It appears that Yuigahama-san wants to make homemade cookies for someone. However, she has no confidence in her ability and would like some help. That is her request," Yukinoshita explained, clearing my doubt.
"Sure. Why not?" I stood up and paced over to the chalkboard and erased my cycles. You could make a fractal out of the Collatz conjecture. That was the real reason I was studying it.
f_{c}(z) = z^{2} + c
"What's that?" Yuigahama asked.
"Just some scribbles. Nothing I can't recreate," I answered.
"Ah..." Yuihagama looked downward, at a loss for words. She then gripped the hem of her skirt, her shoulders trembling slightly. "Ah…Ahaha. It-it's weird, isn't it? Someone like me trying to make homemade cookies…like I'm trying to be some kind of girly girl… Sorry, Yukinoshita-san, it's okay, don't worry about it."
"Well, if that's what you really want, I don't particularly mind… —Oh, I see. If you're worried about him, you don't have to be. He doesn't exactly have a moral compass so I'll force him to help out."
Somehow it seemed like the Japanese constitution didn't apply to me. I mean, what kind of sweatshop-type exploitation was this?
"No, it's really okay! I mean making cookies really doesn't suit me and it would be weird… I asked Yumiko and Mari and they said it's totally old-fashioned." Yuigahama stole a glance at me.
"...Yes. I certainly wouldn't expect that a girl who looks as flamboyant as you do would make cookies," Yukinoshita said, as if to push the already crestfallen Yuigahama further into depression.
"E-exactly! It's weird, isn't it?!" Yuigahama laughed anxiously as if she was waiting for us to react. Her downcast eyes suddenly looked to me, as though she was challenging me. With those eyes looking at me, I felt like she was asking me for some kind of reply.
"Don't look at me. I don't know what's weird or not. I… I don't care about this. About cookies," I made my voice crack for inflection. "I don't give a fuck."
"That's an even more horrible thing to say!" Yuigahama struck the table hard in exasperation. "Hikki, I really can't believe you! I'm seriously pissed off. I would do it if I put my mind to it!"
"That's not something you can say about yourself. That's something your mom says, while getting emotional – tears in her eyes and all. 'I always thought you would do it if you could...but of course you just can't.'"
"Well, it looks like your mom already gave up on you!" Yuigahama declared.
"A reasonably good conclusion." Yukinoshita nodded her head eagerly. Meanwhile, Yuigahama had tears welling up in her eyes.
I narrowed my eyes and chuckled. "You know…"
"Zip it," Yukinoshita evil eyed me.
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-WG