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"That's it," Castle yelled, propelling himself off his perch next to her on her desk, scaring a few years out of her. "This is ridiculous."
"You're ridiculous," Kate hissed at him in disdain, before gathering herself. "But what, dare I ask, are you talking about?"
"Us being together," he said plainly.
She looked at him like he'd grown two heads, one of which was purple and had antennae. "We aren't together."
"I know that."
"I should hope so."
"And you know that. But how many times have we had to clear it up?"
"One time too many."
"Exactly. Yet people accuse us of being together."
"Castle, I feel vaguely offended that you're genuinely frustrated about this. Possibly more than I am."
"I am frustrated."
He really was! But he wasn't about to tell her why. Castle's reasons were none too noble. The source of his frustration was her frustration. When people kept reminding her of their non-relationship, they were also unknowingly reducing his chances of making her forget that she didn't not want a relationship. Why didn't people understand, for crying out loud?!
"Ohhhkay," Kate drew out.
"We should do something about it."
"You want to stop harassing me?" she said with a ridiculously cheesy grin.
If he didn't know her the way he did, he'd be upset. But he did know her. If she was serious, he'd probably convince her otherwise anyway. Something they had already been through. In short, he wasn't worried. "Woah now! Do I want to stop breathing? Kate Beckett, don't be ridiculous."
"A girl could dream."
"Oh. What kind of dreams? Are they raunchy? Do they involve a certain ruggedly handsome author?"
"As if I'd tell you. No. And you wish."
"I do wish. I so do wish," he said, nodding so hard he was getting dizzy.
"Castle, focus?"
"Right. I have a plan."
"Why am I not surprised?"
"Because you have come to realize my brilliance."
"I used to think you have a big ego. Oh, how I underestimated it."
"Do you want to hear the plan?"
"Are you going to leave me alone until I do?"
"What do you think?"
"Get on with it, then."
"I propose we prove ourselves."
"How do we prove we don't have a relationship?"
"We keep denying its existence, but nobody believes us. Why?"
"What do you mean 'why'?"
"Why don't people believe us?"
"Because -," Kate tried to think, coming up short. Could it be that Castle actually had a point? Nah. "Because people are stupid."
"No, my lovely Detective. It's because they don't have a reason not to not believe us."
"Did you hit your head while we were chasing that suspect today?"
"Yes, but that's besides the point. See the people who believe we're in a relationship have seen or heard something to convince them."
"Okay."
"And we have to unconvince them."
"You're finally starting to make a little sense."
"For that we have to know what has them convinced. We find their hypothesis, upon which they have established our relationship, and provide them with the alternative hypothesis to prove the non-existence of said relationship."
"Ah, I see," Kate nodded, as he beamed at her. "Now can we get back to work?"
The smile dropped off his face, and his shoulders sagged. She was trying hard not to simultaneously sock him and laugh at him.
"Beckett!" Castle whined.
She sighed. "Yes, Castle?"
"Did you not hear all of that?"
"I spent a precious few minutes and brain cells on it, all so you would let me get back to this murder we're trying to solve, and possibly join me if you could spare your brilliant mind to such a mundane task."
"Aww, Beckett. You think I have a brilliant mind?" he said, sitting back down next to her as she rolled her eyes at him.
She was lucky Castle could be so easily distracted. Or so she thought.
Kate had forgotten all about Castle's weird plan, if it could be called that. She thought he'd forgotten about it too. That is, until one particularly quiet afternoon at the precinct.
Castle had the habit of disappearing for periods of time so it strangely coincided with Beckett having to do paperwork. Usually, though, he would either tell her he's going home, or he'd bug Esposito or Ryan, or distract some other poor unsuspecting fool. More rarely he'd sit with Montgomery in the name of research. In any case, he always touched base, and made sure not to go more than twenty minutes without bugging her.
And so when it had been an hour and a half of peaceful paperwork completion, Kate knew something was up.
She tossed a scrunched up piece of waste paper at Ryan, hitting him squarely in the forehead. "Ryan, you seen Castle?"
Ryan blinked, and looked around. As if she hadn't done that already. "Um. No. Haven't seen him in a while now. Where is he?"
She rolled her eyes. "I don't know. That's why I'm asking you."
"Miss your boyfriend already, Beckett?" Esposito piped up, looking proud of himself.
"Espo, I swear to God, I will come over there and - what?" What she would go over there and do, Espo never had the chance to find out, because he'd successfully spotted Castle and pointed to him wordlessly, his eyebrow raised in a mix of confusion and suspicion.
Kate had turned around expecting Castle to be heading towards her. Instead she saw his head and half his body poke out from behind a white board as he dragged it into an unused room. The grey room, as they had come to call it, was being refurbished after recently being damaged due to a water leak from the floor above. Really all that was left was for it to be painted and furnished, but funds were tight, and they were able to work without it, so there it sat, grey and unused.
"What's he up to? Kate asked, directing the question at no one in particular.
"Beats me," Ryan said, "he's your partner."
She bit her lip, wondering whether it was better for her sanity to pursue this, or let it go.
She decided to let it go.
Fifteen minutes later, she decided she couldn't let it go, and he'd long since messed with her sanity anyway. That was how she found herself in the grey room, watching Castle make a - a murder board of their relationship? And people called her morbid.
"Castle, what are you doing?"
Castle squeaked and jumped two feet away from her, wielding his marker out like a sword. "Beckett. Hah. You almost scared me."
"Almost?" she smirked, crossing her arms and raising her well sculpted eyebrow.
"This is my plan."
"You're plan to - what exactly?"
"You know, my plan," he waved randomly at the board. "I told you about it already. You even actually listened to it."
"Huh?"
"My theory about unconvincing people who are convinced we're in a relationship, and convincing them that we're not, by disproving whatever proof they have which stands as the foundation to their hypothesis."
"Oh, that plan," she said, rubbing at her temple.
"Yep. So this is the null hypothesis," Castle said, pointing at the large red font.
"Castle, what the hell?"
"What?"
"This says, 'Beckett and Castle are in a relationship'."
"Yes, I know. I can read. Also, I wrote that."
"How is that supposed to convince people we're not in a relationship?" she said a little frantically. The man could drive her insane.
"Because this is the null hypothesis," he said, looking smug. "Does sound nice, doesn't it?"
"I'll tell you what sounds nice," she said, rolling her sleeves up as she advanced on him. He jumped off the plastic covered table rounding it so it stood between them.
"Woah, calm down."
"Richard Castle, do not tell me to calm down while you are spreading lies about our non-existent non-relationship."
"I'm doing the exact opposite. I'm trying to spread the truth about our existent - wait a minute, I think you said that wrong, because the opposite implies - OW!"
"You have two minutes to explain before I hit you where it really hurts."
Castle winced at the thought and nodded his acquiescence. "Fine. Won't even take that long. Have a seat," he said, fighting the urge to shield himself, and added, "please?"
Kate huffed, but sat on the table where he'd been sitting before. He sat down next to her so that their sides touched, even if the table was spacious enough to not have them invading the others personal space. There was dust on some parts of this one. A perfectly reasonable explanation for this plastic-covered hardly-used table. Not so much for her desk that they treated similarly.
"See, this is the null hypothesis. The hypothesis that other people are putting forth, and we are denying. Once we reject the null hypothesis, we thereby accept the alternative hypothesis, which is what we are trying to prove."
"That you and I are not in a relationship."
"Right."
"So we prove that, by disproving this?" she said, pointing at the board.
"Exactly."
"Okay, and how do we do that?"
"By letting people try to prove the null hypothesis."
"Isn't that counterproductive?"
"Not when we disprove their theories. Once we do, there's only the alternative that remains, and they'll finally accept it."
"That - actually makes sense."
"I can be sensible," he said, nudging her with his shoulder.
Kate couldn't help but smile, as she rested her head on his shoulder just for a moment. A slightly prolonged moment. "Careful, Castle. Or I'll expect you to be sensible more often."
He gasped. "Wouldn't want that. What a blip on my well maintained reputation."
"How ever will you recover?"
"I'll just have to be nonsensical more often."
Kate groaned as she straightened up, and pushed him off the table, laughing as he tried to bat away the dust off his bottom.
A/N:
1) Thanks Bot, for having my back, as usual! You really understand my weirdo brain.
2) A Null and Alternate Hypothesis are actually scientific methods of determining the given hypothesis. I learnt it in biostatistics - a subject that I studied because it was mandatory. :| The way Castle is using it, is not quite how it works. BUT, what Beckett doesn't know, won't hurt Castle.
Cheers, and thanks for reading!