All In Your Head (TheNerd & Treasure)

"Yes, because everyone loves their duties," Damien drawled. "I can tell you are just so extremely happy you are working for my mother. It's the greatest duty you ever fulfilled, isn't it?"
 
"Maybe it has, and you just don't see it yet," Celia replied in earnest. Her literal answer to everything just showed how oblivious she actually was, and it was amusing for some, annoying for most.
 
"If this is the greatest duty ever, then you are seriously messed up in the head," Damien stated. He does abruptly and stalked away. The servants moved quickly out of his way as he strode back toward the stairs leading to his room.
 
Celia completely missed the sarcasm this time. She just followed him, making sure he wasn't about to have another presumed episode, wondering where she'll have to retire to for the night. She knew it would probably with some of the other maids, but she couldn't be too sure.
 
Damien hesitated at the stairs only briefly. He set his jaw and climbed up, his steps slow and deliberate. Beads of sweat dotted his forehead, but he'd made it without incident! He took no time to revel in his success, though, going straight into his room and closing the door in Celia's face.
 
Celia, unimpressed, took a shortcut. She'd known about a secret door to her quarters that was disguised as a closet door next to Damien's room, and it had a door straight to Damien's room at the end of it, where there was a keyhole she could peep through. She suspected it would probably be boarded up by the time she settled into the room.
 
Damien was a little surprised Celia didn't try to follow him in, but after a moment of the door staying closed, he decided to let it go and enjoy his space while he had it. He sighed and started undressing for bed. He pulled on his usual pajama wear and a long robe before uncovering his boards and settling down to work. He had a lot to do and so little time to do it in!

He stood before his biggest board and stared at the white lines marching across the dark surface. They lay there, flat and unmoving, mocking him. The answer was here, somewhere, hidden among the letters, numbers, and symbols, but he couldn't find it! He had to find it. He was supposed to find it. Why else had he been given the gift he had? If he could not figure this out, then it was wasted... he was a failure... or perhaps this was their way of torturing him. The problem that would never be solved because it had no answer.

With a tiny shriek, Damien grabbed his head in both hands and pounded his forehead into the board twice. "Why?" he keened. "What is it! I have to find it! I need to know! Why won't you tell me!" He let his head hit the board again then stood there panting, his forehead pressed against the cool, gritty surface.

He took a deep breath then coughed as he inhaled some chalk dust. He straightened and ran a hand over his forehead, smearing the dust more. Never mind. He would find this answer. No question was truly unsolvable. Nightmarishly difficult, perhaps, but not unsolvable. All he had to do was find just one clue, and it would be like the key in the lock. He could do this. The chalk had fallen. He picked it up, wiped down his board, and started again. Letters, symbols, and numbers dashed into being under his frantic hand only to be wiped away and rewritten in a different order. He would solve this. He had to! For the sake of humanity.

"Okay, let's start again from the beginning. Let P be a problem. Assume that given a solution, it is easy to check P is correct. I need to show that P then is easily solved. Assume P is not easily solved. Then we must show the solutions are not easy to verify. Equivalently, we have to show that there is a problem that is hard to solve, but easy to check. Which means we have to show every possible means of solving it. But that is completely absurd, at least in first-order of logic. So that line of proof seems for the moment to be impossible..." He scribbled down the line of proof in the corner of the board and slashed an asterisk next to it. "Later. Come back to this later."

He stood back from the board and crossed one arm over his torso, the other hand picking at his chin stubble fretfully, his brow furrowed. Then he leaned forward. "But is it impossible? Let us try attacking it in a different way. Assume that such a problem exists. Then every algorithm that solves P..." he trailed off for a second, thinking, "is of nonpolynomial time. Let A be the algorithm that varifies solutions of P that has polynomial time, and let A1, A2, A3, and so forth be all the algorithms that solve P."

He stopped, chalk dangling from his fingers, and pondered the white mass on the blackboard. "This is two more assumptions that I need to prove that I can make. First, is it true that a problem that has an algorithm that can check solutions must have an algorithm that can solve it? Secondly, Would the set of those algorithms be countable?" He stared for a moment longer.

In a sudden fit of frustration, he threw the piece of chalk at the board. "More questions! More assumptions! I cannot get anywhere without unearthing more! Every time I think I am getting close, it seems every answer dissolves into three more questions." He ran his hands through his hair in frustration and paced in the room within a room he had created by setting up the blackboards in a square. "What am I missing?"
 
Celia went to her room, being a tad tired. She looked through the little peephole where the other boarded door was, and saw him with the huge math equation. She watched him with all of his keening. His aura felt frazzled to her, and that's about as it should be if you tried to solve the equation of a Lycan's existence. In fact, the only way for him to know if they truly existed is to actually see one. As long as she doesn't act very suspicious for any longer, she'd be fine.
 
It was so late it was early when Damien finally gave up. He covered his boards with old sheets and shoved them up against the wall once more. He dusted off his hands and fell into bed, passing out in an exhausted sleep in seconds.
 
Celia didn't feel so tired, as she was used to staying up certain nights to hunt, but tonight seemed like she'd had a insomnia spell put on her. She whipped out her journal with her copy of "Lycan's Memoir", which was basically the Lycan's bible, containing the history of the Lycans from the perspective of very first of their kind, Hermaeus Lycan, who she'd known as a child. She started to write some quotes down, ones that described her day that day. She meditated on the words, trying to find the wisdom to help her get through the process of gaining his trust.
 
Damien slept late then lay staring at the ceiling. Maybe he wouldn't bother to get up this morning. Who would care?
 
Celia didn't get any sleep that night, promptly getting up out of her seat to secretly bandage her swollen, overused hands, putting on gloves to mask the fact that her quirk was overused on both hands, and they hurt like anything else. They almost looked as if they'd been broken, and somehow she was able to conceal it with compression bandages and gloves. She had to go wake Damien and be the bad guy for a second.
 
"No, don't want probes," Damien mumbled, drooling a little into his pillow. "Feed the turtles the meters, hmm?" He rolled over and flopped diagonally across his narrow bed, still sound asleep.
 
Celia walked out of her little hole in the wall looking a bit tired, going to Damien's door, then giving a firm 3 knocks, which was obviously pretty painful for her. The knocks felt like her hands were going to explode. She winced after the last knock, when she respectfully put her hands behind her back. "Mr. Damien, time to wake up," she called, trying not to sound like a pained puppy.
 
Celia sighed, feeling his aura, knowing it'd be another fight. This was all necessary, and it would be for a few months. "Please sir, you have to. It was your mother's orders to make sure you got up every day," she said. She was trying to hide the pain on her face as her weakened hands held each other a little too tightly behind her back.
 
On the other side of the door, Damien growled as the annoying voice slowly worked its way down to his brain. "Keep it down!" he growled. "I'm trying to sleep. Go away and bother someone else."
 
Celia knew she couldn't do much now, so she might as well try to enjoy taking care of a child like him. She internally chuckled at the thought, him being a man child like most of the other nobles she'd had to take care of, all man children. She was going to put on the sweet face now. "I promise to leave you be after just this one thing," she chirped, toning her voice not to sound annoying.
 
Damien growled and muttered a few not-very-nice things. "What?" he finally rasped out crankily as he hugged his pillow tightly.
 
Celia gestured over for one of the maids, asking her to bring out some breakfast for Damien. She then said, "If it pleases the Mr., I've brought breakfast."
 
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