"Why are you still awake?"

"Why are you asking like you didn't know I was awake?"

"The sarcasm is not appreciated, Donovan. One of my primary objectives is to ensure your health and safety. After the events of today, you need sleep more than anything else."

"YOU THINK I DON'T KNOW THAT?!?!" Donovan slammed a fist on the table, giving the delicate electronics ample space in spite of his frustrated outburst. He then remembered who was in the room with him, and tried to relax. Letting out a deep breath and running his fingers through his hair, Donovan sat back on the couch. "I can't sleep, Arc. If I could, I would be sleeping next to Diana right now."

"Have you-"

"I've done every single thing I know to force myself asleep. I've done it thousands of times, I haven't made a mistake, so it has to be something else." Despite his earlier workout, Donovan still didn't feel tired. It was starting to seriously worry him. "Please contact the Arboreal Maiden. It might be related to what she had me do."

". . . as you wish."

Donovan took a moment to close his eyes, begging to feel tired at this point. Of course, such a brief period of rest yielded nothing. 

"Given the situation you face, what brings the two of you here? I cannot imagine your motive is light conversation, though it would be appreciated."

"That, sorry. We aren't here for that."

"I don't hold it against you." Arc paused for a few seconds, the potential reasons numerous but the truth unknown. "What would like me to do?"

"Titanyana?"

"Huh?"

"Let's practice now. Tell Arc the plan."

"What?"

"Titanyana, you need to become fluent in English if you wish to interact with Arc effectively. That means practice, and practice started the moment you agree to the proposition. Am I understood?"

"Uh, uh, yes sir!"

"Perfect. Now, tell Arc about what we have planned for you." Donovan's eyes remained locked on Titanyana's form, disregarding her less than modest attire to the best of his ability.

"Ah, er, Donovan and . . . me? I? are wanting to speed my learning to make their life less . . . hard? He wants me to learn from you besides sword-ing and teach from that to Wall and Sanna and Len so they has more of time for . . . other, and I learn more from teaching." Titanyana frowned slightly at Donovan's wincing, but she had given it her best shot. As much as she could listen to the words, remembering their meanings and pronunciations and the proper grammar associated with their usage was still a bit beyond her level of comprehension. "W-was that acceptable? I know it wasn't the best."

"I think it was passable for your level and what you were trying to convey. Arc, what did you get from her message?"

"If I may be granted the liberty of enhancing her message to the desired level of eloquence and detail, I interpreted the following - 'Donovan and I wish to accelerate my education in order to make the lives of Donovan and Diana less difficult. He has proposed that I receive additional lessons from you in lieu of practicing swordplay. In addition to this, he suggested that I take the additional knowledge I would acquire and relay to the others during the usual lessons as a way to both reduce Donovan and Diana's work load and cement my understanding of those lessons.' - Is this an acceptable translation?"

"Y-yes!" Already Titanyana was taking notes. Not literally, she didn't have anything to write down on, but it was quite enlightening to hear the message she wished to convey repeated to her at a higher level. It was much more eloquent, and used words that were more specific than her hodge-podge of mumbles.

"More than good enough. Would you be able to accommodate this?"

"Of course. My only concern is the degree to which you wish for her to learn. She is well beyond the optimal age to learn and ingrain habits, so the more traditional education methods and schedules may prove inefficient. How would you prefer I handle that?"

"The basics are the most important. Do not demean her in any way, but treat this as a trial run of how you will educate the Nekh. She will probably be a little bit easier as she can understand your words without misinterpretation, but don't take that to mean you should slack off or cut corners. She is slated to be a lifelong compatriot, and I want her to be competent enough to fulfill that role."

"Naturally. Should we begin now?"

"Pop quiz?"

"I believe he preferred the term, 'Unscheduled Examination', did he not?"

Donovan sighed. He did not want to be reminded of such extracurricular interrogations. On occasion, Doctor Helmsguard would ambush Donovan with an oral examination focused around his education in the midst of some other task. There were pretty severe punishments involved for not providing a sufficient answer to a question, the distraction those punishments provided usually cascading into more unsatisfactory answers.

"Let's go light for now. Gauge where she is truly at and provide a challenging set of questions. I would prefer if you provided them in read format as opposed to verbal in order to train her reading comprehension skills, but if she asks a question about a certain word or the meaning of a question, oblige her."

"So the test will be centered on mathematics and science?"

"Throw in something to test knowledge of synonyms and antonyms or whatever, as well as something to verify her ability to handle abstract concepts like time and patterns."

"So you would like a generalized test?"

"Yes."

"Very well, please hand her a tablet."

- - - - -

Titanyana had not come to this room expecting to be put on the spot. Sure, she had anticipated some level of instruction and/or interrogation of her ability, but only for the purposes of furthering her knowledge. This was different.

'Seven people wish to ride a boat across a stream. The boat has a mass 500 kg and is capable of displacing 1 cubic meter of water before sinking becomes a serious risk. The average mass of a person is taken to be 70 kg. 

A. If we assume that each individual is of an average build, will the boat still float?

B. If we have to account for a factor of safety of 1.1 for the passengers as they shift and rock the boat around, will all seven people be able to ride the boat across the stream in one trip?'

Titanyana kind of understood what it was asking her to do. It wanted her to determine if the weight of the people was enough to sink the boat. The big problem was that she had no idea how much the boat could handle. This question did not mention the weight the boat could carry without sinking, which was key to completing the problem. Her only hint was that little bit about 'displacing' water.

What did that mean?

"Do you have a question?"

"Yes. What does it mean when it says it is . . . that word?" Titanyana didn't know how to say it, so she just pointed at it. "Dis-placking?"

"Displacing. When something is submerged in a liquid, the liquid does not just disappear, it must go somewhere. The volume of water moved, displaced, is the exact same as the volume of the object submerged in the liquid. Anything above the liquid's surface does not count towards this."

"O-okay." Titanyana felt like she had heard that from Donovan at some point in the past, but she couldn't remember if they had done any problems with it as the focus. This had given her an idea though. From what she knew about stuff in water, light stuff would float and heavy stuff would sink. If she had a block of metal and a block of wood of equal sizes, one would float and the other would sink. Floating things had part of their . . . volume? above the water, which means it wouldn't contribute to the displacement according to Arc's definition. 

If she was right in her assumption, and she had no clue if it was correct, then the weight of an object was the same as the weight of the water it displaced if it floated, right?

"What is the, um, the weight of water? If I had a cup of water how much would it weigh?"

"A single US customary unit cup of water would have a metric weight of approximately 2.24 Newtons."

"Arc. Answer the question she is trying to ask."

"My apologies, the density of water is generally taken to be 1 kilogram per liter, or 1000 kilograms per cubic meter. The weight of water would be a force, meaning you would multiply the mass by the acceleration due to gravity at that specific location. Because the intensity of gravity is subject to change between planetary bodies, I have elected to not include it in this problem."

"Th-thank you?" Titanyana made a note of that to the side, deciding to commit it to memory as soon as possible.

"You are welcome."

Returning to the task at hand, she recognized the problem to be pretty easy if her assumptions were correct. The boat was 500 kg, and the combined weight . . . mass . . . of the seven people was 490 kg, meaning the total weight of the boat would be 990 kg, a simple arithmetic problem. A cubic meter of water was 1000 kg, which was the maximum displacement of the boat, which was just barely larger than the combined weight of the boat and people. The answer for part A had to be 'Yes'.

The second part once again introduced an element of uncertainty. What did factor of safety mean? What was she supposed to multiply by it? Given the fact it was a number close to 1 and didn't have units attached to it she could surmise it was a multiplier or divisor of some kind, but she didn't know where to apply it. Because this problem seemed to focus around the boat, she decided to put it there. 

Her final displacement, 1100 kg, was still larger than 990 kg. Because the difference between the weight and the maximum allowable weigth was bigger, it was probably safer, right? Was that how that worked? Titanyana submitted a 'Yes', confident that deliberating over a 50/50 chance would be counterproductive this late at night.

"F-finished." She pressed the little green 'Submit' button at the top right of the tablet while announcing her completion of the problem.

"I rate your response a 7/10 based on process and asked questions."

The rapidity of Arc's response to her submittal was shocking, but not unexpected. It could probably see what Titanyana was doing while she worked.

"Don't give her a score, Arc. Just tell her what she did wrong. She isn't competing for a grade."

"Very well. Disregarding the questions you have asked on account of genuine ignorance to the subjects involved, your only mistake was applying the factor of safety to the capacity of the boat. In this scenario, you should have multiplied the mass of the people and boat or divided the capacity of the boat by it in order to receive an inflated mass value, or a deflated buoyancy value."

"We haven't covered factors of safety, and I doubt I ever would have. They aren't training to become engineers."

"It was a question designed to test her understanding of a few key concepts with both concrete and abstract implications. Multiplication, addition, and an understanding of the limiting state guided the mathematics, while I looked for an understanding of abstract principles such as buoyancy, standardized leeway, and the relationship between density, mass, and volume. I had hoped she remembered the density of water, however I admit it could have been added to the problem statement to clear up some confusion."

Titanyana thought Donovan looked slightly unimpressed with his friend, but he didn't raise any more complaints.

"Shall we move on to the next problem?"

"Please."

"Very well."

Titanyana's tablet beeped, the screen cleared of her previous work. In its place was another problem.

'Two airplanes are maintaining the same constant elevation in flight as they travel to their respective destinations. The first plane, from this point on referred to as A, is flying at a 45 degree angle clockwise to True North. The second plane, from this point on referred to as B, is flying at a 60 degree angle counterclockwise to True South. At 1:00 PM, B is 250 kilometers directly north of A.

A. Please plot a graph of both planes and their projected flight paths at 1:00 PM. For the purposes of simplicity, you may consider A's starting position to be the origin of the graph. The graph is not required to be to scale. 

B. At what point do the paths of A and B intersect?

C. How far is this intersection point from A's position at 1:00 PM?

D. How far is this intersection point from B's position at 1:00 PM?

E. If A travels at a speed of 800 kilometers per hour, how fast would B need to be travelling for them to collide? At what time would this happen? Round to the nearest minute.

F. If B travels at a speed of 800 kilometers per hour, how fast would A need to be travelling for them to collide? At what time would this happen? Round to the nearest minute.

G. If both airplanes are travelling at a speed of 633 kilometers per hour, how long would it take for them to collide? Round to the nearest minute.

H. How far apart will A and B be at 1:15 PM if A flies at 500 kilometers per hour and B flies at 720 kilometers per hour?'

Titanyana stared blankly at the screen for a couple minutes as she attempted to parse together what exactly she was supposed to be doing. She would follow the orders of the problem, and began to dutifully draw out a grid to plot these things on, but she had a question to ask before her head started to hurt.

"What's an airplane?"

cakeonfrosting

Howdy gamers, sorry for the delay. I have been enjoying my break a little too much, and decided I needed to ruin it by introducing some of the most tedious math questions known to man into my novel! I am excited to announce that I have not failed any classes this past semester, which is pretty important, and am beginning the search for a job. Christmas is right around the corner, which means y'all will either get none chapters for a week or so, or you will get ALL of the chapters for a week or so. Those who were around this time last year will understand what I mean, I think I managed to pump out four chapters a day for a whole week.

This also means that I have a limited amount of time to make good on my new year's resolution, which was to publish chapter 310 . . . lets be honest, that aint happening. I may be able to put my head down and chug from time to time, but 7 chapters (about 18 thousand words) a day for ten days straight is simply beyond me, especially when I have a vacation coming up.

That said, I do want to start off the new year with the introduction of the Nekh to Donovan and Diana. I'll try to get pumping.