244 An Evening Coffee (Author – I LOVE MATHEMATICS!!!)
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Donovan rubbed his eyebrows as he went over Titanyana's answers to Arc's little examination. She had left the room some time ago with a limp tail and droopy ears, a sign to him that she didn't feel confident in her performance. The fact Titanyana hadn't grasped that the purpose of the test was and eventual failure didn't surprise Donovan, he wondered how many people in this universe would create a test like that without malice. That said, he still felt a little bad about it.

He knew more than anyone else how shitty it felt to be shown just how little he actually knew. Even towards the end of his education Donovan would sometimes find himself faced with a subject he knew fuck all about. Hell, he was dealing with such a phenomena right now. Split was to him as Science and Mathematics were to Titanyana, a strange field of study that had little bearing on their past yet promised to be incredibly important to their future. 

The biggest difference between their situations was that Titanyana had a group of people more than willing to sit down and teach her this stuff until she got the hang of it. Actually, now that he thought about it, that might be one of Donovan's biggest issues with Split. He didn't have a teacher. 

Sure, the Arboreal Maiden would tell him what to do and could occasionally provide a demonstration, but aside from that he was on his own. Her determination to have him forge his own path in the field of Split was simultaneously infuriating and worrying. He had to wonder why she was so reserved with her instruction, why she didn't display to him the most optimal methods of doing things so that he could catch up to the pack. Were the traditional methods somehow wrong? Was there something about him that made the 'old fashioned way' undesirable somehow?

Donovan understood that there were bound to be some differences on account of his lack of familiarity, but how was he supposed to bridge that gap without the help of someone with experience? 

"What are your thoughts on her current status?" For better or worse, Arc interrupted his spiraling thoughts. "I believe her level of knowledge to be commendable for one with little formal education, but she does not even approach the standards required for a Street Level Bureacrat, much less those necessary to be your Liaison."

"She doesn't need to be perfect just yet, Arc. If she is already admirable in your book, then she is already leagues above most others."

"That may be true, but I cannot help but advocate for-"

"For what? Someone more competent? Don't get me wrong Arc, I would love to have someone with a better specialization take the job, but they just don't exist at the moment."

"A fair point. . ." Donovan shook his head lightly at Arc's backing down. ". . . what if she makes things harder for you and I? Mistakes at this point could prove disastrous."

"Then we should focus on catching them, fixing them, and instructing her on her mistakes so she doesn't make them again. We're training a person here, Arc, not a machine."

"Ah, and what a pity that is."

Donovan didn't bother to stifle the short laugh Arc's sarcastic comment evoked. The poor computer was probably being driven crazy from a lack of meaningful human contact. It had been little else but machines for it ever since they left the Oberlux.

"Hey Arc?"

"I'm listening?"

"You are going to be integral to our bureaucracy, right?"

"Naturally. Why do you ask?"

"Well, I was just wondering how you plan to handle communicating with billions of people all at once. I can't imagine that would be good for you. I mean, I can hardly handle ten people speaking at once."

". . ."

". . ."

". . ."

"Arc?"

"I heard you, and I understand your concerns, I simply don't know how I should answer your question. On the one hand, I can understand how you would worry about me going crazy from the stress of handling all of those interaction, and that you worry about a shift in my priorities, but I don't know how I could convince you that I will be fine when I am not certain myself."

"So it's a bad idea."

"No, it is the best plan we have to deal with such a large population and maintain a cohesive and centralized bureaucratic structure. I am confident in my ability to handle as many separate instances of interaction as my supplied processing power will allow, and I am almost certain that such interactions will not affect me negatively, but I am not absolutely certain. There is still a chance that I may become cynical and detached or overly intrigued by the personal lives of those I am serving. As I understand it, it is most efficient for a bureaucrat to maintain a comfortable distance from the personal lives of the people, but still retain an amicable and flexible approach."

Donovan closed his eyes and took a deep breath. Arc's answer basically told him nothing, which provoked a response in Donovan's mind that was arguably worse than if Arc had admitted it didn't know. In spite of Arc's seemingly infinite knowledge and analytic capability, the best it could do was a 'maybe' From the way that 'maybe' was formatted it sounded a lot more like it was certain that something would happen. Arc didn't intend to lie to Donovan, it just didn't know how to tell him that it knew it didn't know without sounding somewhat incompetent. 

". . . forget it. I can't be bothered to think about it right now. It would just stress me out even more."

"Speaking of, are you still unable to sleep?"

"I don't feel tired, if that's what you're asking."

"I see. Given how long you have been awake at this point, I highly doubt that it is a mental issue. I would like for you to take a blood test so I can analyze your blood chemistry."

"You want me to take a blood test? Right now?"

"I doubt it would be of much use if we did it any later."

"Don't we have a limited number of those?"

"If your are referring to the number of sample charges on your EMHM, there should still be three remaining after the five I used to monitor your status in transit to the Oberlux and the two used to identify differences in blood chemistry after what the Great Csillacra did to you."

"What if we need those three for some other emergency?"

"The Pegasus has a small pharmaceutical manufactory that is nearing completion, and the rondel is nearing its service expiration date. Unless something drastic happens in the next week, there should be no concerns with regards to blood tests. There will be one for each of you."

Donovan mindlessly peeled some dry skin from his lower lip before realizing what he was doing. "Fine. Where did I put it?"

"It should be in a drawer."

"Mhm." Donovan mumbled to himself while he searched for the device that had probably saved his life back then, a funky little medical device that was secured around the elbow. 

click

"Alright, do you want me to push the button?"

"If you so please."

"Will do." Donovan pushed the white button in the center, a white cylinder dropping down as he felt a needle prick the crease of his elbow. He held it for three seconds before releasing the button, bringing a (now) dark red cylinder up before it slid out of view and another white cylinder took its place. 

The Elbow Mounted Health Monitor was a neat little device issued to the pilots and crew of deployable craft in order to regulate and monitor their health while on mission. It consisted of a nine cylinder blood test rondel feeding into a miniaturized rapid result chemistry tester, a pneumatically deployed syringe, and a block meant to hold vials of various injected chemical substances, the most common being a stimulant, a sedative, a painkiller, a blood coagulant, and a blood thinner. 

On account of Donovan's mission, his was a bit more specialized, having a nine-charge rondel instead of the standard five and space for an additional two vials, which he usually filled with stimulant and sedative on account of their frequent use.

That little machine tended to be the second most expensive item inside the cockpit besides the pilot, and was there for to keep them alive and alert during a fight, and increase the chances of survival should something go wrong. Hyperventilation and panic attacks caused by combat stress can be managed by the proper application of sedative, while daze and fatigue can be staved off with stimulants. Painkillers can dilute the effects of damage on performance to an extent, while blood coagulates and thinners are used in tandem to help deal with any internal or external damage that may have occurred. 

Overdoses issued by these devices were not unheard of, but the vast majority of cases that resulted in a death tended to be situations in which death was likely to occur regardless. The most common example being when a craft was subjected to a mobility kill and had not method of returning to base. In such a situation the EMHM was programmed to intentionally over-inject sedatives to send the pilot into a catatonic state to reduce their oxygen consumption and prolong the amount of time available for rescue. 

"What's the damage?"

"Caffeine, a lot of it."

"Caffeine? Coffee caffeine?"

"Yes. The EMHM was not built to measure such high levels of the substance, so I cannot say anything for certain, but it estimates your blood caffeine levels to be around 100 milligrams per liter of blood, around twice the maximum healthy dosage. If we assume a half life of five hours in the blood stream, then I estimate you ingested approximately a kilogram of caffeine, though your body's limited ability to process that much means it was likely closer to 0.8 kilograms."

". . ."

"Knowing this, it is hardly surprising that you are still awake. As a matter of fact, I doubt you will be able to fall asleep for the next few hours."

". . . damn."

"Should I contact the Arboreal Maiden and inform her of this? If her claim to be running a test about this phenomenon is to be taken as truth, I imagine this would be quite enlightening for her."

"Um, sure, please do." Donovan felt a little dazed at this revelation, or was that the caffeine? "How . . . how did that happen? It was only in my stomach for a few minutes."

"One of the notable aspects of caffeine is that it can be rapidly absorbed through the stomach lining. In fact, it can even be absorbed through the skin so long as contact is maintained. I imagine those few minutes were enough."

"No, yeah, I get that much. I was wondering more about how that much caffeine got in there. I drank at most like . . . half a liter of blood, and I don't think the blood and cup weighed a kilogram combined. How could I get that much caffeine out of it?"

Donovan and Arc were vaguely aware that the laws of conservation of energy and mass weren't really applicable anymore (both had witnessed events that were in clear violation of those principles) but that didn't there wasn't anything to indicate when one of those events was happening. 

"So when did the caffeine appear?"

"It had to be once my gut absorbed it, right? Something happened at that point that made a bunch of it."

"Perhaps there was something in the slurry that permitted the synthesis of caffeine?"

"That makes more sense, I think." Donovan didn't much like the concept of a mass suddenly appearing inside of him. Well, he didn't vibe with the concept of 'mass suddenly appearing' in general. "So what should I do?"

"Relax. I don't want you to overwork yourself, so I will be restricting your access for the rest of the night. You should probably take a shower or bathe, and then do something you find enjoyable for a while. Perhaps you could read a book or watch a movie."

Donovan frowned, fully aware of his filth. "I . . . thanks, bud. Sorry I snapped at you earlier."

"I have not taken offense to it. Given your current state, I am more surprised that was the extent of your irritability."

"Yeah . . ."

The two of them were silent for a few moments, neither quite sure where to take the conversation. Despite how long it had been since they had genuinely conversed with each other, neither of them had a new topic. 

"So . . . how about that history lesson?"

"Interesting for sure, but I don't feel she revealed anything particularly intriguing. At the very least, there was nothing in there I would consider to be a ground breaking revelation warranting a change in policy or diplomatic stance. I will still discuss it with Diana tomorrow, perhaps she will have some insight."

"I - er. Diana and I decided that we would take the day off tomorrow." Considering what Diana saw, Donovan didn't want her trying to work so soon after what was liable to be a traumatizing event.

"If that is what you wish. Now, go shower and rest. If you are still unable to sleep in three hours time, I will consider authorizing sedatives to force you to sleep."

"Thanks buddy."

By (un)popular request, I have decided to provide an answer for the previous problem.

A:

A is at (0, 0), flying at an angle of 45 degrees clockwise to true north. The path of the plane is modeled by the equation:

y = x

B is at (0, 250), flying at an angle 60 degrees counterclockwise to true south. The path of the plane is modeled by the equation:

y = 250 - x/sqrt(3) -> x/1.7 (simplified assuming Titanyana doesn't have a calculator

Plot the equations into Desmos or something, I can't be bothered to finagle with a graph right now.

B:

A point of intersection can be found by substitution and solving for the remaining variable.

x = 250 - x/1.7 -> 2.7x/1.7 = 250 -> x = 1.7*250/2.7 = 157.4

Because one of the lines is a direct relationship, y = x, the x and y values are the same.

Point of intersection is (157.4, 157.4)

C:

Determining the linear distance between points is done via the Pythagorean theorem. For a 45/45/90 degree triangle, an easy relationship to remember, the ratio between side lengths is that the leg/leg/hypotenuse relationship is 1/1/sqrt(2).

hypotenuse/(157.4) = sqrt(2)/1 -> hypotenuse = 157.4*sqrt(2)

Assuming Titanyana simplified sqrt(2) to 1.4 if she didn't have a calculator,

Distance = 220.36 km -> 220.4 km

D:

Much the same as the previous section, an easily remembered ratio can be utilized. For a 30/60/90 triangle, the ratio of side lengths is 1/sqrt(3)/2 (the same ratio used to determine the slope). In short, this means that the hypotenuse is twice the length of the shorter leg.

The leg lengths are

|250-157.4| = 92.6

|0-157.4| = 157.4

The shorter side is 92.6, so

Distance = 185.2 km

E:

You can do parameterization for this shit, but I wouldn't recommend it because I've given you lines with clear distance conditions. 

Speed is defined as distance/time. Time, therefore, is defined as distance/speed.

The time taken for A to reach the collision point is, 220.4/800 = 0.2755 hours (16.5 minutes -> 17 minutes)

Reversing this to find the speed of B necessary to reach the collision point at the same time,

185.2/0.2755 = 672.2 kph

Speed of plane B = 672.2 kph

time of collision = 1:17 PM

F:

An alternative method of solving for speed is to do a ratio conversion. Because they have to cover the distance in the same period of time, their speed to distance ratios must be proportional. 

speedA/220.4 = 800/185.2 -> speedA = 800*(220.4/185.2) = 952 kph

You still need to find the time to collision the old fashioned way though.

185.2/800*60 = 13.89 (14 minutes)

Speed of plane A = 952 kph

Time of collision = 1:14 PM

G:

This one is kind of a trick question. Because there is a difference in distance between point of collision, two planes travelling the same exact speed will not collide with each other. A question of this nature is usually added to see if the student is paying attention and is confident in their answer. 

H:

. . . motherfucker, why did I do this one again? Oh, right, parameterization. Parameterization takes into account another variable, time, when calculating the path an object takes. This allows for two lines to intersect without ever actually intersecting, essentially turning them into points that travel along the path defined by the base equation. The easiest method I remember is for objects with a constant speed travelling across a linear path. 

Note here: I am sorry, but I simply cannot be bothered to re-learn the more complex "official" ways of parameterizing equations. I believe it to be a niche field of study with limited use now that computers are so common.

Starting with A, which is travelling at 500 kph.

A linear speed, the rate of change of x per unit time is, once again using the ratios established for a 45/45/90 triangle.

x = 500*t*(1/sqrt(2)) = 500*t/1.4 = 357.1*t

Therefore,

y = x = 357.1*t

After 15 minutes (a quarter of an hour), the coordinates of A are

(89.3, 89.3)

Moving on to B, which is travelling at 720 kph

because of the relationship of the 30/60/90 triangle making it stupid easy to find the change in y

y = 250 - (720*t/2) = 250 - 360*t

Now that we know y with respect to time, we have to find x

250-360*t = 250 - x/1.7

x/1.7 = 360*t -> x = 612 * t

plugging in our time of 0.25, we get the coordinates

(153, 160)

Now we get to find the distance between the two.

deltax = 153-89.3 = 63.7

deltay = 160-89.3 = 70.7

now to pythagorize

(63.7^2+70.7^2)^0.5 = (4058+4998)^0.5 = sqrt(9000) = 30*sqrt(10) = 30*3.2 = 96

The planes are 96 kilometers from each other at 1:15 PM.

 

God, I hate myself for doing that. Why did I ruin my night like this? I hope you enjoyed my suffering.

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