D. N. Angel Fan Fiction ❯ Complex Equations ❯ Complex Equations ( Chapter 1 )

Disclaimer: I don't own DNAngel.

AN: I felt like going about writing a one-shot differently than I usually go about it. Call this experimental. Go ahead, be my guinea pig.

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Over the course of time, one learns that taking one's mind off something unfavorable is, more often than not, a good thing. For Hiwatari Satoshi, it was, more often than not, imperative.

Over the course of time, Hiwatari Satoshi had gathered a collection of what he considered `distractions.' As the named implied, they more often than not, helped him divert his mind to smaller, better things. Because he could often be found needing to think of other things for the most part.

Tonight was not an exception. With cold, familiar laughter still echoing softly in his mind, Satoshi pulled out his single sheet of lined paper. On this paper were written several complex math equations - more often than not with their solutions already written. Satoshi frowned as he realized yet again, that his small list of distractions wouldn't be able to distract him for very much longer.

Mingled in here or there on the long list of solved equations were problems that Satoshi either hadn't gotten to , or he had proclaimed that they had no solution. Either way, the math was a nice alternative, the boy had found, to the background noise in his head. Each of the problems were certain equations that his past professors had pointed out as `unsolvable' or `having no solution.' They had so far been correct on a few of the problems, but on the others Satoshi had been far more successful than they would have believed he could have been. Such was the result of serious concentration, apparently.

Among the remaining equations on the page, Satoshi saw the problems:

i^4 +2 = 0

e^(i*pi) + 1 = 0

Which is truly greater? x or -x?

0/0 =

He decided to tackle them one at a time. First:

i^4 + 2 = 0

He began to think about the values of each symbol represented, the proper way to go about solving an equation was analysis first, after all.

0. 0 was the way to go about representing nothing in mathematics. 0 meant that there was nothing there or nothing left. 2 was a second term on the left of the equation. That would be the first term to be simplified. It could alternatively be shown as 1+1. i. That one was a simple variable normally used to express an imaginary number; usually the square root of -1. The 4 was how many imaginary numbers were to be multiplied.

Satoshi's thoughts suddenly (and not quite voluntarily) returned to that day's history lesson.

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“Who can tell me the four main principals for which the American Revolution began?” One student in the back raised his hand. “Yes?”

“Freedom, Safety, Change, and Peace.”

“Very good. Such irony that a war be fought for the principles of Safety and Peace, I know, but that was the way things had to be decided back then…”

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The lecture had continued on after that, but the only moments that the blue-haired boy found significant were the ones he remembered. Without permission, his brain entered the values into the equation.

Freedom * Safety * Change * Peace + 2 = Nothing

Once again, the boy was reminded that he had to simplify the right side with the 2. He looked at his problem now, and saw that, whatever the principals equaled were apparently canceled out with the addition of that one term, for in the end there was nothing. By just adding that simple 2, there could be no Peace, no Change, no Freedom, and no Safety. Satoshi thought over what the number two represented. 1+1.

Freedom * Safety * Change * Peace + 1+1 = Nothing

Satoshi thought over the number 1. Subconsciously, he thought it to be the single most solitary number. But then again, Satoshi was quite familiar with solitary things. His brain once again took the liberty of modifying his equation in his slow state of mind.

Freedom * Safety * Change * Peace + Satoshi +1 = Nothing

The boy calmly thought over what had just happened, and realized that he, indeed, was quite similar to the number one. So what was it that was added to him that kept him from having Peace, Change, Safety, or Freedom? There was only one…and it canceled out Satoshi's four most basic principals of life…and he never left the boy alone…

Satoshi gave up on this problem. He used these problems as a distraction, so it was totally useless to do the problem if it couldn't keep his mind off matters. The boy moved on to the next problem. It wasn't worth it to answer that last problem anyway; he had already known that to begin with.

e^(i*pi) + 1 = 0

He started by, again, assessing what each symbol represented. 0 and 1 both had the same value as before, and both still represented nothing and a solitary unit. e was the variable to define exponential value. Pi was the mathematical symbol for expressing the non-terminating, irrational number 3.14159...it was used for finding the circumference, area, or surface area of circles. i still represented an imaginary number. Satoshi took the first step in simplifying the problem. It now read:

e^(i*pi) = -1

Automatically, he re-wrote the problem as his brain thought it should be based on past values.

e^(imaginary * irrational) = -Satoshi

Imaginary…something that only existed in the mind…that lived only in the head….

e^(KradIrrational) = -Satoshi

What was e? What made the Krad irrational? What could take away the Satoshi from the picture?

Daisuke^IrrationalKrad = -Satoshi

The boy threw down his pencil when he realized what exactly he had just done. Well, that wasn't exactly the answer he had been looking for, but what could he say to refute it? The equation was true… Satoshi shook his head to try to clear the thoughts that were spawning from the sight of what he had written. He moved on. There was no way he would ever be able to look at that problem again without it being a reminder, anyway.

Which is truly greater? x or -x?

Satoshi took into consideration what the question was asking. It was asking, in terms of both magnitude, and placement on a number line, which was a larger number? There were the terms `x,' and `-x,' which was read as `the opposite of x,' because since they were both variables, it was unknown whether `x' was a positive number to begin with. If `x' was positive, then `-x' was negative. But if `x' was negative, then `-x' was positive.

+So if `x' is happy, then the `opposite of x' is sad, but if `x' is sad, then the `opposite of x' is happy…right? +

Satoshi nearly snapped his pencil at the sudden intrusion. He loved doing math in the presence of Krad (which was always) simply because, out of all of the areas Krad had studied, math did not seem to be one of them. The boy wasn't totally sure if the statement had been somewhat of a joke, or if the wretched being had honestly thought that was a correct response.

-No. `Positive' or `Negative' does not mean `happy' or `sad'. How is it that you have been alive for over three hundred years, and you still don't know this? - The boy enjoyed conversing with the voice in his head only when he could make fun of, or humiliate it.

+…Numbers never really…interested me…+

-Then shut up, if you know nothing about what you speak, fool. - The come back had been a bit curter than anything Satoshi usually said, but he had been speaking to Krad, and he had been slightly shaken by what Krad had said. Satoshi's brain had gone quite a step faster than the boy would have liked, and as he had eyed the problem at the start, the first thing he had noticed was, of course, the `x.' Though, by having a conversation with Krad, slowly, that `x' looked a tad bit more like a…cross. So `x' equaled a cross…which equaled Krad. So…what was the `opposite of Krad?'

-ME.-

His mind nearly shouted to be heard. There was nothing more different than that demon than that demon's host, or…at least the host liked to think so. So the equation quickly mutated into:

 

Which is truly greater? Krad or Satoshi?

Satoshi looked back at what the problem was asking…again. Both in magnitude and on a number line, which was greater? Well, on a number line, `x' would of course be greater than `-x'…a thought that Satoshi was sure incited a gleeful smirk from the curse inside of him. So maybe Krad had been…a little right… `-x' certainly was sad when `x' was happy…

What about greater in comparison by magnitude?

Neither.

Neither `x' nor its opposite was greater when compared by magnitude; they were both `x' units away from zero. Neither of them were greater…

For fear for his sanity, the boy moved on to the last problem on the page. It was a simple problem, but sometimes it was the simple ones that really turned out to be complex. Sometimes, it was the quiet ones in the back that really deserved the most attention…but his thoughts were digressing. This was math he was doing. Nothing else.

0/0 =

So he had a problem with no variables, and nothing that he would have to substitute words in for. All he was being asked was `How many times can you divide zero to get zero?' Simple, right?

Satoshi sat still for a few seconds focused on all the different ways to go about double, and triple-checking his answer before he finally finished.

For some problems, there are no solutions.

These math problems certainly hadn't been a very fine distraction for him at all, this night…