kscans

Chapter 186 - Episode 5: Part 1, Information Can Be Bought with Money

"Simply put, the ultra-high density 'information' of prophecy is an 'ultra-high density' wavelength, and thus, 'ultra-high' energy."

I began my explanation, hoping to persuade Maytyl. That said, I had to make a disclaimer beforehand.

"I think this story is a bit, no, completely different from what you three are expecting. It's a topic so abstract it's almost unimaginable."

"Let's hear it. I will judge after listening."

"It is rare for your stories to stay within the bounds of imagination."

"As for me, um, please go easy on me."

Maytyl nodded, and Fulsy and Noel lined up in front of me as well. I, as if pushed by the three students, all of whom were smarter than me, stood before the slate.

"There are two premises. One, both sorcery and magic are information processing that uses magic power. The other, the prophecy of the crystal, even among such information processing, requires the observation and transmission of vast amounts of information. In other words, it deals with ultra-high density information."

I started off this way, as if organizing my own thoughts.

I cannot use either sorcery or magic. Much less do I know the specific mechanism by which that accursed crystal calculates the future. What I do know is that the information required for that calculation must be precise and vast, and only the physical consequence of information being precise and vast.

Even if I do not understand the intricate workings of an engine, I do know that an enormous amount of energy is required to move a mass of iron at high speed. It is that kind of analogy. In other words, high-density information is equivalent to high-density energy.

"Information... That is the word Ricardo always obsesses over, isn't it? It was the same during the incident with the Spiral Flame. What do you mean by 'information,' Ricardo?"

"That's where we should start, isn't it? I am sorry to ask a question in return, but what do you think 'information' is?"

"...Simply put, I suppose it is something written in text like this?"

Maytyl pointed to the paper pasted on the slate. The characters written on the paper were certainly information. But the "information" I am talking about is not something special that cannot exist without humans.

"Of course, what is on that paper is information. However, the 'information' I am talking about is much broader."

Even before humanity created written language, there was "information." For example, the genetic information in DNA. This means that complex information existed even at the bacterial level. However, what I am about to explain is a matter at the level of physics, not even related to living beings.

"For example, let's say this paper contained 'information' comparing the Kingdom and the Empire. What do you think would be written on it?"

Even so, I deliberately chose a familiar example. ...This is so I can explain it in a way I understand.

"...The ruler of the Empire is the Emperor, and the ruler of the Kingdom is Ricardo, or something like that?"

"This is not the time for jokes, you know."

The content of what I am about to say will be enough of a joke on its own.

"I get it. Like, 'The Empire has many mountains, and the Kingdom has many plains,' or something similar."

"Yes, that is exactly it."

"............"

"I do not understand that."

"I apologize for being unreliable, but I am organizing my own thoughts. ...Um, the current example is good. You would not write, 'Both countries have land,' would you?"

"That is right, of course, because that is obvious."

"Right. Obvious things, in other words, common things, do not become 'information.' Conversely, differences are 'information.'"

When people from the Kingdom introduce themselves to each other, they do not say, "I am Ricardo, a person of the Kingdom," or "I am Noel, a person of the Kingdom."

"Differences are information... It is a story that I understand and yet I do not. For now, let us say information is differences. So?"

"If 'information' is differences, then the simplest difference becomes the 'basic unit of information.' ...To put it in terms of something easily visible..."

I took a copper coin out of my pocket. When I flicked it with my fingertip, it spun in the air with a high-pitched sound.

"The difference between rich and poor people?"

Noel tilted her head. Like a miser... It is enough to make me weep that this is closer to my true nature, to "shounin," than to information theory. Well, expressing everything as information is, if you think about it, somewhat similar to converting human value into money...

"In this case, I am talking about having a front and a back. The most basic difference is a difference between two things. Front and back, yes and no, nothing (sero) and something (ichi). This difference is the 'basic unit of information' for everything. Let us call the use of information that can be expressed by the two sides of a single coin '1 bit.'"

I said, flipping the coin over. I am not talking about computers, the reason computers handle bits is what I just explained.

"In other words, the 'amount' of information can be converted into the number of these coins..."

At my words, all three looked blankly at me. They do not understand, do they? I am even doubtful if I truly understand it myself.

I need another analogy. I looked around. I could see the school building from outside the window. ...There was not a soul in the classroom after school.

"Look at that classroom. Let us say there is a student sitting all alone there."

I pointed to the classroom. Fortunately, no such lonely person was there, but it was an analogy. I do not want to think about why I came up with such an analogy.

"If I were to draw a schematic, it would look like this... To simplify things, let's assume that classroom only has 16 seats, 4 rows by 4 columns."

While receiving their three puzzled gazes, I drew a schematic of the classroom on the slate. And then, I filled in only one seat.

Front □ □ □ □ □ □ □ □ □ □ ■ □ □ □ □ □ Back

"Let us think about how many coins would be needed to describe the position of this student."

I said that, and looked around at the students' faces.

"...He jumps to the wildest conclusions, does he not?"

"I understand what you are saying, but I have no idea what you are trying to say at all. It is always like this, though..."

Fulsy and Noel made thoughtful faces.

"Like a military unit's position being information?"

Maytyl said. Militarily, positional information is the most crucial thing.

"Yes, positional information. Princess Maytyl, you should understand. Positional information has accuracy. At first, it is information that can be expressed with a single coin. How can one student in the classroom be expressed?"

I took out two coins, making one heads and the other tails. I showed the difference on the slate.

Is there a student in the classroom? ● (Yes) ○ (No)

"What can be expressed with one coin is only whether a student is in the classroom or not."

"Yes or no, then."

"Right, in this case, it is expressed as, 'Is there a student in the classroom? ● (Yes).' You only know that a student is in the classroom, but you have no idea where among the 16 seats they are sitting. In other words..."

I "lightly" shaded all 16 seats on the slate.

■ ■ ■ ■ ■ ■ ■ ■ = The student is "somewhere" among the 16 seats
■ ■ ■ ■ ■ ■ ■ ■

"One coin, 1 bit of information, results in this kind of understanding."

Maytyl nodded cautiously. At this point, she was smarter than me. When I first heard this explanation, I complained, asking what information and communication technology had to do with coins.

"So next, I will add one more coin. Then, we can represent information a bit more finely."

Is there a student in the classroom? ● (Yes)
Is there a student in the left half of the classroom? ○ (No)

"In other words, using two coins results in this kind of understanding. Visually, it would be...

□ □ ■ ■ □ □ ■ ■ = The student is somewhere in the right half of the classroom
□ □ ■ ■ □ □ ■ ■

It would be something like this."

I shaded half of the seats, slightly darker than before.

"Certainly, the student is in the latter half, isn't he?"

"But since there are actually four rows of seats in the classroom, information is needed to specify whether it is the left or right of the left half. In other words, one more coin is needed to specify the position of this student. A total of 3 coins."

Does a student exist in the classroom at all? ● (Yes)
Is he in the right half? ○ (No)
Is he in the left half of the left half? ● (Yes)

□ □ ■ □ □ □ ■ □ = The student is somewhere in the third column from the left of the classroom
□ □ ■ □ □ □ ■ □

"However, if we assume the student is in the classroom, two coins are sufficient. With two coins, you can distinguish one out of four possibilities. Next is the vertical axis. We continue by replacing the question with, 'Is he in the front half?' As a result, to specify one out of 16 seats, in other words, one out of 16 possibilities, ultimately requires four coins."

□ □ □ □ □ □ □ □
□ □ ■ □ □ □ ■ □

□ □ □ □ □ □ □ □
□ □ ■ □ □ □ □ □

I returned the schematic to its original state.

Well, what is actually being done is simple. It is like assigning numbers 1 to 16 to the desks, and representing the student's seat number in binary (bits). However, as I just said, precision is the issue.

"The point is, the more you narrow down the student's positional information, the more the amount of information increases. This time, I am expressing it in units of desks, but if you want to express a more precise location, you will need more information, in other words, more coins (bits) to express it."

For example, specifying the classroom's length and width in centimeters would be even more precise, and in millimeters, it would be even finer. If you only want to know who is sitting alone, the seat position would be enough, but if you were to snipe as a sniper, even more detailed information would be required.

"This is incredibly convoluted, but the conclusion is obvious, isn't it? So, what does this have to do with magic power?"

"Hmm, so this connects to prophecy..."

"I have a headache just thinking about what will happen after this..."

The three of them, at least, were interested. Next, I would equate the number of these coins with wavelength and energy.