The Economics of Prophecy

"That's interesting though. First, it's the simplest machining, and I want to know the relationship to size"

I said as I looked sideways at Meer. Even though it was on the top of the Buddha just now, I'm asking for an explanation so I can eat in.

"It's not that simple. As the magnitude increases, so does the amount of magic required."

"I see. What are the specific figures?

"That's what you're gonna do when you know it. It depends on the alchemist's qualities, physical condition, and more. Normally..."

Noel wrote down five numbers, one unit, two units, five units, ten units, and a hundred units of necessary magic. By the way, it seems to take around 100 units to create a single sword.

"Please."

I gave him the paper. Meer sparkled her eyes.

"When the volume is n-fold, the required magic power per unit volume increases by a factor of 1.2 of n"

"I see. Kind of tight."

"Hey, what are you talking about?

He doesn't understand me and Meer's conversation.

"Maybe, but you're writing a plus or minus five percent shift in discipline from what you really need. That pattern of disguise is the same as nothing, so be careful."

"For Meer. By the way, would you?

…………

Noel wrote five numbers again. That's a little better than just now.

"1.1 times n. Excellent, I think."

"That's amazing"

"Hey, you don't know anything. It's not gonna work."

"With 2/3 of the magic that ordinary alchemists apply to the processing of 32 units of magic conductor gold, you can process - just under 60% for 64 units and just over half for 128 units."

"Ugh, you're lying. How do you know?"

Sounds right. They weren't false in Fulsey's publicity complaint.

"I just calculated it from the numbers you wrote"

"... I wonder if that means merchant technology. Yeah, but now you know how amazing I am."

Noel, cooled from surprise, bragged against his chest. Oh, Meer's gaze snapped. Well, let's make this place feel good.

"I found out about the size. You're in shape next. How exactly do you process magic gold when you say alchemy?

I looked over the room. I don't have any of them.

"... I have to use demonic crystals to put it into practice, and I can't waste it on my current authority. I can't say I used it to show merchants."

"I was getting it from the curator. You don't need that much magic if you're talking about less than one unit."

I took out the Demon Crystal Shards.

"The sorcerer deposited it with the civilian..."

Noel took out a table with a platter of hemispheres on the trapezoid. Carefully place the demonic crystal I gave you on the plate. And placed about a quarter of the earlier demonic conductor gold in the center of the table, where the circular pattern was depicted.

"Look. This is alchemy."

Place your hands on the table and the Demonic Crystal will glow red. Light runs along the pattern depicted on the table. Finally, the magic gold emitted a golden glow. At the next moment, the metal that was square was spherical.

"Isn't that amazing? Do you make shapes like you imagined?"

More mysterious than I ever imagined, I was surprised. It's like combining CAD with a precision machining machine.

"You see. By the way, I can't create whatever shape I want at all. I have a very strict theory."

Noel will explain to us the alchemy shapes. Strict theory was very easy to understand.

"In short, you can only make shapes that can be drawn with compass and rules."

"... what the hell are you, really a civilian? I don't think there's any leaks in the magic dorm."

Noel shook his head at Meer's words. This seems to be correct, too. Actually, I'm making 3D. Although it would be a drawing on space, not a drawing on paper.

"Maybe, but according to complexity, magic is going to be inefficient. Even if you draw a line of the same length, for example, the amount of magic you need in a straight line and a circle is different."

"Oh, yeah. Unlike a straight line that can be defined if the length is determined, the circle has a hell of a lot more magic."

Definition. Then there's hope. Me and Meer nodded at each other.

"What exactly are we going to do?"

"... no matter how much, there's no way I can understand this, but I'll tell you. Multiply the special numbers in the diameter of the circle."

"How much is that number, by the way?"

"There's no way you're gonna tell me. The secret of alchemy."

"Maybe you could tell me a few digits. Extreme story, ink the wheels and put it on paper..."

"Three digits!

Noel said like a jerk. Wow, is that primitive? But a triple digit would have put it out pretty hard that way. You won this one. There is no guarantee that it is the same in this world as it was in the original world, but it will probably be fine. In a world of natural logarithms and different numbers around it, I don't think creatures of Earth origin can exist, not even matter.

Plus, if I'm right, I can verify it right away.

"3.14..."

"... from where"

"No, that number is the ratio of the diameter of the circle to the circumference."

It's called circumference, one of the most important numbers in mathematics, no, maybe in the world.

"π If the accuracy of" Pie "increases, won't the necessary magic be diminished? If the circumference rate of the extreme story is determined, the amount of information on that line is the same whether it's a curve or a straight line."

Of course, the circumference rate never becomes a number in the so-called normal sense. Because it's a transcendent number. The description has an infinite number of digits.

Anyway, if magic is super efficient information processing as I imagined it would go well with math.

"Well, π, suppose Pie is 3.142"

"Don't use strange words......, the circlet is 3.142. Yeah, good. I'll give it a try."

Noel returned the sphere he had just made to the cube. I see, don't go back in a flash. That's how different it is with straight lines and curves. And I did the same thing again.

"Liar, this is..."

"How much did you save?"

"... about 80% and half"

Noel said in a face saying he saw something incredible. If it's a sphere, it's a volume π Pie multiplier. No wonder the slightest difference makes a big difference.

"So, next up, 3.1416"

Noel cramped into Meer's words. Still repeat the same thing.

"Hey, seventy percent and a little. What am I looking at right now?"

"3.141592"

"Halved..."

"Bye,"

"Shit, no more, because I can't adjust better. But tell me. Tell me, how did you do it?"

"This is how the circumference rate can be calculated"

Meer writes a square polygon that interfaces with a circle on the paper. As the number of corners of the polygon increases, the sum of the lengths of the sides of the polygon and the circumference approaches. When I taught her this principle, Meer made her calculate to 128 squares. However, the circumference rate of six decimal places cannot actually be achieved to that extent.

I know circumference rates up to six digits because my teacher, who cut to loose education, made Semi students recite π "Pie" up to ten digits. I forgot about the second half of the boulder.

Incidentally, increasing the number of polygons to infinity does not make the polygon exactly the same as a circle. But don't worry about what happens if you use the concept of infinite classroom numbers to define it exactly. Well, what a 1-1/3 + 1/5-1/7 that I know... is the one that lines up odd numbers while inverting positive and negative. There are definitely tens of billions of calculations to converge into a decent π Pie.

"How do you know this?"

Noelle is just hanging on to Meer. I can't help being prestigious just because I'm on the shoulder of a giant.

One human being does both design and manufacturing. That's a harm. Really, I guess I'll be dragged by the actual work. I guess there are times when an alchemist is valuable as a working force to get to the way of studying abstract mathematical theories.

It's like Archimedes making his own crown to experiment with.

By the way, there's no Magimon giant in this world. Maybe. I checked to see if the Neanderthals existed because they said they were orcs or something. There were no orcs, even though there were female knights.

"Then what happens if you make my order by this standard"

"... one can do it. But you didn't tell me. Make a lot of this. How many?"

Ultimately, it's more than a few thousand.

"Oh, you've peeled off your makeup. It's not enough to gather all the demon crystals in the kingdom."

I'm feeling better, Noel. I put my head on it.

"Oh, I forgot to explain. By the way, it's the shape of the sphere, not the sphere that actually gets it made. Six of them and then these two shapes, at the same time, into a magic guide about the size of a brick..."

I spread out the blueprints I've been drawing. There are a total of three types of moulds drawn there. I really need another one, but that should be at the blacksmith in time. And the ingredients of what you actually make are not magic gold.

"You're all using circles. It's impossible."

"So, what do you think?"

"This pie... it wasn't, what if there was a new circuit. But..."

"What's missing?"

"There is a larger medium crystal. Then even the director needs to apply for permission to use it."

"Okay. Do something."

It was definitely in the loot of the Third Knights, the Knights of Warcraft Again. When they become dragons, they have multiple demonic crystals, such as the heart as well as the forehead. You want to talk to that prince? Well, it's important to the other side.

"First, then, I want you to make this third prototype"

"You can do it with the demonic crystals I can use now..."

"Because I will talk to Fulsey about replenishment. I don't know, will you take it"

"... okay, but..."

Noel saw Meer.

"Meer, give him a hand."

"If the seniors say so, we have no choice."

…………

"No. That's how you pull the auxiliary line, you get the answer"

"I see..."

"Because the angle there and the angle here will prove to be the same, similar"

"Sure, but I can't do that, and I'm gonna need more magic here. I can't do this without needlessly crossing the lines."

"Then use this to reduce the calculated amount"

"Then we'll figure it out, but this is the next place..."

Meer and Noel are discussing the blueprints I gave them before. I'm hand-held.

"I'm sorry to interrupt, but I need to know how long the prototype can take."

I said roughly to the two white-hot people.

"Shit, it's a good place right now."

"No, no, no, I'm doing it right now. It's a drawing that has nothing to do with my favor on the way."

"... with"

"Even Meer...... Uh, just the worst part of the ball. Because that's the most important thing to know about accuracy, and you can go to a tree on the side of a prototype."

I'm out. Even though it was so dangerous earlier. I just feel like it. Apparently, Meer's geometric sense goes well with the alchemists who can be described as CAD producers in this world.

"... right. Maybe three days, including the time it takes for the magic to fall out and the shape to settle."

"Infinity has become finite"

Meer laughed mischievously, because it was "absolutely impossible" at first.

".................. what is it? Sure, you're amazing, but"

"Well yeah. We can't practice. So what?"

"What?"

"I want you to stay with me when I show this to the other members."

"Other members are merchants..."

"Uh, well, you're the most common one. But the curator's coming, too. 'Cause if you don't call it, it's gonna sound loud."

"I'm coming."

It was a quick answer.

"Later you'll be talking to a blacksmith or something when you actually make this..."

"Heh, heh. It's nothing compared to teaching a few tricks to civilians. So..., you know, I'll always be."

Noel saw Meer.

"If you want to finish the other two in three days as well as the ball, don't give me a hand"

"Hey, my own magic will drain you.... Okay, I'll try."

"Hey Meer. You don't have to rush that far. The members who show the prototype are members, and they don't know when the meeting will be for the fair."

I told Meer. But Meer has already begun to interact with Noel.

Well, the result is Aurai. But, Noel, that's my precious secretary. Don't forget.

But after all, magic is a super-efficient information manipulation. Maybe we can think the same way about how the crystal of prophecy works.