Twenty Years Later- Bunbunmaru Spirit News archives
Vampire Girl has totally awesome mathematics skills!
Like, I tend to avoid the Scarlet Devil Mansion like a plague, because it's a super-scary place. It's bigger than it is on the outside, its maid can totally stop time and pincushion you with silver knives, and its décor is like, totally ugly!
However, recently, a certain Flandre Scarlet has been, like, becoming smarter and leaving this mansion, something I would, like, totally not expect. Remilia Scarlet had always said that her sister was something to be feared, a total recluse with the power to crush you within a second, but, like, when I saw her, she was not like that at all! She as so adorable, I, like, don't think she could even hurt a fly!
Like, you're probably wondering where I found her, right? Well, I was, like, totally visiting the Netherworld to totally not do suspicious things like stalk Youmu Konpaku, however, when I went to the half-ghosts' house, I found that all of the half-ghosts bar that drummer girl were outside of the house.
I asked Hemi what was going on, knowing I'd get a straight answer, and she told me that they were waiting outside while Point-five stopped her heated argument with another mathematician. I was, like, not afraid of any heated argument, so I totally walked into the room, and like, I was amazed! Flandre was right there, shouting with the drummer and pointing to some kind of diagram that had been drawn onto the wall!
I decided to try and ask what was going on, and this is what happened:
Hatate: Like, hello you two!
Point-five: Go away, I'm busy refuting a false line of mathematical thought!
Flandre: No! Stop being so closed-minded! If the imaginary numbers didn't have a magnitude, how would they form negative numbers when squared?
Point-five: Because they're imaginary! When you have a pile of rocks, you cannot have a set of imaginary rocks, can you?
Flandre: If your line of thought was correct, then only integers would exist, and decimals like your name-sake would mean nothing too!
Point-five: You take that back!
Flandre: What, I'm merely operating by your logic...
Hatate: Like... what are you two arguing about?
Flandre: Hello, Miss Tengu! Have you heard of imaginary numbers?
Hatate: Well... like... I can imagine that there's a number four floating in the air in front of me, if that's what you mean...
Point-five: No, you idiot. What she means is the set of imaginary numbers that act as the square root for negative numbers. For example, the square root of minus four is two I.
Hatate: Isn't the square root of minus four minus two?
Flandre and Point-five: NO! Minus two squared is plus two!
Hatate: Um... I never realised it was that insulting... like, sorry, I'm not very good at maths...
Flandre: It's okay, everyone has their beginnings.
Point-five: Unacceptable. Hmph, square root of a negative number being a real number, preposterous...
Hatate: Okay, so, like, anyway, imaginary numbers are like... weird numbers that you can multiply together to make negative numbers?
Flandre: Wow, you catch on quick! So you managed to deduce that three I times two I would not be six I, but in fact, minus six?
Hatate: Well, I didn't actually deduce that much...
Point-five: However, it is not true to assume that the square root of minus I is one, as minus I times I is one...
Flandre: Although, to be sure, both the square and square root of one is one...
Point-five: Oh, here's yet another point we disagree on...
Hatate: Like... I'm in way over my head here... what's going on?
Flandre: Oh dear, I'm afraid we got sidetracked. What we're discussing is whether or not imaginary numbers have any magnitude.
Point-five: Obviously, they can't have any real magnitude, they're not real numbers!
Flandre: Who said raw magnitude exists in the realm of real or unreal? A vector can look very different to its actual magnitude...
Hatate: Magnitude... beyond reality... what the fu...
Point-five: Ugh! What is the point of likening real and imaginary numbers to vectors? It's a pointless... hey, stop drawing on my formula wall!
Flandre: (draws a pair of axes, the vertical one labelled 'R' and the horizontal labelled 'I') It's very simple. See, here we can find the magnitude of complex numbers easily!
Point-five: I told you, complex numbers are only as large as their real component!
Hatate: Huh? Complex numbers? I though you were talking about imaginary numbers...
Flandre: Complex numbers are numbers with both real and imaginary components. Like... four plus three I! Hey, I know! Let's plot that on the graph! (places an 'X' on the graph)
Point-five: What's the point? The difference between real and imaginary is not a mere angle.
Hatate: Real... and imaginary? Like... at the same time? What... what... I...
Flandre: See, Point-five, this is why you're being closed-minded. The imaginary numbers are merely a perpendicular set of numbers, with its own infinity and minus infinity, and the only way you can 'rotate' between the sets of numbers is by square-rooting the negative of either members...
Point-five: Explain this, then. Why doesn't squaring one result in minus I, not one?
Flandre: I... well, perhaps it does! Perhaps every time you square a number, it results in a negative imaginary number component to it!
Point-five: Your reasoning makes no sense. Rotation-like relationships can go both ways, the reverse process being similar but backwards. Such a relationship doesn't exist between the imaginary and real numbers.
Hatate: Uh... hi, I'm a normal person, are you gonna fill me in on what the hell is going on?
Point-five: Sssh, mathematicians are talking.
Flandre: Okay, okay, the analogy isn't perfect, but just look! If I put a line from the origin... absolute zero, with no imaginary or real components to the point corresponding to four plus three I... look! The line is of length five, which is a value of neither four or three! Therefore, magnitude is beyond definitions like 'real' or 'imaginary', and imaginary components do play a part in magnitude, just as much as real ones!
Point-five: But, as you admitted, the analogy is not perfect, and as mathematicians, we need the model to be as close to absolute truth as possible. Also, as you admitted, when we square real numbers under this model, we have two possible answers, whereas squaring imaginary numbers still only results in one, breaking the model one way or another.
Hatate: I... I... I see why the others left now.
Point-five: Then leave. Molest Youmu while you wait or something.
Hatate: Hey, I didn't...
Flandre: ...anyway, Miss Point-five, your point. I... must take it into account. Your points about the flaws of the model are correct, and it may prove to be that magnitude is only real or imaginary, rather than a concept for both...
Point-five: I am glad you understand. However, Miss Scarlet, your mathematical theories and suggestions are very impressive, surprisingly creative given the way mathematics is. I'd be glad to take you on as an apprentice if you like... well, when I don't have concerts on. Hey, want a free ticket to our show on Saturday?
Flandre: I'd love to! Thank you, Miss Reciprocal!
Hatate: Huh? Are they friends now? What's going on? Why am I still here?
Point-five: Okay, I'll let you get off now. Take that reporter with you, Flandre. She looks ill...
Flandre: Okay!
Flandre then led me out of the house. I was... like, slightly stunned. I... I didn't know what was going on in the slightest, but from what I can gather, maths and philosophy have far more in common than I ever realised at first...
Like... so yeah, Flandre Scarlet really has grown up. Apparently, Remilia is now closer to being the 'shut-in sister' of the two. Apparently Remilia reads a lot of books now that Patchouli's left their house. That's... kinda sad. I wonder if she visits Patchouli every now and then.
Anyway, I left the Netherworld with Flandre, and she then taught me a little more on how these complex number things work. But... like, I don't see the point in them myself. I mean, sure, it's nice to say 'four plus two I times five plus two I equals sixteen', but what does it earn you? Like, I'm not sure...
Article written by Hatate Himekaidou
Present-day hindsight: I should have covered this article. I'm sure I would have understood it perfectly! I mean, imaginary numbers are just numbers that don't exist, right?