As per the usual disclaimer, this tl;dr post will feature some personal analysis on religious topics. If you are offended by such discussions, do not read on. I don’t claim any of what follows to be the truth or the “correct” interpretation. This post merely contains my own thoughts and ramblings on the topics in question.
I just marathoned Rinne no Lagrange, and I must say it has some very interesting themes. Let’s start with the most obvious; the trinity. Those of you more religiously inclined readers out there may be familiar with this concept, but for those who haven’t heard of it before, allow me to explain. The concept of the trinity is one pervasive in many religions. It typically refers to the “division” of a diety into three forms. Whether this is a literal division or merely different aspects of one whole depends on the specific religion at hand, but the underlying idea remains the same.
Rinne no Lagrange features a trinity of its own; the three main leads and their respective mechs. Obviously the show isn’t trying to deify them, but there is clearly something special about the connections between each of the characters and the mechs. What I intend to discuss, however, is the concept of the trinity itself. Just what makes the number “three” so special? Youko mentions that three is the smallest “stable” number, hence its importance. But this kind of explanation isn’t exactly satisfactory, now is it?
My own interpretation of the matter is, again, more scientific. To be precise, it has a mathematical basis. Before I can elaborate, though, we must first address the issue of dimensions. As you probably know, we are three-dimensional beings. This is a poorly worded statement, though, and as such is technically incorrect. While we visually perceive our surroundings in three dimensions, our perceptions do not in any way limit the reality of things. Despite my disclaimer at the top, the fact of the matter is, the world (and the universe) can have many more dimensions than those that we can perceive ourselves.
Just how many dimensions are there? No one knows for sure. You may have heard of String Theory, which asserts that there are eleven stable dimensions, but that is just a scientific interpretation that has yet to be affirmed. In a more mathematical sense, though, there can be as many dimensions as you want there to be. I can tell you’re probably getting confused by now, so I should first define what I mean by “dimension”. A dimension is merely a way to describe an object. Think of it this way; whenever you pick up a ruler to measure something, you are defining one dimension of said object and then assigning a value to this dimension. When you smell something, you are essentially doing the same thing, and the list goes on.
So what about String Theory, then? How can they turn infinity into just eleven? Doesn’t that basically contradict what you just said? Not necessarily. While it is true that we can assign infinitely many dimensions to an object, not all of these “measures” are useful. That said, what String Theory is really claiming is that there are eleven “practical” dimensions with which we can describe the known universe (specifically spacetime), not that there are eleven dimensions period. So just what does any of this have to do with the trinity? Well, the point of it was to establish a proper understanding of what is really meant when we say we are three-dimensional beings.
On to the main topic; the reason why the number three is “important”. Since we are three-dimensional beings, most of our media comes in a two-dimensional form. Sure, we can create statues and models (“3D” movies don’t count), but aside from these, almost all of our media is two-dimensional. This isn’t a random coincidence, though. It is merely a complication of the fact that our visual perception is limited to three-dimensions; any more and we wouldn’t be able to fully comprehend the object in question. So then why don’t we have more three-dimensional media? At this point, it really comes down to a matter of practicality; it is much easier to display things in two dimensions.
With this established, what can we say about the number three? Let’s look back at Youko’s claim that it is the smallest “stable” number. As I’m sure you’ve realized by now, this statement isn’t universally true. Rather, it is “true” within the limits of two dimensions. Within a plane, you need a minimum of three finite points in order to completely confine a region. It’s easy to understand how three points isn’t enough to do the same in higher dimensions, but what about lower dimensions? Well, the number just goes down; you only need two points in a one-dimensional space. So as you can see, we only give the number three significance because of its relevance to our perception. I’m sure that if some “four-dimensional” being also had a religious belief, the number four would hold more significance to it.
But that’s enough science, what about the religious significance of the trinity? Christianity aside, another “major” religion in which the trinity appears is that of Hinduism. Specifically, there is a personification of the three “cosmic functions”; creation, maintenence, and destruction (a theme also present in Dantalian no Shoka). In terms of Rinne no Lagrange, though, don’t all three parts of the trinity cause destruction according to legend? While it’s true that Hinduism may not have been the best example in this case, I picked it for two other reasons; the title contains the term “rinne”, and I took a course in Asian mythology so I know more about Hinduism than Christianity.
Just what is “rinne”? Well, it’s the Japanese term for “samsara”, which refers to the cycle of rebirth. Needless to say, the concept of a cycle is a very important one to Hinduism, and can be represented by the circle. Aha! So there really is more to Madoka’s “maru” than just being cute! Well perhaps, but I’m thinking the cuteness was still more of the point. Anyway, the circle is yet another very important concept. If the triangle (three points) can be considered the “lowest stable state”, then the circle is the exact opposite in a sense.
Just what is a circle? A typical math textbook would say something along the lines of “the set of points equidistant from a center point”. That doesn’t tell you much, does it. In terms of what I’ve been talking about, you can think of it as infinitely many points; quite literally the polar opposite of the triangle. But what makes the circle so unique? This is where things get fun. So you have a set of infinitely many points connected by infinitely many lines to create a circle. Sounds straight forward. But do you really consider a circle to be infinitely many lines? No; you generally think of a circle as one “line”.
Granted, a line isn’t supposed to be curved in the first place, but let’s say we accept this point of view. What does this have to do with anything? Well, if the circle is just one line, what are the points it connects? A triangle clearly connects three distinct points, but what can we say about a circle? Well, the obvious answer is that the circle has no end or beginning. This is a very powerful concept, and yet another one present in many religions. Take the Egyptians, for example. They had the Uroborus; a serpent that eats its own tail.
Of course, you could argue that even your dog chases its own tail, but the underlying concept remains. The circle represents completeness in the sense that it contains infinitely many lines (and points). Yet, the circle looks like just one line, and in that sense can thus represent the one divine being. Even further, when you consider the circle as a single line, you realize that it has no end or beginning, and as such represents eternal emptiness. Thus, we have “reconstructed” an underlying theme in Hinduism; from nothing came one, and from one came everything.
What does this have to do with rinne, or in other words, the cycle of samsara? Well, the “goal” of Hinduism is to fundamentally realize your true self; that you are part of the one, which is simultaneously everything and nothing. By doing so, you will be freed from the cycle of rebirth (also known as the state of suffering) and reunited with “the supreme being”. That’s some really deep stuff right there, and while I can agree that we do go through hardships in life, it’s not as if living is suffering. Well, perhaps with the exception of Lancer.
In any case, all of this goes far beyond the comparatively “simple” themes present in Rinne no Lagrange, but it’s nice to see them referenced. I’m sure some of you will inevitably point out they are also part of other far east religions such as Buddhism and Shintoism, but if you look a little further, you will find that these religions in some way originate from Hinduism. Of course, I’m not here to discuss the origins of religions, though, so I won’t elaborate on that matter. More importantly, we can focus on the other part of the title “Rinne no Lagrange”.
The term “lagrange” doesn’t really have much religious significance to it, as far as I’m aware. It does, however, have a scientific background. I’m sure if you go looking around, you’ll see people saying that “lagrange” refers to Lagrangian points, but they probably won’t elaborate any further. Just what are Lagrangian points? A simple lookup will tell you that they are points in space at which an object in orbit can theoretically remain stationary. How does this connect to the rest of the themes present in Rinne no Lagrange? This one is a bit of a stretch.
In terms of numbers, when you speak of Lagrangian points, you are talking about a set of five points. Well this doesn’t exactly connect with zero, one, three, or infinity, does it? I suppose, then, that the points themselves are sort of a red herring when it comes to trying to find a connection. I’m sure you could attempt to find some long-winded justification by taking Yurikano and Astelia into account in addition to the three leads, but I’ll consider something else completely. Instead of focusing on the Lagrangian points themselves, we should instead look at the framework of the concept as a whole.
Lagrangian points are a consequence of the three-body problem. What is the three-body problem? That gets into some very complicated physics and mathematics, so let’s just say that it is the determination of a model of how three bodies (usually celestial bodies) interact. What does that have to do with anything? Near the beginning of this discourse, I mentioned that there was a special connection between the three main leads and their mechs. Specifically, Rinne no Lagrange focuses on the exchanges between these three characters and how their emotions affect the mechs. And there you have it; the interaction between three bodies!
Alright, I admit that may be as far-fetched as an attempt to bring Yurikano and Astelia into the equation for five points, but at least this interpretation preserves the importance of the trinity and sounds quite poetic. In any case, this discussion has really gone into the deep end of the tl;dr pool. I’m sure it’s more than sufficiently brought some of the major themes present in Rinne no Lagrange to light, so I’ll just cut off before you tune out completely.