Leliel is one of the angels of the Neon Genesis Evangelion anime that comes to Earth with the purpose of annihilating humanity (or at least this is one of the interpretations of his coming). In the count, he is the twelfth angel, preceded by Ireul and succeeded by Bariel, his appearance occurs in episode 16. Initially he looks like a floating sphere full of white and black stripes with different patterns. However, the real manifestation of his body in our three-dimensional universe resembles a completely black circular shadow on the ground, with 680 meters in diameter and a thickness of only 3 nanometers (or 0,000000003 meters). In the anime they conclude that the floating sphere is just the shadow that this entity manifests in our dimension.
In this text we will explain the spatial dimensionality of this character and how it is possible that his “shadow” is projected in the form of a three-dimensional object.
Shadows and projections
A shadow is nothing more than the projection of an object into a smaller spatial dimension. For example, when we light an apple in front of a wall in the dark, the region blocked by the apple, casts a shadow on the wall in the shape of its silhouette. While the apple is an object with height, width and thickness, the shadow of the apple projected on the wall has only two dimensions (height and width).
The projection can also occur in a dimension of size 1. For example, imagine that behind the apple, instead of a wall, there are no obstacles, except an extremely thin wire, positioned horizontally. Now, the shadow of the apple projected on the wire has only one dimension, the width. On the other hand, if the wire was vertical, the shadow cast on the wire would only have the height dimension.
Projection can also occur in a dimension of size 0. For example, imagine that behind the apple, we have a bacterium. Now the shadow of the apple projected on this bacterium has no dimension, it is or is not on the bacterium.
Similarly, let us imagine a universe with four dimensions, that is, height, width, thickness and a fourth direction perpendicular to the other three mentioned. If we take a four-dimensional apple in this universe, and project this four-dimensional apple in a universe with height, width and thickness, the shadow that this four-dimensional apple will make in our universe will be a three-dimensional object. That is, we will see the height, width and thickness of the original four-dimensional apple projected in our universe.
Thus, for the beings of this universe of four dimensions, we, creatures of three dimensions, are equivalent to projections or shadows. Similar to our universe, if another shadow appears in the place where our shadow is projected, it will cover the original projection, however it will not affect the object that projects it in any way.
From the point of view of beings in the four-dimensional universe, for which we are equivalent to the projected shadows, if we interact with the shadows of these beings, we can destroy their original projections by superimposing ourselves on them, but in no way will we affect the object generating the projection . As in the Neon Genesis Evangelion anime, when humans fired at the Angel Leliel’s shadow, it disappeared immediately. For in our three-dimensional universe, when the three-dimensional object (in this case, the launched projectile) overlaps the Angel’s shadow, it momentarily falls apart, similar to when we make our shadow cover the shadow of an apple. We don’t really destroy the apple, however our shadow affects our perception of the apple’s shadow, making it no longer noticeable.
Understanding the shadow of the Angel Leliel
In the case of the Angel Leliel, we have a creature from a universe with at least four dimensions. Two of which are in contact with our universe. It would be the equivalent for a two-dimensional universe, if a three-dimensional creature in the shape of a cube landed touching only one of its edges.
In this two-dimensional universe, creatures have only width and height. Thus, when this three-dimensional cube landed with only one of the edges touching the plane, the inhabitants of this universe would see a line segment appear out of nowhere.
However, the cube being a three-dimensional object, when receiving three-dimensional light, it would cast a shadow in the universe of two dimensions, in the shape of a square.
The inhabitants of this universe would now see a square, which is, for them, a much more complex shape than a simple line segment, as it has two dimensions, also resulting in an area.
Thus, despite the apparent existence of this square in the universe of two dimensions. It is but a shadow of the cube that has landed in this universe. Even though the inhabitants of this universe try to interact with the square, the square is not really a real object, but a projection.
Similarly, in Neon Genesis Evangelion. When Leliel lands on Earth, he is actually a being of at least four dimensions, touching our universe with only two dimensions. Thus, its true point of contact is the apparent shadow of 680 meters in diameter. But since he is a being of at least four dimensions, he casts a shadow of three dimensions in our universe (in the form of a giant floating sphere). That hides from us, this Angel’s point of contact with our universe until we come to interact with the shadow. Similar to what occurs in the two-dimensional universe, when the shadow of the cube blocks from the creatures of this universe, the line segment that is the point of contact between the cube and that universe, until the individuals of this universe come to interact with its shadow (the square).