Summary[]
Dimensional Tiering is the idea of tiering a character based on their spatio-temporal status, more specifically based on what dimensional level they exist in. Based on the concept of a Hausdorff dimension, a higher dimension encompasses infinitely more mass and aspects than a being who inhabits a lower dimensional plane (I.E 3rd Dimensional Humans in relation to 2-D Drawings, whom of which we percieve as flat). When quantifying characters of a higher-dimensional origin, this concept is used to determine how powerful they are. Dimensions are heavily related to the concept of size and it's said that one who inhabits a higher plane will have infinitely greater size than that of a lower dimension being. Note that while dimensions are the means of measuring for this wikia, superiority relative to that level isn't ignored either. If a power has the necessary qualitative superiority over a certain level it can justify corresponding higher rankings in the tiering system
Explanation[]
An easy way to grasp this concept is as follows:
A 1-Dimensional (line) object only has length.
A 2-Dimensional (plane) object has length and width. The area of a 2-D object = length x width. The width of any 1-D object = 0, so its area = 0, even if its length = infinity.
This works in the same manner with 3-Dimensional space. The volume of a 3-D object = length x width x height. Since a 2-D object's height = 0, it doesn't matter if its length or width = infinity. Its volume, and mass, will still = 0.
"Hypervolume"/the 4-Dimensional volume analogue = length x weight x height x a fourth dimension. Since a 3-D object's fourth dimension = 0, its "hypervolume" and "hypermass" = 0
For a 5-Dimensional volume analogue = length x width x height x a fourth dimension x a fifth dimension. Since a 4-D object's fifth dimension = 0, its 5-D volume analogue, and 5-D mass analogue = 0
Basically, what this means is that, just like an entirely flat, two-dimensional square has a more than countably infinite number of times less volume (and mass) than a three-dimensional cube, the cube also has a more than countably infinite number of times less volume (and mass) than a four-dimensional tesseract, which has a more than countably infinite number of times less volume (and mass) than a five-dimensional hypercube, and so onwards.
- This panel from DC Comics demonstrates how much superiority a higher dimensional creature has to a lower one
- Many series such as Flatland and Futurama deal with the topic of dimensions and explain them in simplier terms
- Umineko takes it up a notch and explains the relation of infinity to higher infinities
Notes[]
- Simply existing in a higher dimension doesn’t qualify for a tier. Higher Dimensional stuff have to be determined on a case by case basis, as some writers lack the knowledge in what dimensions are and how they function
- Dimensions can be treated differently from series to series, this means that elaboration of the functions regarding dimensions have to be given within the series
- Characters who create their dimensions will automatically scale one dimensional tier higher then their dimension (For example, someone creates a 4D construct) Whoever created it would scale one dimensional tier higher, in this case it would be 5D