Q: When are higher dimensions not viable to use as evidence for Tier 2 and above?
A: Whether higher-dimensional entities qualify for such high tiers or not depends on several different factors, which may take root both in and out-of-verse. To explain this situation, we must first clarify what exactly being higher-dimensional entails.
Are higher-dimensional beings infinitely larger than lower-dimensional equivalents?
In a way, yes, though not how most would think when using this word. Basically, an arbitrary object of dimension
n is essentially comprised by the total sum of uncountably infinite objects of one dimension less, which may be described as lower-dimensional "slices", each corresponding to one of the infinite points of a line. For instance, a square is made of infinitely many line segments (Lined up on the y-axis), a cube of infinitely many squares (Lined up on the z-axis), and so on.
One may think of it as a multiplication between sets: For instance, the unit square [0,1]² may be expressed as the product of two unit intervals [0,1] x [0,1], which itself can be visualized as taking "copies" of the first interval and lining them up along each point of the second interval, of which there are uncountably infinitely-many, thus forming a square out of infinite line segments.
Are higher-dimensional beings infinitely stronger than lower-dimensional equivalents?
Unintuitive as that may be: Not necessarily, as a number of characteristics through which we quantify the strength or power of a character can remain unchanged when transitioning between higher and lower dimensions. For example: Mass is a quantity that is detached from the dimension of the object which it is inherent to, and unlike volume is not divided in units corresponding to each particular dimension (1-volume [length], 2-volume [area], 3-volume, 4-volume...). It is singular in nature and its units equally apply to
alldimensions; whether it is distributed over an area or a volume only tells us about the span of space in which it is spread, not about the quantity itself.
As a consequence of that, much of the calculation methods which are used to measure strength apply equally to both higher and lower dimensions, as they do not care about the extra variables and often work with a single one of them. Examples of this are kinetic energy (Ek=0.5*M*V^2), force (F=M*A), work (W=F*d), and etc.
An intuitive example of that is found in the general definition of Work as defined in physics: In essence, as work itself denotes the energy applied to an object as it is displaced along a given path, the basic formula for calculating it only takes into account a single variable, and the path itself is treated as an one-dimensional object, regardless of the dimension of the space in which the action itself takes place.
Hence, a higher-dimensional entity can be both stronger or weaker than a lower-dimensional one, and thus, they are usually quantified based on their own feats, instead of dimensionality alone. If a character is merely stated to be higher-dimensional and simultaneously has no other feats to derive anything noteworthy from, then they are put at
Unknown, and the same applies to lower dimensions as well.
Do note, however, that them not qualifying for Tier 2 and above doesn't mean they are "fake" higher-dimensional beings or anything of the sort. It is simply that being higher-dimensional does not inherently mean they have infinite power in the first place, as explained above.
vsbattles.com
