Q: How does this wiki treats higher dimensions?
A: A character that is stated to be N-dimensional will have their tier in accordance to that dimension. For example, a character that is stated to be 5-dimensional would be inherently rated as Low 1-C, unless this is contradicted in some way, such as the dimensions in question being portrayed as compactified.
Q: Do infinite-sized characters get infinite speed by default?
A: Yes. As seen in this blog, speed is proportional to your size at a certain point. The bigger you are the faster you naturally become. So an increase of infinity would result in infinite speed. In addition, any kind of movement in such a scale would by definition cover an infinite distance in a finite time.
Q: Why are dimensions treated as higher infinities/uncountable infinities?
A: Spatial dimensions are defined as powers of the Reals (R; an uncountable infinite set). For example, R^0 would be a point, R^1 would be a line, R^2 would be a plane, R^3 would be tridimensional space, R^4 would be a space-time continuum, etc. The basic construction of a space with n dimensions is a Cartesian Product, A x B, which is basically just taking all of B and attaching a copy of it to each point of A. In the case of a space with 3 spatial dimensions and 1 temporal, this would be R x R³, which means attaching a copy of R³ to each point of R. Another example of this is how a line has R amounts of points attached to it. In more simple terms, a space that is R^2 (for example) is to R^1 what R^1 is to R^0. That is, a difference of uncountable infinite size.
Q: What tier/speed is transcending space and time?
A: While the statement can be used for supporting evidence, by its lonesome, "transcending space-time" doesn't grant any AP or Speed Tier without further context. The reason for this is due to this kind of statement abridging a variety of meanings of which none can be considered the default without being very arbitrary.
Q: Is destroying multiple 2-A structures a better feat than destroying one?
A: No, as said logic doesn't work when it comes to infinite sets. That is to say, a countable infinite structure multipled by countable infinity would always result in the same countable infinity. In this fashion, we can draw the conclusion that [2-A x 2-A x 2-A x 2-A...] = 2-A.
Q: Then how can a 2-A character become "above baseline"?
A: It is possible for a 2-A character to become above baseline if they are part of scaling chain that comes from physically beating up baseline 2-As. Alternatively, the verse might state that a multiverse may be harder to destroy than another, such as how it is portrayed in Maou Gakuin no Futekigousha.
Q: Would a character/structure that is stated or visually shown to be bigger than a 2-A structure be classified as Low 1-C?
A: Yes. When it comes to infinite sets, there is no set whose cardinality is in-between countable infinity and uncountable infinity. A 2-A structure is comprised of a countable infinite amount of universes. For something to be bigger than such thing, it would strictly have to be an uncountable infinite amount, as otherwise it would still result in the same countable infinite cardinality.
Q: Is containing a 2-A structure Low 1-C as well then?
A: By itself, no. It might be counter-intuitive to think that containing something would not result in the container being bigger than it, but when it comes to infinite sets things are quite different. For example, the set of rationals encompasses the set of integers (which is countable infinite) and the latter encompasses/contains the set of naturals as a subset (also countable infinite), but the three are still all the same size. This is the reason as to why the verse needs to state or visually shown that the character/structure in question is actually bigger/larger.
What is Orthogonality?
A: Mathematically, and in simple terms, Orthogonality is the property of 2 lines that are perfectly perpendicular to each other, in other words, they intersect each other at Right Angle. In this way, while normally, a line can be drawn on a 1-D plane or be contained in it, two orthogonal lines must require a 2-Dimensional plane to draw. For example, you cannot draw a right-angle figure in the one-dimensional plane, you need a 2-D plane (i.e. a paper) to do so. Similarly, one cannot draw a 3rd line perpendicular to both of the previous lines simultaneously on that piece of paper, and would instead require one to draw a line perpendicular to the 2-D plane itself, extending to 3-D Space. This process can go on infinitely, and each time, you would need to extend the additional Orthogonal line perpendicular to the previous N-Dimensional plane, thus requiring N+1 Dimensional Space.
Is a universe with more than one Temporal Dimension Tier 1?
A: Yes. As noted above, structures that contain 3 spatial dimensions and 1 temporal (such as a conventional timeline) would be equated to R x R³ in a cartesian product, which means attaching a copy of R³ (tri-dimensional space) to each point of R (the uncountable set that represent the time axis), resulting in timelines being comprised of uncountable infinite 3-D moments, each of which would be akin to a static snapshot instance of the universe. As such, a space-time with three spatial dimensions and two temporal dimensions (for example) would be R x R⁴, resulting in a timeline that contains uncountable infinite 4-D moments, thus Low 1-C 5D(and so on the more temporal dimensions you add).
Is a cosmology that contains universes each with independent time dimensions Tier 1?
A: Being an independent or unique time axis does not necessarily mean said axis is of a higher dimension compared to a conventional timeline. Much like how you can have infinite lines, each with different directions, in a 2-D plane without the necessity of 3-D space, merely being an independent time axis with its own direction does not imply a higher dimension for each additional time axis.
However, there is indeed the case that even if those Time Axis are independent of each other in the sense of having a different direction, even if not orthogonal, then they can qualify for additional higher Dimensions, which would be needed for those time axes to extend to, as explained here in details.
In what cases do additional Temporal Axes require Higher Dimensions?
A: Cases that qualify for additional Higher Dimensions (Tier 1) for Temporal Axes are as follows :
- Overarching Timelines/Hypertimelines (A Timeline containing another Timeline, containing another Timeline.... and so on)
- Unsynchronized Temporal (Finite and Infinite Un-synchrony)
- Temporal Acausality
All such cases are explained here in details.
Q: When is the destruction of a universe considered 3-A?
A: Refer to our Universe page. As long as you have the statement that it is a "universe" or "space-time", creating or destroying such structure would inherently be 3-A.
Q: Is moving in a timeless void considered Infinite speed?
A: No. As we know, the speed formula is defined by [S=D/T]. However, in this case, the "T" would simply not exist, which then becomes impossible to tell how much distance you are actually covering in a quantifiable manner. You could be moving at 10 m/s, 100 m/s, 1000 m/s, etc, and there would be no way to know in such a place. This is different from moving in 0 seconds, since it's a matter of time not existing as opposed to just being stopped.
Q: Where do Alephs scale in regards to tiering?
A: This is a trick question. Because by itself, an aleph won't scale you anywhere. It's no different than asking "What tier is the number 10?". Alephs only become a proper measurement for scaling when used to quantify a certain object. For example, an Aleph-0 (countable infinite) amount of universes would be 2-A, while an Aleph-1 (uncountable infinite) amount of universes would be Low 1-C. However, things get a bit different when it comes to Aleph-2 and beyond, as they would be strictly bigger than all of the spaces mentioned above, by all rigorous notions of size, regardless of what their elements are. At this stage, the quality of the elements don't matter, only the cardinality of the whole. As such, in cases like this, an Aleph-2 (or higher) amount of anything would be High 1-B+.
Q: Are dimensionless characters 1-A?
A: No. This is because 1-A is all about being beyond dimensionality, and not merely lacking it. After all, just because you lack something does not mean you transcend that something. A character who "lacks" dimensions wouldn't possess a "quality" that's too great to be categorized within dimensionality as opposed to just being outside of its influence and confines out of a lack of it. In other words, it's a negative, reductive quality and not necessarily an additive one that would indicate some level of superiority and thus for this reason, it's not considered 1-A. However, it is possible for a dimensionless character/structure to be 1-A if they have an established relationship of superiority over the nature of infinite or uncountable infinite dimensions, or if their non-dimensional nature stems from being akin to a background canvas where any amount of dimensions can be inserted/contained.
Q: Is a character who "transcends dimensions" 1-A?
A: No. A character being stated to "transcend dimensions" or something similar wouldn't qualify. The reasoning for this is given how vague it is as a statement, as it doesn't really tell us anything about how a character would "transcend" them and furthermore, it's vague on the basis that it could be metaphorical, as the term "transcend" is often used to indicate not being bound to something but in a figurative sense. For example, a common saying is that "love transcends time", which obviously isn't meant to be literal but is meant to be a reference to how love exists everywhere and in every time period. On top of this, there's also the fact that "transcend dimensions" also isn't pertaining to the concept of dimensionality. For this reason, it wouldn't be the same as a being who's existence is "alien" to the concept of dimensionality and thus is beyond any extensions of it. Under the premise that "transcend dimensions" is literal, it would at most qualify for a "+ 1 reality level" above the cosmology as opposed to straight up 1-A like how beings who possess a ontological superiority to the concept of dimensionality.
Q: Is transcending the concept of space and time 1-A?
A: A character who transcends both space and time wouldn't qualify for 1-A under the basis that most writers don't bother making a connection between the concept of space-time and dimensionality. In fiction, these two (technically three) things tend to be separated and it would be fallacious to assert that inherently being beyond the concepts of space and time would make one 1-A. In the instance that a writer bothers to qualify that "Space = Dimensions", then a character being able to exist beyond the concept of space and time would then qualify for 1-A as there's explicit evidence that dimensionality is considered a fundamental part of space and thus, the character in question can be considered "alien" in relation to how many dimensions one could theoretically impose on them.
Q: Is apophatic theology 1-A?
A: No. Normally, a being or structure that is regarded as apophatic would only scale a single transcendence higher than the verse's established cosmology. The reason for this is that accepting apophasis as inherently 1-A is largely grounded on NLF, as it is no different than giving 1-A or High 1-A for a character that scales "beyond all concepts". Furthermore, something that cannot be named or given a definition wouldn't be any tier on its own unless there is context provided that makes it scale above structures of the verse in question. However, it can be 1-A or higher if the context of its apophasis makes it clear that it is being beyond the concept/category of dimensions.