This text also something is written by Ultima reality that I agree:
https://vsbattles.com/vsbattles/2760052
The Hausdorff dimension
One of the main justifications for Higher Dimensions equaling greater orders of Infinities is the use of the concept of a
Hausdorff dimension, which, according to our own pages elaborating on this aspect of the Tiering System, proposes that each Higher Dimension is uncountably infinitely greater than a lower one.
However, Felix Hausdorff's formalisms are extremely specific, and assuming all Higher-Dimensions in fiction need to abide to them is frankly an absurd idea that borders on the pseudo-intellectual.
To start with, Hausdorff Dimensions are simply a way of measuring Fractal Sets and Topologies, which usually have non-integer Dimensions and thus can't be measured using regular Euclidean Geometry and all that junk. They have absolutely no relation to Spatio-Temporal Dimensions that are used in Cosmological Models or Manifolds, which is generally what we use when dealing with the rating of fictional verses.
Yes, theoretically you can obviously model a Formalism based on Hausdorff Fractal Topologies, but, as I stated above, it would be an insanely specific framework that is unseen in any notable cosmology, both in Fiction and in Theoretical Physics, and once again, acting like every single Higher-Dimension needs to act like a Hausdorff Dimension is a fine example of Cherry-Picking.
Furthermore, even stating that Hausdorff's Formalisms establish that Higher Dimensions are infinitely superior to lower ones is erroneous anyway. It effectively argues that due to the existence of Non-Integer Dimensions under Fractal Geometry, and the fact you can infinitely extend any subsets and decimals between any two Integer, the distance between 1 and 2 is Uncountably Infinite, something which, as I keep repeating, is not used in any Manifold or Model describing our Universe / Multiverse, and is generally inapplicable to them unless you model a very specific framework.
So, no, Hausdorff Fractal Geometry doesn't state that Higher Dimensions are infinitely greater than lower ones, it just uses Dimensions as a way of measuring the complexity of shapes and nothing more.
Dimensional Tiering in a more General Sense
Now that all of the details about the flaws present in Dimensional Tiering are out of the way, I'd like to ramble a bit on why the Logic and Reasons behind our usage of it are fairly erroneous and, to put it bluntly, an extreme example of cherry-picking and borderline favoritism towards certain works of fiction.
Yes, I am perfectly aware that this Community uses Dimensions as they are (supposedly) defined within Fictional Works such as DC Comics, Umineko no Naku Koro Ni and the Cthulhu Mythos. In fact, some of the Staff Members even stated in the past that the upper bounds of our Tiering System are basically a combination of Umineko and Lovecraft's works, and at first glance, this seems understandable and even justifiable, to a certain extent.
However, in my opinion, this is what constitutes one of the most severe flaws of Dimensional Tiering.
In effect, it is choosing to apply to all of fiction an incredibly specific and erroneous interpretation of how Dimensions are supposed to work, which itself only applies to the cosmologies of a set of specific franchises. Like, I said, this is borderline favortism towards these franchises, and I see absolutely no reason to put the way they treat Dimensions within their Cosmologies as an objective way to Tier all of fiction, rather than a more realistic approach to the concept, which is far more general, unitary and unattached to any specific Cosmology of any specific work of fiction.
In addition, I am fairly sure that Dimensions being used as Higher Infinities in any of those Franchises is a huge misconception. For example, Umineko simply uses Dimensions as a metaphor to describe an hierarchy of Reality-Fiction Layers which can themselves contain any amount of space-time dimensions.
Furthermore, the very concept of Dimensional Tiering is giving our visitors the wrong idea about Dimensions; what we are doing now is making pseudo-intellectual trite and forgetting that VSBW has the responsibility of being truthful and placing accuracy above all. What I am pointing at is expressed very well on our own
Tiering System page, which was the following notes written in it:
| " | Logically, a lower-dimensional character should at best have as much ability to affect a higher-dimensional character as a drawing on a paper has to punch you in the face. However, mostly due to lack of story logic, mere 3-dimensional characters sometimes triumph over forces that are degrees of beyond countable infinity above them. It is usually due to Plot-Induced Stupidity. | " |
| " | There are many different versions of the concept of higher-dimensional entities, each depending on the fictional rules that the author of that particular franchise has laid out. Hence, it is impossible to say that higher-dimensional characters can always beat lower dimensional ones within fiction.
This, however, does not invalidate the system itself. It simply means that the author in question does not particularly care about logical coherence, or does not understand the full implications of the terms that he or she is using.
| " |
Not only are the last two paragraphs extremely self-contradicting, but they are effectively stating that certain Authors are idiots who don't know what Dimensions are just because their Cosmologies and Interpretations aren't aligned to the Cosmology of completely disparate fictional settings.
So, as I keep saying, (for the time being at least) our Wiki
should use a simple, unanimous and realistic system that can apply to all fictional verses, rather than specific ones that happen to be popular enough to have great influence on this wiki.
