Dimensional Duplicitousness

What is Dimensionality? and why is it important?

Dimensionality is The state or characteristic of possessing dimensions. or  The number of dimensions something has    

Which Dimension can be defined as 

1.  A single aspect of a given thing.  

2.  A measure of spatial extent in a particular direction, such as height, width or breadth, or depth 

3.  A construct whereby objects or individuals can be distinguished 

4.  (geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates. 

 (linear algebra) The number of elements of any basis of a vector space. 

5.  (physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.  

6.  (physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.  

7.  (computing) Any of the independent ranges of indices in a multidimensional array. 

8.  (science fiction, fantasy) A universe or plane of existence. 

definition 1-7  are often conflated with definition 8 which refers to an entirely different thing that can't be applied under the definition of Dimensionality unless under the most vague possessive sense 

when something has a Dimensionality of 1 it is usually said to be "1 Dimensional" or "1D" it is also commonly  said that anything that is greater Dimensionally would be infinitely, incomparably, or inaccessibly greater then than the lower Dimensional thing 

99% of people who use this standard do not understand or know the basis or reasoning of this standard and just take it as a base assumption

According to VSBW and CSAPW who both go under the same reasoning  

Dimensions or Dimensional axis are equivalent to ℝ (the real numbers) and more then one Dimensional axis is ℝxℝ which they propose is equivalent to an inaccessible differences or just  ℝ<ℝ^2 which who's relationship holds true for all difference between all Directionalities 

the problem arises that this is just not true at lest under any arithmetic of infinity besides there own 

 ℝ is equal to <ℵ0  which is an infinity 

and  ∞ x  ∞ =  ∞   or  ∞ ^2 =  ∞  or  ∞ ^ ∞ =  ∞ 

but under the continuum hypothesis  there is nothing between ℵ0 and  ℵ1 meaning ℝ is equivalent to ℝ=ℵ1 

which under the Axiom of choice defines the relationship between ℵs (Alephs) as  2^ℵn = ℵn+1 or 2^ℵ0 =ℵ1

which ℝxℝ or ℵ1xℵ1 is not equivalent to 2^ℵ1 = ℵ2

ℵ1xℵ1xℵ1xℵ1....a ℵ1 number of times or ℵ1^ℵ1=ℵ2

and now an even more common geometric argument which is more of an analogy as it isn't a rigorous understand of geometry , that most who don't know or understand the previous example usually assert, is that "there is no amount of squares that stacked together t equals a cube " or some other variation of this point

The problem with this is what is actually being done is taking objects that are equal in 2 aspects or more simply 1 by 1 or 1x1 square and a 1x1x1 cube and seeing how many of the squares nonexistent 3rd number = the 3rd number of the cube which is just a problem in the comparison and  is not a proof of ether the cube is greater then the square, the cube is less then the square, or that the cube and the square are equal

A quick but relatively unconvincing opposing argument is

1x1 = 1 and 1x1x1 =1 

But getting to the real argument 

A square that is allowed to be bent in half orthogonality into the third axis of the cube like putting a bend in a piece of paper which still has the square as a 2-dimensional object, we can then unaccountably infinitely bend the square back and forth well not increasing the size of its interval between (0,1) of its lengths, a thing that is bent like this is call a space-filling curve  meaning geometrically the square and a cube are  equivalent in cardinality or "size" which is an unsurprising result when reinforced by the previous argument for the equality of dimensionalities

Dimensionality has been put into a special position in Power Scaling as it has seemed to put a natural hierarchy above the finite tiers and levels in the scaling system as an inherent extinction of just how Dimensions work but now that Dimensionality has shown to be not reliable as its function does not follow from an inherent way it works, It can by that alone be caveat-ed that it can work that way in some universe and it can work differently in others and that it can not be assumed out right

which we can nail down that function it performed so that we can use it to conclude if one thing or another does or does not fulfill it

the thing or " function " the previous understanding of Dimensionality was trying to convey is that

"A thing processes a quality that makes it inherently superior to any thing that does not have the quality." which we shall call "qualitative superiority "

using this, we can envision a number of cases in which this does and does not apply in specific scenarios

a universe where the number of axis it envelopes is 5 but has never shown any gap in power between things that have 3 axis and things that have 5 under the old standard would be assumed to inherently superior but as there is no reason to assume it to be case under the new standard it just would not be the case

a universe that has another " higher dimension " to it that is but another layer of the universe like a second floor is a higher floor of a building, but that being in the " higher dimension " makes it so that anything that has been to the " higher dimension " is supernaturally great then anything that has only been in the " lower dimension" in the old standard would not automatically be granted dimensional transcendence as they do not have a higher dimensionality, well in the new standard it does fit having a quality "having been to the higher dimension" that is inherently superior to any quantity of something that does not have it