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Dimensional tiering is a popular system of rating Multiversal characters in fiction, but in truth, it is an extremely flawed system that ends up being used to extremely inflate verses such as Warhammer 40K. Here is why:

What is Dimensional Tiering?

For starters, some debating systems have determined that infinite multiversal beings are not the ultimate power level for characters, and they may surpass it through bigger infinities. Through this development, someone had the notion that geometric dimensions also equate to bigger planes of infinity. As such, a 3-D being is 3 orders of infinity larger than a 0-D (which is a misleading term), and a 5-D being is 2 orders of infinity above said 3-D being.

Why is Dimensional Tiering Wrong?

General

Power comes from energy. According to dimensional tiering, a 4-D being would have an infinitely higher form of energy, and that there is "3-D" energy which we use. This is blatantly wrong, as energy, too is mass, is a scalar value. Energy being a scalar means it is not limited or contrained to a value for displacement or direction, meaning there is no limit to its dimensionality.

Vectors

This means that energy has no dimensioned value, and can be applied and permeate through all spatial dimensional axes.

Also, mass is just mass. There is no "hypermass" or anything like that. It's kilograms and has no direction, and has no length like area or volume. The volume might have a 4-D, 5-D, 6-D, or infinity-D hypervolume, but the mass will only correlate with the 3-D volume. Mass, again, is separate from dimensionality.

Furthermore, dimensional tiering is based on the belief that a higher dimensional axis exists infinitely transcendant to a lower dimension in such a way that a lower dimensional object absolutely cannot interact with the higher dimension. This is quite... Misinformed... To put it lightly.

For example, scientists actually have actually theorized that they can detect higher dimensions through our worldly matter

"As gravity is thought to be a force able to probe these extra dimensions, another way in which we may be find evidence for string theory is through the disappearance of gravitons, the hypothesised carrier of gravity, into these other dimensions. The particle might be carried away without a trace, but it would leave behind an imbalance in momentum and energy.




Two of the most fundamental laws of physics are that momentum and energy “are conserved”. In other words, the total momentum and energy before a collision is equal to the total momentum and energy after. So if we add these up in all the observed particles emerging from a collision (in the case of CMS we do this is the sideways “transverse” direction) and it does not equal the amount in the original particles, there must be a missing particle that carried away the momentum and energy: a lost piece leaving a hole in the jigsaw."






Particles most likely could actually fall through or from higher dimensions, which would not happen according to Dimensional Tiering as each dimension is a completely higher infinity


On Quantum-Physics Based Dimensions

Furthermore, higher dimensions are not necessarily larger than lower dimensions:

"Klein’s contribution best addressed the question of why such a fifth dimension would not be observable—consistent with Ehrenfest’s conclusion that space appears three-dimensional. In an idea known as compactification, Klein envisioned that the higher dimension would be rolled up into a tiny, compact loop on the order of 10^-33 centimeters. Thus, while it would supply (in theory, if not in practice) a means of unification, it would be undetectable—like a curled up pill bug camouflaged as a dot on a leaf."

That's right. The 5th dimension, for example, can be 'rolled up' into being the size of a subatomic particle.


Now there is a video which might be used to explain how dimensions work:

Ten Dimensions Explained

Ten Dimensions Explained

I am sorry to burst one's bubble, but this video messes up the second they reach the fourth dimension. It makes the confusion that time is the fourth dimension, when it is not. Rather, time is a temporal dimensions which when addition to the 3 spatial dimensions common to our life, makes the universe '4 dimensional,' but time is not the 4th dimension. Rather, there would be 4-D hyperspace. This also applies for M-Theory, which states there are ten spatial dimensions and one temporal dimension. This video makes a grave mistake making the 4th dimension = time, as it then extrapolates each higher dimensional axis as an extra temporal dimension, which deals with causality and alternate-times, when in reality these extra dimensions are spatial in nature and work as methods of range and displacement like how the 3 spatial dimensions we experience are.

Oh, and there is more proof that higher dimensions are actually compacted instead of large extra-dimensions

"Analyses of results from the Large Hadron Collider severely constrain theories with large extra dimensions.







The Fermi/LAT collaboration, in 2012, published limits on the ADD model of Large Extra Dimensions from astrophysical observations of neutron stars. If the unification scale is at a TeV, then for n < 4, the results presented here imply that the compactification topology is more complicated than a torus, i.e., all large extra dimensions (LED) having the same size. For flat LED of the same size, the lower limits on the unification scale results are consistent with n ≥ 4. The details of the analysis is as follows: A sample of 6 gamma-ray faint NS sources not reported in the first Fermi gamma-ray source catalog that are good candidates are selected for this analysis, based on age, surface magnetic field, distance, and galactic latitude. Based on 11 months of data from Fermi -LAT, 95% CL upper limits on the size of extra dimensions R from each source are obtained, as well as 95% CL lower limits on the (n+4)-dimensional Planck scale M_D. In addition, the limits from all of the analyzed NSs have been combined statistically using two likelihood-based methods. The results indicate more stringent limits on LED than quoted previously from individual neutron star sources in gamma-rays. In addition, the results are more stringent than current collider limits, from the LHC, for n < 4. Further details of the analysis are found in"








https://en.wikipedia.org/wiki/Large_extra_dimension#Empirical_tests

On Geometric-Based Dimensions

One argument for Higher Dimensions is that verses do not use quantum sciences for their dimensionality, and are geometrically based. This is utter nonsense.

For one, higher dimenional volume is based on powers of r. 3-D space is r^3, 4-D space is r^4, 11-D space is r^11, and so on. This is adding a new dimensional axis, but this does not go past Aleph Naut, I.E our conception of infinity beyond all numbers and countless. Aleph Naut would include all squared, cubed, quarted, etc numbers, which means all dimensional axes fall under the first order of infinity.

So dimensions do not equal higher infinities basing it off of Geometry anyways. Regardless, real life and most fictional verses to do not approximate dimensions off of geometric infinity, but off of "bridges" or "higher movement axes" which make things seem flat in comparison.

"How it works in fiction"

Lastly, an argument used by proponents for dimensional tiering is that dimensions in fiction are different from dimensions in reality, and that dimensions in fiction mean higher infinities. While it is true that in fiction, things within higher dimensions are described as 'transcendant' and 'inconcievable' to lower dimensional beings, this is somewhat true. Yeah, you get that when you have an added axis of movement we cannot see or grasp, making it incomprehensible to a lower being and untouchable to them. But this is not raw power, a higher dimensional being is not infinitely more powerful than you. It lives a life with pretty much the same laws of mathematics as you.

One may use Mr. Mxy from DC Comics as an example of dimensional tiering, as he is in fact multiversal and does many things Superman cannot comprehend. Well Mr. Mxy is multiversal just because he has a lot of hax and power feats placing it at this level, which is juxtaposed by the fact that he can literally move in and out on 2 spatial axes 3-D beings cannot comprehend. Him being multiversal does not have to do with him being 5-D, it has to do with his hax and power feats, same with Strange Visitor Superman. His dimensional level just lets him move and do stuff considered outlandish to lower dimensional beings as they literally cannot see the big picture of what he is doing when moving around the 5th dimensional axis.

Plus, DC Comics has a relatively flawed description of the fifth dimension, which is different from how dimensions work from even other fictional sources. Quoting the DC Comics Database

"The Fifth Dimension is an inter-dimensional reality that exists outside of the normally accepted space/time continuum. Due to its five dimensional properties, this reality functions off of a completely different set of physics than those found in typical three dimensional environments.







Zrfff is the home world of a race of impish beings who manipulate the properties of their dimension as a form of super-science"











http://dc.wikia.com/wiki/5th_Dimension

Going from this, it is shown that the Fifth Dimension simply works on different physics which is more lax and permits the crazy powers and abilities Mxy has. The dimension itself has no proof of being 2 orders of magnitudes of infinity larger than reality. Quite the contrary, it seems to be a subspace that simply exists outside our universe.

Another example, which indeed uses dimensions as higher infinities, is for the description of Yog Sothoth and the whole cosmology of Cthulhu Mythos. However, one can simply interpret that these "dimensions" were just wrongly named by Lovecraft. New theories about higher dimensions were only developed around 10 years ago, and a legit cosmological theory would not be formed for another 30 to 40 years. Lovecraft was wrong with his science. This can be seen with his interpreation of the fourth dimension as actually being time, and time itself being lowly to the 5th dimension.

The point being made is that dimensions in fiction do work nary to how scientists describe it, but that gives no credence to the idea of making higher dimensions equal higher infinities, because I doubt even the writers necessarily mean that; they just mean they are transcendental and beyond common understanding, something that can apply for our dimensions in real life.

TL;DR

Because the detractors most likely won't read the above information

  • Energy is a scalar value, which is not bound by any dimensional value.
  • Higher dimensions are not necessarily even large, they can be as small as subatomic particles. In fact, there is more to refute higher dimensions being compressed than large extra dimensions.
  • Temporal Dimensions work completely differently from Spatial Dimensions, and m-theory only has one temporal dimension, meaning being 6-D does not necessarily mean transcending time
  • Regardless if fiction uses higher dimensions differently, seldom do fictional verses show that they really equal higher infinities, and tend to just be inaccessible and transcendental to the standards of the human mind, which is true for even real life higher dimensions which are not higher infinities.


Sources