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STAFF DISCUSSION
Introductio
Hello everyone, hope you're doing well.
As a few users I spoke with off-site may know, I have been increasingly unsatisfied with the current state of our Tiering System, and thus, have been making a Thread to tackle what is certainly the most controversial aspect of it: Dimensional Tiering.
But before discussing this subject, I'd like to note that I am not really trying to dismantle the System, nor do I want deviate too much from it. In fact, most of the Tiers are going to be basically the same even after the revisions I am proposing, save for some name alterations and changes in Tier 11. So I would appreciate if the main subject of this Thread can be discussed in a calm and civilized way, with no shitstorms or anything of the sort.
Furthermore, I would like to give credits to Aeyu, since she assisted a lot with this Thread and basically taught me about most of this stuff I previously knew shit about.
Now, as Jack the Ripper would say: Vamos por partes.
dimenshunal tayeri
Firstly, it is extremely important to note that Dimensions are just Axis of Movement, nothing more and nothing less. Higher Dimensions are not layers or higher levels of existence in any way, they are just additional directions through which individual shapes and entities can displace themselves in. I believe this is explained fairly decently in the Dimensional Tiering page, so I am not going to waste time or space going in-depth about it here.
Secondly, it is important to note that within Mathematics, Dimensions are used to denote the number of values needed to specify the position of a point within some abstract space. A Cartesian Plane, for example, is 2-dimensional because two values are needed to specify the location of some element inside it (x, y), and a Space is 3-dimensional because three values (x, y, z) are needed to do that. You could as well say that an n-dimensional space is the set of all n-tuples of numbers that can possibly be used to indicate a position within said Space.
Now, with these two things in mind, the problems with Dimensional Tiering become incresingly obvious.
To start with the basics, let's see what the Attack Potency page has to say about the levels of energy exerted by Higher-Dimensional Beings:
I will simply start by saying that this notion is completely wrong even when going by our basic understanding of physics: This is due to the fact that Energy is a Scalar Quantity, which means that it is described by only one value, its magnitude, and thus does not depend on direction or displacement of any kind.
A Vector Quantity, on the other hand, is a quantity that is dependent not only on its Magnitude, but on its Direction and Displacement as well. A good example of the distinction between Scalar and Vectors would be the concepts of Speed and Velocity - Speed, as it is commonly defined, is the rating which is used to describe how fast an object is moving, or in more formal terms, the rate in which an object covers distance: this definition is a constant regardless of motion and direction, as it is only defined by Magnitude and nothing else, a car moving at 70 km/h will have the same Speed regardless if it is heading towards North, West or East. Thus, Speed is a Scalar Quantity, one that never changes regardless of directions.
Velocity, on the other hand, is the rating in which an object changes position, that is, it defines not only the rate in which an object covers distance, but also the direction in which it is doing so. Indeed, to shamelessly quote Wikipedia on this:
Now that the difference between Scalar and Vector Quantities is established, it is fairly easy to see where I am going with this, as I mentioned earlier: Energy is a Scalar Quantity, and so are Mass and Speed, the quantities which are used to measure Energy, and by extension, Power, in the first place. Hence, Energy is a dimensionless concept, and is fully independent from direction or displacement, and thus, from Dimensionality as a whole, meaning a punch of 10 joules will still have a value of 10 joules regardless if it is done by a being of Dimension 3, 5 or 100.
Now with this out of the way, It is also important to tackle the simple fact that there is nothing inherently cosmic or godly about Higher-Dimensional Beings. Under ordinary circumstances, they would in no way be what is described in the Higher-Dimensional Existence page.
As a matter of fact, Higher-Dimensional Beings would abide by the same physical and mathematical principles as we do, as stated by actual mathematicians. The fundamental laws of physics are inherently dimensionless, and they would effectively be the same in Higher-Dimensions going by a mathematical, more fundamental sense, they would only operate differently in a physical sense, and that would be due to the additional axis of movement inherent to the Higher-Dimensional Space; say, the newtonian law of gravitation would be the same mathematical principle within a Universe of 4 dimensions, but the way it functions would appear different because, for example, Orbits work differently in more than 3 dimensions.
Furthermore, even the idea of Higher-Dimensional Creatures being always strictly bigger than lower-dimensional ones is faulty at best. Sure, they can potentially be much bigger than us, but this is not because of their Dimensional Parameters make them automatically larger by an infinite amount, but because said parameters allow their mass to extend into different directions entirely which are inaccesible to lower beings.
Additionally, if beings with more than three dimensions were really Infinite in size and scope, and capable of exerting more than infinite energy, their 3-dimensional parameters would also have to be Infinite, which obviously wouldn't always be the case, since we don't have infinitely big 2-dimensional parameters, so the argument that any non-zero size within a Higher Dimension would be uncountably infinite in a lower one simply doesn't hold up.
Now, one may propose the argument that, due to the fact that even an infinite amount of 2-dimensional objects and shapes wouldn't be able to construct a 3-dimensional one, then the difference between Dimensions 2 and 3 must be uncountably infinite. That is, an individual could stack up and combine any amount of 2-D objects, but they would never really be as large as a 3-D one and their collective size would always be 0 in relation to it. By logical extension, this can be applied to any shapes and objects, no matter their number of dimensions.
However, I would like to note that this has little relation to Size per se; rather, it is due to the fact that the 3-dimensional object extends into another direction of space entirely, which the set of 2-dimensional objects can't reach because they lack the parameters needed to do so.
Remember, Dimensions are merely axis of space-time movement, and under Coordinate Spaces the above argument falls apart even much more clearly - Suppose that we have a Coordinate System with Three Axes (System A):
X = 999
Y = 999
Z = 999
W = 0
And then we have another one, comprised of Four Axes (System B):
X = 1
Y = 1
Z = 1
W = 1
Obviously, System B can never be reached by the System A, but this is simply because it has a greater value on the W axis, which the latter System lacks entirely. It doesn't translate to "lol W axis is infinitely more bigger than (999,999,999)", rather, it translates to "W axis is to the left and even if you go infinitely up and up and up it'll never reach it".
Even then, you can just increase the value of the W axis to 1 in System A. You don't need to accelerate the parameters X, Y and Z to infinity to try and make W increase to 1.
In layman's terms, what the argument I detailed above (and Dimensional Tiering as a whole, really) proposes is analogous to saying that North is infinitely far away from West, since you can walk infinitely in the direction of the former and never reach the latter, when this only happens because West is positioned in another direction relative to North, and you can simply take a step in its direction and reach it with no problem whatsoever.
Additionally, we are actually capable of calculating Hypervolume. This is even more evidence that Dimensions don't represent orders of infinity even in a geometrical sense.
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:
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.
Proposals
However, as I clarified in the beginning of this Thread, my intention here isn't to completely change the Tiering System, so my proposals can be summed up to:
Introductio
Hello everyone, hope you're doing well.
As a few users I spoke with off-site may know, I have been increasingly unsatisfied with the current state of our Tiering System, and thus, have been making a Thread to tackle what is certainly the most controversial aspect of it: Dimensional Tiering.
But before discussing this subject, I'd like to note that I am not really trying to dismantle the System, nor do I want deviate too much from it. In fact, most of the Tiers are going to be basically the same even after the revisions I am proposing, save for some name alterations and changes in Tier 11. So I would appreciate if the main subject of this Thread can be discussed in a calm and civilized way, with no shitstorms or anything of the sort.
Furthermore, I would like to give credits to Aeyu, since she assisted a lot with this Thread and basically taught me about most of this stuff I previously knew shit about.
Now, as Jack the Ripper would say: Vamos por partes.
dimenshunal tayeri
Firstly, it is extremely important to note that Dimensions are just Axis of Movement, nothing more and nothing less. Higher Dimensions are not layers or higher levels of existence in any way, they are just additional directions through which individual shapes and entities can displace themselves in. I believe this is explained fairly decently in the Dimensional Tiering page, so I am not going to waste time or space going in-depth about it here.
Secondly, it is important to note that within Mathematics, Dimensions are used to denote the number of values needed to specify the position of a point within some abstract space. A Cartesian Plane, for example, is 2-dimensional because two values are needed to specify the location of some element inside it (x, y), and a Space is 3-dimensional because three values (x, y, z) are needed to do that. You could as well say that an n-dimensional space is the set of all n-tuples of numbers that can possibly be used to indicate a position within said Space.
Now, with these two things in mind, the problems with Dimensional Tiering become incresingly obvious.
To start with the basics, let's see what the Attack Potency page has to say about the levels of energy exerted by Higher-Dimensional Beings:
| Higher Dimensional levels: These levels are not listed because they are not restricted to the same parameters for energy requirement. The energy for such levels cannot be calculated. |
A Vector Quantity, on the other hand, is a quantity that is dependent not only on its Magnitude, but on its Direction and Displacement as well. A good example of the distinction between Scalar and Vectors would be the concepts of Speed and Velocity - Speed, as it is commonly defined, is the rating which is used to describe how fast an object is moving, or in more formal terms, the rate in which an object covers distance: this definition is a constant regardless of motion and direction, as it is only defined by Magnitude and nothing else, a car moving at 70 km/h will have the same Speed regardless if it is heading towards North, West or East. Thus, Speed is a Scalar Quantity, one that never changes regardless of directions.
Velocity, on the other hand, is the rating in which an object changes position, that is, it defines not only the rate in which an object covers distance, but also the direction in which it is doing so. Indeed, to shamelessly quote Wikipedia on this:
| If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified. The big difference can be noticed when we consider movement around a circle. When something moves in a circular path (at a constant speed, see above) and returns to its starting point, its average velocity is zero but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. |
Now with this out of the way, It is also important to tackle the simple fact that there is nothing inherently cosmic or godly about Higher-Dimensional Beings. Under ordinary circumstances, they would in no way be what is described in the Higher-Dimensional Existence page.
As a matter of fact, Higher-Dimensional Beings would abide by the same physical and mathematical principles as we do, as stated by actual mathematicians. The fundamental laws of physics are inherently dimensionless, and they would effectively be the same in Higher-Dimensions going by a mathematical, more fundamental sense, they would only operate differently in a physical sense, and that would be due to the additional axis of movement inherent to the Higher-Dimensional Space; say, the newtonian law of gravitation would be the same mathematical principle within a Universe of 4 dimensions, but the way it functions would appear different because, for example, Orbits work differently in more than 3 dimensions.
Furthermore, even the idea of Higher-Dimensional Creatures being always strictly bigger than lower-dimensional ones is faulty at best. Sure, they can potentially be much bigger than us, but this is not because of their Dimensional Parameters make them automatically larger by an infinite amount, but because said parameters allow their mass to extend into different directions entirely which are inaccesible to lower beings.
Additionally, if beings with more than three dimensions were really Infinite in size and scope, and capable of exerting more than infinite energy, their 3-dimensional parameters would also have to be Infinite, which obviously wouldn't always be the case, since we don't have infinitely big 2-dimensional parameters, so the argument that any non-zero size within a Higher Dimension would be uncountably infinite in a lower one simply doesn't hold up.
Now, one may propose the argument that, due to the fact that even an infinite amount of 2-dimensional objects and shapes wouldn't be able to construct a 3-dimensional one, then the difference between Dimensions 2 and 3 must be uncountably infinite. That is, an individual could stack up and combine any amount of 2-D objects, but they would never really be as large as a 3-D one and their collective size would always be 0 in relation to it. By logical extension, this can be applied to any shapes and objects, no matter their number of dimensions.
However, I would like to note that this has little relation to Size per se; rather, it is due to the fact that the 3-dimensional object extends into another direction of space entirely, which the set of 2-dimensional objects can't reach because they lack the parameters needed to do so.
Remember, Dimensions are merely axis of space-time movement, and under Coordinate Spaces the above argument falls apart even much more clearly - Suppose that we have a Coordinate System with Three Axes (System A):
X = 999
Y = 999
Z = 999
W = 0
And then we have another one, comprised of Four Axes (System B):
X = 1
Y = 1
Z = 1
W = 1
Obviously, System B can never be reached by the System A, but this is simply because it has a greater value on the W axis, which the latter System lacks entirely. It doesn't translate to "lol W axis is infinitely more bigger than (999,999,999)", rather, it translates to "W axis is to the left and even if you go infinitely up and up and up it'll never reach it".
Even then, you can just increase the value of the W axis to 1 in System A. You don't need to accelerate the parameters X, Y and Z to infinity to try and make W increase to 1.
In layman's terms, what the argument I detailed above (and Dimensional Tiering as a whole, really) proposes is analogous to saying that North is infinitely far away from West, since you can walk infinitely in the direction of the former and never reach the latter, when this only happens because West is positioned in another direction relative to North, and you can simply take a step in its direction and reach it with no problem whatsoever.
Additionally, we are actually capable of calculating Hypervolume. This is even more evidence that Dimensions don't represent orders of infinity even in a geometrical sense.
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. |
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.
Proposals
However, as I clarified in the beginning of this Thread, my intention here isn't to completely change the Tiering System, so my proposals can be summed up to:
- Higher-Dimensionality by itself should not warrant a higher tier, unless the Verse in question specifies that Higher Dimensional Beings are qualitatively superior to lower ones, as assuming any 11-D being is capable of destroying / affecting an entire 11-D Multiverse is really the same thing as assuming any 3-D being can affect the entirety of a structure equivalent to our (un)observable Universe in scope. Therefore, if a Higher-Dimensional Being has no feats or showings other than being Higher-Dimensional, and no further context as to the nature of Dimensions within their setting is given, they should be put at 'Unknow'.
- However, if said Higher-Dimensional Being is actually shown to be capable of affecting and manipulating phenomena / structures on their level of existence, then an appropriate Tiering can be given to them (i.e a Cosmic Entity who embodies the totality of an 11-D Multiverse would be High 1-C, so too would a being who created a Multiverse of this scale of complexity)
- For High 2-A and above, instead of Hausdorff Fractal Geometry that has absolutely no relation to Spatio-Temporal Dimensions as they are applied to Manifolds and regular Cosmologies, I suggest we use Brane Cosmology, a model wherein our entire Universe is part of a Higher-Dimensional Membrane whose dimensional complexity can vary, which is itself contained inside a greater "Bulk". It is actually a far easier and more reasonable alternative, and isn't as convoluted and overly technical as arguing the distance between 1 and 2 is infinite because of Non-Integer Dimensions
