- 6,149
- 16,238
also known as vsbw kai abridged, in light of recent events.
By the way, I will suggest you all act like normal people, as in, read the whole thing first, then write down your opinion regarding it. That is all I am going to ask.
Lastly, I'd like to give credits to these three persons. The former for sparking this whole thing in the first place, and the latter for originating the basis for much of the tiering I am about to propose.
Dimensional Tiering
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 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, it is 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-dimensional spaces 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.
Now, 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. This obviously doesn't mean that any higher-dimensional being is about as strong as lower-dimensional ones period, rather, it just means energy is a constant that is independent of dimensionality, and would exist regardless even in a universe of more than three dimensions
Of course, higher-dimensional beings would probably be a lot bigger and stronger than us, but that would be more due to external factors, rather than strictly about their dimensionality per se.
Now, it is true that we cannot calculate the "Area" of a 3-dimensional object, or the "Volume" of 4-dimensional constructs. Trying to do such is indeed a fruitless endeavour that won't get you anywhere, but this is not at all because they are Infinite in size compared to 2 and 3-dimensional objects respectively, far from it.
This is because they have an additional parameter which describes their size and displacement in an area of space, another axis of movement to dislocate themselves through. Thus, another variable has to be taken into account in the context of whatever equation you are using to calculate the size of a given shape. In fact, in most cases you just have to use another equation altogether. It is basically a case of overall incompatibility, not difference in magnitude.
There is also the argument that, since, a higher-dimensional object possess an infinite number of slices of lower-dimensional objects within itself, then they are necessarily infinitely larger than them, and as a consequence of that, you can't really stack up lower-dimensional objects to get yourself a higher-dimensional one.
The former is actually geometrically accurate, there is, say, an infinite number of squares within a cube, but the issue is that this is mostly a very basic geometrical notion that doesn't really conform to how this stuff would play out within the physical world we live in, similar to how any object can be mathematically visualized as an uncountably infinite set of points, no matter how large or small. Higher and lower-dimensional objects are just... arbitrarily large, and can really be of literally any size.
In fact, it is indeed possible to calculate the radius of higher-dimensional spheres without the values accelerating to infinity, so that should tell you something. Of course, there are also examples for actual physics, such as Strings, which are 1-dimensional objects, yet are planck-length, not infinitely smaller than we are.
The latter is also intuitively accurate, but not so much diving deeper into it: Yes, you can't really stack up a lower-dimensional thing to get you a higher-dimensional thing, but this isn't really because the latter is infinitely bigger, rather it is because it has another direction through which its body can displace itself into.
The lower-dimensional object can't actually displace itself in said direction because it doesn't exist to them. It's a matter of position, rather than size: 1 meter in an additional axis isn't really bigger than 2 meters in the other axis, the former is just inaccessible to the latter because it is displaced in another direction, much like how west isn't infinitely far away from north because you can accelerate as far as you want in the direction of one and never reach the other, or how one second of time isn't really bigger than the entire Universe. The distance between them can be better described as "undefined", rather than infinite.
The thing about them is that they exist in different "sets". Dimensions are, for the most part, defined through real coordinate spaces, which are basically coordinate systems that denote said coordinates using the real numbers.
They are denoted as R^n (where R = the line of real numbers, equivalent to an axis of the space, pretty much a line. And n = the number of dimensions, which you get by taking the cartesian product/multiplication of R), with R^3 (R x R x R) being 3-dimensional space, R^4 (R x R x R x R) being 4-dimensional space and so on.
This relates to what I said in the sense that, for example, 4-dimensional objects are subsets of R^4, while 3-dimensional ones are subsets of R^3, and so on. The spaces don't "intermingle", and the difference between subsets in R^3 and subsets in R^4 is undetermined, since, again, they are in different sets altogether with a different number of axes. When you get down to it, you can only rely on the "lol uncountably infinitely larger" thing for the whole set, not just some random subsets of it.
B-but, we already do what you are suggesting! We don't give away a higher tier just for being Higher-D! This revision isn't necessary!
Yeah, so, I've seen this argument quite a lot both in and off-site. My response to it is that, this is exactly the point I am trying to make here: If we don't really give away a higher tier for a character who is just stated to be higher-dimensional, then why even use Dimensional Tiering in the first place?
Literally, the whole premise of it is that higher-dimensional stuff is necessarily infinitely larger and more expansive than stuff with less dimensions. If we just threw this standard out of the window and decided to take a more case-by-case approach a long time ago, then the whole Tiering System is pretty much useless and stupidly outdated in relation to our very own current standards on the matter. These pages are allpointless.
I believe most of you already know the gist of my proposals, but for those who don't:
Yeah, so, our current standards on both 1-A and Tier 0 suck and make no sense whatsoever.
Firstly, I should point to the fact that, according to many members of the Wiki, an 1-A character can be equal to, or even stronger than a Tier 0 character.
This is easily seen when one notices that there are profiles ranked at Tier 0 for being fully transcendent over a basic 1-A cosmology (Such as The One Above All and Kami Tenchi, for example) and standing as their sole supreme being, with maybe a limitation or two. Meanwhile, there are characters who possess identical, or even far better feats than them and scale to a far more expansive cosmology, yet are ranked at 1-A due to having big limitations, such as other beings in their verse who happen to be equal to, or superior to them
Examples of this are The Presence, The Ultimate Gods, Haju, The Leviatha and so on.
In fact, it seems like whether someone is Tier 0 or not is dependent of their standing within their own verse. A character could be 0 in the context of their verse, but weaker than an 1-A in another.
This is an obvious elephant in the room no one wants to address here: Higher Tier = Stronger Character is such a basic notion that I find it weird that I have to be enforcing it here. There is basically no reason for two tiers to be so fluid and arbitrary, especially when the entirety of the system before them is fairly straightforward and set in stone.
Although, even if we fixed this and decided to tier such characters from an out-of-universe, hands-on perspective, we'd still have another problem: The sheer extension of 1-A.
Yes, as many of you know, 1-A is an absurdly extensive tier, much like 1-B and 1-C are, and can extended indefinitely. The problem is that we choose to simply compress all of this into a single rating with no subtiers and leave it at that - If we take this route, we may as well fuse together everything from Low 1-C to High 1-B and call it a day: A tier as big as this one just shouldn't not have subtiers.
Yes, most people here do take into account 1-A hierarchies, but even then, this is extremely inconsistent, as several members have said that 1-A characters are just completely unquantifiable and cannot be put into an hierarchy, while others say that we cannot compare 1-As from different verses for a variety of reasons, so this is something that obviously needs to be settled.
Now, my proposal to fix this issue is, as you probably already gathered, to split 1-A and 0 into multiple subtiers. There are two ways in which this can be done, which are:
Option 1
* 1-B gets fused with 1-C and becomes a single rating with three subtiers (Low 1-C, 1-C and High 1-C), called simply Hyperverse level
* 1-C remains unchanged
We currently define 1-A characters as being those who exist in qualitative, "Beyond-Dimensional" states of existence, basically meaning that they transcend all possible dimensions of space and time, and are unreachable from their perspective, lacking such limitations altogether.
...Except that even this definition has its flaws. The problem here is that existing beyond dimensionality is extremely ill-defined and heavily depends on the verse's setting.
As dimensions are mainly constructs of space and time in the sense we use them, being beyond space and time entirely would already make you "beyond-dimensional", regardless if your verse has 3, 4 or 916 spatio-temporal dimensions in it. Once you jump off the boat, you are in the water, after all. You can't really scale a character to something which straight up doesn't exist in their verse.
Treating existing beyond space and time over a Low 2-C cosmology as being in a higher dimension than it is nonsensical and doesn't conform to what dimensions are in the first place.
This is obviously a fairly glaring issue with 1-A's current, formal definition, since, going by the basics of it, any character described as "beyond space and time" would qualify, as opposed to our current treatment, where a character has to explicitly transcend infinitely-layered structures to warrant such a rating. Due to that, I really think its primary definition should be changed to "a size so big you't can reach it by stacking infinities". It is really far more straightforward, less obtuse, and also encapsulates stuff like the current "transcending all forms of space and time" pretty well.
There is also the fact that, 1-A is apparently this grand, unknowable tier which we cannot comprehend and accurately measure or quantify in any way and all of this blah blah. This results in shit like High 1-B having no endpoint and just going on forever, while its successor just pops up somewhere along the line and has no defined starting point.
I will just note here that whoever thinks that is the case is sorely mistaken. This all starts with the blatant headcanon that 1-A is beyond logic and mathematics, something which is not only completely unprovable in the context of an indexing website, but is also not supported by any of its descriptions present anywhere in this site, with all of them mostly putting emphasis on how it denotes transcendence over spatio-temporal dimensionality, not mathematics and logic as a whole or anything like that.
So, no. There is absolutely no reason us to choose to not quantify 1-A like we do for every other Tier. So, what do I suggest for it? Well...
How To Count Past Infinity
I am sure most of you are familiar with this video already: But, for those who don't know, it is basically describing the concept of infinite sets with different cardinalities, formulated by Georg Cantor and expanded over by various mathematicians over the years and blahblahblablah.
Before delving into a brief explanation on the topic, I'd advise you that it is important to be familiarized with the concept of Countable and Uncountable Infinite sets, which is explained fairly straightforwardly in this video. It is like, 8-minutes long and the relevant part comes after 5 minutes into it, so I don't think pausing to watch it will be a problem, unless you are extremely lazy or already familiar with the idea, in which case...
Basically, according to very smart people, the cardinality (amount of stuff in a set) of a countably infinite set, such as the Natural Numbers, is denoted by the number ÔäÁ(0), or aleph-null. The "smallest" infinity, and the only countable one.
As you can see in the two videos linked above, the set of all real numbers has greater cardinality than the naturals: It is an uncountable set, equivalent to the power set of aleph-null, which, for simplicity's sake we are going to assume equates to aleph-one [ÔäÁ(1)], the successor of aleph-null and the first uncountably infinite number.
ÔäÁ(1) is... a pretty damn big number. Under our assumptions, it is basically what you get when you quantify every single permutation of a countably infinite set, and is basically inaccessible from the smaller infinity through linear operations, as the union of a given of countable sets is still very much countable, and thus falls under aleph-null.
Now, what the **** does this have to do with 1-A?
Well, basically, if one assumes that ÔäÁ(1) is the cardinality of the real numbers, then, from the perspective of the rest of the system (by which I mean, the Low 1-B/New High 1-B tier I described above) and in a very general way, one could say that it is the point where Dimensions stop being relevant, and the ceiling before "beyond-dimensional" states start to appear.
This is because, as far as standard stuff goes, the measures from which we generalize the notion of "dimension" and things such as "volume" are always defined over the reals. They are basically functions which assign real-numbered values to subsets of mathematical spaces, with the Hausdork Measure we currently use to justify dimensional tiering also falling under this.
The aforementioned Real Coordinate Spaces are also prime examples of things which would stop being relevant past uncountably infinite dimensions: Their whole thing is that they are coordinate systems defined over the real numbers, meaning the coordinates in them are *always* denoted by real values (like, "1, 6, 8, 0", or whatever other set of coordinates), and nothing else, and you obviously can't assign such values to something which functionally exceeds the reals.
Hence, a number of dimensions equivalent to the smallest uncountable infinity would be the longest you could go before they become completely arbitrary and mostly unusable/irrelevant, and things start to get all wonky and metaphysical, for our purposes.
That is the reason I proposed a "Low Outerverse level" tier accounting for uncountably infinite higher spaces/realms/dimensions, as this way we could have defined boundaries for both High 1-B and 1-A, and an answer for when the former ends and the latter starts.
Of course, I am not saying Aleph Numbers by themselves are 1-A or something. They are just that: numbers and quantities, and don't actually have fixed tiers: An uncountably infinite number of points can be as low as 11-B, for example, and an uncountably infinite number of Universes would be just High 2-A even by the system I am proposing. It depends on the things contained in the set whose cardinality they denote.
Rather, we'd have to get a little specific here which brings in the concept of a Class, which is basically a generalization of the idea of a collection into something more expansive and specific that sets: They are basically collections defined by a property all of their members share (Such as the class of all things made of chocolate, or the class of all people taller than 1 cm).
Classes are divided into two categories: Small Classes (which are pretty much sets, but slightly more specific) and Proper Classes (which denote collections that are too big to be sets. See this page for more information on that).
Hence, for the purposes of the system, if we assume an uncountably infinite number of dimensions (the ceiling before Outerverse level) is equivalent to R^R, and by extension aleph-one (sorta), then the succeeding tier and its levels could be assumed as arbitrary small classes of objects that are bigger than R^R and equivalent to some infinite cardinal number past aleph-one (or, R ^ R ^ R and up, if you will)
Now, for formally classifying the new 1-A and 0 tiers, there are a few options at hand:
1. Have 1-A be denoted by inaccessible cardinals, which are essentially uncountable, regular cardinal numbers that cannot be reached from smaller numbers, be it through power sets, replacements or whatever. More detailed explanation on them is on the VSauce video linked above
Tier 0, on the hand, would formally be for characters who are equivalent in size to the aforementioned Proper Classes. Essentially, collections of things that are too big to be classified as sets, examples of which are the Class of all Ordinal Numbers, or the Class of All Sets. This would be equivalent to "boundless" characters who exist outside of notions of size and scale, or something of the sort.
so basically
Inaccessible Cardinals = 1-A
Proper Classes = 0
2. Have 1-A be denoted by Worldly Cardinals, which are essentially a weaker cardinal axiom than Inaccessible Cardinals that can act as a proper entry into the realm of large cardinals, which exist as unreachable fixed points in relation to the hierarchy of Aleph / Beth Numbers, much like inaccessibles are. The difference is that, Worldly Cardinals don't share the more technical characteristics of their successors, and can be "singular" in nature, which means they can be defined as the union of cardinals smaller than themselves, while Inaccesibles... well, can't.
Worldly Cardinals themselves are divided into an hierarchy (called the a-worldly hierarchy, with a being a placeholder for any ordinal number, be it finite or infinite). What I just described classify as 0-Worldy Cardinals, while limits of the enumeration of those are 1-Worldly, and so on. This whole hierarchy is superseded by the a-inaccessible hierarchy, with 0-inaccessibles being basically what Vsauce describes in the video above.
So
Worldly Cardinals = 1-A
Inaccessible Cardinals = 0
Tally
Yay:
Nay:
By the way, I will suggest you all act like normal people, as in, read the whole thing first, then write down your opinion regarding it. That is all I am going to ask.
Lastly, I'd like to give credits to these three persons. The former for sparking this whole thing in the first place, and the latter for originating the basis for much of the tiering I am about to propose.
Dimensional Tiering
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 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, it is 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-dimensional spaces 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.
Now, 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. |
Of course, higher-dimensional beings would probably be a lot bigger and stronger than us, but that would be more due to external factors, rather than strictly about their dimensionality per se.
Now, it is true that we cannot calculate the "Area" of a 3-dimensional object, or the "Volume" of 4-dimensional constructs. Trying to do such is indeed a fruitless endeavour that won't get you anywhere, but this is not at all because they are Infinite in size compared to 2 and 3-dimensional objects respectively, far from it.
This is because they have an additional parameter which describes their size and displacement in an area of space, another axis of movement to dislocate themselves through. Thus, another variable has to be taken into account in the context of whatever equation you are using to calculate the size of a given shape. In fact, in most cases you just have to use another equation altogether. It is basically a case of overall incompatibility, not difference in magnitude.
There is also the argument that, since, a higher-dimensional object possess an infinite number of slices of lower-dimensional objects within itself, then they are necessarily infinitely larger than them, and as a consequence of that, you can't really stack up lower-dimensional objects to get yourself a higher-dimensional one.
The former is actually geometrically accurate, there is, say, an infinite number of squares within a cube, but the issue is that this is mostly a very basic geometrical notion that doesn't really conform to how this stuff would play out within the physical world we live in, similar to how any object can be mathematically visualized as an uncountably infinite set of points, no matter how large or small. Higher and lower-dimensional objects are just... arbitrarily large, and can really be of literally any size.
In fact, it is indeed possible to calculate the radius of higher-dimensional spheres without the values accelerating to infinity, so that should tell you something. Of course, there are also examples for actual physics, such as Strings, which are 1-dimensional objects, yet are planck-length, not infinitely smaller than we are.
The latter is also intuitively accurate, but not so much diving deeper into it: Yes, you can't really stack up a lower-dimensional thing to get you a higher-dimensional thing, but this isn't really because the latter is infinitely bigger, rather it is because it has another direction through which its body can displace itself into.
The lower-dimensional object can't actually displace itself in said direction because it doesn't exist to them. It's a matter of position, rather than size: 1 meter in an additional axis isn't really bigger than 2 meters in the other axis, the former is just inaccessible to the latter because it is displaced in another direction, much like how west isn't infinitely far away from north because you can accelerate as far as you want in the direction of one and never reach the other, or how one second of time isn't really bigger than the entire Universe. The distance between them can be better described as "undefined", rather than infinite.
The thing about them is that they exist in different "sets". Dimensions are, for the most part, defined through real coordinate spaces, which are basically coordinate systems that denote said coordinates using the real numbers.
They are denoted as R^n (where R = the line of real numbers, equivalent to an axis of the space, pretty much a line. And n = the number of dimensions, which you get by taking the cartesian product/multiplication of R), with R^3 (R x R x R) being 3-dimensional space, R^4 (R x R x R x R) being 4-dimensional space and so on.
This relates to what I said in the sense that, for example, 4-dimensional objects are subsets of R^4, while 3-dimensional ones are subsets of R^3, and so on. The spaces don't "intermingle", and the difference between subsets in R^3 and subsets in R^4 is undetermined, since, again, they are in different sets altogether with a different number of axes. When you get down to it, you can only rely on the "lol uncountably infinitely larger" thing for the whole set, not just some random subsets of it.
B-but, we already do what you are suggesting! We don't give away a higher tier just for being Higher-D! This revision isn't necessary!
Yeah, so, I've seen this argument quite a lot both in and off-site. My response to it is that, this is exactly the point I am trying to make here: If we don't really give away a higher tier for a character who is just stated to be higher-dimensional, then why even use Dimensional Tiering in the first place?
Literally, the whole premise of it is that higher-dimensional stuff is necessarily infinitely larger and more expansive than stuff with less dimensions. If we just threw this standard out of the window and decided to take a more case-by-case approach a long time ago, then the whole Tiering System is pretty much useless and stupidly outdated in relation to our very own current standards on the matter. These pages are allpointless.
I believe most of you already know the gist of my proposals, but for those who don't:
- Higher-Dimensional Beings shouldn't be automatically in a higher tier unless further context as to their nature is shown. They can either scale off of their best feats or be placed at Unknow
- However, meaningfully affecting a higher-dimensional space that is either provably infinite in size or explicitly defined as beyond lower-dimensional spaces by the verse itself can indeed warrant a higher tier. The exception to this nitpicking are infinite-dimensional spaces, for obvious reasons, unless the verse they're from says they are somehow finite.
Yeah, so, our current standards on both 1-A and Tier 0 suck and make no sense whatsoever.
Firstly, I should point to the fact that, according to many members of the Wiki, an 1-A character can be equal to, or even stronger than a Tier 0 character.
This is easily seen when one notices that there are profiles ranked at Tier 0 for being fully transcendent over a basic 1-A cosmology (Such as The One Above All and Kami Tenchi, for example) and standing as their sole supreme being, with maybe a limitation or two. Meanwhile, there are characters who possess identical, or even far better feats than them and scale to a far more expansive cosmology, yet are ranked at 1-A due to having big limitations, such as other beings in their verse who happen to be equal to, or superior to them
Examples of this are The Presence, The Ultimate Gods, Haju, The Leviatha and so on.
In fact, it seems like whether someone is Tier 0 or not is dependent of their standing within their own verse. A character could be 0 in the context of their verse, but weaker than an 1-A in another.
This is an obvious elephant in the room no one wants to address here: Higher Tier = Stronger Character is such a basic notion that I find it weird that I have to be enforcing it here. There is basically no reason for two tiers to be so fluid and arbitrary, especially when the entirety of the system before them is fairly straightforward and set in stone.
Although, even if we fixed this and decided to tier such characters from an out-of-universe, hands-on perspective, we'd still have another problem: The sheer extension of 1-A.
Yes, as many of you know, 1-A is an absurdly extensive tier, much like 1-B and 1-C are, and can extended indefinitely. The problem is that we choose to simply compress all of this into a single rating with no subtiers and leave it at that - If we take this route, we may as well fuse together everything from Low 1-C to High 1-B and call it a day: A tier as big as this one just shouldn't not have subtiers.
Yes, most people here do take into account 1-A hierarchies, but even then, this is extremely inconsistent, as several members have said that 1-A characters are just completely unquantifiable and cannot be put into an hierarchy, while others say that we cannot compare 1-As from different verses for a variety of reasons, so this is something that obviously needs to be settled.
Now, my proposal to fix this issue is, as you probably already gathered, to split 1-A and 0 into multiple subtiers. There are two ways in which this can be done, which are:
Option 1
* 1-B gets fused with 1-C and becomes a single rating with three subtiers (Low 1-C, 1-C and High 1-C), called simply Hyperverse level
- 1-B becomes the new Outerverse level, and starts to have three subtiers:
- Low 1-B: Characters whose size cannot be reached by stacking infinities, but who still exist in the same "level" as the things they dwarf. Equivalent to an uncountably infinite number of dimensions/planes, and is pretty much a middle ground between High 1-C and 1-B. I will elaborate on why it exists later.
- 1-B: More or less a better defined current "baseline" Outerversal, up to any finite number of higher levels above it
- High 1-B: Infinite levels of existence above baseline Outerversal. Though it doesn't necessarily have to be layers/levels, sheer power/size equivalent to this also qualifies
- 1-A is made into a tier of its own, denoting characters who exist above Outerversal hierarchies altogether, and lie beyond any scale.
- 0 becomes a tier for all-encompassing characters who exist fully beyond the scope of the rest of the system
* 1-C remains unchanged
- The current 1-B becomes Low 1-B
- The current High 1-B becomes 1-B
- High 1-B becomes the tier for up to uncountably infinite higher planes/dimensions/stuff
- Low 1-A becomes baseline Outerversal and up, with infinite hierarchies on this scale receiving a "+" modifier next to the rating
- 1-A and 0 are basically the same as Option 1
We currently define 1-A characters as being those who exist in qualitative, "Beyond-Dimensional" states of existence, basically meaning that they transcend all possible dimensions of space and time, and are unreachable from their perspective, lacking such limitations altogether.
...Except that even this definition has its flaws. The problem here is that existing beyond dimensionality is extremely ill-defined and heavily depends on the verse's setting.
As dimensions are mainly constructs of space and time in the sense we use them, being beyond space and time entirely would already make you "beyond-dimensional", regardless if your verse has 3, 4 or 916 spatio-temporal dimensions in it. Once you jump off the boat, you are in the water, after all. You can't really scale a character to something which straight up doesn't exist in their verse.
Treating existing beyond space and time over a Low 2-C cosmology as being in a higher dimension than it is nonsensical and doesn't conform to what dimensions are in the first place.
This is obviously a fairly glaring issue with 1-A's current, formal definition, since, going by the basics of it, any character described as "beyond space and time" would qualify, as opposed to our current treatment, where a character has to explicitly transcend infinitely-layered structures to warrant such a rating. Due to that, I really think its primary definition should be changed to "a size so big you't can reach it by stacking infinities". It is really far more straightforward, less obtuse, and also encapsulates stuff like the current "transcending all forms of space and time" pretty well.
There is also the fact that, 1-A is apparently this grand, unknowable tier which we cannot comprehend and accurately measure or quantify in any way and all of this blah blah. This results in shit like High 1-B having no endpoint and just going on forever, while its successor just pops up somewhere along the line and has no defined starting point.
I will just note here that whoever thinks that is the case is sorely mistaken. This all starts with the blatant headcanon that 1-A is beyond logic and mathematics, something which is not only completely unprovable in the context of an indexing website, but is also not supported by any of its descriptions present anywhere in this site, with all of them mostly putting emphasis on how it denotes transcendence over spatio-temporal dimensionality, not mathematics and logic as a whole or anything like that.
So, no. There is absolutely no reason us to choose to not quantify 1-A like we do for every other Tier. So, what do I suggest for it? Well...
How To Count Past Infinity
I am sure most of you are familiar with this video already: But, for those who don't know, it is basically describing the concept of infinite sets with different cardinalities, formulated by Georg Cantor and expanded over by various mathematicians over the years and blahblahblablah.
Before delving into a brief explanation on the topic, I'd advise you that it is important to be familiarized with the concept of Countable and Uncountable Infinite sets, which is explained fairly straightforwardly in this video. It is like, 8-minutes long and the relevant part comes after 5 minutes into it, so I don't think pausing to watch it will be a problem, unless you are extremely lazy or already familiar with the idea, in which case...
Basically, according to very smart people, the cardinality (amount of stuff in a set) of a countably infinite set, such as the Natural Numbers, is denoted by the number ÔäÁ(0), or aleph-null. The "smallest" infinity, and the only countable one.
As you can see in the two videos linked above, the set of all real numbers has greater cardinality than the naturals: It is an uncountable set, equivalent to the power set of aleph-null, which, for simplicity's sake we are going to assume equates to aleph-one [ÔäÁ(1)], the successor of aleph-null and the first uncountably infinite number.
ÔäÁ(1) is... a pretty damn big number. Under our assumptions, it is basically what you get when you quantify every single permutation of a countably infinite set, and is basically inaccessible from the smaller infinity through linear operations, as the union of a given of countable sets is still very much countable, and thus falls under aleph-null.
Now, what the **** does this have to do with 1-A?
Well, basically, if one assumes that ÔäÁ(1) is the cardinality of the real numbers, then, from the perspective of the rest of the system (by which I mean, the Low 1-B/New High 1-B tier I described above) and in a very general way, one could say that it is the point where Dimensions stop being relevant, and the ceiling before "beyond-dimensional" states start to appear.
This is because, as far as standard stuff goes, the measures from which we generalize the notion of "dimension" and things such as "volume" are always defined over the reals. They are basically functions which assign real-numbered values to subsets of mathematical spaces, with the Hausdork Measure we currently use to justify dimensional tiering also falling under this.
The aforementioned Real Coordinate Spaces are also prime examples of things which would stop being relevant past uncountably infinite dimensions: Their whole thing is that they are coordinate systems defined over the real numbers, meaning the coordinates in them are *always* denoted by real values (like, "1, 6, 8, 0", or whatever other set of coordinates), and nothing else, and you obviously can't assign such values to something which functionally exceeds the reals.
Hence, a number of dimensions equivalent to the smallest uncountable infinity would be the longest you could go before they become completely arbitrary and mostly unusable/irrelevant, and things start to get all wonky and metaphysical, for our purposes.
That is the reason I proposed a "Low Outerverse level" tier accounting for uncountably infinite higher spaces/realms/dimensions, as this way we could have defined boundaries for both High 1-B and 1-A, and an answer for when the former ends and the latter starts.
Of course, I am not saying Aleph Numbers by themselves are 1-A or something. They are just that: numbers and quantities, and don't actually have fixed tiers: An uncountably infinite number of points can be as low as 11-B, for example, and an uncountably infinite number of Universes would be just High 2-A even by the system I am proposing. It depends on the things contained in the set whose cardinality they denote.
Rather, we'd have to get a little specific here which brings in the concept of a Class, which is basically a generalization of the idea of a collection into something more expansive and specific that sets: They are basically collections defined by a property all of their members share (Such as the class of all things made of chocolate, or the class of all people taller than 1 cm).
Classes are divided into two categories: Small Classes (which are pretty much sets, but slightly more specific) and Proper Classes (which denote collections that are too big to be sets. See this page for more information on that).
Hence, for the purposes of the system, if we assume an uncountably infinite number of dimensions (the ceiling before Outerverse level) is equivalent to R^R, and by extension aleph-one (sorta), then the succeeding tier and its levels could be assumed as arbitrary small classes of objects that are bigger than R^R and equivalent to some infinite cardinal number past aleph-one (or, R ^ R ^ R and up, if you will)
Now, for formally classifying the new 1-A and 0 tiers, there are a few options at hand:
1. Have 1-A be denoted by inaccessible cardinals, which are essentially uncountable, regular cardinal numbers that cannot be reached from smaller numbers, be it through power sets, replacements or whatever. More detailed explanation on them is on the VSauce video linked above
Tier 0, on the hand, would formally be for characters who are equivalent in size to the aforementioned Proper Classes. Essentially, collections of things that are too big to be classified as sets, examples of which are the Class of all Ordinal Numbers, or the Class of All Sets. This would be equivalent to "boundless" characters who exist outside of notions of size and scale, or something of the sort.
so basically
Inaccessible Cardinals = 1-A
Proper Classes = 0
2. Have 1-A be denoted by Worldly Cardinals, which are essentially a weaker cardinal axiom than Inaccessible Cardinals that can act as a proper entry into the realm of large cardinals, which exist as unreachable fixed points in relation to the hierarchy of Aleph / Beth Numbers, much like inaccessibles are. The difference is that, Worldly Cardinals don't share the more technical characteristics of their successors, and can be "singular" in nature, which means they can be defined as the union of cardinals smaller than themselves, while Inaccesibles... well, can't.
Worldly Cardinals themselves are divided into an hierarchy (called the a-worldly hierarchy, with a being a placeholder for any ordinal number, be it finite or infinite). What I just described classify as 0-Worldy Cardinals, while limits of the enumeration of those are 1-Worldly, and so on. This whole hierarchy is superseded by the a-inaccessible hierarchy, with 0-inaccessibles being basically what Vsauce describes in the video above.
So
Worldly Cardinals = 1-A
Inaccessible Cardinals = 0
Tally
Yay:
Nay:
