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Analyzing the Tiering System
- Thread starter Ultima_Reality
- Start date
- Status
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"Literal Cardinality also ain't all that useful for measuring the global sizes of objects either, since literally anything has cardinality equal to the real numbers if we go by it. If you wanted to use infinite numbers as a measuring stick it would be more appropriate to say a given object has size analogous to a given number, rather than pointing at its cardinality."
Any thoughts on this?
Any thoughts on this?
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It is impossible to properly compare 1-A/0 and 1-A/0 from different settings. No one can make a proper argument to support one or another character. Isn't it the reason why we don't add 1-A matches to the character pages?Sera EX said:
And the new tiering system is even worse simply because we will not be able to compare the stuff especially with more fanmade limits.
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i mean it's going to be talked in the future where they gods will beZephyrosOmega said:
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@Jockey-1337, it is the opposite; adding more Tier 1-A makes it easier to compared characters from other fictional settings. So, the new system is better.
Removing many Tier 1 and Tier 0 would make less sense and is way worse since proper comparison will be will harder to understand under this simplified system
Removing many Tier 1 and Tier 0 would make less sense and is way worse since proper comparison will be will harder to understand under this simplified system
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extrapolate more on the idea of it would be worse bcuz we cant compare, if you say we cant compare crossverse 1-A's power then you're wrong, this system heavily supports how HIGH someone can get in tier 1-B and up in the new tiering.Jockey-1337 said:
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not necessarily, it can be based on both since cardinality is the size meanwhile ordinality is more like how many are there within a set, which if we go with high 1-B in the new thing it would be based on both cardinality and ordinality.Elizhaa said:
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@Jockey
Your idea will just make it even more of a mess you know.....one of the points of this revision is to categorize Outerversal better. Before that be it baseline, finite "transcendences", Infinite-Outerversal, above the whole hierarchy, etc was contained in one tier : 1-A. And some 1-As could beat other verses' Tier 0s, which go against the goal of a Tiering System in the first palce, in which the higher you are the stronger you're supposed to be. Now, we'll have a proper one for Baseline Outerversal till any finite "transcendence" (Low 1-A), one for Infinite Outerversal (1-A), one for characters being above the whole hierarchy itself (High 1-A), and characters transcendent of High 1-As, which I guess would mean being above that hierarchy as well, Tier 0s.
Your idea on the other hand, is like saying "Why don't we just fuse current 1-A with High 1-B, 1-B and the whole 1-C stuff". I'm not sure that solves anything, rather the opposite.
And maybe you skimmed it, but Math was used for the reasoning, so I don't think it's that fanmade
.
Your idea will just make it even more of a mess you know.....one of the points of this revision is to categorize Outerversal better. Before that be it baseline, finite "transcendences", Infinite-Outerversal, above the whole hierarchy, etc was contained in one tier : 1-A. And some 1-As could beat other verses' Tier 0s, which go against the goal of a Tiering System in the first palce, in which the higher you are the stronger you're supposed to be. Now, we'll have a proper one for Baseline Outerversal till any finite "transcendence" (Low 1-A), one for Infinite Outerversal (1-A), one for characters being above the whole hierarchy itself (High 1-A), and characters transcendent of High 1-As, which I guess would mean being above that hierarchy as well, Tier 0s.
Your idea on the other hand, is like saying "Why don't we just fuse current 1-A with High 1-B, 1-B and the whole 1-C stuff". I'm not sure that solves anything, rather the opposite.
And maybe you skimmed it, but Math was used for the reasoning, so I don't think it's that fanmade
.
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Ok, let's get to this. To say it in advance: I will give my opinion on every mathematical detail I see as wrong, even if it is for the sole purpose of mathematical correctness.
Firstly, it is extremely important to note that Dimensions are just Axis of Movement, nothing more and nothing less.
There are many definitions of dimensions used, depending on the objects one wishes to apply them to. The one you mention here is probably the one for vector spaces, where the description is pretty fitting. For other things it doesn't work quite as well.
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.
Wrong. One can use even just 1 number to specify position in the 2,3,4,5… dimensional plane.
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.
You are misinterpreting that article a bit. That article for example notes how EM waves are usually considered 3D and how generalizing forces on higher dimensions would result in inverse cube laws instead of inverse square laws.
In fact not just electromagnetism, but the weak and strong force as well are usually considered 3D only.
He then goes on explaining how things would be if they were not 3D (which isn't really what we are talking about for our purposes), though they in reality are. And as he notes, under these assumption the interactions between fundamental particles would be pretty different.
That is of course not to say that it is justified by physics for higher dimensional stuff to be superior to lower dimensional ones. Though, as I always enjoy mentioning, according to physics there is no level above High 3-A, so every system of higher levels is wrong by physics.
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.
You're misinterpreting the intention behind that statement a bit. Physically you can also calculate the energy of destroying a multiverse, but surely you don't suggest that we should list energy requirements for multiverse level, right?
That's because for our uses we don't rank multiverse level by physics anymore, which of course means that energy for these levels can't be calculated anymore.
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.
I mean, if the average density of their 3-D slices isn't 0 they have infinite mass. ┬»\_(Òâä)_/┬»
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.
Our basic idea regarding the size of an object is based on the approach to take base objects which's size we can easily calculate (For 2-D that could for example be all rectangles), lay out the thing we want to measure with them and then sum up the size of all the base objects we used to lay them out. You can lay out higher dimensional objects with lower dimensional ones just fine, it's just that the sum of the size of base objects you laid it out with goes towards infinity, meaning they have infinite size.
Even the most standard measure allows for the measurement of lower dimensional objects and the Hausdorff measure allows for the measurement of higher dimensional ones. (And is actually also a core to our understanding of 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.
You are talking about the 1D size of 1D objects. (Or in case of the radius a 1D path through an object) That has nothing to do with their 3D size. Literally nothing ever claimed these would be 0.
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.
Completely false equivalence. Nobody claimed any of that. In regards to what I said above: Rotate the base objects into any dimension you want, it neither makes a different to their size nor to how many you need to lay out an object with them.
And I can displace 1D lines in arbitrary directions just fine…
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.
Wrong. The surface of a ball with radius 1 is a subset of R^3 (It's the set {(x,y,z) in R^3|x^2+y^2+z^2=1}), but is definitely 2 dimensional.
Or to make it even more obvious. Take a 1D object, say the interval (0,1) = {x| 0 < x < 1}. Now add two coordinates, which are both constantly 0. You get {(x,y,z)| 0 < x < 1, y = z = 0}. This is a subset of R^3, but still a 1D line.
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.
Again, disagreed for reasons above. Also, nobody said anything of uncountably infinite larger, though that's a distinct difference.
In total I'm fine with reformulating our tiering system, we should just not do it for misinformed reasons.
The reason relates to the last point made in that section: Fictions deal with ideas of above multiversal cosmologies in vastly different ways. Ideally we should reformulate our system in a way that it doesn't depend strongly on a specific idea, which some fictions agree more with than others, but instead focus on it being scale for which systems roughly equate to which other systems in scale. In other words, we shouldn't have a system and try to squeeze in composite hierarchies. Instead, composite hierarchies should be part of the system. Furthermore whether the fiction itself treats something as higher level or not should be a general consideration.
In regards to the gist of the proposal: Yeah, I'm fine with it, with one exception.
Our own universes dimensional axis' aren't necessarily infinite, neither are our timelines axis'. It makes in my opinion no sense to start demanding infinite axis from higher onwards.
I can understand wanting to sort out the entirely empty microscopic higher dimensions that some physics theories use, but what we should demand is large extra dimensions, not infinite extra dimensions.
Personally I would be most happy to just have 1-A and 0 as beyond the system tiers and leave it as that. IMO it's over-segregating things into tiers, instead of just having each verse explain its power on the profile.
But that might be an opinion I'm alone with.
If I gotta chose I guess Option 2.
Something I can agree with is that we should do away with the idea that being beyond dimensional, and I mean even qualitatively being beyond dimensional, is (what today is) 1-A.
Especially if we bring cardinality into this, transcending space of any size translating to our high tier understanding of what that would mean in a verse is in my opinion makes vastly more assumptions about the fictions understanding than everything regarding higher dimensions. One has to consider that we are talking about transcending infinite infinite infinite (repeat this infinite times) infinite hierarchies and more. Such a thing needs much more evidence than just "is qualitatively above all space and dimensions" IMO.
In this context I wonder which kind of feats are envisioned for a tier like Low 1-A, 1-A and 0 in option 2.
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.
I have to disagree. There are euclidean Hilbert spaces of a dimensionality above any given cardinal number (note: any given. Not all at once!), which then have real valued coordinates.
One can certainly also define a few measures on them, though I don't know if any of those quantifies size in an intuitive fashion.
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).
I wish to point out that classes can only contain sets. "Classes" that could actually contain everything that has a certain property are paradox!
Proper Classes (which denote collections that are too big to be sets.
Technically a proper class doesn't necessarily need many members. It's only important that it can't be constructed by ZFC. Given, I don't really know an example for a class with few members either.
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)
Wait, now I'm confused. Why are you using classes if you are working with cardinals. For a start a non-set class has no cardinality regardless of its size.
And why does uncountable end at aleph one?!? All other cardinals are also uncountable?
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
Inaccessible cardinals makes things way too complicated. I have honestly no idea which practical consequences you envision that has. Just state where 1-A starts by giving the concrete cardinal, or better yet describe what the cardinal means in terms of difference of scale.
E.g. If N are the natural numbers and P() denotes the powerset, one could use something like |{N, P(N), P(P(N)), P(P(P(N))),...}|. In words that would equate to transcending an infinite hierarchy. (Whether in terms of points, order, or by replacing each with a space with correspondingly many dimensions)
Though I personally would try to put it into simpler terms than actually pulling out cardinals. If that doesn't end up specific enough to use one can still consider explaining it in reference to cardinals.
Firstly, it is extremely important to note that Dimensions are just Axis of Movement, nothing more and nothing less.
There are many definitions of dimensions used, depending on the objects one wishes to apply them to. The one you mention here is probably the one for vector spaces, where the description is pretty fitting. For other things it doesn't work quite as well.
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.
Wrong. One can use even just 1 number to specify position in the 2,3,4,5… dimensional plane.
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.
You are misinterpreting that article a bit. That article for example notes how EM waves are usually considered 3D and how generalizing forces on higher dimensions would result in inverse cube laws instead of inverse square laws.
In fact not just electromagnetism, but the weak and strong force as well are usually considered 3D only.
He then goes on explaining how things would be if they were not 3D (which isn't really what we are talking about for our purposes), though they in reality are. And as he notes, under these assumption the interactions between fundamental particles would be pretty different.
That is of course not to say that it is justified by physics for higher dimensional stuff to be superior to lower dimensional ones. Though, as I always enjoy mentioning, according to physics there is no level above High 3-A, so every system of higher levels is wrong by physics.
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.
You're misinterpreting the intention behind that statement a bit. Physically you can also calculate the energy of destroying a multiverse, but surely you don't suggest that we should list energy requirements for multiverse level, right?
That's because for our uses we don't rank multiverse level by physics anymore, which of course means that energy for these levels can't be calculated anymore.
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.
I mean, if the average density of their 3-D slices isn't 0 they have infinite mass. ┬»\_(Òâä)_/┬»
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.
Our basic idea regarding the size of an object is based on the approach to take base objects which's size we can easily calculate (For 2-D that could for example be all rectangles), lay out the thing we want to measure with them and then sum up the size of all the base objects we used to lay them out. You can lay out higher dimensional objects with lower dimensional ones just fine, it's just that the sum of the size of base objects you laid it out with goes towards infinity, meaning they have infinite size.
Even the most standard measure allows for the measurement of lower dimensional objects and the Hausdorff measure allows for the measurement of higher dimensional ones. (And is actually also a core to our understanding of 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.
You are talking about the 1D size of 1D objects. (Or in case of the radius a 1D path through an object) That has nothing to do with their 3D size. Literally nothing ever claimed these would be 0.
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.
Completely false equivalence. Nobody claimed any of that. In regards to what I said above: Rotate the base objects into any dimension you want, it neither makes a different to their size nor to how many you need to lay out an object with them.
And I can displace 1D lines in arbitrary directions just fine…
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.
Wrong. The surface of a ball with radius 1 is a subset of R^3 (It's the set {(x,y,z) in R^3|x^2+y^2+z^2=1}), but is definitely 2 dimensional.
Or to make it even more obvious. Take a 1D object, say the interval (0,1) = {x| 0 < x < 1}. Now add two coordinates, which are both constantly 0. You get {(x,y,z)| 0 < x < 1, y = z = 0}. This is a subset of R^3, but still a 1D line.
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.
Again, disagreed for reasons above. Also, nobody said anything of uncountably infinite larger, though that's a distinct difference.
In total I'm fine with reformulating our tiering system, we should just not do it for misinformed reasons.
The reason relates to the last point made in that section: Fictions deal with ideas of above multiversal cosmologies in vastly different ways. Ideally we should reformulate our system in a way that it doesn't depend strongly on a specific idea, which some fictions agree more with than others, but instead focus on it being scale for which systems roughly equate to which other systems in scale. In other words, we shouldn't have a system and try to squeeze in composite hierarchies. Instead, composite hierarchies should be part of the system. Furthermore whether the fiction itself treats something as higher level or not should be a general consideration.
In regards to the gist of the proposal: Yeah, I'm fine with it, with one exception.
Our own universes dimensional axis' aren't necessarily infinite, neither are our timelines axis'. It makes in my opinion no sense to start demanding infinite axis from higher onwards.
I can understand wanting to sort out the entirely empty microscopic higher dimensions that some physics theories use, but what we should demand is large extra dimensions, not infinite extra dimensions.
Personally I would be most happy to just have 1-A and 0 as beyond the system tiers and leave it as that. IMO it's over-segregating things into tiers, instead of just having each verse explain its power on the profile.
But that might be an opinion I'm alone with.
If I gotta chose I guess Option 2.
Something I can agree with is that we should do away with the idea that being beyond dimensional, and I mean even qualitatively being beyond dimensional, is (what today is) 1-A.
Especially if we bring cardinality into this, transcending space of any size translating to our high tier understanding of what that would mean in a verse is in my opinion makes vastly more assumptions about the fictions understanding than everything regarding higher dimensions. One has to consider that we are talking about transcending infinite infinite infinite (repeat this infinite times) infinite hierarchies and more. Such a thing needs much more evidence than just "is qualitatively above all space and dimensions" IMO.
In this context I wonder which kind of feats are envisioned for a tier like Low 1-A, 1-A and 0 in option 2.
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.
I have to disagree. There are euclidean Hilbert spaces of a dimensionality above any given cardinal number (note: any given. Not all at once!), which then have real valued coordinates.
One can certainly also define a few measures on them, though I don't know if any of those quantifies size in an intuitive fashion.
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).
I wish to point out that classes can only contain sets. "Classes" that could actually contain everything that has a certain property are paradox!
Proper Classes (which denote collections that are too big to be sets.
Technically a proper class doesn't necessarily need many members. It's only important that it can't be constructed by ZFC. Given, I don't really know an example for a class with few members either.
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)
Wait, now I'm confused. Why are you using classes if you are working with cardinals. For a start a non-set class has no cardinality regardless of its size.
And why does uncountable end at aleph one?!? All other cardinals are also uncountable?
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
Inaccessible cardinals makes things way too complicated. I have honestly no idea which practical consequences you envision that has. Just state where 1-A starts by giving the concrete cardinal, or better yet describe what the cardinal means in terms of difference of scale.
E.g. If N are the natural numbers and P() denotes the powerset, one could use something like |{N, P(N), P(P(N)), P(P(P(N))),...}|. In words that would equate to transcending an infinite hierarchy. (Whether in terms of points, order, or by replacing each with a space with correspondingly many dimensions)
Though I personally would try to put it into simpler terms than actually pulling out cardinals. If that doesn't end up specific enough to use one can still consider explaining it in reference to cardinals.
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@DonTalk Sera also suggestion an option three; which we don't change the tier names of High 1-B or below but slightly alter some definitions. But we add Low 1-A and High 1-A for explaining borders of Outerversal or beyond stacking higher infinities.
Sera EX said:
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i explained why it's confusing and will lead t o more confusion rather than simplifcation.Malomtek said:
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Only when measurint characters that are above outerversal such as Featherine, etc.Malomtek said:
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Only when measurint characters that are above outerversal such as Featherine, etc.
I really don't understand the definition above outerverse.
I really don't understand the definition above outerverse.
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Only when measurint characters that are above outerversal such as Featherine, etc.
I really don't understand the definition above outerverse.
Ultima hopefully will extrapolate on the tiering and their requirements.
I really don't understand the definition above outerverse.
Ultima hopefully will extrapolate on the tiering and their requirements.
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Surprised theres not much talk of Cantor or Cardinals going on.
Thats what the system was going to be based on according to the others.
Thats what the system was going to be based on according to the others.
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Actually, change my vote to option 3. Sera is right, this way we separate 1-A characters into diferent tiers while affecting less the tiers below it.
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I agree with @Nepuko and @SeraEx. I choose Option 3.
Nepuko said:
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now voting option 3, but how about characters who are above baseline but aren't infinite outerversal
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Also agree with option 3.
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OK then, which characters will be in revised Tier 0?
In my opinion, Azathoth,The Writer,The Creator,and the Anime teenager girl should be in New Tier 0.
In my opinion, Azathoth,The Writer,The Creator,and the Anime teenager girl should be in New Tier 0.
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I'm also for option 3 based on Sera's suggestion and DonTalkDT's input.
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Hmmm...
To clarify, if Option 3 is what we're going with, the only Tier that's getting substantially changed at all, from all of this, will be 1-A. Or am I missing something?
To clarify, if Option 3 is what we're going with, the only Tier that's getting substantially changed at all, from all of this, will be 1-A. Or am I missing something?
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well with a new option 3 available i'll go for that as well after seeing what it is
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I think we should wait until going all out on voting for options.
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So under @Sera's suggestions where would characters who view 1-A's as weak as dimensional characters like CM characters go? Just higher into "infinitely above 1-A"? In addition, wasn't it discussed in the Dark Tower thread that most of the tier 0s are where they are because they view 1-A as no different from the other tiers? Effectively transcending outervse hierarchies already?
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Infinite outerversal is translated into "above infinite outerversal or infinite outerversal hierarchy so its not merely "infinite above baseline" viewing another 1-A as fiction does not equate to infinite layers of outerversal or hierarchyLightbuster30 said:
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I don't know if that was your question, but characters above Outerversal Hierarchy would go to High 1-A if my suggestion goes through :
High 1-A : Above the Outerversal hierarchy </div> an creature above the outerversal hierarchy, but in their world there is another hierarchy, that character is 1-A or high 1-A?.
High 1-A : Above the Outerversal hierarchy </div> an creature above the outerversal hierarchy, but in their world there is another hierarchy, that character is 1-A or high 1-A?.
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