On the Many, Many Incoherences of the Tiering System

[Ultima_Reality]

That's not a well-defined notion of dimensionality, if it's not within the theory and not something external to it that you can point to and which we can investigate the limits of. Which would then loop us back to my earlier post about how something so general that it can apply to any arbitrary extensions of axioms, should also be able to apply to R>F differences.

You responded to that by beginning discussion about Cartesian Products, but here I'm gesturing at "would it ever be possible to add axioms to ZFC such that you cannot take the Cartesian Product of certain newly-introduced ordinals".

That doesn't necessarily make it ill-defined. For example, "dimension" can be simply defined as the cardinality of a vector space's basis (i.e. How many linearly independent vectors the space has), and that's in fact the definition that our current usage of them aligns to. "Dimensionality" is indeed a pretty well-defined thing under such terms.

I believe what you're referring to might find its closest approximation in axioms that are inconsistent with the Axiom of Choice. And as you might probably know, denying the Axiom of Choice (i.e. Literally just the statement "The union of non-empty sets is non-empty") causes all hell to break loose, everywhere in the Universe of Sets.

It depends on which definition of "dimensionality" you use, since that's a very loose and arbitrary term.

Without further in-verse context, I'd just cap it at standard ones used within real-world theories, R^R. And I believe that's where our Tiering System currently limits it; didn't we, in the past year, have a thread about this topic where we came to that conclusion? That you needed some sufficient amount of statements, but at some points, you could generalise to Low 1-A/1-A without infinite dimensions?

What exactly do you mean by "loose and arbitrary"? I wouldn't say "The quality of having dimensions" is at all loose once you already have a notion of what "Dimension" is.

 

[Agnaa]

That doesn't necessarily make it ill-defined. For example, "dimension" can be simply defined as the cardinality of a vector space's basis (i.e. How many linearly independent vectors the space has), and that's in fact the definition that our current usage of them aligns to. "Dimensionality" is indeed a pretty well-defined thing under such terms.

Then, leading from my earlier posts, I would then seek to construct an extension of ZFC, that invokes an analogue of "cardinality", that functions largely as we expect, but is distinct. Just in the same way that you posit there being differences in size/power/AP past 1-A that function largely as we expect.

If this is usable, it would represent that R>F would be able to be squeezed into dimensions in the same way.

If it's not usable, it would represent an extension of ZFC that isn't relevant to "above all dimensions" talk.

I believe what you're referring to might find its closest approximation in axioms that are inconsistent with the Axiom of Choice. And as you might probably know, denying the Axiom of Choice (i.e. Literally just the statement "The union of non-empty sets is non-empty") causes all hell to break loose, everywhere in the Universe of Sets.

As far as I'm aware, this isn't true? ZF is used for a lot of mathematical theorems, it's not some chaotic nonsense out of which nothing cohesive can be derived.

What exactly do you mean by "loose and arbitrary"? I wouldn't say "The quality of having dimensions" is at all loose once you already have a notion of what "Dimension" is.

I don't think what you said above is always what is meant by "dimension". I think that sometimes, people also include certain allowable transformations that can be applied to those dimensions, with equations for how those would turn out, that would break if arbitrarily large cardinals were chucked into them. I think this is why we talk about dimensions stopping at R^R on the wiki.

 

[Ultima_Reality]

Then, leading from my earlier posts, I would then seek to construct an extension of ZFC, that invokes an analogue of "cardinality", that functions largely as we expect, but is distinct. Just in the same way that you posit there being differences in size/power/AP past 1-A that function largely as we expect.

If this is usable, it would represent that R>F would be able to be squeezed into dimensions in the same way.

If it's not usable, it would represent an extension of ZFC that isn't relevant to "above all dimensions" talk.

I don't believe that's really a useable notion, no. I don't really know how you would even begin to define such a thing. Unless one of us goes ask about this in Math Stack Exchange or MathOverflow, or something.

As far as I'm aware, this isn't true? ZF is used for a lot of mathematical theorems, it's not some chaotic nonsense out of which nothing cohesive can be derived.

Never said it was utterly nonsensical. But it does lack many of the notions that are fundamental to us. If you go "~AC", then R (Or any uncountable ordinal) can be a countable union of countable sets. There can be cardinals that are simply incomparable to each other. An union of non-empty sets, of course, is not necessarily non-empty. And so on.

I don't think what you said above is always what is meant by "dimension". I think that sometimes, people also include certain allowable transformations that can be applied to those dimensions, with equations for how those would turn out, that would break if arbitrarily large cardinals were chucked into them. I think this is why we talk about dimensions stopping at R^R on the wiki.

What exactly is the basis for that thought? Every sensible definition of dimension would, when transcended, result in transcendence over all of ZFC's cardinals, and R^R doesn't provide a cap to that. So when you say that, you're either not talking about "dimension" at all or be appealing to a very obscure (And thus nonstandard) definition of the term.

 

[Agnaa]

I don't believe that's really a useable notion, no. I don't really know how you would even begin to define such a thing. Unless one of us goes ask about this in Math Stack Exchange or MathOverflow, or something.

I mean, you're already asserting that there IS an extension of size/power/etc. that functions outside of ZFC.

I think the only room to contest would be whether ZFC can be extended into something like that.

And so, I think regardless, we can say that your definition of "all dimensions" only extends to "all mathematical systems which are similar enough to ZFC for Cartesian Products to be able to apply to their cardinals".

I'd really prefer we take this compromise, since I don't want us getting into the weeds of whether ZFC can be extended into such a system or not.

What exactly is the basis for that thought? Every sensible definition of dimension would, when transcended, result in transcendence over all of ZFC's cardinals, and R^R doesn't provide a cap to that. So when you say that, you're either not talking about "dimension" at all or be appealing to a very obscure (And thus nonstandard) definition of the term.

I don't think every sensible definition would, and I just provided one that I don't think would.

Like, all I'm really doing here is to referring back to the reason why we chose R^R in the first place. So if you have an issue with that reason, please try to tackle that more clearly than saying "there's no basis" or "that's not sensible".

 

[Ultima_Reality]

I mean, you're already asserting that there IS an extension of size/power/etc. that functions outside of ZFC.

I think the only room to contest would be whether ZFC can be extended into something like that.

And so, I think regardless, we can say that your definition of "all dimensions" only extends to "all mathematical systems which are similar enough to ZFC for Cartesian Products to be able to apply to their cardinals".

I'd really prefer we take this compromise, since I don't want us getting into the weeds of whether ZFC can be extended into such a system or not.

Honestly that seems to be more of a semantical compromise than anything else, since it stems from the fact you're uncertain if "all mathematical systems which are similar enough to ZFC for Cartesian Products to be able to apply to their cardinals" really constitutes "All dimensionality," while I am quite certain that it does. So, sure, I'll take that. Cartesian Products are fundamentally how dimensions as we treat them are structured, anyway.

I don't think every sensible definition would, and I just provided one that I don't think would.

Like, all I'm really doing here is to referring back to the reason why we chose R^R in the first place. So if you have an issue with that reason, please try to tackle that more clearly than saying "there's no basis" or "that's not sensible".

The issue is pretty much that "certain allowable transformations that can be applied to those dimensions, with equations for how those would turn out, that would break if arbitrarily large cardinals were chucked into them" is not a definition of "dimension" to begin with.
R^R was picked because 2^c is the maximum cardinality of a space that's both Separable and Hausdorff, both of which are properties that are present in the usual modelings of the spacetime manifold in physics, but that doesn't really have anything to do with dimensions at all, just with stuff about arrangements of points in space.

 

[DarkDragonMedeus]

For clarity's sake: I never said comparisons between two different things are false equivalences. If you say "X is superior to Y," then you're still making a comparison between X and Y. Saying X and Y are equal due to sharing some superficial similarity, however, is indeed a false equivalence. That gets into the topic of "Does X need to be equivalent to some number or volume to be superior to Y at all?", but that's something still being discussed.

---

As for the other stuff: I've already answered all of these questions before and my whole point in this thread is that qualitative superiorities (So, R>F and Type 2 BDE) are 1-A regardless of whether or not infinite dimensions are mentioned in the verse, so I feel no need to repeat myself at length here.

That said, to address DDM now: One thing I have to note is that I don't think "genuine" R>F Transcendences require -verbal- statements of Type 2 BDE to qualify for 1-A under these revamps. However, there does need to be some very good indication that the beings in the higher layers exist above the dimensions of the lower ones.
So, like I mentioned before: An example would be a case where the higher being is, literally, an author of books, and not a cosmic entity simply perceived as an author, which would mean that their layer has its own set of dimensions exclusively contained in it, and thus isn't really related to other layers by dimensional differences at all. In a way where even lower-dimensional things in their world would be above whatever exists in a lower layer.

Are you fine with that? @DarkDragonMedeus

I might have slightly worded the detail wrong yeah. I didn't mean to suggest the statement needed to be said, only I paraphrased the part where you basically said "That if someone isn't beyond dimensional existence then there can't really be a true evidence of a R>F level of qualitive superiority. But the author comparison statement does make sense and looks good to me.

 

[Agnaa]

The issue is pretty much that "certain allowable transformations that can be applied to those dimensions, with equations for how those would turn out, that would break if arbitrarily large cardinals were chucked into them" is not a definition of "dimension" to begin with.
R^R was picked because 2^c is the maximum cardinality of a space that's both Separable and Hausdorff, both of which are properties that are present in the usual modelings of the spacetime manifold in physics, but that doesn't really have anything to do with dimensions at all, just with stuff about arrangements of points in space.

I guess that's not a definition of dimension? In the same way that "our current physics" isn't a definition of "physics", but when a piece of fiction still gives a vague "above all dimensions" claim, I'd default that to one with similar properties to IRL, so separable Hausdorff spaces or smth.

 

[Ultima_Reality]

I guess that's not a definition of dimension? In the same way that "our current physics" isn't a definition of "physics", but when a piece of fiction still gives a vague "above all dimensions" claim, I'd default that to one with similar properties to IRL, so separable Hausdorff spaces or smth.

That still doesn't really work, imo, since the point is that because these two properties are separate topological things that don't impact on any definition of "dimension" whatsoever, exceeding the limits of either of them doesn't really... Have anything to do with being "Above dimensions" either. You can have Non-Hausdorff spaces that only differ from Hausdorff spaces because of really silly things (A line with two origins is a classical example of one, for instance).

In general, if a verse says something is "Beyond dimensionality" and means it in the sense we're talking about here, it makes the most sense to say the verse is talking about a standard and actual definition of the word. In this case, that'd be "The number of points required to specify a location" or "Number of directions" or some equivalent thing, all of which are totally unchanged by whether a space is Hausdoff and Separable or not.

 

[Agnaa]

That still doesn't really work, imo, since the point is that because these two properties are separate topological things that don't impact on any definition of "dimension" whatsoever, exceeding the limits of either of them doesn't really... Have anything to do with being "Above dimensions" either. You can have Non-Hausdorff spaces that only differ from Hausdorff spaces because of really silly things (A line with two origins is a classical example of one, for instance).

In general, if a verse says something is "Beyond dimensionality" and means it in the sense we're talking about here, it makes the most sense to say the verse is talking about a standard and actual definition of the word. In this case, that'd be "The number of points required to specify a location" or "Number of directions" or some equivalent thing, all of which are totally unchanged by whether a space is Hausdoff and Separable or not.

I think "impact the definition" is a weird framing, since they're properties of the typical examples of them that we model and experience.

And there being some differences that aren't really size-related doesn't seem too relevant either, since you're latching onto the differences that are size-related.

Is the difference between us just "Above dimensions means above dimensions, as we typically know and experience them" compared to "Above dimensions means above the generalised root definition of dimensions, whether how we typically know and experience them or not"?

Given the general nature of the fictional series we're talking about, I'd expect the typical baggage to be a part of it. I don't think most authors invoking that even know enough about the difference to try to mean the latter instead of the former.

But idk if this is something we'll be able to talk into an agreement on.

 

[Antvasima]

I still support the fundamental principle of Ultima's revision, as long as it focuses on solving my concerns about our current system that I tried to explain to Ultima and DontTalk in private.

Will it do so, Ultima?

However, as I think I have stated previously, my support is also contingent on that I receive assurances that we will keep all of our current tiering system definitions with different titles than currently, in addition to tiers for Ultima's new definitions; and I also want assurances that we take precautions by installing very good safeguard definitions so lots of characters do not reach our highest tiers via unreliable claims or statements, for example.

I also definitely do not want us to open the doors for allowing the creation of top tiered pages featuring mostly irrelevant self-insert characters such as Grant Morrison, Akira Toriyama, and otherwise. That should still be prohibited. We should focus on featuring fiction, not pretend that real world humans are omnipotent entities via their physical bodies who can go around beating up any characters that they want to. That has far too strong delusional power-tripping Suggsverse wibes for my tastes.

 

[Agnaa]

From what I've heard, it doesn't sound like it'd contain the current definitions in addition to Ultima's new ones. It sounds like it will combine every character who reaches 1-A/High 1-A/0 but is still bound by mathematics into a lower tier, and add new tiers beyond that purview for reality-fiction differences, being beyond all dimensions, and being more real.

I don't think these changes would make such irrelevant self-inserts suddenly indexable, considering our rules against that, but it would make most of them 1-A if they do cross the threshold of relevancy.

But I think Ultima and I aren't too far off being able to finish our discussion and write up summaries for evaluation. If Ultima's not too busy, I think we could do so by the end of the year.

 

[Antvasima]

Well, the way I understood things previously, I was given assurances by Ultima that we would not lose the precision of our current tiers by mashing them together with each other.

I just want to make certain regarding this and the other issues of concern that I mentioned above.

Also, I want us to continue to only make exceptions to the self-insert rule if it genuinely is absolutely necessary, such as in the case of Andrew Hussie. I definitely do not want us to do a fanon mishmash that turns Grant Morrison into the supreme being of DC Comics again, for example.

 

[Ultima_Reality]

From what I've heard, it doesn't sound like it'd contain the current definitions in addition to Ultima's new ones. It sounds like it will combine every character who reaches 1-A/High 1-A/0 but is still bound by mathematics into a lower tier, and add new tiers beyond that purview for reality-fiction differences, being beyond all dimensions, and being more real

Not quite. I've been planning to introduce a few more tiers/tier modifiers in order to differentiate between levels of infinity that are notably far apart from each other (Or are differentiated from each other by certain reasons). But that's likely something to discuss after the basic concepts are settled, imo.

Also, I want us to continue to only make exceptions to the self-insert rule if it genuinely is absolutely necessary, such as in the case of Andrew Hussie. I definitely do not want us to do a fanon mishmash that turns Grant Morrison into the supreme being of DC Comics again, for example.

I'm not particularly sympathetic to gag feats and most author avatar characters in general, as I've said at the beginning of the thread, so I don't believe this thread would make things we consider unindexable suddenly valid to index (And I can see a few characters losing their positions due to it, as well)

 

[Antvasima]

Thank you for your reply. I would appreciate responses to the other questions that I asked about above as well.

 

[Ultima_Reality]

I think "impact the definition" is a weird framing, since they're properties of the typical examples of them that we model and experience.

And there being some differences that aren't really size-related doesn't seem too relevant either, since you're latching onto the differences that are size-related.

Is the difference between us just "Above dimensions means above dimensions, as we typically know and experience them" compared to "Above dimensions means above the generalised root definition of dimensions, whether how we typically know and experience them or not"?

Given the general nature of the fictional series we're talking about, I'd expect the typical baggage to be a part of it. I don't think most authors invoking that even know enough about the difference to try to mean the latter instead of the former.

But idk if this is something we'll be able to talk into an agreement on.

"Dimensions as we experience them" is a pretty bad benchmark, I'd say, since by that logic you could say 4-dimensional things qualify for being above dimensionality, which is obviously silly. "Dimensions as we know them" (Which I assume refers to modelling) also doesn't really meet a cap at R^R, either, since then the definition of that is, in fact, just what I said above. The nature of dimensions doesn't change when you get past a certain size (And in fact you can have Hausdorff Spaces of any size, too, all defined over the field of the reals)

This also seems to be where our experiences with fiction diverge. I'd say that cases of what I'd consider Type 2 BDE are, generally speaking, ones where "Beyond dimensions" is convertible to "Above space," where "space" just means the general "A continuum where numbers are used to specify locations," which is also not exactly something that meets its cap at R^R or what have you.
I wouldn't say it makes sense to equate a timeless, spaceless void that's depicted as containing and dwarfing all existence to "Dimensional spaces with a slightly weird topology that doesn't really impact on what dimensions are or what space is."

 

[Ultima_Reality]

Thank you for your reply. I would appreciate responses to the other questions that I asked about above as well.

I assume you're referring to your concern regarding the highest tiers having "safeguards" to them, since that's the only question I seem to have missed. With regards to that: I have no problem with the high tiers having solid requirements that prevent unwarranted upgrades and the like.

Really, my problems only arise when those requirements turn into something ridiculous like "The verse needs to have infinite dimensions or an insinuation thereof [i.e. "Even if those things existed, they'd be below this guy"] to be 1-A, no matter how impressive of a definition it gives or how robust its metaphysics are." This treatment of cardinal numbers as the pinnacle of pinnacles and of anything else as fallacious is not something I'm at all fond of.

 

[Antvasima]

I assume you're referring to your concern regarding the highest tiers having "safeguards" to them, since that's the only question I seem to have missed. With regards to that: I have no problem with the high tiers having solid requirement that prevent unwarranted upgrades and the like.

Really, my problems only arise when those requirements turn into something ridiculous like "The verse needs to have infinite dimensions or an insinuation thereof [i.e. "Even if those things existed, they'd be below this guy"] to be 1-A, no matter how impressive of a definition it gives or how robust its metaphysics are." This treatment of cardinal numbers as the pinnacle of pinnacles and of anything else as fallacious is not something I'm at all fond of.

Okay. That seems reasonable. Thank you for your reply.

The only remaining question that I would like a confirmation regarding is that we will not suddenly have to compress our current tier definitions. We need to create more tiers when your revision is eventually applied, as well as move them around a bit, rather than merge them together.

 

[Ultima_Reality]

Okay. That seems reasonable. Thank you for your reply.

The only remaining question that I would like a confirmation regarding is that we will not suddenly have to compress our current tier definitions. We need to create more tiers when your revision is eventually applied, as well as move them around a bit, rather than merge them together.

I wouldn't have a problem with that. Granted, our current Tier 0 will likely have to go, in one way or another, since it quite simply adds no new definitions to the Tiering System whatsoever. It's just "Do High 1-A but again." Having multiple tiers with the exact same definition just seems redundant to me.

 

[Agnaa]

"Dimensions as we experience them" is a pretty bad benchmark, I'd say, since by that logic you could say 4-dimensional things qualify for being above dimensionality, which is obviously silly.

I don't think so. Just as how I don't think "outside of time" means that they can't participate in any more complex forms of or meta analogues for time. In fact, we see the latter quite a lot in fiction.

"Dimensions as we know them" (Which I assume refers to modelling) also doesn't really meet a cap at R^R, either, since then the definition of that is, in fact, just what I said above. The nature of dimensions doesn't change when you get past a certain size (And in fact you can have Hausdorff Spaces of any size, too, all defined over the field of the reals)

You agreed with the idea that separable Hausdorff spaces do, and I already agreed with the idea that a more broad definition of dimensions goes further. Repeating such adds nothing to the conversation.

This also seems to be where our experiences with fiction seem to diverge. I'd say that cases of what I'd consider Type 2 BDE are, generally speaking, ones where "Beyond dimensions" is convertible to "Above space," where "space" just means the general "A continuum where numbers are used to specify locations," which is also not exactly something that meets its cap at R^R or what have you.

This ain't just Type 2 BDE, it's all forms of qualitative differences.

I wouldn't say it makes sense to equate a timeless, spaceless void that's depicted as containing and dwarfing all existence to "Dimensional spaces with a slightly weird topology that doesn't really impact on what dimensions are or what space is."

I know? When I last talked about them I said they were not relevant.

And there being some differences that aren't really size-related doesn't seem too relevant either

I would equate a timeless, spaceless void that's depicted as containing and dwarfing all existence to either "A place where spacetime hax doesn't operate, which can be destroyed by attacks uncountably infinitely more powerful than the existence that is being dwarfed", if there's no evidence of hierarchy bypassing, or "As before, but it requires attacks uncountably infinitely more powerful than a structure with R^R dimensions".

 

[Ultima_Reality]

I don't think so. Just as how I don't think "outside of time" means that they can't participate in any more complex forms of or meta analogues for time. In fact, we see the latter quite a lot in fiction.

You agreed with the idea that separable Hausdorff spaces do, and I already agreed with the idea that a more broad definition of dimensions goes further. Repeating such adds nothing to the conversation

I know? When I last talked about them I said they were not relevant.

When I mentioned "Dimensional spaces with a slightly weird topology that doesn't really impact on what dimensions are or what space is," I did in fact mean spaces that large, as well. Going past a cardinality of 2^c doesn't bring you to a "meta analogue" of either space or time.
So, for clarification's sake, I ask you: Can you tell me, in detail, what exactly you think changes past uncountably infinite dimensions that makes you shift definitions of "dimension"? Especially when the factors you bring up have nothing to do with dimensionality at all.

This ain't just Type 2 BDE, it's all forms of qualitative differences.

That seems related to your last point, so I'll clarify this one first: Why exactly do you say that? You've already accepted that "ZFC and all its large cardinal extensions" is a coherent thing to transcend, to the point where you're only warry of calling it "All dimensionality" because "It may be possible to define systems where cartesian products of high enough ordinals are undefinable." Coordinates (Numbers denoting locations, which I was referring to) and Cartesian Products are pretty tightly bound, so why the backpedal there?

 

[Agnaa]

When I mentioned "Dimensional spaces with a slightly weird topology that doesn't really impact on what dimensions are or what space is," I did in fact mean spaces that large, as well. Going past a cardinality of 2^c doesn't bring you to a "meta analogue" of either space or time.
So, for clarification's sake, I ask you: Can you tell me, in detail, what exactly you think changes past uncountably infinite dimensions that makes you shift definitions of "dimension"? Especially when the factors you bring up have nothing to do with dimensionality at all.

The applicability of certain transformations, the accuracy of certain equations, the truth of certain correspondences.

If it acts differently to the dimensions we're familiar with in those ways, I think it's fair enough to say it's not really the same.

That seems related to your last point, so I'll clarify this one first: Why exactly do you say that? You've already accepted that "ZFC and all its large cardinal extensions" is a coherent thing to transcend, to the point where you're only warry of calling it "All dimensionality" because "It may be possible to define systems where cartesian products of high enough ordinals are undefinable." Coordinates (Numbers denoting locations, which I was referring to) and Cartesian Products are pretty tightly bound, so why the backpedal there?

If you're asking why the backpedal from "ZFC and its large cardinal extensions is a coherent definition of being beyond all dimensions" and "R^R is a reasonable default definition of being beyond all dimensions", I'd point to the words I've bolded.

 

[Ultima_Reality]

Well, there has been a slight delay. Sorry, everyone. Christmas and all, so, you know how it is.

The applicability of certain transformations, the accuracy of certain equations, the truth of certain correspondences.

If it acts differently to the dimensions we're familiar with in those ways, I think it's fair enough to say it's not really the same.

It's not "fair enough" at all when those things don't actually have anything to do with the underlying notion of dimensionality. At that point you're pretty much just inventing a definition for yourself based on unrelated things.

It's one thing to say "There are several avaliable definitions for X that we can pick. In the absence of evidence indicating others, we should go with the lowball", and another to just say "Let's invent our own definition of X based on random things and then use that one as the standard." The fact you can go on Google and look at several ways to define the dimension of a space, none of which are remotely close to what you're talking about right now, should be pretty telling.

If you're asking why the backpedal from "ZFC and its large cardinal extensions is a coherent definition of being beyond all dimensions" and "R^R is a reasonable default definition of being beyond all dimensions", I'd point to the words I've bolded.

Not really what I asked. I'm asking why exactly is it that you think transcending the notion of space as in "A continuum of numbers that are used to indicate a physical location" (i.e. Coordinates) encompasses all possible qualitative differences. I wasn't talking about "space" in its most generic possible form as "A set of things," if that's what you were thinking.

Onto more pressing matters:

I would equate a timeless, spaceless void that's depicted as containing and dwarfing all existence to either "A place where spacetime hax doesn't operate, which can be destroyed by attacks uncountably infinitely more powerful than the existence that is being dwarfed", if there's no evidence of hierarchy bypassing, or "As before, but it requires attacks uncountably infinitely more powerful than a structure with R^R dimensions".

Yeah, that doesn't makes any sense, because that depiction is, in-and-of-itself, the evidence of the "hierarchy-bypassing." If a thing doesn't have volume, you can't really equalize it to a volume.

And here we come to how you seem to make a weird distinction between being "Above dimensionality" and being "Above dimensions" in the sense of basic Type 2 BDE, seeing as you think equating the latter to a dimensional jump is fine, but don't think the same of the former. What's the difference being made here, exactly? Because there isn't any.

 

[Agnaa]

It's not "fair enough" at all when those things don't actually have anything to do with the underlying notion of dimensionality. At that point you're pretty much just inventing a definition for yourself based on unrelated things.

It's one thing to say "There are several avaliable definitions for X that we can pick. In the absence of evidence indicating others, we should go with the lowball", and another to just say "Let's invent our own definition of X based on random things and then use that one as the standard." The fact you can go on Google and look at several ways to define the dimension of a space, none of which are remotely close to what you're talking about right now, should be pretty telling.

Not the underlying notion of it, but the instances of it which we're familiar with.

I don't think we have to go with the underlying notions, which most aren't familiar with the distinctions of.

I'd expect that when people ask how things work in certain-dimensional spaces, they don't always get the answer of "We don't know, because 'dimension' has no ascribed properties or transformations by default, it's just a bunch of points on an axis."

Not really what I asked. I'm asking why exactly is it that you think transcending the notion of space as in "A continuum of numbers that are used to indicate a physical location" (i.e. Coordinates) encompasses all possible qualitative differences. I wasn't talking about "space" in its most generic possible form as "A set of things," if that's what you were thinking.

I don't understand the way you're phrasing things. I don't know what you mean by me thinking that "transcending the notion of space encompasses all possible qualitative differences". Could you point me to the post of mine that gave you this idea, so I could see that idea in my words?

Yeah, that doesn't makes any sense, because that depiction is, in-and-of-itself, the evidence of the "hierarchy-bypassing." If a thing doesn't have volume, you can't really equalize it to a volume.

No, I do not think that we should rate every single aspatiotemporal character's AP/Dura as either Unknown or 1-A or above, when their feats of interacting with reality are consistently 9-A. And I don't think such 9-A feats would contradict them being aspatiotemporal either.

And sometimes when we're talking about things across verses, we do have to equalize things that are "Above all X" to "X". The strongest human in one verse can be fodder in another. An undefeatable technique can be easily resisted in another.

EDIT: Since it has come to my attention that this section is unclear, I should clarify. Despite the conversation having focused on Type 2 BDE, I'm taking a brief detour into Type 1 BDE, to demonstrate a contradiction with the way you're suggesting to treat Type 2 BDE. If you agree that we can equalize something "without volume" to something with a volume for Type 1, you should agree that we can do that for Type 2, at least when, in the case of Type 2, the volume-analogue we're equalizing to is above the volume that's transcended in the character's original setting. And if you don't allow that for Type 1, I'd view your suggested system as quite absurd.

And here we come to how you seem to make a weird distinction between being "Above dimensionality" and being "Above dimensions" in the sense of basic Type 2 BDE, seeing as you think equating the latter to a dimensional jump is fine, but don't think the same of the former. What's the difference being made here, exactly? Because there isn't any.

Whether it can reasonably extend to all dimensions, for a given definition of that, or whether it only applies to the dimensions instantiated in the verse.

 

[Antvasima]

I wouldn't have a problem with that. Granted, our current Tier 0 will likely have to go, in one way or another, since it quite simply adds no new definitions to the Tiering System whatsoever. It's just "Do High 1-A but again." Having multiple tiers with the exact same definition just seems redundant to me.

That seems fine to me in that case. I just don't want any drastic changes in this regard.

 

[Ultima_Reality]

Not the underlying notion of it, but the instances of it which we're familiar with.

I don't think we have to go with the underlying notions, which most aren't familiar with the distinctions of.

I'd expect that when people ask how things work in certain-dimensional spaces, they don't always get the answer of "We don't know, because 'dimension' has no ascribed properties or transformations by default, it's just a bunch of points on an axis."

The vast majority of people think of spatial dimensions as either "Directions of space," "The minimum number of points required to specify a location" or "A measurable extent of some kind, like length, breadth, height and width."

I don't think "Well, that's what most people think of when they hear the word" is a particularly good argument to begin with, either for or against me, but if you want to use it, unironically saying "Actually, most people would think of a dimensional space as a set with the topological properties of being both Separable and Hausdorff" is... a pretty weird way to go about it, to say the least.

I don't understand the way you're phrasing things. I don't know what you mean by me thinking that "transcending the notion of space encompasses all possible qualitative differences". Could you point me to the post of mine that gave you this idea, so I could see that idea in my words?

.

No, I do not think that we should rate every single aspatiotemporal character's AP/Dura as either Unknown or 1-A or above, when their feats of interacting with reality are consistently 9-A. And I don't think such 9-A feats would contradict them being aspatiotemporal either.

And sometimes when we're talking about things across verses, we do have to equalize things that are "Above all X" to "X". The strongest human in one verse can be fodder in another. An undefeatable technique can be easily resisted in another.

EDIT: Since it has come to my attention that this section is unclear, I should clarify. Despite the conversation having focused on Type 2 BDE, I'm taking a brief detour into Type 1 BDE, to demonstrate a contradiction with the way you're suggesting to treat Type 2 BDE. If you agree that we can equalize something "without volume" to something with a volume for Type 1, you should agree that we can do that for Type 2, at least when, in the case of Type 2, the volume-analogue we're equalizing to is above the volume that's transcended in the character's original setting. And if you don't allow that for Type 1, I'd view your suggested system as quite absurd.

Yeah, you can't equate the "size" of a character with Type 1 BDE to any volume, since they have no size at all. You can equate their power output to a volume, though, since that's unrelated to their sizelessness in the case of Type 1.
Ironically, that's a point I already anticipated in the OP, so to restate it: A character with Type 1 BDE can be 6-B for destroying Britain. They can't be 6-B for being as large as Britain, though, since that contradicts their alleged lack of dimensions. So the absurdity you're trying to demonstrate doesn't exist.

That analogy you made is also pretty terrible (Though I imagine the approachable set-up of it got you points with some of the audience). Being human is an ill-defined characteristic that doesn't inherently say anything about you, especially in fiction, unlike dimensions. Same with being an unbeatable technique.

Anyway, to go further: A higher-dimensional volume isn't equated to an uncountably infinite superiority for random reasons, as you know. It's treated as such because that's simply how volumes work when going up dimensions.
Since those mechanics can't apply to something with no volume at all, then, obviously, the claim "Type 2 BDE can be equated to a dimensional difference" is false. And this destroys your previous claim that, actually, the equalizations we do aren't shoddy compromises at all, and are perfectly reasonable lowballs.

Whether it can reasonably extend to all dimensions, for a given definition of that, or whether it only applies to the dimensions instantiated in the verse.

Ontop of the other points I've made, an argument for that is already up there: If a character is in a verse with a strictly finite cosmology (Say, a 5-B-sized universe), and then is stated to be "Above all finite things" (With no caveat), then treating them as finitely above the rest of the verse is absurd, since that would mean they are, themself, a finite thing. Basic application of Russell's Paradox: Something above all things X cannot be a X.
The lowest reasonable tier for that character would be High 3-A, and yet your insistence on applying statements such as these only to things that physically exist would mean they're only slightly higher into 5-B, which is plainly silly.

 

[Agnaa]

The vast majority of people think of spatial dimensions as either "Directions of space," "The minimum number of points required to specify a location" or "A measurable extent of some kind, like length, breadth, height and width."

I don't think "Well, that's what most people think of when they hear the word" is a particularly good argument to begin with, either for or against me, but if you want to use it, unironically saying "Actually, most people would think of a dimensional space as a set with the topological properties of being both Separable and Hausdorff" is... a pretty weird way to go about it, to say the least.

I don't think they'd say that, but I think they'd implicitly assume that. Just as how I'd think that the vast majority of people, when talking about "space", would implicitly be thinking of something that operates as a Euclidean space.

Yeah, you can't equate the "size" of a character with Type 1 BDE to any volume, since they have no size at all. You can equate their power output to a volume, though, since that's unrelated to their sizelessness in the case of Type 1.
Ironically, that's a point I already anticipated in the OP, so to restate it: A character with Type 1 BDE can be 6-B for destroying Britain. They can't be 6-B for being as large as Britain, though, since that contradicts their alleged lack of dimensions. So the absurdity you're trying to demonstrate doesn't exist.

That analogy you made is also pretty terrible (Though I imagine the approachable set-up of it got you points with some of the audience). Being human is an ill-defined characteristic that doesn't inherently say anything about you, especially in fiction, unlike dimensions. Same with being an unbeatable technique.

Anyway, to go further: A higher-dimensional volume isn't equated to an uncountably infinite superiority for random reasons, as you know. It's treated as such because that's simply how volumes work when going up dimensions.
Since those mechanics can't apply to something with no volume at all, then, obviously, the claim "Type 2 BDE can be equated to a dimensional difference" is false. And this destroys your previous claim that, actually, the equalizations we do aren't shoddy compromises at all, and are perfectly reasonable lowballs.

Just as you'd say that the absurdity I'm trying to demonstrate with Type 1 BDE doesn't exist, I'd say the time for Type 2 BDE.

I'm not trying to assign that size to something beyond volume, I'm trying to assign that necessary power to destroy to something beyond volume. That's why I used terms like "uncountably infinitely more powerful" or "uncountably infinite power increase".

And I guess the analogy isn't really needed now, we can put off the "unbeatable technique" stuff unless/until we get onto the topic of omnipotence/apophatic theology.

Ontop of the other points I've made, an argument for that is already up there: If a character is in a verse with a strictly finite cosmology (Say, a 5-B-sized universe), and then is stated to be "Above all finite things" (With no caveat), then treating them as finitely above the rest of the verse is absurd, since that would mean they are, themself, a finite thing. Basic application of Russell's Paradox: Something above all things X cannot be a X.
The lowest reasonable tier for that character would be High 3-A, and yet your insistence on applying statements such as these only to things that physically exist would mean they're only slightly higher into 5-B, which is plainly silly.

I think this is a weird argument to make, but I think the root of you making it is in thinking I meant to equalize such things to a certain "size" rather than a certain "power". Let me know whether you'd still want me responding to this in light of that.

 

[Ultima_Reality]

I don't think they'd say that, but I think they'd implicitly assume that. Just as how I'd think that the vast majority of people, when talking about "space", would implicitly be thinking of something that operates as a Euclidean space.

Hardly. I doubt you yourself can even tell me what exactly a space being "Separable" means, and even if you could I doubt you'd know how it helps form the mysterious-and-yet-supposedly-popular notion of "dimensionality" that you claim exists. The Hausdorff property is slightly closer to the layman's mind (Since it literally just means "Every single point in a space is contained in a neighborhood of points that's separate from the neighborhoods of other points"), but even that one is hardly a fundamental property of what people often think of as "dimensionality."

As said, I dislike arguments of this style (Appeal to popular knowledge and etc), but even if we were to use it, that line of thought far more easily supports me, not you. "Actually most people would implicitly think [p.s They wouldn't] of these obscure topological properties when thinking of dimensional spaces, so there is a notion of dimensionality that is constrained to them" has as much impact as "Most people instinctively imagine 3-dimensional space when thinking of dimensionality at all, so there is a notion of dimensionality that's constrained to 3-D space alone!"

Just as you'd say that the absurdity I'm trying to demonstrate with Type 1 BDE doesn't exist, I'd say the time for Type 2 BDE.

I'm not trying to assign that size to something beyond volume, I'm trying to assign that necessary power to destroy to something beyond volume. That's why I used terms like "uncountably infinitely more powerful" or "uncountably infinite power increase".

I think this is a weird argument to make, but I think the root of you making it is in thinking I meant to equalize such things to a certain "size" rather than a certain "power". Let me know whether you'd still want me responding to this in light of that.

That doesn't change anything whatsoever and is just a rephrasing of the same nonsense as before. At these tiers, you equalize things to a certain "power" because they're of a certain "size." For example you infer a timeline takes Low 2-C power to destroy because it's Low 2-C-sized, and it's Low 2-C-sized because of how 4-dimensional volumes work. Pull out the last thing (Volume) and this whole sequence crumbles.

So, either the character has no size whatsoever that can be compared to dimensional things, and has their AP be just raw destructive feats (That can indeed be equated to such things), or their AP is directly from their ontological superiority over dimensions (As in the case of the aforementioned hypothetical void, or characters who'd scale to it), and is thus 1-A. That's all there is to it.

Overall I noticed the opposition to this just leads back to the weird view of Type 2 BDE as being just Type 1 BDE + More AP than whatever dimensions exist in your cosmology, which is incorrect. Having greater AP than all the dimensional structures in your verse is certainly a necessary condition for Type 2, don't get me wrong, but it's by no means a sufficient one. And it's also an extremely haphazard interpretation of most cases of BDE in general.

 

[Agnaa]

Hardly. I doubt you yourself can even tell me what exactly a space being "Separable" means, and even if you could I doubt you'd know how it helps form the mysterious-and-yet-supposedly-popular notion of "dimensionality" that you claim exists. The Hausdorff property is slightly closer to the layman's mind (Since it literally just means "Every single point in a space is contained in a neighborhood of points that's separate from the neighborhoods of other points"), but even that one is hardly a fundamental property of what people often think of as "dimensionality."

As said, I dislike arguments of this style (Appeal to popular knowledge and etc), but even if we were to use it, that line of thought far more easily supports me, not you. "Actually most people would implicitly think [p.s They wouldn't] of these obscure topological properties when thinking of dimensional spaces, so there is a notion of dimensionality that is constrained to them" has as much impact as "Most people instinctively imagine 3-dimensional space when thinking of dimensionality at all, so there is a notion of dimensionality that's constrained to 3-D space alone!"

As I said, I don't think most people (until fairly recently) knew what a space being "Euclidean" meant, but they still get kinda freaked out when they see things that violate it. I didn't mean that they knew those properties enough to define/describe them, just that they'd notice the consequences of their absence and think of them unusual.

I don't really go for the 3-D thing since I already apply something similar for different reasons; for a verse to be considered for "above all dimensions" taken to a point beyond their cosmology, they'd already have statements indicating that more dimensions can be added without changing their superiority.

That doesn't change anything whatsoever and is just a rephrasing of the same nonsense as before. At these tiers, you equalize things to a certain "power" because they're of a certain "size." For example you infer a timeline takes Low 2-C power to destroy because it's Low 2-C-sized, and it's Low 2-C-sized because of how 4-dimensional volumes work. Pull out the last thing (Volume) and this whole sequence crumbles.

That's how we tier most things, but for things without "size", we rate them based on their "power". Since "power" is more generalizable. It's the root of our entire AP system, really.

Comparisons between verses don't crumble just because not all constructs that exist in one verse exist in the other.

Timelines are Low 2-C because we treat each point in them as containing an entire universe, and so, by the way geometry works, they have an uncountably infinite amount of mass/energy. Since Low 2-C is defined as one realm that takes a power of R to destroy, that's where we'd rate it. That's why we could rate statements of power without reference to size ("uncountably infinitely powerful") and geometries that don't really align with a dimensional hierarchy ("aleph-1 number of cubes in this space") appropriately. Volumes are the map, power is the territory.

Overall I noticed the opposition to this just leads back to the weird view of Type 2 BDE as being just Type 1 BDE + More AP than whatever dimensions exist in your cosmology, which is incorrect. Having greater AP than all the dimensional structures in your verse is certainly a necessary condition for Type 2, don't get me wrong, but it's by no means a sufficient one. And it's also an extremely haphazard interpretation of most cases of BDE in general.

That's literally exactly how we define it right now.

Type 2: Characters whose nature is defined by lacking spatiotemporal features and being superior to them in nature. These characters aren't necessarily superior to spacetime on every level, but just within the scope which they are shown.

 

[Ultima_Reality]

As I said, I don't think most people (until fairly recently) knew what a space being "Euclidean" meant, but they still get kinda freaked out when they see things that violate it. I didn't mean that they knew those properties enough to define/describe them, just that they'd notice the consequences of their absence and think of them unusual. And this matters if you want to substantiate the claim of "Well most people would think of that one way or another."

I don't really go for the 3-D thing since I already apply something similar for different reasons; for a verse to be considered for "above all dimensions" taken to a point beyond their cosmology, they'd already have statements indicating that more dimensions can be added without changing their superiority.

I am aware you're claiming that people would just implicitly think of those properties in concept, even if not in name, but that's just sidestepping the fact you can't actually seem to articulate what those properties substantially add to a space, that makes them so fundamental as to constitute a whole notion of "dimensionality" centered entirely around them, which is important if you want to substantiate the claim of "Well, these things are bonded enough to the notion of dimensionality as to be already in people's minds when they think of the very concept."

You're claiming those things are fundamental without even having any real knowledge of what they entail, which is poor form when added to the fact you're inventing definitions as is (Which is why this part of the argument is honestly the silliest by far). The bit about the 3-D thing is already being discussed down below, though even then the argument is nonetheless about on par with what you are saying right now, even with the different context here.

That's how we tier most things, but for things without "size", we rate them based on their "power". Since "power" is more generalizable. It's the root of our entire AP system, really.

Comparisons between verses don't crumble just because not all constructs that exist in one verse exist in the other.

Timelines are Low 2-C because we treat each point in them as containing an entire universe, and so, by the way geometry works, they have an uncountably infinite amount of mass/energy. Since Low 2-C is defined as one realm that takes a power of R to destroy, that's where we'd rate it. That's why we could rate statements of power without reference to size ("uncountably infinitely powerful") and geometries that don't really align with a dimensional hierarchy ("aleph-1 number of cubes in this space") appropriately. Volumes are the map, power is the territory.

This is incorrect. Size is indeed the foundation of power, which is why the Tiering System page starts the description of each and every high tier with: "Characters or objects that can universally affect, create and/or destroy structures whose size is equivalent to...".
The example you use changes nothing because it really just says the opposite of what you claim it demonstrates (See: The fact even the idea of "an uncountably infinite amount of mass/energy" is dependent on there being a higher-dimensional volume extending over where the countable mass is). So you're really just saying "We don't rate the ontology of things without size based on size, but on something based on size."

The other examples are also pretty bad. "Uncountably infinitely powerful" is just equivalent to "Their raw power could destroy a realm infinitely greater than High 3-A" (Which leads back to size, again) and "Aleph-1 cubes lying around" is just a dismantled hypervolume.

Though, you are not wholly wrong about what the Tiering System does: It claims to not base itself on higher-dimensional jumps, in particular, but on the more ill-defined idea of "levels of infinity," which is the primary thing that higher-dimensional volumes, R>F Transcendences and BDE are all just equated to. Thing is: That, itself, is nonsense, and the very thing whose usage I am critiquing with this thread, so in any case I don't think appealing to tradition makes for a very strong defense of your principles.
It ultimately goes back to what I said before: You seem to think volume is some magical element that you just "have," and that you can be comparable to even without, when in reality it's in-and-of-itself a description. Being able to be equated to volume in a real way is having volume.

And the current way it's treated does indeed just leads to true contradictions. Adding a dimension to a space, in terms of "levels of infinity," would be adding infinitely more points to it, while a being that exists beyond volume entirely would be made up of no points of space at all. I don't believe I have to say that "Infinitely more points = No points" is literally incoherent.

That's literally exactly how we define it right now

Notice the "and being superior to them in nature", which is indeed because Type 2 is meant to be for characters whose very ontology is beyond dimensions. Type 1 is for characters who lack that, not characters who lack dimensions but have their AP at Unknown or only AP equal to all the dimensions in their verse.

 

[Antvasima]

Ultima, please try to be more respectful in your rebuttals. Thank you.

 

[Ultima_Reality]

Ultima, please try to be more respectful in your rebuttals. Thank you.

My apologies. Will keep that in mind.

 

[Antvasima]

Thank you.

 

[Agnaa]

I am aware you're claiming that people would just implicitly think of those properties in concept, even if not in name, but that's just sidestepping the fact you can't actually seem to articulate what those properties substantially add to a space, that makes them so fundamental as to constitute a whole notion of "dimensionality" centered entirely around them, which is important if you want to substantiate the claim of "Well, these things are bonded enough to the notion of dimensionality as to be already in people's minds when they think of the very concept."

You're claiming those things are fundamental without even having any real knowledge of what they entail, which is poor form when added to the fact you're inventing definitions as is (Which is why this part of the argument is honestly the silliest by far). The bit about the 3-D thing is already being discussed down below, though even then the argument is nonetheless about on par with what you are saying right now, even with the different context here.

I don't think it is "fundamental", as in, that beings with exceedingly different laws of physics would write stories where that matters.

It's just a typical property that people expect, and one which places bounds on the size of such spaces.

I don't think the tier we provide to "above all dimensions" has to be about the fundamental properties of that, just the typical things people mean when they say that.

This is incorrect. Size is indeed the foundation of power, which is why the Tiering System page starts the description of each and every high tier with: "Characters or objects that can universally affect, create and/or destroy structures whose size is equivalent to...".
The example you use changes nothing because it really just says the opposite of what you claim it demonstrates (See: The fact even the idea of "an uncountably infinite amount of mass/energy" is dependent on there being a higher-dimensional volume extending over where the countable mass is). So you're really just saying "We don't rate the ontology of things without size based on size, but on something based on size."

Not fundamentally, no. Otherwise your notions of 1-A would be unsuited to the Tiering System.

There has to be something deeper at play, which it's truly based on, which "size" is only a common emanation of. I don't care which term you give to it, which is why I tried to use "power" here, and off-site have used "size or whatever meta analogue you use that functions exactly how we would expect size to function but works in cases where the piece of fiction says that it's beyond size", shortened to sowmayutfehwwestfbwicwtpofstibs.

Literally all that I'm trying to do with this is the exact same thing which you take no issue with suggesting your new system does; applying a broader principle than "size" to the Tiering System.

And the current way it's treated does indeed just leads to true contradictions. Adding a dimension to a space, in terms of "levels of infinity," would be adding infinitely more points to it, while a being that exists beyond volume entirely would be made up of no points of space at all. I don't believe I have to say that "Infinitely more points = No points" is literally incoherent.

If we were saying they literally had that, it would be, but we explicitly say they lack that, and only compare their AP/Dura to that. I don't think such comparisons of the fundamental-property-underlying-the-entire-Tiering-System-manifested-at-most-levels-as-size leads to a contradiction.

Notice the "and being superior to them in nature", which is indeed because Type 2 is meant to be for characters whose very ontology is beyond dimensions. Type 1 is for characters who lack that, not characters who lack dimensions but have their AP at Unknown or only AP equal to all the dimensions in their verse.

I just see "more AP" (in this context, of being a qualitative superiority) and "superior to them in nature" as the exact same thing.

 

[Ultima_Reality]

I don't think it is "fundamental", as in, that beings with exceedingly different laws of physics would write stories where that matters.

It's just a typical property that people expect, and one which places bounds on the size of such spaces.

I don't think the tier we provide to "above all dimensions" has to be about the fundamental properties of that, just the typical things people mean when they say that.

Separability is something only mathematicians and people actually working on analysis care about. It's not really "a typical property people would expect" even implicitly, and the same goes for Hausdorffness to a degree. What people typically mean when they talk about dimensions or dimensional things is simply coordinate spaces and coordinate axes. That's about it. (And you still haven't really demonstrated that you actually know what those terms entail to the degree you need to substantiate the claims you're making)

So, to draw from the point above: By your logic, "above the notion of dimensionality itself" is actually just a 4-dimensional non-euclidean space, or something, since it's larger than what people instinctively think about when imagining dimensions (3-D space), and also has different properties than the spaces they're used to. That's pretty absurd, to say the least.

I just see "more AP" (in this context, of being a qualitative superiority) and "superior to them in nature" as the exact same thing.

If we were saying they literally had that, it would be, but we explicitly say they lack that, and only compare their AP/Dura to that. I don't think such comparisons of the fundamental-property-underlying-the-entire-Tiering-System-manifested-at-most-levels-as-size leads to a contradiction.

They aren't really the same thing, no. There is a difference between a character who simply lacks spacetime (And thus has a state of existence that simply cannot be compared to any size, by virtue of lacking size) and then displays destructive feats that are tiered separately from that nature, and a thing whose aspatial and atemporal nature is the direct cause of their superiority over things (See the argument here, which you gave a rather poor answer to), as the aforementioned hypothetical void would be.

The latter (Type 2) would constitute a superiority that is, as the Reality-Fiction Transcendence page puts it, "strictly one of quality, not quantity," and which as such can't be equated to a gap in quantity at all. Meanwhile, the former (Type 1) wouldn't constitute any superiority whatsoever, since their non-dimensional nature is unrelated to their AP. Their AP would be quantitative by virtue of coming from affecting quantitative things.

Not fundamentally, no. Otherwise your notions of 1-A would be unsuited to the Tiering System.

There has to be something deeper at play, which it's truly based on, which "size" is only a common emanation of. I don't care which term you give to it, which is why I tried to use "power" here, and off-site have used "size or whatever meta analogue you use that functions exactly how we would expect size to function but works in cases where the piece of fiction says that it's beyond size", shortened to sowmayutfehwwestfbwicwtpofstibs.

Literally all that I'm trying to do with this is the exact same thing which you take no issue with suggesting your new system does; applying a broader principle than "size" to the Tiering System.

It would only be unsuited if the term "size" was applied to 1-A in the same way it was applied to lower tiers, which isn't the case under these proposals. There's an analogy between both usages of the word, but that doesn't guarantee equality, nor total sameness of meaning. "Power," even then, is still just a measure of the scope of size you can affect (Referring to both dimensional size and the meta-size that applies to 1-A), meaning it is dependent on size, and not the primary thing.

By that same token, what I am doing is not at all the same thing as what you are trying to do, no. I maintain that this "meta analogue" of size is not only broader than dimensional size but also fundamentally different to the point that dimensions aren't even included in its definition. You, meanwhile, want to somehow say this analogue can be equated to a volume, which is nonsense either way. Refer to the analogy here.

 

[Agnaa]

Separability is something only mathematicians and people actually working on analysis care about. It's not really "a typical property people would expect" even implicitly, and the same goes for Hausdorffness to a degree. What people typically mean when they talk about dimensions or dimensional things is simply coordinate spaces and coordinate axes. That's about it. (And you still haven't really demonstrated that you actually know what those terms entail to the degree you need to substantiate the claims you're making)

Welp, if you and @DontTalkDT think that lacking those properties wouldn't cause any changes to how dimensional spaces operate that ordinary people would notice, then fair enough. I'll defer to you two since I don't know enough about the topic.

So, to draw from the point above: By your logic, "above the notion of dimensionality itself" is actually just a 4-dimensional non-euclidean space, or something, since it's larger than what people instinctively think about when imagining dimensions (3-D space), and also has different properties than the spaces they're used to. That's pretty absurd, to say the least.

I'd usually only accept statements as implying that sort of essence if they included wording about "any number of dimensions, no matter how many" or something like that, so I wouldn't accept such a comparison as following my logic.

They aren't really the same thing, no. There is a difference between a character who simply lacks spacetime (And thus has a state of existence that simply cannot be compared to any size, by virtue of lacking size) and then displays destructive feats that are tiered separately from that nature, and a thing whose aspatial and atemporal nature is the direct cause of their superiority over things (See the argument here, which you gave a rather poor answer to), as the aforementioned hypothetical void would be.

The latter (Type 2) would constitute a superiority that is, as the Reality-Fiction Transcendence page puts it, "strictly one of quality, not quantity," and which as such can't be equated to a gap in quantity at all. Meanwhile, the former (Type 1) wouldn't constitute any superiority whatsoever, since their non-dimensional nature is unrelated to their AP. Their AP would be quantitative by virtue of coming from affecting quantitative things.

I agree that there's a difference, but in my words, Type 1 lacks the "more AP" in terms of a qualitative superiority.

It would only be unsuited if the term "size" was applied to 1-A in the same way it was applied to lower tiers, which isn't the case under these proposals. There's an analogy between both usages of the word, but that doesn't guarantee equality, nor total sameness of meaning. "Power," even then, is still just a measure of the scope of size you can affect (Referring to both dimensional size and the meta-size that applies to 1-A), meaning it is dependent on size, and not the primary thing.

By that same token, what I am doing is not at all the same thing as what you are trying to do, no. I maintain that this "meta analogue" of size is not only broader than dimensional size but also fundamentally different to the point that dimensions aren't even included in its definition. You, meanwhile, want to somehow say this analogue can be equated to a volume, which is nonsense either way. Refer to the analogy here.

If dimensions aren't included in its definition, then it shouldn't be the basis of the tiering system, as even after your revisions, you'd still want to incorporate dimensions

You can't have it both ways. You can't have it be the fundamental basis of tiering, and inapplicable to most of the tiering system.

If you think that analogue can't be equated to volume, then you're saying that the analogue is unsuitable for a tiering system involving volume.

 

[DontTalkDT]

Welp, if you and @DontTalkDT think that lacking those properties wouldn't cause any changes to how dimensional spaces operate that ordinary people would notice, then fair enough. I'll defer to you two since I don't know enough about the topic.

I see my name mentioned. Can you briefly summarize the point of debate this relates to?

 

[Agnaa]

I see my name mentioned. Can you briefly summarize the point of debate this relates to?

Whether a space being "Hausdorff" and/or "separable" results in any changes in typical operation, such that ordinary people would notice the absence of them, and find them weird.

Ultima's currently arguing that both are mainly mathematical curiousities, rather than something like "angles of a triangle add up to 180 degrees" that everyone would notice being off.

 

[Ultima_Reality]

Jumping here for a little bit to clarify:

Ultima's currently arguing that both are mainly mathematical curiousities, rather than something like "angles of a triangle add up to 180 degrees" that everyone would notice being off.

To be more specific: I am saying that "A space that is Hausdorff and Separable" is hardly something that constitutes its own definition of "dimensionality," either formally or in the average people's head. The former for obvious reasons (No one defines it that way) and the latter because most people quite simply don't think of dimensions or dimensional spaces while using these two properties as foundational things, either explicitly or implicitly.

 

[Agnaa]

To be more specific: I am saying that "A spaces that is Hausdorff and Separable" is hardly something that constitutes its own notion of "dimensionality," either formally or in the average people's head. The former for obvious reasons (No one defines it that way) and the latter because most people quite simply don't think of dimensions or dimensional spaces while using these two properties as foundational things, either explicitly or implicitly.

Well yeah, for it to be something that people don't implicitly include within people's beliefs, it would have to not be something they'd notice the absence of and find strange. That's what it means for it to implicitly be part of it.

 

[Ultima_Reality]

Well yeah, for it to be something that people don't implicitly include within people's beliefs, it would have to not be something they'd notice the absence of and find strange. That's what it means for it to implicitly be part of it.

I find it odd that you mention "People noticing" things, though. Obviously, people would notice the difference between a 3-D space and a 4-D space, and yet that wouldn't constitute a breach in the common conception of dimensionality to you. At that point I'd ask what exactly it is you think the average person even conceives of when they think of spatial dimensions as a concept.

I'd usually only accept statements as implying that sort of essence if they included wording about "any number of dimensions, no matter how many" or something like that, so I wouldn't accept such a comparison as following my logic.

It's pretty much identical, I might note. Since "4-dimensional + Non-Euclidean" follows exactly the same format as "Has more than c dimensions + Non-Separable." That format being "Bigger than what came before it + Has a property that makes it kinda weird compared to the things it dwarves."

I agree that there's a difference, but in my words, Type 1 lacks the "more AP" in terms of a qualitative superiority.

That doesn't really change my point. This being that you seem to view even things like "This void is timeless, spaceless and beyond dimensions, and is depicted as surrounding and infinitely dwarfing dimensional space" in terms of some Dragon Ball-styled thing where the void simply has "More power" than it things it dwarves in some nebulous ill-defined sense, and since "power" to you is measured in volume, then that can be equated to volume even if the void itself has no volume to speak of.

I'm saying that's not really coherent. If the hypothetical beyond-dimensional void's non-quantitative "size" is one and the same with its "power," then its power likewise isn't a quantitative thing (By transitivity), and can't be equated to a quantitative measure such as volume. The other arguments I've done follow suit after this.

If dimensions aren't included in its definition, then it shouldn't be the basis of the tiering system, as even after your revisions, you'd still want to incorporate dimensions

You can't have it both ways. You can't have it be the fundamental basis of tiering, and inapplicable to most of the tiering system.

If you think that analogue can't be equated to volume, then you're saying that the analogue is unsuitable for a tiering system involving volume.

Not exactly sure what you mean by that. The basis of the Tiering System below 1-A would be just dimensional jumps, and the basis of the Tiering System from 1-A and onwards would be the aforementioned notion of "meta-size." Both of those would simply be grounded on the basic notion of "X is bigger than Y," which in fiction has to extend further than simple comparisons of volume and measure. It's simple, really.