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Berkely Cardinal

No, it does mean it's not a part of everything.

The Tellurian is literally everything. Capital R reality, Capital E everything. The High Umbra does not extend beyond the Horizon Realms.

The Far Umbra is where it stops, and the High Umbra contains the Tegmark Multiverse.

Objectively, the Tegmark Multiverse does not contain everything in WoD, there are structures larger than it.

Everything that has, will, could be or might be thought of exists with in the High Umbra.

Tegmark Multiverse cannot extend beyond Imagination, because the definition for the Type 4 Multiverse is all Mathematically coherent phenomena.

Mathematics is very much so a construction of Human Imagination.

No, it does mean it's not a part of everything.

The Tellurian is literally everything. Capital R reality, Capital E everything. The High Umbra does not extend beyond the Horizon Realms.

The Far Umbra is where it stops, and the High Umbra contains the Tegmark Multiverse.

Objectively, the Tegmark Multiverse does not contain everything in WoD, there are structures larger than it.

Everything that has, will, could be or might be thought of exists with in the High Umbra.

Tegmark Multiverse cannot extend beyond Imagination, because the definition for the Type 4 Multiverse is all Mathematically coherent phenomena.

Mathematics is very much so a construction of Human Imagination.

Mathematics is a construct of human imagination that's completely fine.

I still don't see how the Tegmark Multiverse cannot extend beyond human imagination, though. One can think about what would happen if you were to combine every known mathematical construct possible, but that would still not mean they'd be able to necessarily imagine the true biproduct of said combination, only a part of it. However, this "construct" would still, technically be, a part of mathematics.

Thank you for the rebuttal by the way, I really appreciated your input in this discussion truly 😁
 
Question: Would the dimensioned space of the Cthulhu Mythos count as a Tegmark 4 multiverse? I mean, it's infinite universes with infinite dimensions, all of which are mathematically understandable. If not, where would it fall on the Tegmark scale, if at all?
 
Question: Would the dimensioned space of the Cthulhu Mythos count as a Tegmark 4 multiverse? I mean, it's infinite universes with infinite dimensions, all of which are mathematically understandable. If not, where would it fall on the Tegmark scale, if at all?
https://vsbattles.fandom.com/wiki/User_blog:KingPin0422/Cthulhu_Mythos_Blog#Beyond_the_Ultimate_Void

However, this is only for the Ultimate Void it seems as this is before the Tiering System revision IIRC.
 
Question: Would the dimensioned space of the Cthulhu Mythos count as a Tegmark 4 multiverse? I mean, it's infinite universes with infinite dimensions, all of which are mathematically understandable. If not, where would it fall on the Tegmark scale, if at all?
Nope. Even basic type 3 multiverse can be infinite dimensional. Also Tegmark was literally born after Lovecraft died lol.
 
Nope. Even basic type 3 multiverse can be infinite dimensional. Also Tegmark was literally born after Lovecraft died lol.
Well, I never thought Lovecraft specifically said anything about Tegmark-style multiverses. But even if the baseline multiverse is only a type 3, wouldn't the cosmology reach Tegmark 4 levels by the Ultimate Void? I mean, there are the Dreamlands that transcend dimensioned space, the Outer Extension transcending the Dreamlands to the point they're illusions, and the Ultimate Void transcending that to an infinite degree. I guess I'm wondering what the difference between WoD and the Lovecraft universes is that would make WoD so much higher, given that, to me, they seem to have a similarly constructed cosmos.

https://vsbattles.fandom.com/wiki/User_blog:KingPin0422/Cthulhu_Mythos_Blog#Beyond_the_Ultimate_Void

However, this is only for the Ultimate Void it seems as this is before the Tiering System revision IIRC.
I am aware of that page, but beyond stating the Ultimate Void "might" reach levels of cardinality, I don't really see how it answers my question. Does WoD have official statements explicitly saying it's a Tegmark 4, or is there a description that makes it conclusively such? I'm asking out of genuine curiosity and I'm just trying to wrap my head around everything, trying to understand things like the levels of Tier 0, what feats/statements count as such, and so on.

I really do appreciate the answers and help so far. I know this probably comes across as me trying to wank the Cthulhu Mythos, but that's not my intent; I just want to have a full understanding of the tiering of the verse, which is easiest through comparisons to other universes. Again, thank you for your patience with me.
 
I mean, there are the Dreamlands that transcend dimensioned space, the Outer Extension transcending the Dreamlands to the point they're illusions, and the Ultimate Void transcending that to an infinite degree.
That's not really how you define a Type 4 Multiverse. It's not really about transcendence on top of transcendence, nor by seeing stuff as illusions. The only way for a verse to have Type 4 is if it has statements of implications of such. Manifold has it because it has numerous statements of Mathematics being the basis of all reality in which all physical things springs from, from every mathematical possibility. While WoG has a straight up statement and mention of Tegmark himself.
Does WoD have official statements explicitly saying it's a Tegmark 4
Yes.
 
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Possibly Gilman ought not to have studied so hard. Non-Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of the Gothic tales and the wild whispers of the chimney-corner, one can hardly expect to be wholly free from mental tension. Gilman came from Haverhill, but it was only after he had entered college in Arkham that he began to connect his mathematics with the fantastic legends of elder magic.
~ The Dreams in the Witchhouse
Gilman is stated to be doing Calculus D, which is akin to Vector Calculus, Riemann Equations, and the like. However, given he is into occult and more obscure sciences, it would not be too absurd for him to have heard and studied the works of Georg Cantor's set theory, a shunned and repudiated mathematical branch during his time which is right up his alley. This means he could possibly know of the concept of an absolute infinity (And we will get back to this eventually) and yet the outer void is so foreign that he deigns to justifying it even with the concepts of dimensionality or, if he possibly knows it, of higher infinities. In other words, the outer void may possibly be above cantorian cardinality.

The main inhabitant of the Ultimate Void are the Ultimate Gods:

The Ultimate Gods​

It was dark when the galley passed betwixt the Basalt Pillars of the West and the sound of the ultimate cataract swelled portentous from ahead. And the spray of that cataract rose to obscure the stars, and the deck grew damp, and the vessel reeled in the surging current of the brink. Then with a queer whistle and plunge the leap was taken, and Carter felt the terrors of nightmare as earth fell away and the great boat shot silent and comet-like into planetary space. Never before had he known what shapeless black things lurk and caper and flounder all through the aether, leering and grinning at such voyagers as may pass, and sometimes feeling about with slimy paws when some moving object excites their curiosity. These are the nameless larvae of the Other Gods, and like them are blind and without mind, and possessed of singular hungers and thirsts.




This is from the blog if you read as it mention a certain set theory made by a certain mathematician I think. Let me check
 

Yeah, here is the set theory.

Basically to summarize what the set theory is.


It basically consists of all cardinals I think including Mahlo:

“3.1 Cardinals​

A cardinal is an ordinal that is not bijectable with any smaller ordinal. Thus, every finite ordinal is a cardinal, and ωω, ω1ω1, ω2ω2, etc. are also cardinals. The infinite cardinals are represented by the letter aleph (ℵℵ) of the Hebrew alphabet, and their sequence is indexed by the ordinals. It starts like this

ℵ0ℵ0, ℵ1ℵ1, ℵ2ℵ2, …, ℵωℵω, ℵω+1ℵω+1, …, ℵω+ωℵω+ω, …, ℵω2ℵω2, …, ℵωωℵωω, …, ℵω1ℵω1, …, ℵω2ℵω2, …
Thus, ω=ℵ0ω=ℵ0, ω1=ℵ1ω1=ℵ1, ω2=ℵ2ω2=ℵ2, etc. For every cardinal there is a bigger one, and the limit of an increasing sequence of cardinals is also a cardinal. Thus, the class of all cardinals is not a set, but a proper class.

An infinite cardinal κκ is called regular if it is not the union of less than κκ smaller cardinals. Thus,ℵ0ℵ0 is regular, and so are all infinite successor cardinals, such as ℵ1ℵ1. Non-regular infinite cardinals are called singular. The first singular cardinal is ℵωℵω, as it is the union of countably-many smaller cardinals, namely ℵω=⋃n<ωℵnℵω=⋃n<ωℵn.

The cofinality of a cardinal κκ, denoted by cf(κ)cf(κ) is the smallest cardinal λλ such that κκ is the union of λλ-many smaller ordinals. Thus, cf(ℵω)=ℵ0cf(ℵω)=ℵ0.

By the AC (in the form of the Well-Ordering Principle), every set AA can be well-ordered, hence it is bijectable with a unique cardinal, called the cardinality of AA. Given two cardinals κκ and λλ, the sum κ+λκ+λ is defined as the cardinality of the set consisting of the union of any two disjoint sets, one of cardinality κκ and one of cardinality λλ. And the product κ⋅λκ⋅λ is defined as the cardinality of the Cartesian product κ×λκ×λ. The operations of sum and product of infinite cardinals are trivial, for if κκ and λλ are infinite cardinals, then κ+λ=κ⋅λ=maximum{κ,λ}κ+λ=κ⋅λ=maximum{κ,λ}.

In contrast, cardinal exponentiation is highly non-trivial, for even the value of the simplest non-trivial infinite exponential, namely 2ℵ02ℵ0, is not known and cannot be determined in ZFC (see below). The cardinal κλκλ is defined as the cardinality of the Cartesian product of λλ copies of κκ; equivalently, as the cardinality of the set of all functions from λλ into κκ. König’s theorem asserts that κcf(κ)>κκcf(κ)>κ, which implies that the cofinality of the cardinal 2ℵ02ℵ0, whatever that cardinal is, must be uncountable. But this is essentially all that ZFC can prove about the value of the exponential 2ℵ02ℵ0.

In the case of exponentiation of singular cardinals, ZFC has a lot more to say. In 1989, Shelah proved the remarkable result that if ℵωℵω is a strong limit, that is, 2ℵn<ℵω2ℵn<ℵω, for every n<ωn<ω, then 2ℵω<ℵω42ℵω<ℵω4 (see Shelah (1994)). The technique developed by Shelah to prove this and similar theorems, in ZFC, is called pcf theory (for possible cofinalities), and has found many applications in other areas of mathematics.”

Basically, it is a mess unto itself already.
 
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Well, I never thought Lovecraft specifically said anything about Tegmark-style multiverses. But even if the baseline multiverse is only a type 3, wouldn't the cosmology reach Tegmark 4 levels by the Ultimate Void? I mean, there are the Dreamlands that transcend dimensioned space, the Outer Extension transcending the Dreamlands to the point they're illusions, and the Ultimate Void transcending that to an infinite degree. I guess I'm wondering what the difference between WoD and the Lovecraft universes is that would make WoD so much higher, given that, to me, they seem to have a similarly constructed cosmos.
None of that is Type 4. You can't reach type 4 just by stacking more transcendence.
Gilman is stated to be doing Calculus D, which is akin to Vector Calculus, Riemann Equations, and the like. However, given he is into occult and more obscure sciences, it would not be too absurd for him to have heard and studied the works of Georg Cantor's set theory, a shunned and repudiated mathematical branch during his time which is right up his alley. This means he could possibly know of the concept of an absolute infinity (And we will get back to this eventually) and yet the outer void is so foreign that he deigns to justifying it even with the concepts of dimensionality or, if he possibly knows it, of higher infinities. In other words, the outer void may possibly be above cantorian cardinality.
Meh this is just extremely exaggerated for so many reasons. Gilman considered even simple mathematics dealing with algorithms involving some higher dimensions beyond human comprehension

What made the students shake their heads was his sober theory that a man might—given mathematical knowledge admittedly beyond all likelihood of human acquirement—step deliberately from the earth to any other celestial body which might lie at one of an infinity of specific points in the cosmic pattern.
Such a step, he said, would require only two stages; first, a passage out of the three-dimensional sphere we know, and second, a passage back to the three-dimensional sphere at another point, perhaps one of infinite remoteness

But I have long since accepted the fact that Cthulhu Mythos will continue to get exaggerated on this website and I honestly don't care
 
None of that is Type 4. You can't reach type 4 just by stacking more transcendence.

Meh this is just extremely exaggerated for so many reasons. Gilman considered even simple mathematics dealing with algorithms involving some higher dimensions beyond human comprehension



But I have long since accepted the fact that Cthulhu Mythos will continue to get exaggerated on this website and I honestly don't care
I myself personally think Set Theory is technically in the range of Tier 1A and Tier High 1A as I am kinda unsure about inaccessible cardinals at Tier 0 tbh.


However, I will have to ask Ultima Reality for that matter.
 
I myself personally think Set Theory is technically in the range of Tier 1A and Tier High 1A as I am kinda unsure about inaccessible cardinals at Tier 0 tbh.


However, I will have to ask Ultima Reality for that matter.
What? The tiering system (mostly Tier 1 and 0) is based on set theory, why would it stop at High 1-A?
 
What? The tiering system (mostly Tier 1) is based on set theory, why would it stop at High 1-A?
Probably because of this description of Tier High 1A currently:

High 1-A | High Outerverse level: Characters who can affect and create/destroy states or realms which are completely transcendent over infinitely-layered Outerversal hierarchies and any extensions thereof, as well as the framework in which such entities are defined in the first place. Note that simply adding more "layers" to an already infinite 1-A hierarchy (or some structure of equivalent size) is not enough to reach this tier, and one must be completely external and unreachable by it in any form
 
Probably because of this description of Tier High 1A currently:

High 1-A | High Outerverse level: Characters who can affect and create/destroy states or realms which are completely transcendent over infinitely-layered Outerversal hierarchies and any extensions thereof, as well as the framework in which such entities are defined in the first place. Note that simply adding more "layers" to an already infinite 1-A hierarchy (or some structure of equivalent size) is not enough to reach this tier, and one must be completely external and unreachable by it in any form
Okay, so what? Tier 0 follows the same logic
 
Okay, so what? Tier 0 follows the same logic
Are you sure about Tier 0 following the same logic? I will probably have to double check something as again, it probably stems from the fact it is confusing anyway since set theory has been used in physics and not just math too.

“In as much as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the rôle of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (Church-Turing thesis) related to the possible `solution of supertasks'', and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvantages for physical applications are discussed: Cantorian naive'' (i.e., non-axiomatic) set theory, constructivism and operationalism. In the author's opinion, an attitude of suspended attention'' (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same time, physicists should be open to bizarre'' or `mindboggling'' new formalisms, which need not be operationalizable or testable at the time of their creation, but which may successfully lead to novel fields of phenomenology and technology.”


 
Yes, if you read carefully, Tier 0 is to a High 1-A what a High 1-A is to a 1-A. It is just a larger cardinal than High 1-A. There is no character on this wiki that is above set theory. Not even the Mathiverse is.
 
Yes, that is assuming set theory has been used in fiction all the time (which it isn’t) and do keep in mind as set theory do have certain paradoxes although that is for another time.
 
Paradoxes? My dude this wiki accepts bullshit like nonexistent physiology and transduality. Consistent language has been thrown out of the window long ago. Some minor paradoxes or issues in an otherwise extremely technical and closest to actual real life mathematics based tiering isn't gonna be an issue anytime soon
 
Paradoxes? My dude this wiki accepts bullshit like nonexistent physiology and transduality. Consistent language has been thrown out of the window long ago. Some minor paradoxes or issues in an otherwise extremely technical and closest to actual real life mathematics based tiering isn't gonna be an issue anytime soon

Not to mention the extreme bias some verses have on this wiki and regardless of how good of an argument you have, it will simply get closed because of the most stupid reason ever
 
None of that is Type 4. You can't reach type 4 just by stacking more transcendence.

Meh this is just extremely exaggerated for so many reasons. Gilman considered even simple mathematics dealing with algorithms involving some higher dimensions beyond human comprehension



But I have long since accepted the fact that Cthulhu Mythos will continue to get exaggerated on this website and I honestly don't care
Really? Why is that? How do you reach Tier 4 without an explicit statement that it's a Tegmark 4 in the material itself? There has to be a way; there's far too much fiction that has no idea what a Tegmark 4 is but still reaches to ridiculous heights the tier system. By my reading of the Tegmark definitions, the Lovecraft Mythos seem to fit. They lack definitive statements like the WoD, but are described in almost the exact same way if you look at the language being used.

You're free to believe the Mythos is getting exaggerated, but I'm equally free to think that they're underpowered, based on the language used and how they aren't supposed to be comprehensible by a human mind at such a low level of the cosmology. But I will admit they're short on feats outside of the expanded universe. Though, frankly, I haven't really seen a Tier 0 with any strong feats. They're just rarely the focus of any story they're a part of for pretty obvious reasons. But I guess I'll wait for the Cthulhu revisions @Ultima_Reality is working on.

Anyway, I do appreciate the help with this stuff. Sorry to keep asking 'why?', but I really do want to learn this stuff. I've just never been that great at math, especially abstract math like set theory.
 
Really? Why is that? How do you reach Tier 4 without an explicit statement that it's a Tegmark 4 in the material itself? There has to be a way; there's far too much fiction that has no idea what a Tegmark 4 is but still reaches to ridic
Tier 4 involves destroying a star or larger like a solar system or 4A if it involves multiple solar systems as it is simply physics at its core so…
 
Really? Why is that? How do you reach Tier 4 without an explicit statement that it's a Tegmark 4 in the material itself? There has to be a way; there's far too much fiction that has no idea what a Tegmark 4 is but still reaches to ridiculous heights the tier system. By my reading of the Tegmark definitions, the Lovecraft Mythos seem to fit. They lack definitive statements like the WoD, but are described in almost the exact same way if you look at the language being used.
There isn't really a way to reach it without directly mentioning it or copy pasting it's definition. It doesn't have a defined plane of existence that can be reached by stacking infinity.

As for how this wiki interprets type 4 multiverses, think of them as substitute for "all possible extensions of the system" on which the verse works. If a verse has only shown simple higher dimensions in its system then they are equated to low 1-A/1-A. And if they show 1-A stuff then type 4 multiverses would be High 1-A.


You're free to believe the Mythos is getting exaggerated, but I'm equally free to think that they're underpowered, based on the language used and how they aren't supposed to be comprehensible by a human mind at such a low level of the cosmology.
That's true for any cosmic beings in fiction. We are only able to gauge their power levels in a very reduced and restricted theoretrical form. Practically we will never ever be able to completely accurately visually model even the 4th dimension. While theoretrically we can even comprehend the highest possible power achievable (omnipotence). "Beyond comprehension" in general is one of the worst metrics you can ever use to measure these beings.
 
Tier 4 involves destroying a star or larger like a solar system or 4A if it involves multiple solar systems as it is simply physics at its core so…
I meant Tegmark 4, not tier 4. My mistake.

There isn't really a way to reach it without directly mentioning it or copy pasting it's definition. It doesn't have a defined plane of existence that can be reached by stacking infinity.

As for how this wiki interprets type 4 multiverses, think of them as substitute for "all possible extensions of the system" on which the verse works. If a verse has only shown simple higher dimensions in its system then they are equated to low 1-A/1-A. And if they show 1-A stuff then type 4 multiverses would be High 1-A.
Hmm. I guess I have a problem with something like that. But, I can accept it. Still, even by those standards, I would think that the Cthulhu Mythos would be Tier 1 at its lowest level, right? A cosmology of infinite universes with infinite spatial dimensions is Tier 1, correct?

That's true for any cosmic beings in fiction. We are only able to gauge their power levels in a very reduced and restricted theoretrical form. Practically we will never ever be able to completely accurately visually model even the 4th dimension. While theoretrically we can even comprehend the highest possible power achievable (omnipotence). "Beyond comprehension" in general is one of the worst metrics you can ever use to measure these beings.
That's a very good point.
 
Hmm. I guess I have a problem with something like that. But, I can accept it. Still, even by those standards, I would think that the Cthulhu Mythos would be Tier 1 at its lowest level, right? A cosmology of infinite universes with infinite spatial dimensions is Tier 1, correct?
Well yes it's Tier 1. Cthulhu Mythos is so explicit that you can't really lowball it below High 1-B
 
Tbh alot of the top tier characters from the top tier verses all boil down to the same Ein Sof type being, from a philosophical point of view anyways. They're all boundless entities above thought and language, free of any restrictions, etc etc etc.
But yeah that's not how the wiki does things. I can certainly see how one could potentially wank certain characters to that level based on hyperbolic descriptions and what not and how it could lead to alot of wank on several different profiles, but personally I wouldn't mind if those were the standards for tier 0
 
So things beyond it don't count as part of "everything"?
No.

What is beyond is completely beyond conception.
Mathematics is a construct of human imagination that's completely fine.
More than that. It's nothing more than an effect of the Weaver existing.

Things like Computers, science, logic, and mathematics are examples of the Weaver’s influence on the material plane.



And I can tell you, the Weaver does not extend to the Void.


I still don't see how the Tegmark Multiverse cannot extend beyond human imagination, though. One can think about what would happen if you were to combine every known mathematical construct possible, but that would still not mean they'd be able to necessarily imagine the true biproduct of said combination, only a part of it. However, this "construct" would still, technically be, a part of mathematics.
The definition is "Mathematically coherent phenomena"

Anything that is mathematically coherent would have to be within Human understanding, otherwise it wouldn't be coherent.

All Mathematical constructs are within Human understanding, even if not known, because Mathematics is a product of Human Understanding.

Does WoD have official statements explicitly saying it's a Tegmark 4, or is there a description that makes it conclusively such?
Oh yes.

"Ensemble Space: Called the “Astral Plane” by Reality Deviants, Ensemble Spaces contain objects generated by human minds that lack the characteristics required to instantiate in material reality. This dimension includes fundamental mathematical objects: the Platonic “ultimate ensemble” predicted by mathematician Max Tegmark. The prevalence of “unreal” mathematical constructs gives rise to spatial distortions and subdimensions containing similar data sets, superstitiously referred to “conceptual realms,” “Epiphamies,” and “kingdoms of the gods.”"

Post Script:

Btw, I am not (meaning to be) as sharp or angry as I might come across in text, inflection and tone is harder to convey in text.
 
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Lmao how can tiering system be broken
Just think it's ******* high into baseline tier 0 and call it a day
Generally speaking, it would be really high above Tier 0. The way you say it makes it sound like a Berkeley Cardinal is high into a Mahlo Cardinal, which generally makes no sense, but I get where you are coming from. A better way of saying it would be it's way above Tier 0 as Tier 0 is a Mahlo Cardinal, and Berkeley is the highest known Cardinality in ZFC Set Theory.
 
Ya, no. Berkeley and Reinhardt Cardinal's are the known to be way above a 0=1 cardinal. But, if your talking about the most highest cardinality that's consistent with ZFC, then I agree.
There is no large cardinal beyond a weakly inaccessible consistent with ZFC (zemelo’s axiom of choice). I don’t understand your initial point. And not at all, a 0=1 cardinal in consistency strength is noted to be larger than rank into rank as well.
A 0=1 is pretty much the same/= to the formation as the universe of sets. And “The Higher Infinite” explicitly has 0=1 as the cardinal with the most consistency strength, as large cardinals are not measured by size, they’re measured by how much can proved in it. And well, 0=1 literally makes anything true in it so.
 
And also about the first thing you asked me to quote.

Speed tiering! Irrelevant speed is granted to anyone above low 1-A automatically. If a 3d human with tier 0 ap came along, they'd be granted irrelevant speed even though they're unable to do what the irrelevant speed tier is exactly, due to them being 3 dimensional. So either the wiki is inconsistent or your argument is inconsistent, but since your argument is in reference of the wiki the first one isn't possible without invalidating your premise
Why would 3d human with tier 0 hax be granted with irrelevant speed ? irrelevant speed required the character existence itself, not hax.
 
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