The Truth of Dimension Tiering and the Sources that effectively deal with the currently ongoing arguments favoring against it.

[Jakob_C._Brown]

Recently, I have been back in the whole battleboard discussion in part of my own - for curiosity's sake - research in the nature of dimensions and how it leads to dimensional tiering.

I have noticed for a somewhat long while that the dimensional tiering is heavily criticized or questioned outside of VBW but initially I thought the arguments were rather superficial such as dimensions being "the new omnipotence" or that it cannot be applied because not every fictional work uses dimensions or utilizes them in the same way, but this can also be said about such thing as universes, multiverses and especially terms like "meta verses" and "mega verses". Not every fictional work revolves around having "infinite universes inside infinite universes inside infinite universes" or "infinite universes within a collective of infinite universes" and so on, but you got to work with some sort of tiering system or a hierarchy to make sense of what's up.

Besides, at initial glance, dimensional tiering makes sense if a 4D universe is infinitely greater than an infinite collection of 3D universes or a 5D universe being infinitely greater than an infinite collection of 4D universes. However, beyond this website I haven't really found this reasoning and it might be that I am also misinterpreting VBW's reasoning but I digress. Because I am not sure of myself whether I can just drop the discussion threads here, I will try to summarize and/or quote the counter arguments and criticism to the best of my understanding:

- A 3D being could still attack and affect the length, width, and height of a 5D being, therefore causing significant if not lethal damage due to having 3 of their 5 dimensions destroyed.

- Mathematically, infinity * infinity * infinity would still be infinity since infinity encompasses all whether you say just infinity, infinity + 1 or infinity * infinity.

- They argue that a vector of (1/1/1/1) pales in comparison to a vector (99/99/99/0) despite the former just having one dimension more. "If I have a glass cube with a volume of 1 dm3and Cthulhu folds it into higher dimensions a billion trillion time, it will still shatter if I hit it with a sledgehammer."

- "Beings and objects are not geometrical entities, geometry is more about space than the objects within," furthermore do they add that for example "four-dimensional entities can not be composed of an infinite amount of three-dimensional objects, because the fermions (electrons / probability waves) in those entities would have to occupy the same space, which violates the Pauli principle"

- Mass and velocity, i.e. the key components of kinetic energy, are unrelated to dimensions they assert, meaning that "A 4D man can weigh just 100 kg and run only 5 m/s, and that'd hurt just as much as a 100 kg 3D man running 5 m/s."

- Mass is not a dimensional unit because the mass of an object is not dependent on how big said object is. While density is a thing, there are cases of there being large volumes having moderate mass yet small volumes having immense mass.

- "Even string theory outright states that higher dimensions are actually smaller than our own dimensions."

- "The idea of a 2d infinitely flat plane of existence is impossible since the very mass of these 2d objects would have to eventually interject into a solid 3d mass since they would be made up of 3d subatomic particles & atoms. The very idea of an infinite amount of mass separating a 2d object from a 3d one is wrong since there is only a finite amount of mass in the human body and the assumption that their are an infinite amount of planes separating a 3d one with a 2d one would only imply that we are infinitely reusing the very same subatomic particles for each plane and thus would contradict our very claim." I suppose this reasoning can be used to argue against the notion of infinite 3D volume or infinite 4D or infinite 5D and so forth.

Also, I'm afraid I haven't found any, most preferably scientific, sources that state that a higher dimension being would possess energy, power or force at an infinitely greater magnitude compared to us 3-dimensions beings. The only information that I could have ascertained thus far is that a 4th or 5th dimension being for instance has more than 3 options in terms of movement according to the dimensional axis (just like how we could side-step around a 2-dimensional being for instance) but I don't know how that should exactly translate in said being have more energy or force at their disposal compared to a 3D entity.

Mind you, I am not here to "dismantle" the dimensional tiering system of VBW in case this post may have invoked some feelings of anxiety. I just want to find out the truth. Also, in the case I write fictional stories revolving around dimensional and multiversal power shenanigans, I'd like to know as much as possible to make it seems as logical or reasonable as possible. Fiction is fiction of course, but I'd like to see how far the dimensional tiering system can be argued from rather scientific or hard sci-fi perspective.

So yeah, any further information or sources on this matter that go in detail in favor of dimensional tiering or would "argue" in favor of it - or that it sheds light on the aforementioned counter arguments - would be more than welcome.

 

[Promestein]

I'm not very well-versed in this stuff, but to my understanding, though our own dimensional tiering system takes from things such as projective geometry, it is mostly based in how fiction treats dimensions and "layers" that exist as higher planes of existence.

 

[Antvasima]

We are well aware of that dimensions do not work in this manner from a physics standpoint, but according to infinity in projective geometry and the principle of a Hausdorff dimension our tiering system does seem to make sense from a purely geometric "volume"/size viewpoint.

In addition, several fictions, such as Umineko, the Dark Tower, and the works of H.P. Lovecraft use principles of increasing degrees of infinity, so this is the best option we seem to have available to integrate that concept.

The old system's "Megaverse" and "Omniverse" terms are simply too small to contain the sheer scale of these concepts.

However, DontTalkDT and DarkLK are much more well-versed in this subject than I am.

 

[RavenSupreme]

Not to forget that we, even in the real world, have confirmed layers of infinity, where one layer of infinity will never reach even the starting point of the other layer of infinity.

Thats not just mere fiction, thats applied in real life

Its called countable and uncountable infinity.

Example:

-> Countable infinity is simple stuff like counting numbers from 1..2..3...etc. theoretically, given an infinite amount of numbers you could contrast an infinite numbers of counters.

-> Uncountable infinity however is simply that: Imagine the numbers from 0 to 1.

Is it 0.1..0.02...? Or is it 0.01....0.002...? Or even 0.0000001...0.000002...?

You get what i mean. You can always fill in another 0 before the dot, making the entire concept uncountable and this infinity greater in aspect, since you can not assing a corresponding amount of counters, given you had an infinite amount of them..

 

[DontTalkDT]

Regarding anything involving physics:

You can have a Tiering System based on physics entirely. But in that case you will have to accept that there is no tier above high 3-A. From a physics perspective there is no level above infinite energy/force.

I always consider it rather funny if other battleboards argue "muh physics" and then have a multiverse level, even though from a physics perspective multiverse level isn't actually above universe level.

If you want to have a system were all characters that rank multiverse level or higher are equal or inferior to those that destroyed an (infinite) universe, you can have that with a purely physics based approach. If you want to reflect that there are countless fictions that have levels higher than universe level, though, you will have to use some concept aside from physics, but the fact that physics won't agree with that concept in some aspects is obvious, as otherwise you could have actually used physics.


When it comes to the mathematical justification: Well, for one thing the analogy makes sense and is used in a few pieces of fiction. At the same time we are able to include fictions which don't include it explicitly in a decent fashion into it.

Using size of the things a character can destroy as the way to classify character power in the realms were physics makes no distinction is a decent concept.

And there it turns out that one can say that higher dimensional objects are indeed infinitely larger.

To be more specific: The Hausdorff dimension assigns each subset (and with it every real life form and volume) of the n-dimensional real number space a dimension as such that, in terms of the m-dimensional Hausdorff measure, its size is infinite, if m<n, and its size is 0 if n<m.

That the n-dimensional Hausdorff measure is the same as the n-dimensional Lebesgue-measure on any set within the Borel Algebra and its proper classification of the surface area of submannifolds, which justifies its use as intuitive size for all sets relevant for our purposes.

 

[Antvasima]

Thank you very much for the clarification help DontTalk.

 

[Antvasima]

Would you like to insert a version of your text into a preexisting or new explanation page?

 

[Antvasima]

We have needed to move the explanation in the Higher-Dimensional Manipulation page to a separate page for quite a while now anyway.

Would you be willing to incorporate the information there with an expanded version of your text, and place both in a page titled "Dimensional Tiering" or somesuch, that can be linked to via the front page and our wiki navigation bar?

I would really appreciate the help, and could clean up the grammar and structure if necessary.

 

[ProspectX]

Mass is not a dimensional unit? It has no dependent variable?

There exists no thing as dependency on "real life" mathematical theorems in literature. No thing prevents a verse from having a whole another prefix, and set of laws exclusive only to them.

However, From a logical standpoint the Hausdorff concept of spatial layers would make sense in most of them.

 

[Jockey-1337]

Interesting

 

[Antvasima]

Since DontTalk and Raven have answered this question, I think that we should close the thread.