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Bringing Xenosaga to a Higher Dimension: Cosmology

Apologies. I haven't had time for a proper reading.

Working from the bottom up, I'm trying to understand your jump from 4-D to 8-D between the Real and Imaginary Number Domain.
No problem, and thank you so much for the time and attention. It's ok to take time since I know this is a pretty long effort and reading the whole blog can be a time-consuming beast. Right now I'm working, but once I'm home in the afternoon I'll answer this, if that is ok.
 
Alright, I'm home now.
Working from the bottom up, I'm trying to understand your jump from 4-D to 8-D between the Real and Imaginary Number Domain.
This happens because of the Dual Structure of these two domains. It is explained in the Perfect Guide passages that the Imaginary Number Domain has a counterpart to everything that exists in the Lower Domain.
The ability of Testament is something that alters the imaginary domain, and as a result, it has influence in the real number domain. This is why they could perform numerous miracle-like deeds and cause phenomena that disregarded the physical laws of the real number domain. This is also proof that all existence exists in both the real and imaginary number domains. There is no exception to this, even for artificial structures and products.
These two domains exist as two sides of the same coin, and all things that exist in the real domain, the material domain, also exist in the imaginary domain, the spiritual domain. This would have been considered similar to the world of the soul spoken about by religions that existed in many numbers in the era of Lost Jerusalem.
(— Xenosaga's Perfect Guide, << What kind of Connection is there between the Real and Imaginary number domains? >>)
Then it's repeated when talking about Momo's consciousness.
All things that exist in the real number domain have an imaginary number domain existence. In other words, what exists in the real domain must always also exist in the imaginary domain.This is a law that does not change, whether it may be living or non-living, natural or artificial. There is no exception to this rule, even if, for example, it is something incorporeal like software. (— Xenosaga's Perfect Guide, << The Dual-Layers of All Existence >>)
Finally, Imaginary space and Imaginary time heavily influence the plot. Thus confirming that they are not exceptions. Hence, there should be an equivalent counterpart to the dimensions of the Real World Domain in the Imaginary Number One, making it a total of eight.

Of lesser importance but still worth mentioning, the creator makes a comparison between domains as being relative to how dimensions are to one another as well in the perfect guide, something that he says is true even when it comes to the relationship between the Lower and Upper Domains.
The given names <<Upper>> and <<Lower>> for the domains are nothing more than relative names. It is like how the third dimension is to the second, or how the fourth dimension is to the third. Each possess an individual time axis and space axis, but as a whole, they are elements that form one universe. In addition, it is unknown even whether or not the lower domain's concept of time exists in the upper domain in the first place.
In the section of the blog, Superiority of Imaginary Space and Time, I detail the many reasons why Imaginary Space and time are portrayed as thorough transcendent to their Real Domain Counterparts. Furthermore, all of the standard space and time model, all existing phenomena are within bounds of the Real Number Domain. Beyond that range are the contents of Y-Data which begins to cover transcendent events possible only through interference with the Imaginary Number domain and beyond.
 
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Let's say we have a 3-D cube in Real Space. Does it still appear as 3-D in Imaginary Space?
There'll be a whole cube counterpart in the imaginary number domain. One example of this are the Gnosis, the human consciousness of rejection. They are still tridimensional forms in the Imaginary Number Domain and following the flow of imaginary time, even though in the Real Number Domain their lesser counterparts are mostly composites of sodium chloride (salt) and occasionally water.
 
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Speaking of “imaginary Space” is that something related to the idea of “Space of all possible ideas”?
 
Speaking of “imaginary Space” is that something related to the idea of “Space of all possible ideas”?
Not sure what you mean with the Space of All Possible Ideas. Whether you mean what you've written in a literal sense — a space of all possibilities — or that being a theory that I don't know about. Could you clarify to me about that? Because Xenosaga's imaginary terminology, while being its own thing and having its own set of rules, was inspired by Hawking's conceptualization of Imaginary Time. Here Imaginary is approached not as something unreal, instead being something that challenges logic.

Until then, what I could tell you is that Imaginary Space is like a second reality that proceeds along an imaginary temporal axis. It complements the lower one but beings from the RND can not perceive it. << — Database Entry of Imaginary Space, Episode III. >> From a purely physical approach, imaginary Domain is what's found past planck units, a world of nothing but what's beyond the predictions of the Standard Model, quantum field theory and general relativity.

It's why the surface of the Hypersphere being connected to Imaginary Space made it immune to any interference from the Real Number Domain regardless of scale. The Hilbert Effect has a verbatim explanation of weaponizing waves that exist in both domains ❝to generate A Finitely-Bound Realm, within the limits of the senses, enabling an intersection with the Imaginary Number Domain❞.

Beyond the physical way of looking at it, the imaginary domain covers everything outside the range of existing phenomena of reality. The only potential exception being non-existence which is called the Phase Space. For example, when a human body is formed in the real number domain, its corresponding parts of the imaginary number domain are the consciousness and its concept of individuality. When someone dies they are absorbed into the Collective Unconscious that also exists in the Imaginary Domain. If they reject this merging with will, they become Gnosis that are freed from material world limitations rather than a part of the whole. In most extraordinary cases they turn into Testament retain even their reason and memories. In fact, consciousnesses are described as being limited by the flesh because while someone is alive their sensory-body counterpart narrows their consciousness perception of the Imaginary Domain.

In summary physically speaking the Imaginary Number Domain has everything beyond the normal bounds of physics and Xenosaga's reality, where even leaks of energy from it are infinite in the real number domain. But it also is where things without any scientific explanation to begin with like the soul, consciousness and concepts are.
 
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There'll be a whole cube counterpart in the imaginary number domain. One example of this are the Gnosis, the human consciousness of rejection. They are still tridimensional forms in the Imaginary Number Domain and following the flow of imaginary time, even though in the Real Number Domain their lesser counterparts are mostly composites of sodium chloride (salt) and occasionally water.
Is there any demonstrable example of the Real Domain space being infinitesimal in size to the Imaginary Domain space?
 
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Is there any demonstrable example of the Real Domain being infinitesimal in size to the Imaginary Domain?
There's a variety from different sources of the lore that indicate that.

The database's lore on Hilbert Effect that I mentioned to CNBA above explains that imaginary domain existences like the Gnosis must be forcefully captured into a finitely bound realm before they can be interacted with.

When infected by U-DO, Albedo was going to produce a Matter Shift and Anomaly between the Real and Imaginary Number Domains, which he describes as the lower dimensional creatures obtaining what they lack. Most blatant, he was going to shove the entire 3rd dimension to the imaginary one through a matter shift. An act that he described as the evolution of mankind and of the world itself. (Episode 2, Final Boss). And Albedo had been causing a Space-Time anomaly at the time, with the Database entry of Episode III describing it as a phenomenon where the boundary between real and Imaginary Space warps. The same database also says that such a thing can be caused for example by the Zohar going out of control, something that generates infinite amounts of energy.

There is a structure in the plot called an Hypersphere that becomes invulnerable to any intervention from the Real Number Domain by simply being connected to imaginary space. The only power outputs that can pierce through come from even higher in the cosmology, at a level of energy that can only come from interaction with the Upper Domain and U-DO. But Imaginary Number Domain beings can cross the surface as they please without extra effort.

It's also stated that dimensions of imaginary space and time are their own side of reality without beginning nor end, and the researcher Juli Mizrahi has a plot-relevant statement which describes the process of something shrinking to Planck Scale size before disappearing altogether from the dimension when a shift is occurring, something that happens because the only accessible area between dimensions is planck sized at best. The mass of the Abel's Ark, an U-DO terminal existence created in the imaginary number domain is simply Immeasurable even when materializing into normal space.

Xenosaga thus approaches the differences between dimensions as infinite or immeasurable in energy outputs, mass and size, the Real Number Domain consistently considered the lower of the two. Only by binding the superior beings to finite limits of the lower one and expanding the area of the Imaginary that is accessible from the physical world is interaction possible. The imaginary domain is also described multiple times as having no material limitation.

Finally, everytime that Hyperspace jumps are executed they must pseudo-construct the Real Number Domain inside the Imaginary Number Domain, to make it possible without the lower domain people imploding upon their own structure the moment they try access.
This is why, when an object that has a complicated structure in the imaginary number domain is to be transmitted, there must be protection from interference from the imaginary domain by using an isolated environment such as hyperspace and a spaceship.

"Hyperspace" is a protective tube so that interference from the imaginary domain is immediately prevented. The image of its boundary is like the inner wall of a shining tube, and it is recognized during transference as the boundary with the imaginary domain. Perhaps it can be thought to be like something that pseudo-constructs the real domain on a tube inside the imaginary domain, so to speak. (— Xenosaga's Perfect Guide, << Substance Transmission through the UMN >>)
In the Superiority of Imaginary Space Time subsection of the blog, I also explain this all in more detail. If anyone else is interested.
 
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From what I understand, 1-B seems to work for Xenosaga. That being said, I can't help but wonder if the Upper Domain's transcendence of all dimensions and the like is enough to qualify for 1-A, given our new standards on the subject matter.
Counted the vote, and thank you! About the new standards, I couldn't tell you for sure either. I'm also getting a better grasp of these changes as they come not to stake a claim that I am any expert of the standards so far either. There are reasons to believe it but there are also a contest or two to that interpretation. They make me question myself about how solid a 1-A rating would be even in the new one. If that bridge ever needs to be discussed I'll help from a neutral position or get in the way since my practical doubts are a few as well.
 
To clarify, shrinking is required to leave which dimension?
That is actually a hard one to call. It happened when the Hypersphere was passing through a space-time cleft between real and imaginary. The hypersphere itself, as mentioned above was a real domain structure with a surface connected to imaginary space. It shrunk to planck size because that's the only accessible area between two dimensions (or rather, of the imaginary number domain that is accessible from the real one), then it was converted to imaginary space that is immune to interference from real space according to the imaginary pocket entry of Episode III.
 
That is actually a hard one to call. It happened when the Hypersphere was passing through a space-time cleft between real and imaginary. The hypersphere itself, as mentioned above was a real domain structure with a surface connected to imaginary space. It shrunk to planck size because that's the only accessible area between two dimensions (or rather, of the imaginary number domain that is accessible from the real one), then it was converted to imaginary space that is immune to interference from real space according to the imaginary pocket entry of Episode III.
I see.

Is Real Space described as infinite 3-D space?
 
I see.

Is Real Space described as infinite 3-D space?
At least off the top of my mind I can't remember a verbatim statement about infinite 3-D space. The Real Number domain has the 4 standard dimensions and an origin point of the Big Bang, which the main antagonist eternally returns to before the entirety of the dimensional universe is destroyed by the power of Anima.
 
From what I've read so far, my impression is that Imaginary Time might give +1D if it meets our Higher Time Requirements.

At the moment, I only see Imaginary Space as being maybe +1D.
 
From what I've read so far, my impression is that Imaginary Time might give +1D if it meets our Higher Time Requirements.

At the moment, I only see Imaginary Space as being maybe +1D.
I'm only counting a +1 from Imaginary Time, indeed. But a +1 rather than a +3 from Imaginary Space would however run contrary to the rule of everything in the Lower Domain having an at least equal counterpart. Wouldn't that be a counter-intuitive conclusion, taking how the lore behaves in every other aspect and the author's frequent underlining of there being no exceptions? It seems divergent to the lore's observed rules that the imaginary space would only have 1 dimension when real domain space has 3.
 
I'm only counting a +1 from Imaginary Time, indeed. But a +1 rather than a +3 from Imaginary Space would however run contrary to the rule of everything in the Lower Domain having an at least equal counterpart. Wouldn't that be a counter-intuitive conclusion, taking how the lore behaves in every other aspect and the author's frequent underlining of there being no exceptions? It seems divergent to the lore's observed rules that the imaginary space would only have 1 dimension when real domain space has 3.
I don't follow your concerns.

A 3-D space and objects can fit in a 4-D Space.
 
I don't follow your concerns.

A 3-D space and objects can fit in a 4-D Space.
It's simply that the Imaginary Number Domain, specifically, has a counterpart to everything. It seems contrary to this rule of the lore to conclude that Imaginary Space only has 1 dimension because the Real Number Domain's space has three of them. That would make it so that only one out of the three dimensions of real space have a counterpart, which does break the pattern presented by the franchise whenever it speaks about these correlations.
 
It's simply that the Imaginary Number Domain, specifically, has a counterpart to everything. It seems contrary to this rule of the lore to conclude that Imaginary Space only has 1 dimension because the Real Number Domain's space has three of them. That would make it so that only one out of the three dimensions of real space have a counterpart, which does break the pattern presented by the franchise whenever it speaks about these correlations.
I didn't say that Imaginary Space has only 1 dimension. I said that it's likely a 4D space. A 4D space still has dimension 1-3.
 
I may be getting this wrong, but I believe what Magic's trying to say is that the Imaginary Number Domain contains the 4 dimensions of the Real Number Domain as an infinitesimally small part of it, and then also has 4 more dimensions, each one being an Imaginary Number Domain counterpart to said dimension in the Real Number Domain - resulting in a total of 8 dimensions
 
@Celestial_Pegasus @DarkDragonMedeus

Your further assistance in this matter is appreciated.
Currently tied up ATM, but given the Upper Domain > Lower Domain > Imaginary Numbers Domain > Real Numbers Domain with Imaginary ND having face value statements about transcending time and space; this was 1-C at minimum based on what I talked with Aeyu about years ago in Discord. And the OP added more elaborate context about each of those domains having multiple layers which basically results in 1-B minimum. Also some "Beyond Dimensions" statements might be 1-A based on some of those same conversations I had.
 
I may be getting this wrong, but I believe what Magic's trying to say is that the Imaginary Number Domain contains the 4 dimensions of the normal world as an infinitesimally small part of it, and then also has 4 more dimensions, each one being an Imaginary Number Domain counterpart to said dimension in the normal world - resulting in a total of 8 dimensions
From what I read here, 3D objects in Real Space are still seen as 3D object in Imaginary Space. It's not depicted as infinitesimal, 1D, 2D, or the like.
 
From what I read here, 3D objects in Real Space are still seen as 3D object in Imaginary Space. It's not depicted as infinitesimal, 1D, 2D, or the like.
Could be my personal view of the matter, but I feel like we would be expecting too much to say that the franchise should say word by word that objects are infinitesimally small sized rather than simply inferring that difference in scale from how things are portrayed in the series. Even if Xenosaga does have an habit of saying things verbatim a number of times.

A. Juli Mizrahi's statement regarding the passage between the cleft that separates real and imaginary.
B. The quote from the database of Hilbert Effect which does in fact call the real number domain a finitely bound realm compared to the universe without a beginning or end of the imaginary. And even fodder Gnosis can't be touched without this forced downgrade happening first.
C. Hyperspace transfer requiring a pseudo-construction of the real number domain within it. And being a realm free of all material limitations and laws of physics since otherwise they can't even exist there.
D. Something of the Imaginary Number Domain when materialized into normal space, like the Abel's Ark example above, having immeasurable mass.
Among others like the examples above.
I may be getting this wrong, but I believe what Magic's trying to say is that the Imaginary Number Domain contains the 4 dimensions of the Real Number Domain as an infinitesimally small part of it, and then also has 4 more dimensions, each one being an Imaginary Number Domain counterpart to said dimension in the Real Number Domain - resulting in a total of 8 dimensions
That is correct, yes.
 
To reitterate, do you have examples of 3-D objects in Real Space being depicted as lesser when in Imaginary Space? Are they depicted as miniscule, flat, etc?
 
That is correct, yes.
HUZZAH I UNDERSTOOD DIMENSIONALITY SHENANIGANS FOR ONCE

Anyways I'm with Magic on the fact that I don't really see how one would realistically apply this to a game outside of the most direct statement in existence. Unless I'm mistaken, 3-D beings are only really seen from the lens of other 3-D beings. It makes for much better clarity that way.
 
HUZZAH I UNDERSTOOD DIMENSIONALITY SHENANIGANS FOR ONCE

Anyways I'm with Magic on the fact that I don't really see how one would realistically apply this to a game outside of the most direct statement in existence. Unless I'm mistaken, 3-D beings are only really seen from the lens of other 3-D beings. It makes for much better clarity that way.
To take an example from comics, higher beings/spaces would depict the 3-D world as flat or miniscule.
 
To reitterate, do you have examples of 3-D objects in Real Space being depicted as lesser when in Imaginary Space? Are they depicted as miniscule, flat, etc?
I feel that the Juli Mizrahi quote about the Hypersphere that we discussed before does carry the implication that it was at best Planck-Scale Sized before disappearing altogether once it was converted to imaginary space. It being originally a huge structure rather easily seen from space. I took a new look around my folders to find the entry to the Hilbert Effect in episode III once more, and it appears to support that, since KOS-MOS's expands the absolute minimal accessible area to several million Astronomical Units.

That interpretation would also be most coherent with it being necessary for beings like Gnosis to be bound to finite and the laws of physics before they can be even interacted with. Also important is that when the previously brought up matter shift happened to the whole Earth (Lost Jerusalem), it was just shrunk to planck scale and then gone. There wasn't a planet sized Earth in the Imaginary Domain, it vanished despite very specifically being shifted to the imaginary number domain until it was shifted back nearing the end of the series.
Editing: After looking around, there is confirmation that the matter-shifted Lost Jerusalem was Planck Scale once it had shifted to the Imaginary.
Not even imaginary-domain existences can escape from the complete disappearance of the Dimensional Universe caused by the Failsafe. There is no exception to this, not even Lost Jerusalem shrunk down to Planck-scale. (— Xenosaga's Perfect Guide, << Is Lost Jerusalem safe? >>)
Other than that, I can't give you many examples of objects from the Real Number Domain existing explicitly in the Imaginary Number Domain because lore dictates that simply put, that is not possible. And judging from the entries on UMN transfer from Episode 3, even the less complex, exposed kind of transfer is done by just converting everything into information form first before having it reappear at the intended location, rather than the objects existing fully physically in the Imaginary Number Domain at any moment.
 
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(Unrelated, tomorrow is an important day here and I can not be active. Monday there's work again so I don't think that I'll be able to reply again before that late afternoon. Thank you again for the feedback from everyone so far, and until then I wish everyone a great weekend.)
 
I feel that the Juli Mizrahi quote about the Hypersphere that we discussed before does carry the implication that it was at best Planck-Scale Sized before disappearing altogether once it was converted to imaginary space. It being originally a huge structure rather easily seen from space. I took a new look around my folders to find the entry to the Hilbert Effect in episode III once more, and it appears to support that, since KOS-MOS's expands the absolute minimal accessible area to several million Astronomical Units.
From what you said earlier, "the only accessible area between dimensions is planck sized at best." To reiterate, going from Real Space to Imaginary space involves shrinking to Planck size to fit through the dimensional hole?

Let's say we have Object A of 1m size in Real Space. It shrinks to 1 Planck to pass through the area between dimensions end enters Imaginary Space. Does Object A remain planck size or is there size adjustment afterward?
 
From what you said earlier, "the only accessible area between dimensions is planck sized at best." To reiterate, going from Real Space to Imaginary space involves shrinking to Planck size to fit through the dimensional hole?

Let's say we have Object A of 1m size in Real Space. It shrinks to 1 Planck to pass through the area between dimensions end enters Imaginary Space. Does Object A remain planck size or is there size adjustment afterward?
That is correct, it becomes an imaginary number domain existence of planck scale. It is what happened to planet Earth (Lost Jerusalem) of the example above.
 
That is correct, it becomes an imaginary number domain existence of planck scale. It is what happened to planet Earth (Lost Jerusalem) of the example above.
Since that's the case, this example wouldn't fulfill the size difference requirement in the site FAQ since the object actively shrinks to appear that way.
 
Since that's the case, this example wouldn't fulfill the size difference requirement in the site FAQ since the object actively shrinks to appear that way.
It doesn't seem to me that that interpretation would work since otherwise there would be no explanation as to how Lost Jerusalem was perfectly planet sized when it was domain shifted back to the Real Number Domain at the end of the story. As the quote presented in the example goes, the planet became an imaginary domain existence, and it was a planck sized one there when it did.

When it was shifted back to the Real Number Domain it was once more a full on planet. If we operated on the logic that it was permanently shrunk specifically by the process of transfer, and not by the fact that it happens because that's the absolute extent of what the Real Number Domain can access of the Imaginary Number Domain, there would be no reason for the planet to suddenly grow in size and be perfectly habitable as it happened in the end, with the cast setting out on a journey to find them again and KOS-MOS's body drifting closer to it. It would have just stayed a planck length structure.

There would also have been no need to explain that the lower dimensions can only access a Planck Scale of the Higher Ones. Or objects and existences from the Imaginary manifested in the Real Number one having Immeasurable mass as is the case for Abel's Ark, Albedo describing the lower dimensions as lacking and being able to shift the whole dimension. The perfect guide stating that the imaginary domain has no material or physical limitations, the verbatim explanation of the Real Number Domain being a finitely bound realm in constrast to the Imaginary One.

From all that can be gathered from statements, the guide and how it behaves whenever it interacts with normal space, it appears particularly counter-intuitive to disregard them and conclude that these dimensions would be at all similar in scale.
 
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