Translation of this article.
Singularity (Singular Surface) [Fourth Dimensional Concept]
What is a Singularity?
Singularity refers to an [impossible crash point in space] that is caused due to [distortions] in the tridimensional universe's space.
Thanks to the Singularities, it's possible to completely bind together two points in space that are physically separated by astronomical distances. But given that both spatial areas are in a state of [Fourth Dimensional crossover], they are normally invisible to the eye.
If we had the ability to freely configure the spacetime angles in the Fourth Dimension, we would be able to go back and forth between the planets Ar Ciel and Ra Ciela in a way as easy as going to a row of doors and opening one.
Put in simpler terms, this is called a [Warp].
The Orgel of Origins also draws an astounding amount of energy from the areas around Ra Ciela's location and sends it to Ar Ciel, but this only happens because the Orgel of Origins was an item that [was capable of changing the configuration of multidimensional angles] by mere chance.
After all, the Orgel of Origins as it was originally made by the "Father of Sound Science" didn't have a power output as large as the one required to put the entire Tower of Ar tonelico in operation.
It was only later on, thanks to the extraordinary amount of research he conducted with several engineers and technicians that the Orgel's own power output could be increased to that level.
It was told to the people of that world that this increase was carried out through [D-Wave amplification techniques], but strictly speaking it was done through a technique similar to a prism that allowed to change the [multidimensional crossover] angles in multiple ways.
It was something similar to electromagnetic wave tuning, so it was tuned to end up pointing at the spatial angle where Ra Ciela was located.
Harmful Effects of the Singularities
Singularities are the main cause for the universe's contraction.
The more energy Ar tonelico uses, the more matter around Ra Ciela will be absorbed.
As matter and energy hold the same meaning under this context, it would be easier to understand if we said it is actually absorbing matter that has been converted into energy.
All in all, this is one of the laws that keep the universe in existence.
Ultimately, the proportion of existing energy and mass isn't a large problem from the universe's point of view.
For starters, the proportion of mass to energy existing in the current universe accounts for a little more than a 3% of everything that exists in it.
In other words, more than 96% of the universe is made up by energy, so to the universe, matter would be something similar to [the impurities that float within a puddle of water].
However, this would actually become a great problem for the [matter] that inhabits it. Ar tonelico has unconsciously kept on converting matter into energy ever since it started functioning, and this hasn't changed at all in the Third Era.
If it ever started using tremendous amounts of power and did so incessantly, it would ultimately cause the material universe to contract further and further, up to the point in which the entirety of the matter in it would end up converted into energy.
The only short-term solution for this would be to completely stop the source of the conversion (in both space and time).
In Ar Ciel's case, this would mean stopping the time for the Orgel of Origins and spatially isolating it.
It shouldn't ever be destroyed, as destroying it would make any means to restrain the conversion ineffective, as there is a large probability of it ending up converting the entire universe into energy at once should it ever happen.
And for a long-term solution, it would be necessary to completely eliminate the spatial singularity (make it into a Fourth Dimensional space where there are no spatial crossovers) it's connected to.
Ways for Repairing a Singularity
Given a Singularity is a crash point for tridimensional space, it would be more accurate to call it a [Singular Surface].
As we can't grasp the Fourth Dimension, we'll explain it using the bidimensional world that is located one dimension below than ours, following the logic established by the Law of Dimensional Resemblance.
By warping a bidimensional surface, we can make a line with a part where two surfaces cross over each other. This would be a Singularity in bidimensional terms, or more strictly speaking, a [Singular Line].
So by returning that warp to its original form, it would return these areas to the state they were prior to the appearance of the Singularity.
So to summarize, the current incident created a spatial distortion due to astonishing amounts of [Fourth Dimensional energy], and this generated a [Singular Surface].
This Singular Surface can be thought of as being an infinite surface existing upon a certain coordinate system.
And Ar Ciel is the planet that is riding [upon that Singular Surface].
(Strictly speaking, given the Singular Surface is a completely bidimensional plane (WH Plane) that has a zero D-width, the planet passing over it would happen only twice during the year caused by its rotational period, and it would happen in just one instant.
However, due to the effective range of the Singular Surface, even a rotational radius would become a microscopic distance small enough to be attributed to a measurement error).
Ultimately, if we could find three planets where [the Ra Cielans could live], including Ar Ciel, since the three points where they each are located had Surfaces created upon them, it would be necessary to apply a kickback at them using a force equal in strength to the one that created them, which would restore normalcy to each of these spaces.
However, the effects of the energy used for the kickback would completely pulverize all the matter existing over the Surface, including the entirety of Ar Ciel.
External Universes [Seventh Dimensional Concept]
An External Universe is strictly speaking a [world existing in a different layer of the universe].
The world where planets like Ar Ciel are and the world where Earth is exist in the same Universe of EXA_PICO, but it isn't possible for them both to see each other. The reason for this is because we and the Ar Cielans are formed by entirely different wave structures.
For example, while matter uses D-Waves for its composition in Ar Ciel, Earth uses completely different waves for that purpose (which haven't been discovered yet).
And no matter how much the Ar Cielans work into it or how much their civilization advances, the wave types they can feel are limited only to 24 specific types.
This is because the planet Ar Ciel, the creator of the Ar Cielans is formed by these 24 specific wave types, which is why they can't recognize any other waveforms that aren't comprised in the ones that give them form.
And the so-called visible [universe] the humans call the world is only a world that is visible because [a Will unexpectedly decided to maintain the existence of the D-Waves].
These maintenance and definition methods are very varied and chosen by each different Will, but it's almost unmistakable that what gives planets their characteristic globe shape is a [Will that defines D-Waves as matter].
(There also are Wills that define D-Waves as [feelings] and [energy]. We could see the jets emitted from the quasars and the nebulas as a part of them.)
It is due to these reasons that the universe is so empty as well.
The energies that are thought to exist in the darkness of the universe, called the [Dark Matter] and the [Dark Energy] are most likely made up in their entirety from waveforms we can't grasp.
And since Ar Ciel and our planet Earth are defined by different wave types (matter isn't defined by D-Waves in Earth... and it goes without saying that D-Waves don't exist in it), they can't see each other.
From the viewpoint of Earth, Ar Ciel wouldn't be more than another piece of [Dark Matter].
To explain this concept in a simpler way that focuses on tridimensional lifeforms, let's use Photoshop layers as an example.
Each layer would be separated in categories created [by the waveforms that define matter in them], so tridimensional beings wouldn't be able to see planets existing in layers different from the one they live in.
However, if there was someone who could oversee all the waveforms (all the layers) at once, they would see the universe as an incredibly crowded place.
Planets Ar Ciel, Ra Ciela and Earth
Planets Ar Ciel and Ra Ciela could be called [neighbors].
Even so, they are separated in the tridimensional plane by a distance of about 6000 light years. However, the reason we call them [neighbors] in this context is because they share similar wave compositions.
Among the 24 wave types that form Ar Ciela and Ra Ciela, roughly an 80% is common to both planets.
Therefore, these two planets (and their star systems) could be said to be siblings under the Seventh Dimensional context. Furthermore, this also makes Ar Ciel and Ra Ciela sibings under the tridimensional context.
And the reason why we are calling them siblings under both contexts is because it's relatively easy to move from one to the other.
For the sake of argument, saying that objects are siblings under the Seventh Dimensional context has a wide definition, naturally. Under this viewpoint, Ra Ciela's Sun and Ar Ciel could be also called siblings (due to them having very similar wave compositions). However, they would naturally be quite unlike from each other under the tridimensional context (due to the Sun being inhospitable for any sort of lifeform).
However, Earth would be in a very faraway position from these two planets under the Seventh Dimensional context.
This is because Earth barely contains about two or three of the waveforms that give form to Ar Ciel and to any other planets like it.
In other words, moving from either of these planets to the other would be impossible.
Even so, and leaving out the completely lack of resemblance when it comes to wave composition, it's possible that some sort of encounter or contact could be established between them.
And the [Ar nosurge Tube] that appeared this time around is a device that was created to make the link between them possible in a way similar to shooting a thread through a microscopic hole.
Connecting with External Universes
The External Universes are a concept that is grounded on a Seventh Dimensional way of thought.
Just like we just explained, they are fellow [worlds where the waves that rule over all creation carry out completely different roles].
But there are methods for establishing contact if these worlds happen to share even just one common waveform.
We'll now explain it giving a more concrete example:
Let's suppose that Ra Ciela and Earth both have [Tz-Waves] in their composition, or in other words, that it is the sole wave type they both happen to share.
And following the premise given above, if Ra Ciela possessed devices that could convert [D-Waves] into [Tz-Waves] and Earth had equipment that could convert [Tz-Waves] into [elementary particles], both material worlds would be connected.
It could be a good analogy to compare these devices to the NAT Converter feature that the Internet routers are equipped with.
So we can conclude that the [Ar nosurge Tube] that links up the external universes was the device created for that very purpose.