TenSura LN Major Revision - Slime-Verse Salvation - Tier 1 Upgrade

[Worthless]

Infinite cycles where already accepted,

Yeah I remember now, no wonder why I felt de javu

. If you want to somewhat downgarde 2A to 2B then open you own crt in the future, we need to discuss 1C here.

Bet

 

[Robo432343]

i agree with 5-D

 

[Digital_Franz]

Oh come on. Can you wait for the OP to show up? The conversation is going in circles here.

 

[Mizuki67]

This will be my last reply to you. Infinite cycles where already accepted, it isn't something that we need to talk about here (and tecnically it doesn't really metter). If you want to somewhat downgarde 2A to 2B then open you own crt in the future, we need to discuss 1C hehere.

Bro stop it you are not helping .

anyways I will give my thoughts on this later

 

[Mizuki67]

I don’t even feel like reading everything he said because much of what he initially stated doesn’t match what the scans show. Besides, no amount of context can save this one, as the initial argument and the first scan from second argument strongly contradict the idea of multiple parallel worlds existing

And no, I was only addressing the 2A justification.

Please forgive berga he is new to the wiki. I believe I should add one more evidence here since you still have doubts regarding tensura infinite size. If this isn't enough then idk what is

The time compression of the mask is Infinite. Skip to 13.40


and to further clarify the mask is a subject of paradox which should be enough to prove those cycles or loops are infinite

Also the idea or the existence of parallel universes was proven somewhere in Volume 17. I believe the op explained it very well Why it follows one world theory. The rest is up to you to comprehend

 

[Bernkastelll]

Agree

 

[DarkDragonMedeus]

Looks alright

 

[CodeCCLL]

Looks alright

Can you elaborate on your thoughts? We had the necessary discussion in the comments as to why there is not enough proof for hyperspace.

 

[Robo432343]

Looks alright

 

[Astral_Trinity439]

Can you elaborate on your thoughts? We had the necessary discussion in the comments as to why there is not enough proof for hyperspace.

Hadn't we discussed that already?

Please forgive berga he is new to the wiki. I believe I should add one more evidence here since you still have doubts regarding tensura infinite size. If this isn't enough then idk what is

The time compression of the mask is Infinite. Skip to 13.40


and to further clarify the mask is a subject of paradox which should be enough to prove those cycles or loops are infinite

Also the idea or the existence of parallel universes was proven somewhere in Volume 17. I believe the op explained it very well Why it follows one world theory. The rest is up to you to comprehend

Thanks for helping while I was asleep, homie

 

[Astral_Trinity439]

Bet

One point to note, however, is that it won't effect anything whether the timelines are "Infinite" or not. Since each Timeline has its own direction of time[in-verse explained] that is unsynchronized from all other timelines, the timelines collectively, whether finite or infinite, would still be 5D. Meanwhile the encompassing Hypertimeline would also be 6D regardless.

Now, for the earlier comments

A universe : A "Timeline"
A world : A "bundle" of said timelines, self-enclosed.
I believe this scan makes that pretty damn clear, as well as the fact on how the Timeline was over at beyond space and time, yet the World hadn't reached its end, not until it reached the End of Space and Time [Beyond and End in this case are different, even the kanji is different].

Thats the simplest explanation I can give you. Other then that, I won't be replying further on questions related to this, unless it brings something new to context. A staff has agreed as well.

 

[CodeCCLL]

Hadn't we discussed that already?

Even if I assume this is the correct translation, there is no proof that the empty space in question has a structure that extends infinitely perpendicular to the timelines.

Still not enough proof for Hyperspace.

 

[Astral_Trinity439]

Still not enough proof for Hyperspace.

Using the same analogy as before in the OP, the existence of a 5th Dimensional hyperspace would be proved BY NECESSITY because the timelines' time axis extend in different directions

In such a case, the Time Axes between those Worlds, while not parallel or overlapping, would also not be Orthogonal to each other. However, there is indeed the fact that if those Time Axis are independent of each other in the sense of having a different direction, even if not orthogonal, then they can qualify for additional higher Dimensions, which would be needed for those time axes to extend to.

Basically, this is because you can draw as many "Lines" on top of each other in a 1-Dimensional Plane, and all those lines would still be in the same direction, even Anti-Parallel Lines would essentially be extending in the same direction, only difference being, simply in reversed flow. Therefore, they can still be represented in a 1-D plane. This is also why in cases where there's a Multiversal construct containing many Space-Time Continuums, by default, we assume that the Time Dimension of each of those Space-Times extends in the same direction, and therefore would not qualify for an additional Higher Dimension, as there's no need for such a higher Dimension to exist for those individual temporal Dimensions to extend to.

However, what if you draw 2 lines that are non-Parallel or "completely" overlapping? This results in you requiring a 2-Dimensional Plane to contain or draw those lines, because those lines, even if intersecting, must have some "Space" between them, if they are not parallel or completely overlapping. Even if one of the lines is parallel or overlapping with the X-Axis (and thus having its Y-coordinates as 0), the second line, which is not parallel or overlapping to it, must have "some" Y-Coordinates. Resultantly, 2 such lines would always require a 2-Directional plane to represent

And the "2-Dimensional Plane" here is referring to the hyperspace in the direction of which the Timeline's Axes extend

 

[CodeCCLL]

Using the same analogy as before in the OP

Please don't make me repeat myself again. This is a non-significant 5D space, not a Hyperspace (Low 1-C). Hyperspaces should have an axis that extends infinitely orthogonal to the timelines.

 

[Astral_Trinity439]

Please don't make me repeat myself again. This is a non-significant 5D space, not a Hyperspace (Low 1-C). Hyperspaces should have an axis that extends infinitely orthogonal to the timelines.

A time axis itself extends infinitely in its direction, spawning snapshots. If timeline A's time axis extends in the 4th Dimensional direction infinitely, that of timeline B will extend in the 5th dimension. How is that hard to understand?
The diagram makes it clear

Since the 2nd Timeline's Axis extends "Infinitely"[by nature of being a time dimension and spawning snapshots in that direction] in a direction different then the 1st timeline's direction
Tho this does not repeat with every time axis, just the first two, as explained in OP.

 

[CodeCCLL]

How is that hard to understand?

A time axis itself extends infinitely in its direction, spawning snapshots. If timeline A's time axis extends in the 4th Dimensional direction infinitely, that of timeline B will extend in the 5th dimension. How is that hard to understand?
The diagram makes it clear

Since the 2nd Timeline's Axis extends "Infinitely"[by nature of being a time dimension and spawning snapshots in that direction] in a direction different then the 1st timeline's direction
Tho this does not repeat with every time axis, just the first two, as explained in OP.

The person who doesn't understand is you. For a 5D space to be a Hyperspace, it needs proof that the additional spatial axis orthogonal to the timelines extends to infinity. I explained quite obviously in previous comments why this works the way it does.

 

[Astral_Trinity439]

The person who doesn't understand is you. For a 5D space to be a Hyperspace, it needs proof that the additional spatial axis orthogonal to the timelines extends to infinity. I explained quite obviously in previous comments why this works the way it does.

I'm pretty sure I have mentioned this before in the thread that by Hyperspace I don't mean an additional Spatial Axis, strictly speaking, but instead an axis for the Timeline to extend to. It does not have to be spatial in nature, much like the time axis in a regular space-time. I understand that well enough. The term "Hyperspace" is used for convivence........ ig I should call it temporal space at this point instead, if that term makes sense in itself to begin with[which is why I stuck with "hyperspace"].

 

[CodeCCLL]

I'm pretty sure I have mentioned this before in the thread that by Hyperspace I don't mean an additional Spatial Axis, strictly speaking, but instead an axis for the Timeline to extend to.

This my last answer unless I see anything new.

First, you presented proof for the existence of empty space at a point where the standard space-time continuum is destroyed, for a spatial axis that is orthogonal to the timelines, but when you cannot show proof that this spatial axis extends orthogonally to infinity, you mention that this could be a temporal axis. At this point, you claim that there may be 3 spatial + 3 temporal axes to obtain 1-C, but there is no proof for this, Hypertimeline (Low-1C), which has an orthogonal temporal axis to the timelines, already covers everything.

 

[Astral_Trinity439]

First, you presented proof for the existence of empty space at a point where the standard space-time continuum is destroyed, for a spatial axis that is orthogonal to the timelines, but when you cannot show proof that this spatial axis extends orthogonally to infinity,

The existence of Timeline B's time axis itself proves that, since it cannot extend in the same 4th Dimension as Timeline A. As I explained in the OP, quoting it once again, you DO NOT need direct orthogonal axes as a necessity to reach 5D. 2 non-orthogonal but unsynchronized lines need as much of an Infinite 2-Dimensional plane as a 2 orthogonal such lines. Although, once again, this does not repeat beyond once, for the first and second line.

you mention that this could be a temporal axis.

It is assumingly the "Space" containing the Timelines, that was left after the timeline was destroyed.

At this point, you claim that there may be 3 spatial + 3 temporal axes to obtain 1-C

3, yes, but not quite in the sense you're putting it. I'm referring to something like this :
3 Spatial Axes
2-Dimensional additional temporal plane required for all the timelines to extend their time dimension into, aka, this adds two dimensions to the previous 3. Total 5-D
Then another +1 Dimension for the Hypertimeline encompassing all the timelines at the same time.

I won't be replying further either if its the same points despite me explaining them in the OP and the replies many times.

 

[CodeCCLL]

you DO NOT need direct orthogonal axes as a necessity to reach 5D.

You don't really know how the mathematical dimensions work.

 

[Meli_Tempest]

Additional 5D Time Axis

Spoiler: Sum up

Since it seems that this is the most controversial point of the OP, thinking that this is a spatial dimension and not understanding that it is just an analogy, then I will show that this "other timeline" is in fact orthogonal and not only that, but it MUST exist in order to embody the view of cosmology that the OP proposes.

What the OP proposes is the idea of an additional time dimension that "holds" the non-orthogonal "streams" of time flowing in "different directions", so let's simplify it this way:

So under that idea we have two 4-dimensional spaces, represented by the coordinates (X, Y, Z, T) for the first and (X', Y', Z', T') for the second. Where each coordinate can be any real value (R). In order to represent what the OP states it is necessary to add a fifth dimension (u) which is equal to the rest in its real values.

Then in this way we can represent the two systems flowing in a different direction as a subspace within a 5-dimensional Euclidean space, so we can express each point in the space as a tuple of 5 real numbers (X, Y, Z, T, U) and (X', Y', Z', T').

About orthogonality

Spoiler: Sum up

Let's talk about orthogonality:

In this simplification, where we embody each vector of the universal tetradimensional space it is possible to demonstrate the orthogonality of the new value (u) by representing the vectors, functions and calculations that nobody here is interested in, so I will simplify it:

To prove that a vector is orthogonal to another it is necessary that its scalar product is equal to 0.

Let's consider a vector in this 5-dimensional space represented by the coordinates (x, y, z, t, u). We can define two vectors:

1. The vector representing the spatial and temporal coordinates (x, y, z, t).

2. The vector representing only the time coordinate u, i.e. (0, 0, 0, 0, 0, u).

Then we calculate its scalar product:

Scalar product = (x * 0) + (y * 0) + (z * 0) + (t * 0) + (u * 0) = 0.

Since this is a simplification of the real time line we are talking about, and a simplification of the equations needed to prove orthogonality, and will not convince many, we must also consider the following:

In order to "accommodate" two tetradimensional spaces that "flow" in non-orthogonal directions it becomes necessary to have a space in which to accommodate such a "change".

Let's simplify it further by using the analogy of the OP: to represent two lines going in two non-orthogonal directions requires the idea of a two-dimensional plane, where each line can have its own specific direction in that plane.

However, in order for this to be possible, and for each line to follow its direction properly, it is necessary that the newly added dimension be orthogonal to the first. This is because only orthogonal dimensions allow directions to be separated and represented without interfering with each other, intersecting or confusing each other. (Just as we know what happens with slime timelines).

How this works in timelines and counterarguments.

Spoiler: Sum up

However we are looking at this from a simplified, and "spatial" form so how would it work in timelines?

Let's look at it abstractly: Recall that each coordinate can be expressed as a tuple of 5 real numbers, and that each coordinate is itself a set of real numbers, i.e. it is possible to "divide" each dimension into points of the lower dimension where each can be represented by a real number. Then we can look at it in the following way:

Just as changes in time (T) affect the 3-dimensional set, changes in the second dimension of time (u) represent alterations in the 4-dimensional sets, and by varying the value of (u), changes in the coordinates of both sets will be observed. To visualize this better, we can understand that "changing the value of u" would be equivalent to choosing any number between [0 and ], and such a "change" is equal to "choosing any time" of the 4-dimensional set.

But some questions arise:

Is (u) really necessary for the two sets to "flow" in different directions?

Yes, in fact it is absolutely necessary. Let's see:

The flow of each 4-dimensional set, implies that their states change over time (u) (in fact, the Q&A page addresses this as a proof of orthogonality). We can then understand that "as u changes" the states of both sets also change. This is what allows each set to evolve and move in its own direction, even if they are not orthogonal to each other.

That is, if u does not exist, it would not be possible for two timelines (or 4D sets) to move in directions not orthogonal to each other.

How can this be asserted? Let's see:

Without the u-coordinate, there is no time dimension connecting both 4D sets, this means that there is no common frame of reference that would allow both sets to "flow" in any other apparent direction.
-
Without the u-coordinate or its orthogonal properties, it implies that the sets are in a space where their trajectories can intersect, interact; (which we know does not happen in the slime) without u, such trajectories could not be defined since there would be no "time" that allows both sets to move in their respective directions.

But, if they are orthogonal, how are the 4D sets "affected" by changes of values in u?

This is possible because of the function of u as a parameter describing the evolution and change of each set over time:

U is orthogonal in the sense that there is no direct or cross influence between changes in u and changes in the other coordinates, this means that a change in u does not directly affect X, Y, Z, T and vice versa. However, although changes in u do not directly affect the other coordinates, they do determine the state of the set at a given time.

Then we can understand that as u changes, the states of the 4-dimensional sets can be described as functions of u. Or in other words:

Even if u is orthogonal, its change causes the state of the 4-dimensional space to "update".

Conclusions:

Spoiler: Sum up

The (u) coordinate and its orthogonal properties are fundamental to allow timelines to flow in different directions not orthogonal to each other. Without this orthogonality, the 4-dimensional sets would constantly interfere with each other, which is not the case in slime. This ensures that each set maintains its own trajectory without crossing or blurring with the other.

The coordinate (u)represents the changes in the states of the 4-dimensional sets, functioning as their temporal "flow". As (u)varies, the states of both sets update and evolve, allowing each to move in its own direction over time.

Being a timeline where each point is a "moment" of the 4-dimensional set is represented by a real number, we can understand that it is an uncountable set.

Then we understand that the time dimension in which "flow through different directions" the timelines, is orthogonal and an uncountable set, thus fulfilling the necessary requirements for L1-C.

I hope that with this, it is clearer to everyone what the OP is referring to. Please I want to remind everyone that this is based entirely on what the OP posits, and the proofs for all of this are already in the thread, this is just "another way" of understanding the 5 dimensions that the OP posits. But I may still be wrong in my interpretation of the thread, so I would be grateful to Astral if he corrects me if that is the case.



I would also like to remind that much of what he posed here are simplifications or analogies to make it simpler to understand, and I fully understand the difference between the dimensions of time and space, and have posed all of it in this.



Regarding the 6 dimension, that one seems more accepted. So I don't think I need to explain it, the OP did that already very well.

 

[Digital_Franz]

Additional 5D Time Axis



Since it seems that this is the most controversial point of the OP, thinking that this is a spatial dimension and not understanding that it is just an analogy, then I will show that this "other timeline" is in fact orthogonal and not only that, but it MUST exist in order to embody the view of cosmology that the OP proposes.



What the OP proposes is the idea of an additional time dimension that "holds" the non-orthogonal "streams" of time flowing in "different directions", so let's simplify it this way:



So under that idea we have two 4-dimensional spaces, represented by the coordinates (X, Y, Z, T) for the first and (X', Y', Z', T') for the second. Where each coordinate can be any real value (R). In order to represent what the OP states it is necessary to add a fifth dimension (u) which is equal to the rest in its real values.



Then in this way we can represent the two systems flowing in a different direction as a subspace within a 5-dimensional Euclidean space, so we can express each point in the space as a tuple of 5 real numbers (X, Y, Z, T, U) and (X', Y', Z', T').



Let's talk about orthogonality:



In this simplification, where we embody each vector of the universal tetradimensional space it is possible to demonstrate the orthogonality of the new value (u) by representing the vectors, functions and calculations that nobody here is interested in, so I will simplify it:



To prove that a vector is orthogonal to another it is necessary that its scalar product is equal to 0.



Let's consider a vector in this 5-dimensional space represented by the coordinates (x, y, z, t, u). We can define two vectors:



1. The vector representing the spatial and temporal coordinates (x, y, z, t).

2. The vector representing only the time coordinate u, i.e. (0, 0, 0, 0, 0, u).



Then we calculate its scalar product:



Scalar product = (x * 0) + (y * 0) + (z * 0) + (t * 0) + (u * 0) = 0.



Since this is a simplification of the real time line we are talking about, and a simplification of the equations needed to prove orthogonality, and will not convince many, we must also consider the following:



In order to "accommodate" two tetradimensional spaces that "flow" in non-orthogonal directions it becomes necessary to have a space in which to accommodate such a "change".



Let's simplify it further by using the analogy of the OP: to represent two lines going in two non-orthogonal directions requires the idea of a two-dimensional plane, where each line can have its own specific direction in that plane.



However, in order for this to be possible, and for each line to follow its direction properly, it is necessary that such a new added dimension be orthogonal to the first one. This is so that only orthogonal dimensions are separated and represented without interfering with each other, intersecting or confusing each other. (Just as we know what happens with slime timelines).



However we are looking at this from a simplified, and "spatial" form so how would it work in timelines?



Let's look at it abstractly: Recall that each coordinate can be expressed as a tuple of 5 real numbers. Then we can look at it in the following way:



Just as changes in time (T) affect the 3-dimensional set, changes in the second dimension of time (u) represent alterations in the 4-dimensional sets, and by varying the value of (u), changes in the coordinates of both sets will be observed.



But some questions arise:



Is u really necessary for the two sets to "flow" in different directions?



Yes, in fact it is absolutely necessary. Let's see:



The flow of each 4-dimensional set, implies that their states change over time (u) (in fact, the Q&A page addresses this as a proof of orthogonality). We can then understand that "as u changes" the states of both sets also change. This is what allows each set to evolve and move in its own direction, even if they are not orthogonal to each other.



That is, if u does not exist, it would not be possible for two timelines (or 4D sets) to move in directions not orthogonal to each other.



How can this be asserted? Let's see:



Without the u-coordinate, there is no time dimension connecting both 4D sets, this means that there is no common frame of reference that would allow both sets to "flow" in any other apparent direction.



Without the u-coordinate or its orthogonal properties, it implies that the sets are in a space where their trajectories can intersect, interact; (which we know does not happen) without u, such trajectories could not be defined since there would be no "time" that allows both sets to move in their respective directions.



But, if they are orthogonal, how are the 4D sets "affected" by changes of values in u?



This is possible because of the function of u as a parameter describing the evolution and change of each set over time:



U is orthogonal in the sense that there is no direct or cross influence between changes in u and changes in the other coordinates, this means that a change in u does not directly affect X, Y, Z, T and vice versa. However, although changes in u do not directly affect the other coordinates, they do determine the state of the set at a given time.



Then we can understand that as u changes, the states of the 4-dimensional sets can be described as functions of u. Or in other words:



Even if u is orthogonal, its change causes the state of the 4-dimensional space to "update".



I hope that with this, it is clearer to everyone what the OP is referring to. Please I want to remind everyone that this is based entirely on what the OP posits, and the proofs for all of this are already in the thread, this is just "another way" of understanding the 5 dimensions that the OP posits. But I may still be wrong in my interpretation of the thread, so I would be grateful to Astral if he corrects me if that is the case.



I would also like to remind that much of what he posed here are simplifications or analogies to make it simpler to understand, and I fully understand the difference between the dimensions of time and space, and have posed all of it in this.



Regarding the 6 dimension, that one seems more accepted. So I don't think I need to explain it, the OP did that already very well.

Bro absolutely cooked . For 6-D it's clear. If each cycle already has its own time axis then 6-D follows.

 

[Shiraito983]

ill be neutral since im not expert on this topic

 

[Astral_Trinity439]

Additional 5D Time Axis



Since it seems that this is the most controversial point of the OP, thinking that this is a spatial dimension and not understanding that it is just an analogy, then I will show that this "other timeline" is in fact orthogonal and not only that, but it MUST exist in order to embody the view of cosmology that the OP proposes.



What the OP proposes is the idea of an additional time dimension that "holds" the non-orthogonal "streams" of time flowing in "different directions", so let's simplify it this way:



So under that idea we have two 4-dimensional spaces, represented by the coordinates (X, Y, Z, T) for the first and (X', Y', Z', T') for the second. Where each coordinate can be any real value (R). In order to represent what the OP states it is necessary to add a fifth dimension (u) which is equal to the rest in its real values.



Then in this way we can represent the two systems flowing in a different direction as a subspace within a 5-dimensional Euclidean space, so we can express each point in the space as a tuple of 5 real numbers (X, Y, Z, T, U) and (X', Y', Z', T').



Let's talk about orthogonality:



In this simplification, where we embody each vector of the universal tetradimensional space it is possible to demonstrate the orthogonality of the new value (u) by representing the vectors, functions and calculations that nobody here is interested in, so I will simplify it:



To prove that a vector is orthogonal to another it is necessary that its scalar product is equal to 0.



Let's consider a vector in this 5-dimensional space represented by the coordinates (x, y, z, t, u). We can define two vectors:



1. The vector representing the spatial and temporal coordinates (x, y, z, t).

2. The vector representing only the time coordinate u, i.e. (0, 0, 0, 0, 0, u).



Then we calculate its scalar product:



Scalar product = (x * 0) + (y * 0) + (z * 0) + (t * 0) + (u * 0) = 0.



Since this is a simplification of the real time line we are talking about, and a simplification of the equations needed to prove orthogonality, and will not convince many, we must also consider the following:



In order to "accommodate" two tetradimensional spaces that "flow" in non-orthogonal directions it becomes necessary to have a space in which to accommodate such a "change".



Let's simplify it further by using the analogy of the OP: to represent two lines going in two non-orthogonal directions requires the idea of a two-dimensional plane, where each line can have its own specific direction in that plane.



However, in order for this to be possible, and for each line to follow its direction properly, it is necessary that such a new added dimension be orthogonal to the first one. This is so that only orthogonal dimensions are separated and represented without interfering with each other, intersecting or confusing each other. (Just as we know what happens with slime timelines).



However we are looking at this from a simplified, and "spatial" form so how would it work in timelines?



Let's look at it abstractly: Recall that each coordinate can be expressed as a tuple of 5 real numbers. Then we can look at it in the following way:



Just as changes in time (T) affect the 3-dimensional set, changes in the second dimension of time (u) represent alterations in the 4-dimensional sets, and by varying the value of (u), changes in the coordinates of both sets will be observed.



But some questions arise:



Is u really necessary for the two sets to "flow" in different directions?



Yes, in fact it is absolutely necessary. Let's see:



The flow of each 4-dimensional set, implies that their states change over time (u) (in fact, the Q&A page addresses this as a proof of orthogonality). We can then understand that "as u changes" the states of both sets also change. This is what allows each set to evolve and move in its own direction, even if they are not orthogonal to each other.



That is, if u does not exist, it would not be possible for two timelines (or 4D sets) to move in directions not orthogonal to each other.



How can this be asserted? Let's see:



Without the u-coordinate, there is no time dimension connecting both 4D sets, this means that there is no common frame of reference that would allow both sets to "flow" in any other apparent direction.



Without the u-coordinate or its orthogonal properties, it implies that the sets are in a space where their trajectories can intersect, interact; (which we know does not happen) without u, such trajectories could not be defined since there would be no "time" that allows both sets to move in their respective directions.



But, if they are orthogonal, how are the 4D sets "affected" by changes of values in u?



This is possible because of the function of u as a parameter describing the evolution and change of each set over time:



U is orthogonal in the sense that there is no direct or cross influence between changes in u and changes in the other coordinates, this means that a change in u does not directly affect X, Y, Z, T and vice versa. However, although changes in u do not directly affect the other coordinates, they do determine the state of the set at a given time.



Then we can understand that as u changes, the states of the 4-dimensional sets can be described as functions of u. Or in other words:



Even if u is orthogonal, its change causes the state of the 4-dimensional space to "update".



I hope that with this, it is clearer to everyone what the OP is referring to. Please I want to remind everyone that this is based entirely on what the OP posits, and the proofs for all of this are already in the thread, this is just "another way" of understanding the 5 dimensions that the OP posits. But I may still be wrong in my interpretation of the thread, so I would be grateful to Astral if he corrects me if that is the case.



I would also like to remind that much of what he posed here are simplifications or analogies to make it simpler to understand, and I fully understand the difference between the dimensions of time and space, and have posed all of it in this.



Regarding the 6 dimension, that one seems more accepted. So I don't think I need to explain it, the OP did that already very well.

Spoiler: Sum up

Yeah, this pretty much follows the OP from the gist of it. Although I might have missed some parts while reading this, so will give it a reread later.

Other then that, it would be better if you used less "Spaces"[line-breaks] between lines, and separate each section, optionally with a heading, and separate those sections with Spoilers tags to compress the message as much as possible. That's also why I used the spoiler tags in the OP.
And, most importantly, thank you for writing all this, goat

On the other hand, I think you can divide the sections like this
Section 1 : Basis of the OP and Simplified form

Additional 5D Time Axis

Since it seems that this is the most controversial point of the OP, thinking that this is a spatial dimension and not understanding that it is just an analogy, then I will show that this "other timeline" is in fact orthogonal and not only that, but it MUST exist in order to embody the view of cosmology that the OP proposes.

What the OP proposes is the idea of an additional time dimension that "holds" the non-orthogonal "streams" of time flowing in "different directions", so let's simplify it this way:

So under that idea we have two 4-dimensional spaces, represented by the coordinates (X, Y, Z, T) for the first and (X', Y', Z', T') for the second. Where each coordinate can be any real value (R). In order to represent what the OP states it is necessary to add a fifth dimension (u) which is equal to the rest in its real values.

Then in this way we can represent the two systems flowing in a different direction as a subspace within a 5-dimensional Euclidean space, so we can express each point in the space as a tuple of 5 real numbers (X, Y, Z, T, U) and (X', Y', Z', T').

Section 2 : OP's Analogy

Let's talk about orthogonality:

In this simplification, where we embody each vector of the universal tetradimensional space it is possible to demonstrate the orthogonality of the new value (u) by representing the vectors, functions and calculations that nobody here is interested in, so I will simplify it:

To prove that a vector is orthogonal to another it is necessary that its scalar product is equal to 0.

Let's consider a vector in this 5-dimensional space represented by the coordinates (x, y, z, t, u). We can define two vectors:
1. The vector representing the spatial and temporal coordinates (x, y, z, t).
2. The vector representing only the time coordinate u, i.e. (0, 0, 0, 0, 0, u).

Then we calculate its scalar product:
Scalar product = (x * 0) + (y * 0) + (z * 0) + (t * 0) + (u * 0) = 0.

Since this is a simplification of the real time line we are talking about, and a simplification of the equations needed to prove orthogonality, and will not convince many, we must also consider the following:
In order to "accommodate" two tetradimensional spaces that "flow" in non-orthogonal directions it becomes necessary to have a space in which to accommodate such a "change".

Let's simplify it further by using the analogy of the OP: to represent two lines going in two non-orthogonal directions requires the idea of a two-dimensional plane, where each line can have its own specific direction in that plane.

However, in order for this to be possible, and for each line to follow its direction properly, it is necessary that such a new added dimension be orthogonal to the first one. This is so that only orthogonal dimensions are separated and represented without interfering with each other, intersecting or confusing each other. (Just as we know what happens with slime timelines).

Section 3 : Non-simplified Explanation and Counter Arguments

However we are looking at this from a simplified, and "spatial" form so how would it work in timelines?

Let's look at it abstractly: Recall that each coordinate can be expressed as a tuple of 5 real numbers. Then we can look at it in the following way:

Just as changes in time (T) affect the 3-dimensional set, changes in the second dimension of time (u) represent alterations in the 4-dimensional sets, and by varying the value of (u), changes in the coordinates of both sets will be observed.

But some questions arise:

Is u really necessary for the two sets to "flow" in different directions?

Yes, in fact it is absolutely necessary. Let's see:

The flow of each 4-dimensional set, implies that their states change over time (u) (in fact, the Q&A page addresses this as a proof of orthogonality). We can then understand that "as u changes" the states of both sets also change. This is what allows each set to evolve and move in its own direction, even if they are not orthogonal to each other.
That is, if u does not exist, it would not be possible for two timelines (or 4D sets) to move in directions not orthogonal to each other.

How can this be asserted? Let's see:

Without the u-coordinate, there is no time dimension connecting both 4D sets, this means that there is no common frame of reference that would allow both sets to "flow" in any other apparent direction.

Without the u-coordinate or its orthogonal properties, it implies that the sets are in a space where their trajectories can intersect, interact; (which we know does not happen) without u, such trajectories could not be defined since there would be no "time" that allows both sets to move in their respective directions.

But, if they are orthogonal, how are the 4D sets "affected" by changes of values in u?

This is possible because of the function of u as a parameter describing the evolution and change of each set over time:

U is orthogonal in the sense that there is no direct or cross influence between changes in u and changes in the other coordinates, this means that a change in u does not directly affect X, Y, Z, T and vice versa. However, although changes in u do not directly affect the other coordinates, they do determine the state of the set at a given time.
Then we can understand that as u changes, the states of the 4-dimensional sets can be described as functions of u. Or in other words:

Even if u is orthogonal, its change causes the state of the 4-dimensional space to "update".

I think that should sum it up.
You can do this by editing your own comment.

 

[Meli_Tempest]

Yeah, this pretty much follows the OP from the gist of it. Although I might have missed some parts while reading this, so will give it a reread later.

Other then that, it would be better if you used less "Spaces"[line-breaks] between lines, and separate each section, optionally with a heading, and separate those sections with Spoilers tags to compress the message as much as possible. That's also why I used the spoiler tags in the OP.
And, most importantly, thank you for writing all this, goat

On the other hand, I think you can divide the sections like this
Section 1 : Basis of the OP and Simplified form


Section 2 : OP's Analogy

Section 3 : Non-simplified Explanation and Counter Arguments

I think that should sum it up.
You can do this by editing your own comment.

Okay, I'll edit it now

 

[Compsito]

Additional 5D Time Axis



Since it seems that this is the most controversial point of the OP, thinking that this is a spatial dimension and not understanding that it is just an analogy, then I will show that this "other timeline" is in fact orthogonal and not only that, but it MUST exist in order to embody the view of cosmology that the OP proposes.



What the OP proposes is the idea of an additional time dimension that "holds" the non-orthogonal "streams" of time flowing in "different directions", so let's simplify it this way:



So under that idea we have two 4-dimensional spaces, represented by the coordinates (X, Y, Z, T) for the first and (X', Y', Z', T') for the second. Where each coordinate can be any real value (R). In order to represent what the OP states it is necessary to add a fifth dimension (u) which is equal to the rest in its real values.



Then in this way we can represent the two systems flowing in a different direction as a subspace within a 5-dimensional Euclidean space, so we can express each point in the space as a tuple of 5 real numbers (X, Y, Z, T, U) and (X', Y', Z', T').



Let's talk about orthogonality:



In this simplification, where we embody each vector of the universal tetradimensional space it is possible to demonstrate the orthogonality of the new value (u) by representing the vectors, functions and calculations that nobody here is interested in, so I will simplify it:



To prove that a vector is orthogonal to another it is necessary that its scalar product is equal to 0.



Let's consider a vector in this 5-dimensional space represented by the coordinates (x, y, z, t, u). We can define two vectors:



1. The vector representing the spatial and temporal coordinates (x, y, z, t).

2. The vector representing only the time coordinate u, i.e. (0, 0, 0, 0, 0, u).



Then we calculate its scalar product:



Scalar product = (x * 0) + (y * 0) + (z * 0) + (t * 0) + (u * 0) = 0.



Since this is a simplification of the real time line we are talking about, and a simplification of the equations needed to prove orthogonality, and will not convince many, we must also consider the following:



In order to "accommodate" two tetradimensional spaces that "flow" in non-orthogonal directions it becomes necessary to have a space in which to accommodate such a "change".



Let's simplify it further by using the analogy of the OP: to represent two lines going in two non-orthogonal directions requires the idea of a two-dimensional plane, where each line can have its own specific direction in that plane.



However, in order for this to be possible, and for each line to follow its direction properly, it is necessary that the newly added dimension be orthogonal to the first. This is because only orthogonal dimensions allow directions to be separated and represented without interfering with each other, intersecting or confusing each other. (Just as we know what happens with slime timelines).

However we are looking at this from a simplified, and "spatial" form so how would it work in timelines?

Let's look at it abstractly: Recall that each coordinate can be expressed as a tuple of 5 real numbers. Then we can look at it in the following way:

Just as changes in time (T) affect the 3-dimensional set, changes in the second dimension of time (u) represent alterations in the 4-dimensional sets, and by varying the value of (u), changes in the coordinates of both sets will be observed.

But some questions arise:

Is (u) really necessary for the two sets to "flow" in different directions?

Yes, in fact it is absolutely necessary. Let's see:

The flow of each 4-dimensional set, implies that their states change over time (u) (in fact, the Q&A page addresses this as a proof of orthogonality). We can then understand that "as u changes" the states of both sets also change. This is what allows each set to evolve and move in its own direction, even if they are not orthogonal to each other.

That is, if u does not exist, it would not be possible for two timelines (or 4D sets) to move in directions not orthogonal to each other.

How can this be asserted? Let's see:

Without the u-coordinate, there is no time dimension connecting both 4D sets, this means that there is no common frame of reference that would allow both sets to "flow" in any other apparent direction.
-
Without the u-coordinate or its orthogonal properties, it implies that the sets are in a space where their trajectories can intersect, interact; (which we know does not happen in the slime) without u, such trajectories could not be defined since there would be no "time" that allows both sets to move in their respective directions.

But, if they are orthogonal, how are the 4D sets "affected" by changes of values in u?

This is possible because of the function of u as a parameter describing the evolution and change of each set over time:

U is orthogonal in the sense that there is no direct or cross influence between changes in u and changes in the other coordinates, this means that a change in u does not directly affect X, Y, Z, T and vice versa. However, although changes in u do not directly affect the other coordinates, they do determine the state of the set at a given time.

Then we can understand that as u changes, the states of the 4-dimensional sets can be described as functions of u. Or in other words:

Even if u is orthogonal, its change causes the state of the 4-dimensional space to "update".




I hope that with this, it is clearer to everyone what the OP is referring to. Please I want to remind everyone that this is based entirely on what the OP posits, and the proofs for all of this are already in the thread, this is just "another way" of understanding the 5 dimensions that the OP posits. But I may still be wrong in my interpretation of the thread, so I would be grateful to Astral if he corrects me if that is the case.



I would also like to remind that much of what he posed here are simplifications or analogies to make it simpler to understand, and I fully understand the difference between the dimensions of time and space, and have posed all of it in this.



Regarding the 6 dimension, that one seems more accepted. So I don't think I need to explain it, the OP did that already very well.

I think with this everything is clear. Excellent work

 

[Fixxed]

What the OP proposes is the idea of an additional time dimension that "holds" the non-orthogonal "streams" of time flowing in "different directions", so let's simplify it this way:

The problem here is OP use how spatial dimension work to prove other axis of time dimension, thats not how its work

Even if we consider it is true, the other problem here is, it is just insinigficant space. We already agreed that all multiverse or all space or whataver that contain more than 1 universe are 5D by default due 2 lines must be displaced in 2D plane, but not as sifnificant space so cannot be low 1C

 

[Fixxed]

Slime's timeline still facing the same direction of time here
All time in every timelines are flow to the future or to the past. There are no other direction that the time flow that not to future or it reverse/past

There are no different direction of time, just OP confuse what is time axis and space axis
The standard already clear about this, about what the meaning of different time direction. Just read

Outside of explanations which state that multiple time dimensions exist it is difficult to show that a fiction has more than one. The key point that has to be established is that there is a kind of time that flows in a different direction than the past or the future or any of the spatial directions.

Things like timelines having time that passes at different rates would not qualify, as even the theory of general relativity already establishes that with just one regular time dimension time can flow at different rates in different places. Time flowing backwards in another universe would also not qualify it to have an additional time dimension, as it would still use the same directions of past and future as regular time, just with events playing out in reverse.

 

[Meli_Tempest]

The problem here is OP use how spatial dimension work to prove other axis of time dimension, thats not how its work

Even if we consider it is true, the other problem here is, it is just insinigficant space. We already agreed that all multiverse or all space or whataver that contain more than 1 universe are 5D by default due 2 lines must be displaced in 2D plane, but not as sifnificant space so cannot be low 1C

No, it is just an analogy.

The problem is that you are considering it as something spatial and not temporal, the temporal dimensions are not insignificant, and they are an uncountable set always, hence, now that I have demonstrated orthogonality, its size as a temporal axis proves itself. If it were something spatial you would have a valid point, but that is not how we treat timelines.

 

[Meli_Tempest]

Slime's timeline still facing the same direction of time here
All time in every timelines are flow to the future or to the past. There are no other direction that the time flow that not to future or it reverse/past

There are no different direction of time, just OP confuse what is time axis and space axis
The standard already clear about this, about what the meaning of different time direction. Just read

You completely missed the point, I literally explained why said timeline is orthogonal, how they work, I literally went through each point you mention step by step.

I explained the reasoning behind it in the simplest way I could find, please read carefully, that's all I will ask.

 

[LuffyRuffy46307]

I definitely agree with that completely.

 

[Fixxed]

No, it is just an analogy.

The problem is that you are considering it as something spatial and not temporal, the temporal dimensions are not insignificant, and they are an uncountable set always, hence, now that I have demonstrated orthogonality, its size as a temporal axis proves itself. If it were something spatial you would have a valid point, but that is not how we treat timelines.

Bruh the thing is the anology are not work, temporal dimension direction are not work like spatial dimension

Just a question arent every timelines in slime series have time that flow to the future or it reverse? Or it have any timeline that not flow like that?

You completely missed the point, I literally explained why said timeline is orthogonal, how they work, I literally went through each point you mention step by step.

I explained the reasoning behind it in the simplest way I could find, please read carefully, that's all I will ask.

Bruh i understand what you trying to explain, i just say your reasoning are wrong because you use spatial dimension reasoning for proving the time dimension are have different direction

The reason are makes sense but it just work for spatial dimension

 

[Meli_Tempest]

However we are looking at this from a simplified, and "spatial" form so how would it work in timelines?

Let's look at it abstractly: Recall that each coordinate can be expressed as a tuple of 5 real numbers. Then we can look at it in the following way:

Just as changes in time (T) affect the 3-dimensional set, changes in the second dimension of time (u) represent alterations in the 4-dimensional sets, and by varying the value of (u), changes in the coordinates of both sets will be observed.

But some questions arise:

Is (u) really necessary for the two sets to "flow" in different directions?

Yes, in fact it is absolutely necessary. Let's see:

The flow of each 4-dimensional set, implies that their states change over time (u) (in fact, the Q&A page addresses this as a proof of orthogonality). We can then understand that "as u changes" the states of both sets also change. This is what allows each set to evolve and move in its own direction, even if they are not orthogonal to each other.

That is, if u does not exist, it would not be possible for two timelines (or 4D sets) to move in directions not orthogonal to each other.

How can this be asserted? Let's see:

Without the u-coordinate, there is no time dimension connecting both 4D sets, this means that there is no common frame of reference that would allow both sets to "flow" in any other apparent direction.
-
Without the u-coordinate or its orthogonal properties, it implies that the sets are in a space where their trajectories can intersect, interact; (which we know does not happen in the slime) without u, such trajectories could not be defined since there would be no "time" that allows both sets to move in their respective directions.

But, if they are orthogonal, how are the 4D sets "affected" by changes of values in u?

This is possible because of the function of u as a parameter describing the evolution and change of each set over time:

U is orthogonal in the sense that there is no direct or cross influence between changes in u and changes in the other coordinates, this means that a change in u does not directly affect X, Y, Z, T and vice versa. However, although changes in u do not directly affect the other coordinates, they do determine the state of the set at a given time.

Then we can understand that as u changes, the states of the 4-dimensional sets can be described as functions of u. Or in other words:

Even if u is orthogonal, its change causes the state of the 4-dimensional space to "update".




I hope that with this, it is clearer to everyone what the OP is referring to. Please I want to remind everyone that this is based entirely on what the OP posits, and the proofs for all of this are already in the thread, this is just "another way" of understanding the 5 dimensions that the OP posits. But I may still be wrong in my interpretation of the thread, so I would be grateful to Astral if he corrects me if that is the case.



I would also like to remind that much of what he posed here are simplifications or analogies to make it simpler to understand, and I fully understand the difference between the dimensions of time and space, and have posed all of it in this.



Regarding the 6 dimension, that one seems more accepted. So I don't think I need to explain it, the OP did that already very well.

Bruh the thing is the anology are not work, temporal dimension direction are not work like spatial dimension

Just a question arent every timelines in slime series have time that flow to the future or it reverse? Or it have any timeline that not flow like that?

Bruh i understand what you trying to explain, i just say your reasoning are wrong because you use spatial dimension reasoning for proving the time dimension are have different direction

The reason are makes sense but it just work for spatial dimension

You are not understanding it at all. I am aware of the difference between time, space and their functioning and therefore I treated them as such, using a conceptual simplification since it is impossible to represent time in any other way.

It is simply that "a conceptual simplification", however do not forget how time works, treating (T) and (U) as representations of the alterations of the three-dimensional and four-dimensional spaces respectively. Nor do I treat it the way space is treated, since I established the difference between the operation between (X, Y, Z) and (T) and (U).

Everything was established, so the logic you use does not apply.

 

[Fixxed]

You are not understanding it at all. I am aware of the difference between time, space and their functioning and therefore I treated them as such, using a conceptual simplification since it is impossible to represent time in any other way.

It is simply that "a conceptual simplification", however do not forget how time works, treating (T) and (U) as representations of the alterations of the three-dimensional and four-dimensional spaces respectively. Nor do I treat it the way space is treated, since I established the difference between the operation between (X, Y, Z) and (T) and (U).

Everything was established, so the logic you use does not apply.

Hah...
Firstly, are you know what we consider as direction of time here are the flow to future or it reverse/past?

Secondly you say it get new time dimension because it hold timelines that have different direction. The thing is all timelines in here are same direction

Just tell me where in the slime verse that have other flow of time that are not past to future or reverse. Because the standard that we use literally say like that

And then, i dont know if this is just a assumtion or there are proof of that. But 4 dimensional sets? You dont mean it are the timelines right?

 

[Meli_Tempest]

Hah...
Firstly, are you know what we consider as direction of time here are the flow to future or it reverse/past?

Secondly you say it get new time dimension because it hold timelines that have different direction. The thing is all timelines in here are same direction

Just tell me where in the slime verse that have other flow of time that are not past to future or reverse. Because the standard that we use literally say like that

And then, i dont know if this is just a assumtion or there are proof of that. But 4 dimensional sets? You dont mean it are the timelines right?

Alright, I have made the issue you are concerned about clearer, you can revisit my original post if you wish.

And I have put my conclusions based entirely on the data given by the OP, if you are still left with doubts I don't know what else to do honestly.

You completely miss the point of what I am saying.

 

[Fixxed]

Alright, I have made the issue you are concerned about clearer, you can revisit my original post if you wish.

And I have put my conclusions based entirely on the data given by the OP, if you are still left with doubts I don't know what else to do honestly.

You completely miss the point of what I am saying.

Bruh i literally say based on our wiki standard. If your or OP argument dont match with that then it cannot qualify

 

[Meli_Tempest]

Bruh i literally say based on our wiki standard. If your or OP argument dont match with that then it cannot qualify

Everything established not only follows the standards established by the wiki, but I explained it so that it was possible to understand the relationship, it is literally all very clear in the conclusions. That is all I am going to mention.

You overlook what I say, you overlook features of the time dimension standards below in the Q&A. You limit yourself to straightforward statements of orthogonal directions without looking to see that everything I have stated here meets the requirement below:

“Of particular consideration are instances in which timelines as a whole are changed, such that there is a timeline (or multiple timelines) before they were changed and after they were changed or created / destroyed. As the timelines as a whole are changed, the before and after in this context can't be the past and future the timelines usually use, but should be a separate direction."

Without realizing that what the OP and I state follows that requirement, for as I stated, "For two timelines to flow in two directions not orthogonal to each other, you need the coordinate (u)" which is an additional dimension of time, it's all there. This dimension (u) serves as a representation of the changes in the sets, i.e. their flow.

Everything necessary to prove that it is orthogonal, everything necessary to prove that it is an uncountable set, everything is there, I can't do more if you don't read carefully.

 

[Fixxed]

Everything established not only follows the standards established by the wiki, but I explained it so that it was possible to understand the relationship, it is literally all very clear in the conclusions. That is all I am going to mention.

You overlook what I say, you overlook features of the time dimension standards below in the Q&A. You limit yourself to straightforward statements of orthogonal directions without looking to see that everything I have stated here meets the requirement below:

“Of particular consideration are instances in which timelines as a whole are changed, such that there is a timeline (or multiple timelines) before they were changed and after they were changed or created / destroyed. As the timelines as a whole are changed, the before and after in this context can't be the past and future the timelines usually use, but should be a separate direction."

Without realizing that what the OP and I state follows that requirement, for as I stated, "For two timelines to flow in two directions not orthogonal to each other, you need the coordinate (u)" which is an additional dimension of time, it's all there. This dimension (u) serves as a representation of the changes in the sets, i.e. their flow.

Everything necessary to prove that it is orthogonal, everything necessary to prove that it is an uncountable set, everything is there, I can't do more if you don't read carefully.

That are hypertimeline argument bruh, this has nothing to do with your and OP argument. I think you must read even below it

If you want second dimension of time than i think just use hypertimeline argument for both 5D and 6D, argument like orthogonal line or whataver like that are not work

Additional time dimension in here mean "bigger time-line", where the entirety of time in some timeline are only subject to other flow of time, past-present-future of timeline are inside another flow of time. So if you use time travel, instead you go to the past of timeline, you will go even more past than the past. Thats why if whole timeline get changed, there are one timeline before that, before and after in here are different

However, caution is necessary. As explained above, we require that the additional time dimension is "a line comprised of uncountably infinitely many points." If new versions of timelines are only created if they are changed, due to time travel for example, then the number of "snapshots" of the timeline would be far more limited. The amount of snapshots would be one more than the times the timeline was changed. So, for example, if the timeline is rewritten 2 times, there would be 3 snapshots of the timeline: the original, the timeline after the first rewrite and the timeline after the second rewrite. That are far less than the required uncountably infinitely many.

Aside from direct statements, the easiest way to confirm that the line is comprised of uncountably infinitely many points/"snapshots" is to show that the development of the timelines is time-like. I.e. typically one would want a statement indicating that the alteration of the timelines is subject to its own flow of time, or that special time travel can go to prior versions of the timelines instead of the past. The keyword in the latter case is time travel, as that specifies that the action happens through movement through something like time. Note that such statements can be considered contradicted if the fiction specifies that new versions of the timeline, i.e. additional snapshots, are only created when the timeline is altered or similar.
One other pitfall to consider is the case of branching timelines, where one can return to a past with fewer timelines by just going back to a point in the regular past that was before the split happened. In such cases one has to decide based on context if that is meant or if a prior version where the splits also didn't exist in the regular future is meant. The former case doesn't qualify for an additional time dimension, while the latter might if it meets the other outlined criteria.

 

[Fixxed]

Yeah i think i dont explain what i mean correctly here about the orthogonal argument here

What i mean every time are flow to the future or it reverse. Proving it has different direction are very hard without direct statement, some analogy are not work honestly

Lets see in slime case, the argument for proving different direction of time are because there are many timeline that have different event it also stated have other direction and axis

The problem here are direction and axis here are not mean for actual time axis but for different possibilities that branch, events that could happen, it clear because tensura use MWI cosmology. The argument trying to prove this branch of possibilities are the literal time's axis, but the nature of every timelines still the same where time that flow in every timelines still facing the future, it mean there are no other direction here and they still use the same time axis here

If we use the OP argument, because this is time dimension then X axis are flow to future or reverse direction and Y axis are flow to other direction, then the lines are not facing both X and Y axis, but just facing the X axis alone, it is very very clear the other timelines not show any different nature in time dimension with the default timeline it just show different in event that happen

I think the mistake is taking the branch of the world as literal axis of time taking the "parallel worlds" as direction of time. This is self-evident by the fact every timeline are just other event in tensura

In conclusion timelines in tensura are just branching timelines that have different events each other. They still facing the same direction or axis where time of every timelines are flow to the future and not to the different direction

 

[Meli_Tempest]

Yeah i think i dont explain what i mean correctly here about the orthogonal argument here

What i mean every time are flow to the future or it reverse. Proving it has different direction are very hard without direct statement, some analogy are not work honestly

Lets see in slime case, the argument for proving different direction of time are because there are many timeline that have different event it also stated have other direction and axis

The problem here are direction and axis here are not mean for actual time axis but for different possibilities that branch, events that could happen, it clear because tensura use MWI cosmology. The argument trying to prove this branch of possibilities are the literal time's axis, but the nature of every timelines still the same where time that flow in every timelines still facing the future, it mean there are no other direction here and they still use the same time axis here

If we use the OP argument, because this is time dimension then X axis are flow to future or reverse direction and Y axis are flow to other direction, then the lines are not facing both X and Y axis, but just facing the X axis alone, it is very very clear the other timelines not show any different nature in time dimension with the default timeline it just show different in event that happen

I think the mistake is taking the branch of the world as literal axis of time taking the "parallel worlds" as direction of time. This is self-evident by the fact every timeline are just other event in tensura

In conclusion timelines in tensura are just branching timelines that have different events each other. They still facing the same direction or axis where time of every timelines are flow to the future and not to the different direction

You are forgetting that this is not how things work in TenSura, so let's go deeper into the idea of "different non-orthogonal directions" of time by simplifying the matter into a geometrical model:

Consider a tetra-dimensional space where:

• X-axis represents the spatial dimensions.
• The Y-axis represents the ordinary time dimension, with the future upwards.

Now imagine:

• A straight line L1 extending along the Y-axis, representing the flow of ordinary time.
• A second straight line L2 moving parallel to L1, but on a different plane inclined at an angle of 0 with respect to Y.

L2 will never intersect L1, but moves "next to" it in an alternate time direction, as mentioned in the verse Each point on L2 represents a different "now" than L1, although both move in the "same general direction into the future".

From a physical point of view, this representation in geometric space suggests:

• Multiple "arrows of time" advancing in slightly different directions in space-time.
• Each arrow represents a slightly different notion of causality and time evolution.
• Observers in L1 and L2 would experience the "sense" of time in subtly but perceptibly different ways.

If we consider this idea of timelines moving in non-parallel temporal directions, then the idea of introducing an additional coordinate in order to adequately represent these different notions of time becomes necessary. Then we have to simplify (again) the model I already established in my first post, along with the new one we have:

• The X-axis represents the spatial dimensions.
• The Y-axis represents the ordinary time dimension.
• A line L2 moves in a direction not parallel, neither "superimposed" nor orthogonal to L1 (Y-axis) on a plane inclined at an angle of 0.

Now we must add:

- A fourth axis U perpendicular to the XY and XL2 planes.

Each point in space now has coordinates (x, y, z, u), where:

• (x, y, z) represents the spatial position.
• y represents the ordinary time.
• u represents the "alternative time direction" along L2.

And everything else I already established above.