Why is Aleph0 > Aleph1 considered a 1d gap?

[Ezaru]

Afaik, if you have an uncountably infinite amount of universes, that makes it a low 1-C structure

Why?

I assume its the logic of uncountably infinite lines make a square

But isnt r^3 and r^4 the same cardnality?

 

[SweetDao]

But isnt r^3 and r^4 the same cardnality?

It is. What gives the "higher tier" with dimensions is solely due to how the "new points of space" are arranged. A line and a plane technically has the same cardinality, but the later one is "bigger" solely due to how it is placed (perpendicular).

Uncountably infinite universes (space-time continuums) is Low 1-C because they would need an additional dimension to be accommodated, otherwise they would just end up being interlaced in a weird way, I suppose.

 

[MasterOfArda]

The Cantor set is an example of a set with continuum-many elements, but is "nowhere dense": in practical terms, it takes up 0 space.

 

[Ezaru]

The Cantor set is an example of a set with continuum-many elements, but is "nowhere dense": in practical terms, it takes up 0 space.

How is that relevant? Im confused

I know you can divide amything like into aleph1 points, like a line segment

But I meant specifically Aleph1 amount of universes

 

[Ezaru]

It is. What gives the "higher tier" with dimensions is solely due to how the "new points of space" are arranged. A line and a plane technically has the same cardinality, but the later one is "bigger" solely due to how it is placed (perpendicular).

Uncountably infinite universes (space-time continuums) is Low 1-C because they would need an additional dimension to be accommodated, otherwise they would just end up being interlaced in a weird way, I suppose.

I guess that makes sense? Would love if anyone could explain further

 

[MasterOfArda]

Actually, I was kinda agreeing with you. What I was saying is an uncountably infinite number of Low 2-C universes could still take up zero Low 1-C space.

 

[DontTalkDT]

Cause size and cardinality are different things.

The Cantor set is an example of a set with continuum-many elements, but is "nowhere dense": in practical terms, it takes up 0 space.

One can construct sets of that nature, yes. Even ones whose Hausdorff dimension is 0, I believe.
It's a bit of nuance that was lost when the last Tiering System revision tried to simplify the explanations.

 

[MasterOfArda]

My point is it is entirely possible for a character to be able to create uncountably infinitely many Low 2-C universes, and yet still be totally incapable of affecting a Low 1-C space.

 

[Vietthai96]

Because you need a "space" with a larger size that is comparable to that of a significant Low 1-C space to contain uncountable infinite amount of low 2-c. Kinda like an equalizer. It is also somewhat based on set theory iirc, where uncountable infinite amount of point make a 1D line, uncountable infinite amount of 1D line make a 2D plane, uncountable infinite amount of 2D plane make a 3D cube, and well, continuing up to whatever D want

My point is it is entirely possible for a character to be able to create uncountably infinitely many Low 2-C universes, and yet still be totally incapable of affecting a Low 1-C space.

This is kinda verse specific thing, which is an exception, not general rule. But again i have yet too see such a thing

 

[MasterOfArda]

• you need a "space" with a larger size that is comparable to that of a significant Low 1-C space to contain uncountable infinite amount of low 2-c

You don't, though. The rules notwithstanding, uncountably infinite Low 2-C universes can be an insignificant, in fact 0-volume, Low 1-C space. A 1D line (segment) has uncountably infinite points, but the reverse is not true - uncountably infinite points do not necessarily make a 1D line (segment). In fact, uncountably infinite points can form a segment of 0 length, uncountably infinite lines can have 0 area, uncountably infinite planes can have 0 volume, and so forth.

 

[Vietthai96]

While i do agree that uncountable infinite points can form a segment of 0 length, because point is literal 0D and lack volume

The thing is, in our current standard, we need default assumption, an equalizer, so like you said, a 1D line has uncountable infinite points, Low 1-C (5D) should be uncountable infinitely > Low 2-C (4D), thus we assume that uncountable infinite amount of Low 2-C equal to a Low 1-C sized space, unless fiction went deep into this and actually clear thing up, we do some default assumption

there is a reason i always said, the insignificant 5D is bad, cause no matter how small 5D space is, it is still >>>>>>> 4D

 

[MasterOfArda]

The system is arbitrary - any method of categorization is valid. It is important to understand, thought, that in Low 1-C currently there are two types of characters:

• characters how can destroy uncountably infinite 4-D universes
• characters who can affect a 5-D universe

Characters in the second category are infinitely more powerful than the first category, but they are both grouped together in the same tier.

 

[Ezaru]

Actually, I was kinda agreeing with you. What I was saying is an uncountably infinite number of Low 2-C universes could still take up zero Low 1-C space.

Can you explain more? I am quite interested

I got you were kinda agreeing. I just figured that because they were universes they would take up more space

I read the other comments and I am still a bit confused

 

[MasterOfArda]

Here's how it works. Imagine a line - that's a 1D universe. Now let's say that line is the line X = 0. That line has infinite 1D space, but 0 2D space. The same goes with a plane in three dimensions, or a universe in four dimensions. For a concrete example, the current instant of time is an entire 3D universe, but takes up 0 space along the axis of time and thus 0 space in four dimensions. Likewise, a 4D universe takes up 0 space in five dimensions.

By the same method you can "tuck" a lower dimensional universe into a higher dimension with 0 space, you can do the same with 2, 3, 100, even countably infinite lower universes. What about uncountably infinite universes? The answer is yes! The Cantor set is a set that contains uncountably infinite points, while still taking up 0 space. Using that same set, you can tuck away uncountably infinite points in a line, lines in a plane, planes in a space, and so forth, while still taking up 0 space.

The upshot is energy in higher dimensions transcends lower dimensions, and no amount of lower dimensional space, not countably infinite, uncountably infinite, uncountably infinite universes, uncountably infinite universes of uncountably infinite universes, etc. - will ever amount to even the most miniscule amount of space or energy on a higher dimension. Therefore, characters who can create uncountably infinite 4D universes are infinitely inferior to 5D characters, even though they are in the same tier (Low 1-C).

 

[Ezaru]

Here's how it works. Imagine a line - that's a 1D universe. Now let's say that line is the line X = 0. That line has infinite 1D space, but 0 2D space. The same goes with a plane in three dimensions, or a universe in four dimensions. For a concrete example, the current instant of time is an entire 3D universe, but takes up 0 space along the axis of time and thus 0 space in four dimensions. Likewise, a 4D universe takes up 0 space in five dimensions.

Yeah that makes sense 0+0, even uncountably infinitely many times = 0?

But then why does a square have uncountably infinite lines?

I thought the uncountably infinite part like

"Bridged the gap"

By the same method you can "tuck" a lower dimensional universe into a higher dimension with 0 space, you can do the same with 2, 3, 100, even countably infinite lower universes. What about uncountably infinite universes? The answer is yes! The Cantor set is a set that contains uncountably infinite points, while still taking up 0 space. Using that same set, you can tuck away uncountably infinite points in a line, lines in a plane, planes in a space, and so forth, while still taking up 0 space.

Interesting, Ill have to look into that set

The upshot is energy in higher dimensions transcends lower dimensions,

Does it? Isnt energy scalar and non-dimensional?

and no amount of lower dimensional space, not countably infinite, uncountably infinite, uncountably infinite universes, uncountably infinite universes of uncountably infinite universes, etc. - will ever amount to even the most miniscule amount of space or energy on a higher dimension. Therefore, characters who can create uncountably infinite 4D universes are infinitely inferior to 5D characters, even though they are in the same tier (Low 1-C).

Hmmm, so you think uncountably infinite and 4d should be different tiers?

 

[Vietthai96]

Yeah that makes sense 0+0, even uncountably infinitely many times = 0?

well, for example, a line is infinite in 1 direction, but is 0 in other direction. no matter how many you stacking the line up, the other direction will not add up, because no matter how many times you stack up 0, it is still 0

But then why does a square have uncountably infinite lines?

"Uncountable infinite" is just a term that means you will never be able to count to infinity even if you have infinite amount of time to count; anything that is real number and above are all considered as uncountable infinite

so, a square have uncountable infinite number of lines since it already have volume, length in 2 directions, which, can contains infinitely many of such 1D line, but stacking up 1D line will never get you one more direction, cause it is zero in the other directions and stacking up 0 will result in 0

well it is really depend on what kind of "set' you using

 

[Ezaru]

well, for example, a line is infinite in 1 direction, but is 0 in other direction. no matter how many you stacking the line up, the other direction will not add up, because no matter how many times you stack up 0, it is still 0

Then why is uncountably infinite 1-C at all?

"Uncountable infinite" is just a term that means you will never be able to count to infinity even if you have infinite amount of time to count; anything that is real number and above are all considered as uncountable infinite

Isnt it more to due with the bijection between sets?

so, a square have uncountable infinite number of lines since it already have volume, length in 2 directions, which, can contains infinitely many of such 1D line, but stacking up 1D line will never get you one more direction, cause it is zero in the other directions and stacking up 0 will result in 0

well it is really depend on what kind of "set' you using

Why does it go one way but not the other? If a square has aleph1 lines, why are aleph1 lines not a square?

I know square can vary in size so it gets kinda weird the same way that technically destroying a 4d cube and a 4d multiverse are uncountably infinite but at different levels

 

[MeiouHades]

As others have already answered, I just want to point out that Set theory and Measure theory are different things. Many members misinterpret our tiering system and think it's all just set theory when it's not. As DT already highlighted earlier, we use the concept of a measure (hence the sigma-algebra, it's related to a measurable space R) as well to assign a "size" to these structures

 

[Ezaru]

As DT already highlighted earlier, we use the concept of a measure (hence the sigma-algebra, it's related to a measurable space R) as well to assign a "size" to these structures

Can you link any further reading or explain further? Quite interested as its the basis of the entire 2-A - 1A tier ( or 1-C to Low 1-A/H1B)

 

[Astral_Trinity439]

To put it simply, you can completely fill an infinite X-dimensional plane with a countably infinite amount of "things" that have finite non-zero extensions in those X-dimensions.

I think a simple example of dots and lines can explain this.

I think you already know the basics, a point is 0-Dimensional with zero extensions in any direction/dimension. A line segment is a set of countably infinitely many points, while a line is an a countably infinite amount of points.

But a point has zero extensions in any dimension, so let's drop that and move to another unit. A line segment.

It has a finite extension in a 1-dimensional plane. Now, if you take a countably infinite amount of line segments, it'll make a line. This is equivalent to how you can fill an infinite 4D space (2-A) with a countably infinite amount of universes.

Now, let's move on. What if there's an uncountably infinite amount of line segments? Well, we know that a set of cardinality Aleph1 cannot be put on a one-to-one correspondence with a set of cardinality Aleph0.

To explain a one-to-one correspondence in case you don't know, it's basically when you can assign one unique element of Set A to one unique element of set B, insofar as that each and every unique element of Set A is in with each and every unique element of set B, such that there's no "extra" elements from either set that don't make a pair with an element of the other set, and neither are there any overlapping elements. (Like for example, a set of 12 apples is in one-to-one correspondence with a set of 12 oranges, but a set of 11 apples is not in a one-to-one correspondence with a set of 12 oranges).

Now that that's explained, we can already see that you can't fit an uncountably infinite amount of line segments such that they occupy space equivalent to only a single line. So where do all the extra elements go? They move to another dimensional direction!

Simply put, you can just add them not in "length" but I'm "height" then, and that'll give you a higher dimension: 2-D.

In the same sense, you can't put an uncountably infinite(Aleph0) amount of universes in a countably infinite 4D plane. So you add a new direction for those universes to take place.

You can apply the same to any arbitrarily higher dimension and Infinity, upto any arbitrary layer of high 1-B+. ¯⁠\⁠⁠(⁠ツ⁠)⁠⁠/⁠¯

 

[ExcelsisBerny]

Afaik, if you have an uncountably infinite amount of universes, that makes it a low 1-C structure

Why?

That’s a valid doubt because it is technically wrong, but it’s one of those things that’s never going to be changed since doing so would mean changing the whole system and basically every tier 1 profile on the wiki lol.

 

[Vietthai96]

That’s a valid doubt because it is technically wrong, but it’s one of those things that’s never going to be changed since doing so would mean changing the whole system and basically every tier 1 profile on the wiki lol.

Actually, not that many profiles have low 1-C via uncountable infinite space-time universes or timelines. Most having either extradimension, higher dimensional stuff, or having direct 5th dimension or 5-dimensional stuffs, some have structure that trivialized/viewed tier 2 structure as insignificant thing, the last are hypertimeline thing

But yeah, could change the half the system

 

[Nekobako]

Now that that's explained, we can already see that you can't fit an uncountably infinite amount of line segments such that they occupy space equivalent to only a single line. So where do all the extra elements go? They move to another dimensional direction!

I don't get why it would be another direction instead of the bigger size. It's like uncountable infinity in size doesn't allow to exist under the same dimension when Aleph-1 set is just only bigger than Aleph-0 set.

For example with 2D square with infinite size = infinity x infinity
but a square with uncountable infinite size = Uncountable infinity x Uncountable infinity which is just only bigger than a square with infinite size but they're still 2D and only the size is different like 3x3 square is bigger than 2x2 square

If it was explained like the size of 2D is the biggest possible size which can't be bigger anymore so bigger than this 2D only the size of 3D, then it's understandable.

 

[Agnaa]

Afaik, if you have an uncountably infinite amount of universes, that makes it a low 1-C structure

Why?

I assume its the logic of uncountably infinite lines make a square

But isnt r^3 and r^4 the same cardnality?

You're tugging on a real issue here.

Yes, both of those structures have the same amount of 0-d points in them.

We try to get around this by not letting certain higher-dimensional objects get big tiers, a construct must satisfy at least one of:

1. Have the series explain that higher dimensions correspond to extreme jumps in power. If the series makes that connection, we're just following their logic.
2. Have infinitely-many dimensions. Once you cross into infinity things get weird, any movement across all these dimensions would involve traveling an infinite distance. Such odd consequences make treating such beings as superior fairly reasonable.
3. Have each zero/infinitesimal-size slice of the construct comprised of non-zero/infinitesimal mass. We assume temporal dimensions function this way, with each instant of time representing a physical copy of the universe. This lets us work off the baseline of mass/energy, making higher-dimensional constructs of this kind vastly superior, but this logic is already shaky. It isn't particularly physically meaningful to talk about repeating this process. And worse, in some fictional examples, this is established through things like "This 7-D being has a 3-D shadow with mass", but that doesn't necessarily imply that there are multiple stacking degrees of mass for each additional dimension.
4. Have the construct being affected cover all of space (and maybe also require that space to be infinite? I don't remember such fine details of our standards). This is the biggest loophole in our reasoning, imo. The fundamental idea is that, once we're talking about all of space, higher dimensions are more stuff. But the problem I see is with which other constructs we equalise this sort of thing to; is it really fair to say that a universe stated once to have 7 dimensions, would be indestructible to a 6-D character from a series where each dimension makes them unassailably more powerful?

But ultimately, it's hard to find particularly good alternatives. Alephs themselves are unwieldy due to how each new one is the power set of the previous, resulting in the gaps between them increasing, rather than staying constant, which isn't a good thing to equalise verses to. Ultimately, we'd kind of have to create our own pseudo-math to have proper structures to equalise series to, and would that really be better than moderately butchering math and physics as we are now? I think that's an open question.

 

[Ezaru]

You're tugging on a real issue here.

Yes, both of those structures have the same amount of 0-d points in them.

We try to get around this by not letting certain higher-dimensional objects get big tiers, a construct must satisfy at least one of:

1. Have the series explain that higher dimensions correspond to extreme jumps in power. If the series makes that connection, we're just following their logic.
2. Have infinitely-many dimensions. Once you cross into infinity things get weird, any movement across all these dimensions would involve traveling an infinite distance. Such odd consequences make treating such beings as superior fairly reasonable.
3. Have each zero/infinitesimal-size slice of the construct comprised of non-zero/infinitesimal mass. We assume temporal dimensions function this way, with each instant of time representing a physical copy of the universe. This lets us work off the baseline of mass/energy, making higher-dimensional constructs of this kind vastly superior, but this logic is already shaky. It isn't particularly physically meaningful to talk about repeating this process. And worse, in some fictional examples, this is established through things like "This 7-D being has a 3-D shadow with mass", but that doesn't necessarily imply that there are multiple stacking degrees of mass for each additional dimension.
4. Have the construct being affected cover all of space (and maybe also require that space to be infinite? I don't remember such fine details of our standards). This is the biggest loophole in our reasoning, imo. The fundamental idea is that, once we're talking about all of space, higher dimensions are more stuff. But the problem I see is with which other constructs we equalise this sort of thing to; is it really fair to say that a universe stated once to have 7 dimensions, would be indestructible to a 6-D character from a series where each dimension makes them unassailably more powerful?

But ultimately, it's hard to find particularly good alternatives. Alephs themselves are unwieldy due to how each new one is the power set of the previous, resulting in the gaps between them increasing, rather than staying constant, which isn't a good thing to equalise verses to. Ultimately, we'd kind of have to create our own pseudo-math to have proper structures to equalise series to, and would that really be better than moderately butchering math and physics as we are now? I think that's an open question.

Yeah, the issues with dimensional tiering seem to be pretty vast. Ive read over the few major threads by Ultima about it.

The standards one you are basically summarizing here, with added stuff, and then the r>f change

In this case (alpeh1 amount of universes being 1-C, or uncountably infinite things being 2-C) it seems like we are just roughly equating things I guess?

Like aleph1 amount of universes is above an infinite amount, but I'm not sure how that equates to 5d

Stuff gets too complicated past 2-A I swear, but its fun trying to get the math to work so I was curious

 

[Astral_Trinity439]

I don't get why it would be another direction instead of the bigger size. It's like uncountable infinity in size doesn't allow to exist under the same dimension when Aleph-1 set is just only bigger than Aleph-0 set.

That's practically the same as asking why a block of 100 meter cube cannot exist inside a space that, in all extensions, is only 10 meter cube.

For example with 2D square with infinite size = infinity x infinity

If you mean an infinite line x infinite line, yes, I get your PoV up till this point;

but a square with uncountable infinite size = Uncountable infinity x Uncountable infinity which is just only bigger than a square with infinite size but they're still 2D and only the size is different.

Thing is, we by default assume that a dimension (R) is made up of uncountably infinitely many points, so compared to a line segment (a non-zero finite length), it's only countably infinitely bigger. Like we assume a High 3-A Space is equivalent to a countably infinitely sized cube or something equivalent.

Same applies to squares; a Square that is countably infinitely bigger than a finite square is equivalent to the 2-Dimensional plane (uncountably infinitely bigger compared to a single line still).

So a square that's uncountably infinitely bigger than a finite non-zero area square won't be able to fit in a regular 2-dimensional plane. So it's a default assumption that anything bigger than the infinite plane of any X-dimension (insofar as the difference between Aleph0 and Aleph1) is 1 dimension higher than X.

Or at least this is what I understand of it.

 

[Ezaru]

That's practically the same as asking why a block of 100 meter cube cannot exist inside a space that, in all extensions, is only 10 meter cube.

If you mean an infinite line x infinite line, yes, I get your PoV up till this point;

Thing is, we by default assume that a dimension (R) is made up of uncountably infinitely many points, so compared to a line segment (a non-zero finite length), it's only countably infinitely bigger. Like we assume a High 3-A Space is equivalent to a countably infinitely sized cube or something equivalent.

Same applies to squares; a Square that is countably infinitely bigger than a finite square is equivalent to the 2-Dimensional plane (uncountably infinitely bigger compared to a single line still).

So a square that's uncountably infinitely bigger than a finite non-zero area square won't be able to fit in a regular 2-dimensional plane. So it's a default assumption that anything bigger than the infinite plane of any X-dimension (insofar as the difference between Aleph0 and Aleph1) is 1 dimension higher than X.

Or at least this is what I understand of it.

I dont really see why bigger ( cardnality wise ) = extra dimension though

 

[Vietthai96]

I dont really see why bigger ( cardnality wise ) = extra dimension though

Mathematically?, no, but the matter is not about mathematically but about how the site currently applying these thing, of which is, well, we arbitrary applies measure, space to the set, as Hades had said

As others have already answered, I just want to point out that Set theory and Measure theory are different things. Many members misinterpret our tiering system and think it's all just set theory when it's not. As DT already highlighted earlier, we use the concept of a measure (hence the sigma-algebra, it's related to a measurable space R) as well to assign a "size" to these structures

 

[Astral_Trinity439]

I dont really see why bigger ( cardnality wise ) = extra dimension though

Because you'll need an extra dimension to fit the extra stuff that can't fit otherwise due to size.

 

[IDK3465]

To put it simply, you can completely fill an infinite X-dimensional plane with a countably infinite amount of "things" that have finite non-zero extensions in those X-dimensions.

I think a simple example of dots and lines can explain this.

I think you already know the basics, a point is 0-Dimensional with zero extensions in any direction/dimension. A line segment is a set of countably infinitely many points, while a line is an a countably infinite amount of points.

But a point has zero extensions in any dimension, so let's drop that and move to another unit. A line segment.

It has a finite extension in a 1-dimensional plane. Now, if you take a countably infinite amount of line segments, it'll make a line. This is equivalent to how you can fill an infinite 4D space (2-A) with a countably infinite amount of universes.

Now, let's move on. What if there's an uncountably infinite amount of line segments? Well, we know that a set of cardinality Aleph1 cannot be put on a one-to-one correspondence with a set of cardinality Aleph0.

To explain a one-to-one correspondence in case you don't know, it's basically when you can assign one unique element of Set A to one unique element of set B, insofar as that each and every unique element of Set A is in with each and every unique element of set B, such that there's no "extra" elements from either set that don't make a pair with an element of the other set, and neither are there any overlapping elements. (Like for example, a set of 12 apples is in one-to-one correspondence with a set of 12 oranges, but a set of 11 apples is not in a one-to-one correspondence with a set of 12 oranges).

Now that that's explained, we can already see that you can't fit an uncountably infinite amount of line segments such that they occupy space equivalent to only a single line. So where do all the extra elements go? They move to another dimensional direction!

Simply put, you can just add them not in "length" but I'm "height" then, and that'll give you a higher dimension: 2-D.

In the same sense, you can't put an uncountably infinite(Aleph0) amount of universes in a countably infinite 4D plane. So you add a new direction for those universes to take place.

You can apply the same to any arbitrarily higher dimension and Infinity, upto any arbitrary layer of high 1-B+. ¯⁠\⁠⁠(⁠ツ⁠)⁠⁠/⁠¯

Sorry to barge in here, and this is pretty off-topic, but based on my limited knowledge, I'm 99% sure that both a finite line segment and a full infinite line contain an uncountably infinite number of points, so I just wanted some clarification on that

 

[MasterOfArda]

Sorry to barge in here, and this is pretty off-topic, but based on my limited knowledge, I'm 99% sure that both a finite line segment and a full infinite line contain an uncountably infinite number of points, so I just wanted some clarification on that

You are 100% correct.

 

[HammerStrikes219]

Sorry to barge in here, and this is pretty off-topic, but based on my limited knowledge, I'm 99% sure that both a finite line segment and a full infinite line contain an uncountably infinite number of points, so I just wanted some clarification on that

This is referring to the continuous time model for Tier 2 shenanigans.

I have sent a DM to DarkDragon regarding what I can find regarding not just one type of time model, but two types of time model.

https://proceedings.systemdynamics.org/2008/proceed/papers/OSSIM407.pdf

To quote what I can find from this particular article I find on the subject of time itself and solely on that one.

““Typically the time axis is divided into a number of adjacent time-segments (which are usually are of fixed length). Both the number of time intervals and time points that are specified are finite.”

The quoted part is from the Discrete Time model being used instead of continuous time model.

However, there are attempts at combining the two types of time models using both continuous and discrete time models.

Edit: Referring to the Finepoint’s point when it comes to Finite Space Time which isn’t impossible to say the least.

 

[Agnaa]

Hammer, your post is very off the mark.

This is referring to the continuous time model for Tier 2 shenanigans.

It's not. It's applicable to time, but it applies to any continuous values, and was talked about here in relation to higher tiers in general, not just time and Tier 2.

I have sent a DM to DarkDragon regarding what I can find regarding not just one type of time model, but two types of time model.

https://proceedings.systemdynamics.org/2008/proceed/papers/OSSIM407.pdf

To quote what I can find from this particular article I find on the subject of time itself and solely on that one.

““Typically the time axis is divided into a number of adjacent time-segments (which are usually are of fixed length). Both the number of time intervals and time points that are specified are finite.”

The quoted part is from the Discrete Time model being used instead of continuous time model.

You can model time as being discrete. You can also model the Earth as being hollow. This does not ultimately relate to physical reality.

The paper you post isn't even about physics, it's about system dynamics. In this case, largely relating to ideal ways of predicting the movements of stocks.

Them suggesting using discrete time to make their financial calculations easier is completely and utterly irrelevant to our website.

However, there are attempts at combining the two types of time models using both continuous and discrete time models.

That is complete and utter nonsense, when used in reference to physical reality.

The vast majority of contemporary models for a proper physical description of time have time be continuous, since relativity makes it so that different observers will agree on the duration of events, resulting in a "smallest possible unit of time" being incoherent. A few hypotheses try to figure out ways around this (in ways too mind-bending for me to reiterate right now), but they haven't had much success.

 

[Astral_Trinity439]

Sorry to barge in here, and this is pretty off-topic, but based on my limited knowledge, I'm 99% sure that both a finite line segment and a full infinite line contain an uncountably infinite number of points, so I just wanted some clarification on that

Strange. By this logic, a 3-A universe with a Time axis that isn't infinite (like for example if it's X years of time only) should also be Low 2C, yet we only consider it as such if Time is infinite like a line, and not finite like a Line segment, as in the latter case we only consider it as High 3A.

I also remember reading an article that said otherwise about a line and line segment. Will try to find it and link it when I do find it, cuz I'm pretty sure I used it in one of my sandboxes on some other wiki.

 

[HammerStrikes219]

Hammer, your post is very off the mark.

It's not. It's applicable to time, but it applies to any continuous values, and was talked about here in relation to higher tiers in general, not just time and Tier 2.

You can model time as being discrete. You can also model the Earth as being hollow. This does not ultimately relate to physical reality.

The paper you post isn't even about physics, it's about system dynamics. In this case, largely relating to ideal ways of predicting the movements of stocks.

Them suggesting using discrete time to make their financial calculations easier is completely and utterly irrelevant to our website.

That is complete and utter nonsense, when used in reference to physical reality.

The vast majority of contemporary models for a proper physical description of time have time be continuous, since relativity makes it so that different observers will agree on the duration of events, resulting in a "smallest possible unit of time" being incoherent. A few hypotheses try to figure out ways around this (in ways too mind-bending for me to reiterate right now), but they haven't had much success.

The discrete-time physics hiding inside our continuous-time world | Santa Fe Institute

physicists at the Santa Fe Institute and MIT have shown that Markov processes, widely used to model complex systems, must unfold over a larger space than previously assumed.

www.santafe.edu

It is still applicable in the realm of physics, I just using the paper for what Discrete Time means and what it has been used for.


There is also the existence of Time Crystals using Discrete Time here.

https://link.aps.org/doi/10.1103/PhysRevX.15.011055

I getting off topic here

 

[HammerStrikes219]

Strange. By this logic, a 3-A universe with a Time axis that isn't infinite (like for example if it's X years of time only) should also be Low 2C, yet we only consider it as such if Time is infinite like a line, and not finite like a Line segment, as in the latter case we only consider it as High 3A.

I also remember reading an article that said otherwise about a line and line segment. Will try to find it and link it when I do find it, cuz I'm pretty sure I used it in one of my sandboxes on some other wiki.

Line Segments & Rays | Differences & Measurement - Lesson | Study.com

Grasp the fundamentals of line segments and rays in our video lesson. Discover the differences between these geometric concepts, then test your knowledge with a quiz!

study.com

Difference Between a Line and a Line Segment: Charts and Examples

The difference between a line and line segment is that a line has no endpoints, but a line segment has two endpoints. Learn all the points of comparison in detail.

www.splashlearn.com

Mathematically wise, you are correct regarding lines and line segments in basic form of it.


Edit: There is also the open ended line segment as I kinda forget about my Basic Geometry if I gonna been honest.

 

[Agnaa]

The discrete-time physics hiding inside our continuous-time world | Santa Fe Institute

physicists at the Santa Fe Institute and MIT have shown that Markov processes, widely used to model complex systems, must unfold over a larger space than previously assumed.

www.santafe.edu

It is still applicable in the realm of physics, I just using the paper for what Discrete Time means and what it has been used for.

Wrong. Quoting from the page you linked:

physicists at the Santa Fe Institute and MIT have shown that in order for such two-time dynamics over a set of “visible states” to arise from a continuous-time Markov process, that Markov process must actually unfold over a larger space, one that includes hidden states in addition to the visible ones. They further prove that the evolution between such a pair of times must proceed in a finite number of “hidden timesteps”, subdividing the interval between those two times. (Strictly speaking, this proof holds whenever that evolution from the earlier time to the later time is noise-free — see paper for technical details.)

To illustrate the role of these hidden states, co-author Jeremy A. Owen (MIT) gives the example of a biomolecular process, observed at hour-long intervals: If you start with a protein in state ‘a,’ and over an hour it usually turns to state ‘b,’ and then after another hour it usually turns back to 'a,' there must be at least one other state ‘c' — a hidden state — that is influencing the protein's dynamics. "It's there in your biomolecular process,” he says. “If you haven’t seen it yet, you can go look for it.”

The authors stumbled on the necessity of hidden states and hidden timesteps while searching for the most energy-efficient way to flip a bit of information in a computer. In that investigation, part of a larger effort to understand the thermodynamics of computation, they discovered that there is no direct way to implement a map that both sends 1 to 0 and also sends 0 to 1. Rather, in order to flip a bit of information, the bit must proceed through at least one hidden state, and involve at least three hidden time steps.

“These kinds of models really do come up in a natural way,” Owen adds, “based on the assumptions that time is continuous, and that the state you’re in determines where you’re going to go next.”

This isn't actually saying that time is discrete. But that, for certain specific processes, that are looked at in discrete steps of time for simplicity's sake, if it's apparently oscillating between two states, there must be other hidden intermediary states (and intermediary times where it occupies those states). All the while, it's fundamentally working off of the assumption that time is physically continuous.

The paper itself, in its very introduction, says:

Throughout, we suppose that the underlying dynamics of the system are continuous-time and Markovian.

They did not use the assumption of continuous time to prove that time is discrete.

There is also the existence of Time Crystals using Discrete Time here.

https://link.aps.org/doi/10.1103/PhysRevX.15.011055

But at that point, we getting off topic here

A crystal is a system where atoms repeat periodically in space. A time crystal is a system where atoms repeat periodically in space-time.

Crystals can be thought of to break "continuous translation symmetry"; if you move an atom a little bit, that changes how it relates to its environment, because it wants to line up with the crystal lattice, and so it will behave differently. They can be thought of as instead having a "discrete translation symmetry"; if you move an atom a specific finite distance, it will be at another comparable place in the crystal structure, and so it will behave the same.

A "discrete time crystal" is a reflection of that property in time crystals.

It has nothing to do with time itself being discrete, in the same way that crystals having a regular lattice has nothing to do with space being discrete.

Your post really just reads like you searched "discrete time physics" and posted the first articles that popped up, without actually checking whether they had any relevance to the topic at hand.

Don't do that. It's a waste of everyone else's time since it takes 10x longer to debunk this nonsense than it takes for you to post it, and in that interim, it gives these false ideas more credence than they're due, by them supposedly having evidence attached.

 

[HammerStrikes219]

Wrong. Quoting from the page you linked:




This isn't actually saying that time is discrete. But that, for certain specific processes, that are looked at in discrete steps of time for simplicity's sake, if it's apparently oscillating between two states, there must be other hidden intermediary states (and intermediary times where it occupies those states). All the while, it's fundamentally working off of the assumption that time is physically continuous.

The paper itself, in its very introduction, says:

They did not use the assumption of continuous time to prove that time is discrete.

A crystal is a system where atoms repeat periodically in space. A time crystal is a system where atoms repeat periodically in space-time.

Crystals can be thought of to break "continuous translation symmetry"; if you move an atom a little bit, that changes how it relates to its environment, because it wants to line up with the crystal lattice, and so it will behave differently. They can be thought of as instead having a "discrete translation symmetry"; if you move an atom a specific finite distance, it will be at another comparable place in the crystal structure, and so it will behave the same.

A "discrete time crystal" is a reflection of that property in time crystals.

It has nothing to do with time itself being discrete, in the same way that crystals having a regular lattice has nothing to do with space being discrete.

Your post really just reads like you searched "discrete time physics" and posted the first articles that popped up, without actually checking whether they had any relevance to the topic at hand.

Don't do that. It's a waste of everyone else's time since it takes 10x longer to debunk this nonsense than it takes for you to post it, and in that interim, it gives these false ideas more credence than they're due, by them supposedly having evidence attached.

I wasn’t trying to prove time is discrete though.

As mentioned, time is believed by most scientists to being continuous, not discrete and I even say this in my initial post on the continuous time being used for Tier 2.

Granted, the wording on my end is just poor tbh.

Well, either way, I have no further input regarding that specific part there.

 

[Agnaa]

You can model the Earth as containing 99.99% of its mass in a point at its center. This would be useful for some people in certain cases to make their calculations easier.

It still has absolutely nothing to do with VSBW. And if you brought that up in a thread discussing GBE or something, it would properly be looked at with giant question marks. It has no bearing to physical reality, and no reason to be discussed. While you could say it has the tenuous link of being "a model for the planet's mass distribution", that does not make it relevant, and here, the tenuous link of "there's a model for discrete time used in some places" is completely irrelevant to this thread.

 

[HammerStrikes219]

You can model the Earth as having a single point containing 99.99% of its mass in a point at its center. This would be useful for some people in certain cases to make their calculations easier.

It still has absolutely nothing to do with VSBW. And if you brought that up in a thread discussing GBE or something, it would properly be looked at with giant question marks. It has no bearing to physical reality, and no reason to be discussed. While you could say it has the tenuous link of being "a model for the planet's mass distribution" does not make it relevant, and here, the tenuous link of "there's a model for discrete time used in some places" is completely irrelevant to this thread.

Time is part of physical reality though otherwise we wouldn’t been using space time as 4D in our current tiering system as it stands.

And the initial question was about the theoretical Low 1C being related to higher dimensional and why it qualifies as that rating.

Anyway, I will stop derailing the thread now since I did start it and all.