The commoners thread: Discussing Ultima's "On the Many, Many Incoherences of the Tiering System"

[Ben_CleverName]

Dimensions are not directions, but they correlate heavily enough to where that's mostly just semantics anyway, at least under most definitions of the word "dimension".

Saying that A>C and B>C does not imply that A and B are equivalent. It just implies that they're comparable in the sense that they're both greater than C. That alone says nothing about how much greater A and B are or the extent to which A and B are alike. Regarding the inverse example of "no matter how much 'realer' it is, it wouldn't be given extra dimensions", that's besides the point. The dimensions of the "real" object are inherently superior to the dimensions of the unreal object per Ultima's arguments. They aren't the same type of dimensions. It wouldn't really make sense to try to assign "real" dimensionality to something that is inherently unreal, anyway.

 

[Arnoldstone18]

Dimensions aren't inherently separate from realness, nah.

did anyone say otherwise?

 

[Georredannea15]

Dimensions are not directions, but they correlate heavily enough to where that's mostly just semantics anyway, at least under most definitions of the word "dimension".

Saying that A>C and B>C does not imply that A and B are equivalent. It just implies that they're comparable in the sense that they're both greater than C. That alone says nothing about how much greater A and B are or the extent to which A and B are alike. Regarding the inverse example of "no matter how much 'realer' it is, it wouldn't be given extra dimensions", that's besides the point. The dimensions of the "real" object are inherently superior to the dimensions of the unreal object per Ultima's arguments. They aren't the same type of dimensions. It wouldn't really make sense to try to assign "real" dimensionality to something that is inherently unreal, anyway.

Bro...

 

[Arnoldstone18]

It wouldn't really make sense to try to assign "real" dimensionality to something that is inherently unreal, anyway.

That was exactly my point

I recommended just making a new type for "dimensions beyond dimensions"

Which is synonymous to the meta-space @Phoenks proposed anyway, but i think modifying BDE is better.

 

[Arnoldstone18]

Bro...

Technically speaking why do we keep defining dimensions as directions and not coordinates or axes of lengths. yeah directions are related but eh.. they aren't dimensions?

 

[Georredannea15]

Technically speaking why do we keep defining dimensions as directions and not coordinates or axes of lengths. yeah directions are related but eh.. they aren't dimensions?

Both are same things bro. Those coordinate axes are the directions of movement

 

[Arnoldstone18]

Lmao...

Welp, agree to disagree i guess. Its not a big deal at the end of the day.

directions reference coordinates or axes but they aren't actually coordinates or axes themselves and idgaf enough to argue semantics. Message is still properly conveyed regardless.

 

[Phoenks]

did anyone say otherwise?

I don't honestly even know I kinda just glanced over the text and wrote down an idea... I just wanted to speak

 

[Arnoldstone18]

I don't honestly even know I kinda just glanced over the text and wrote down an idea... I just wanted to speak

Yeah we have the same idea, just different ways of going about it i guess.

What do you think of modifying BDE to add a type 3 to accommodate your meta-space idea?

 

[Iamunanimousinthat]

You could have a fiction where there are infinite dimensions, and then a reality above that where there are infinite dimensions. However, the concept of dimensions in both of those layers of reality would be separated by some kind of existential superiority.

I would argue the concept of dimensions are exactly the same. One is just real and one is less real. It's like a red ball and blue ball. Both balls, the concept of ball is the same for each of them. But one has the concept of red and one has the concept of blue.

First of all, are we still talking about Beyond Dimensional Existence here or attack potency?

I've veered off course and started talking about attack potency. No relevant to the conversation about BDE. But the second message is more general.

 

[Arnoldstone18]

I've veered off course and started talking about attack potency. No relevant to the conversation about BDE. But the second message is more general.

womp womp
you were confusing folks who just glanced through.

I would argue the concept of dimensions are exactly the same. One is just real and one is less real. It's like a red ball and blue ball. Both balls, the concept of ball is the same for each of them. But one has the concept of red and one has the concept of blue.

nobody is arguing that the concept of the ball is different. We are arguing that the concept of the blue should be separated from the red.

In other words they are simply different balls. The red isnt blue.

Does your analogy even consider that the distinction lies in the fact that "red transcends blue"? the space above is and will never be the space below.

I know you hate transcendence in R>F transcendence so bear with me here

 

[Phoenks]

What do you think of modifying BDE to add a type 3 to accommodate your meta-space idea?

hm. well, it's interesting. Here's my idea but heavily simplified because I don't want to type.

Type 1 - Simply a lack of space without necessarily transcending it.
Type 2 - A lack of space via transcending space.
Type 3 - A meta-spatial existence.
Type 4 - For perfect transduals that transcend everything by lacking everything.

So like, type 3 is a spatial entity, but it's through a different, existentially concept of space, I guess.

And Type 4 is for Tier 0s. Though it may not be necessary.

 

[Alexander]

hm. well, it's interesting. Here's my idea but heavily simplified because I don't want to type.

Type 1 - Simply a lack of space without necessarily transcending it.
Type 2 - A lack of space via transcending space.
Type 3 - A meta-spatial existence.
Type 4 - For perfect transduals that transcend everything by lacking everything.

So like, type 3 is a spatial entity, but it's through a different, existentially concept of space, I guess. For 1-As and above.

And Type 4 is for Tier 0s. Though it may not be necessary.

trascending the concept of dimensions

 

[Georredannea15]

These things are basically almost prove to impossible, but anyway...

 

[Arnoldstone18]

hm. well, it's interesting. Here's my idea but heavily simplified because I don't want to type.

Type 1 - Simply a lack of space without necessarily transcending it.
Type 2 - A lack of space via transcending space.
Type 3 - A meta-spatial existence.
Type 4 - For perfect transduals that transcend everything by lacking everything.

So like, type 3 is a spatial entity, but it's through a different, existentially concept of space, I guess.

And Type 4 is for Tier 0s. Though it may not be necessary.

Type 4 is definitely necessary since they also transcend the concept of space.

We should probably change the definition of BDE too. Welp, Ultima says he'll come around to it when he's done with stuff.

 

[Iamunanimousinthat]

nobody is arguing that the concept of the ball is different. We are arguing that the concept of the blue should be separated from the red.

In other words they are simply different balls. The red isnt blue.

Does your analogy even consider that the distinction lies in the fact that "red transcends blue"? the space above is and will never be the space below.

My argument is the distinction only lies in that red transcends blue and nothing more.

The arguments of "no matter how many dimensions you stack, a fictional setting will never be real" is an empty argument because dimensions have nothing to do with real and unreality. And the argument, "no matter how much real you make a setting, the amount of dimensions it has will remain the same" is also equally true.

 

[Phoenks]

Type for is definitely necessary since they also transcend the concept of space.

The reason I said that is because it's almost the same as Type 2 but with extra steps.

My idea is that Type 2s are essentially "voids" that don't have spatial properties but still necessarily transcend them.

Type 4s are the same, but require you to not only transcend the baseline concept of space, but any higher-extension of it, like meta-space, or meta-meta-meta-space, and etc. Since, Tier 0s can't be really be identified with any concepts at all given their nature is similar to things like negative theological objects.

 

[Iamunanimousinthat]

Sidenote, this site needs to have an objective definition of what "transcendence" is.

 

[IdiosyncraticLawyer]

Can you find a piece of fiction that explicitly states "this infinity that we're working with is aleph-0"? Aleph numbers are not the only notion of infinity. In most cases I would even assume that infinity is in reference to limits or something similar, which, no, infinity in limits is not aleph-0, or any aleph, really. To see this in action you can just multiply by 0. Aleph-0 * 0 is 0 whereas "infinity" * 0 is undefined. It's also kind of weird that you say I'm bringing "nothing new to the table" as though my ideas are irrelevant or off-topic. I am literally expanding upon ideas that Ultima himself already had. I know this, both because of what he has said on the thread and because of what we have spoken about in private.

@Ultima_Reality Could you help me here? I'm tired.

 

[Ben_CleverName]

Bro...

They literally aren't, so I don't get why the skull emoji is there. To use Wikipedia as an example, direction is described as "part of the description of how an object is placed in the space it occupies" whereas dimension is described as "the minimum number of coordinates needed to specify any point within it". Another definition that I've seen for dimension is "the least integer n for which every point has arbitrarily small neighborhoods whose boundaries have dimension less than n".

 

[Georredannea15]

They literally aren't, so I don't get why the skull emoji is there. To use Wikipedia as an example, direction is described as "part of the description of how it is placed in the space it occupies" whereas dimension is described as "the minimum number of coordinates needed to specify any point within it". Another definition that I've seen for dimension is "the least integer n for which every point has arbitrarily small neighborhoods whose boundaries have dimension less than n".

These movement directions are valid along the axis along which they extend.

For example, the 1D plane only allows you to move in the left and right directions, while the 2D plane allows you to move up and down with an extra direction of movement. Dimensions consist of axes, and axes extend along a certain direction of movement

 

[Arnoldstone18]

My argument is the distinction only lies in that red transcends blue and nothing more.

The arguments of "no matter how many dimensions you stack, a fictional setting will never be real" is an empty argument because dimensions have nothing to do with real and unreality. And the argument, "no matter how much real you make a setting, the amount of dimensions it has will remain the same" is also equally true.

okay then,

i don't mind if the concept of space persists at any R>F level, just that the dimensions of space being completely separated and independent of the space it transcends should have "BDE type 3". Hence why i said "dimensionality beyond dimensionality"...

Sidenote, this site needs to have an objective definition of what "transcendence" is.

i mean, it objectively means beyond the limits of something. Shouldn't be hard as long as we know the context of that something.

if something is a number of dimensions then occupying space beyond those dimensions qualify as transcendence. (HDE)
If something is dimensionality or the concept of dimensions then existing despite independence from those concepts qualifies as transcendence. (also qualifies for type 2 BDE too)
If something is fictional, being real is beyond fiction so that qualifies as transcendence (hence why i propose type 3 BDE)

"Transcendence" doesn't even need to apply to levels of existence, could also be applied to Attack Potency if those levels of existences are significantly affected, created or destroyed i guess.

So wdym?

 

[Ben_CleverName]

These movement directions are valid along the axis along which they extend.

For example, the 1D plane only allows you to move in the left and right directions, while the 2D plane allows you to move up and down with an extra direction of movement. Dimensions consist of axes, and axes extend along a certain direction of movement

1D can be left and right or up and down, or even forward and back, technically. What matters is that there's only one dimension and thus "two directions", in a sense, not where those directions are. The rest of what you said doesn't attack or change what I presented. I literally started my post by saying that they aren't the same things, but that they correlate heavily enough to where it doesn't technically matter for what we're using them for. All you need to do to demonstrate that they are not the same concepts is look around whatever room you're in and compare your position and orientation to the objects in question (inside your room). If we assumed they were the same thing, then there would only be three possible directions for you to be looking at, and if we took the earlier logic of assuming that each dimension gives two more directions then that would mean there are only six directions that you could be looking at. Both are obviously absurd.

 

[Agnaa]

Can you find a piece of fiction that explicitly states "this infinity that we're working with is aleph-0"?

Unsong.

This reading we derive from Georg Cantor, the German mathematician who explored the cardinality of infinite sets. He found that though the natural numbers – 1, 2, 3 and so on – were infinite, still there were fewer of them than there were “real” numbers like root 2, pi, and 0.239567990052… Indeed, not only were there two different levels of infinity, but it seemed likely that there were an infinite number of different infinities (and maybe one extra, to describe the number of infinities there were?)

[...]

“It has seemed to me for many years indispensable to fix the transfinite powers or cardinal numbers by some symbol, and after much wavering to and fro I have called upon the first letter of the Hebrew alphabet, aleph. The usual alphabets seem to me too much used to be fitted for this purpose; on the other hand, I didn’t want to invent a new sign.”

A pragmatic account, utterly without reference to a two-thousand-year-old tradition of using the aleph to signify God. Nothing is ever a coincidence. The genealogies say his grandparents were Sephardic Jews, and if they weren’t kabbalists I will eat my hat.

- Interlude ג: Cantors and Singers

SCP.

See, sometimes the infinite can be reduced to something simpler. Look here: ℵ0 and ℵ1 and ℵ2 and so on. Simple, yes, but they can each contain the world. You can glimpse it, if you look hard enough. Just breathe in, breathe out. Think about infinity. Not just countable, but uncountable, and the dimension of it goes up into uncountability too. If you think you've really understood it, you aren't thinking hard enough. Sure, zoom past the pitstops. 5, 23, 3333. They're all beautiful, but so horrendously finite. Fly past it all and keep going and going. Minds have died wishing for a fraction of what I can see. So breathe slowly, and think about it.

- Acidverse Hub, About Section-

And not exactly the same, but The Princess, the Songstress, and the Plushie mentions beths, which are typically equivalent.

"There aren't any real coincidences when dealing with other universes," Michelle explained, reciting what her magic teacher had told her. "There's an infinite number of them." It was actually an trans-infinitely high version of infinity, beth omega, but neither of them would have had the slightest clue what she was talking about. "Whatever one we get to has to have lots of things to do with us. Otherwise, we wouldn't get there." The metaphysics, expressed in mathematical terms, were beyond even her.

- Chapter 3

I know that there's many others.

 

[Arnoldstone18]

snip

thanks for listing what not to read to prevent further powerscaling brain rot

 

[Georredannea15]

1D can be left and right or up and down, or even forward and back, technically. What matters is that there's only one dimension and thus "two directions", in a sense, not where those directions are. The rest of what you said doesn't attack or change what I presented. I literally started my post by saying that they aren't the same things, but that they correlate heavily enough to where it doesn't technically matter for what we're using them for. All you need to do to demonstrate that they are not the same concepts is look around whatever room you're in and compare your position and orientation to the objects in question (inside your room). If we assumed they were the same thing, then there would only be three possible directions for you to be looking at, and if we took the earlier logic of assuming that each dimension gives two more directions then that would mean there are only six directions that you could be looking at. Both are obviously absurd.

1-D = moving in one direction of movement through that space, if you are a 1-D being, there cannot be a direction of movement like up and down, no.

Even if it moved up and down, it would still be perceived as "right-left" for that 1-D being.

Also, one dimension does not provide two directions, only one "direction of movement".

You can position a 1-dimensional line to be in the "up-down" and "forward-backward" directions for 3D beings because we can perceive these directions of motion, but a 1-dimensional line would not be able to perceive these directions of motion that we perceive, the directions of motion that are "up-down" or "forward-backward" for us would still be "left-right" for this line.

They cannot move in up-down or forward-backward directions.

 

[Ben_CleverName]

Unsong.

SCP.

And not exactly the same, but The Princess, the Songstress, and the Plushie mentions beths, which are typically equivalent.

I know that there's many others.

I know there are, too. My question wasn't meant to be interpreted as a literal "there are no verses that outright state they're talking about aleph-0" but rather that in the majority of cases "infinity" is taken to mean aleph-0 without further context to it. I don't think it's an unreasonable standard to have, given that aleph-0 is an infinite number, but it isn't infinity itself. I was mainly attacking the statement that aleph-0 specifically was what was common in fiction rather than just the notion of something that is endless or infinite in some way. Though I'm curious, Agnaa, do you know of any that explicitly mention inaccessible cardinals? I imagine a few of the ones you already listed do that, but I'm still curious. The rarity of their appearance was also part of the discussion.

 

[Agnaa]

I know there are, too. My question wasn't meant to be interpreted as a literal "there are no verses that outright state they're talking about aleph-0" but rather that in the majority of cases "infinity" is taken to mean aleph-0 without further context to it. I don't think it's an unreasonable standard to have, given that aleph-0 is an infinite number, but it isn't infinity itself. I was mainly attacking the statement that aleph-0 specifically was what was common in fiction rather than just the notion of something that is endless or infinite in some way.

I'm not really sure what you mean by this. Aleph-0 is chosen because it's the smallest concretely defined infinite quantity. Why would we choose something else, assuming something far larger?

Though I'm curious, Agnaa, do you know of any that explicitly mention inaccessible cardinals? I imagine a few of the ones you already listed do that, but I'm still curious. The rarity of their appearance was also part of the discussion.

Nope. None of the verses I mentioned above mention inaccessible cardinals.

To go to those I'd have to try to recall verses other people have mentioned to me, they probably come up in Flatterland and some of Rudy Rucker's stuff, but I haven't read either and so couldn't give quotes.

 

[Ben_CleverName]

1-D = moving in one direction of movement through that space, if you are a 1-D being, there cannot be a direction of movement like up and down, no.

There are no 1D beings (or 1D spaces) for us to observe and come to any conclusion regarding the nature of "movement" unless you're using that word under a context I'm not familiar with at present.

Even if it moved up and down, it would still be perceived as "right-left" for that 1-D being.

You can position a 1-dimensional line to be in the "up-down" and "forward-backward" directions for 3D beings because we can perceive these directions of motion, but a 1-dimensional line would not be able to perceive these directions of motion that we perceive, the directions of motion that are "up-down" or "forward-backward" for us would still be "left-right" for this line.

So in other words, the exact specifics of them being up and down or right and left are not important, as I already said (or was trying to say, at any rate). Those words rely on a specific frame of reference, though if I were to describe it, I'd say it would be perceived as forward-back (or only forward since they can't really "turn" themselves around) since we "look" forward to see what's in front of us. But again, that distinction isn't important.

They cannot move in up-down or forward-backward directions.

They cannot move in any direction, because they do not exist. I'm unaware of any mathematical models or axioms that would simulate movement for lower-dimensional entities and then restrict that movement by saying they can only move in one direction.

Regardless, this still doesn't change the fact that dimension and direction are not the same things, but I would prefer we not flood the thread with this conversation, as I don't want to inadvertently steer it off-topic. Whether or not they are the same things doesn't impact Ultima's revisions much, if at all.

 

[Ben_CleverName]

I'm not really sure what you mean by this. Aleph-0 is chosen because it's the smallest concretely defined infinite quantity. Why would we choose something else, assuming something far larger?

I don't think you should want to, I was just saying that the option existed since alephs are not the only example of infinity being used in a mathematical context (see the earlier comment I made for another example).
But as for my personal opinion, I think it would be strange to try and define something in a cardinal sense when it's not meant to be treated as a set, such as an object's measure in volume. An object's volume isn't a measure of its "cardinality" but I still see some people say things like "this object has aleph-0 volume". There might be some other notions of "aleph-0" that aren't specifically linked to cardinality which would be applicable here, in which case, feel free to mention them, but I'm not aware of any.

 

[Ben_CleverName]

Nope. None of the verses I mentioned above mention inaccessible cardinals.

To go to those I'd have to try to recall verses other people have mentioned to me, they probably come up in Flatterland and some of Rudy Rucker's stuff, but I haven't read either and so couldn't give quotes.

I meant to add this to my last post but I forgot--

I'm surprised SCP doesn't have at least some mentioning of it, personally. But regardless, the original discussion seems to have died down or at least been put on hold.

 

[Agnaa]

I don't think you should want to, I was just saying that the option existed since alephs are not the only example of infinity being used in a mathematical context (see the earlier comment I made for another example).
But as for my personal opinion, I think it would be strange to try and define something in a cardinal sense when it's not meant to be treated as a set, such as an object's measure in volume. An object's volume isn't a measure of its "cardinality" but I still see some people say things like "this object has aleph-0 volume". There might be some other notions of "aleph-0" that aren't specifically linked to cardinality which would be applicable here, in which case, feel free to mention them, but I'm not aware of any.

I was under the impression that cardinality was related to the size of sets, which makes it seem pretty applicable to something like volume.

I meant to add this to my last post but I forgot--

I'm surprised SCP doesn't have at least some mentioning of it, personally. But regardless, the original discussion seems to have died down or at least been put on hold.

Maybe SCP does actually, I haven't kept up with it for years.

 

[Oblivion_Of_The_Endless]

I'm surprised SCP doesn't have at least some mentioning of it

It does actually

 

[Arnoldstone18]

1-D = moving in one direction of movement through that space, if you are a 1-D being, there cannot be a direction of movement like up and down, no.

Even if it moved up and down, it would still be perceived as "right-left" for that 1-D being.

Also, one dimension does not provide two directions, only one "direction of movement".

You can position a 1-dimensional line to be in the "up-down" and "forward-backward" directions for 3D beings because we can perceive these directions of motion, but a 1-dimensional line would not be able to perceive these directions of motion that we perceive, the directions of motion that are "up-down" or "forward-backward" for us would still be "left-right" for this line.

They cannot move in up-down or forward-backward directions.

Oh my days bro...

There is no "right-left" or "left-right" for a 1-D being. Directions don't exists to them.

moving only up and down is still 1 direction of movement through space
moving only back and forth is still 1 direction of movement
moving only left and right is still 1 direction of movement

All of the above is 1-D and can be perceived by a 1-D being just not as directions but as path with no orientation. No orientation means no direction. Thats why i told you dimensions are not technically directions of movement but are only heavily related because directions (up down left right front back) do not matter when it comes to a 1-D being's perception or movement. It only matters to us because we have the ability to describe "orientation" via referencing dimensions.

thats why i said we are only arguing semantics. lets drop this lame ass debate. If you respond to me by boldening a specific phrase or sentence i hope you receive a slap.

 

[Georredannea15]

Oh my days bro...

There is no "right-left" or "left-right" for a 1-D being. Directions don't exists to them.

moving only up and down is still 1 direction of movement through space
moving only back and forth is still 1 direction of movement
moving only left and right is still 1 direction of movement

All of the above is 1-D and can be perceived by a 1-D being just not as directions but as path with no orientation. No orientation means no direction. Thats why i told you dimensions are not technically directions of movement but are only heavily related because directions (up down left right front back) do not matter when it comes to a 1-D being's perception or movement. It only matters to us because we have the ability to describe "orientation" via referencing dimensions.

thats why i said we are only arguing semantics. lets drop this lame ass debate. If you respond to me by boldening a specific phrase or sentence i hope you receive a slap.

Lmao no, no no no... Even the X axis in the coordinate system, the 1D axis, extends in the "right-left" direction.

Even if we 3D beings extend this line in a different way, a 1D line will always be able to grasp the right-left direction.

 

[Ben_CleverName]

I was under the impression that cardinality was related to the size of sets, which makes it seem pretty applicable to something like volume.

You don't measure an object's volume in terms of sets or cardinals. I mean, it's not impossible to try and make a set like that, I guess, but it's definitely not standard practice and it's not exactly useful without predefining some things. For example, let's say an object's volume is 2.5 cubic inches (doesn't matter the object). 2.5 obviously can't be its cardinality because decimal numbers are not cardinal numbers. A finite cardinal number has to be a natural number. You could try and create a different kind of set to compare its volume another way, but even then you wouldn't really be measuring an object's volume, you'd just be creating a set that compares to its volume.

 

[Agnaa]

Lmao no, no no no... Even the X axis in the coordinate system, the 1D axis, extends in the "right-left" direction.

Even if we 3D beings extend this line in a different way, a 1D line will always be able to grasp the right-left direction.

You're wrong.

Those names we give are arbitrary labels. There is no objective left-right or up-down.

On top of that, dimensions are not ordered. There is no "First dimension" which is labelled "left-right" by convention. There are three dimensions of space, we can't say which comes "before" or "after" others". The only distinction we can draw are between spatial dimensions and temporal dimensions.

 

[Georredannea15]

You're wrong.

Those names we give are arbitrary labels. There is no objective left-right or up-down.

On top of that, dimensions are not ordered. There is no "First dimension" which is labelled "left-right" by convention. There are three dimensions of space, we can't say which comes "before" or "after" others". The only distinction we can draw are between spatial dimensions and temporal dimensions.

Yes, that's not what I meant, for us 3-dimensional beings this is the case, but from the perspective of the 1-dimensional line this is not the case, for them there is always one direction of movement. That's what I wanted to say and that there was always only one movement of direction for them, i hope that's clear.

 

[Agnaa]

Yes, that's not what I meant, for us 3-dimensional beings this is the case, but from the perspective of the 1-dimensional line this is not the case, for them there is always one direction of movement.

Under certain assumptions, probably, but that's mainly due to real beings existing as emanations of fields which fill up however many dimensions actually exist in their reality. So a one-dimensional being would require a one-dimensional reality.

I don't think it's actually incoherent, under vastly different laws of physics, for beings to be able to move through higher-dimensional spaces.

 

[IdiosyncraticLawyer]

Nope. None of the verses I mentioned above mention inaccessible cardinals.

SCP does. From SCP-7650 (fifth footnote):

A significant one is that of a hierarchy of alephs dictated by their mathematical size. Under recent research, this hierarchy stretches to all possible uncountables prior the Inaccessible Cardinal.