PureBasic Forums - English

Maybe I may be wrong but I share you my images to better to understand it

1D is only left or right and 2D left, right, up and down :



3D is left, right, up, down, forward and back



4D is an extrusion of 6D, each sub 3D is 18D (6D * 3D), same as 3D but adding extra dimension to make 4D in 18D, it is most complicate to explain here




What is your thought of that ?

PS : Each dimension I extrude to extra dimension so it looks like that instead of shift

I make 7D => 42D !!!



It looks like more and more a spherical

threedslider wrote: Sat Jan 03, 2026 12:05 pm 4D is an extrusion of 6D, each sub 3D is 18D (6D * 3D), same as 3D but adding extra dimension to make 4D in 18D, it is most complicate to explain here
What is your thought of that ?
PS : Each dimension I extrude to extra dimension so it looks like that instead of shift

No, you can not extrude the 4th dimension into a direction (dimension) you already did an extrusion.

STARGÅTE wrote: Sat Jan 03, 2026 12:24 pm No, you can not extrude the 4th dimension into a direction (dimension) you already did an extrusion.

Why not ? 4D is not a cube, it is more complicate than the 3D (cube, the very low approximation), i mean 4D is as double of 3D so it is 6D, this extra dimension adding the sub of 3D and more and more extra dimension it looks like spherical higher dimension

However I would like to know your version of 4D, what is meaning for you ?

4D is relative to time and space.
Like this:

6D is 3D with 6 faces, but i think is not called 6D.
From your perspective only can see 3 faces at time.
And 4D is relative to the position in space at time. Second one is in 0,0,0 and in second 10 is in 10,0,0.
I think 4D is not volume, except if the volume is animated too.

minimy wrote: Sat Jan 03, 2026 12:42 pm 4D is relative to time and space.
Like this:

Ok but your 4D is more like 3d + time than the 4D ! Because of cube translate from A to B, difficult to explain

My interpretation of 4D is an universe has 3D inside de box + the sub 3D are outside the box, the 6D are something everywhere of sides

Your picture has 1D, 2D and 3D of lines but not 4D...

minimy wrote: Sat Jan 03, 2026 12:45 pm 6D is 3D with 6 faces, but i think is not called 6D.
From your perspective only can see 3 faces at time.
And 4D is relative to the position in space at time. Second one is in 0,0,0 and in second 10 is in 10,0,0.
I think 4D is not volume, except if the volume is animated too.

Thanks for your thought, I think 4D is something curved than line as 3D cube, difficult to show it...

the extra 4D is showing a "ghost" as 3D real world and plus 1D "invisible world", the 1D is something as time (left or right, or better past or futur...), not needed to be straight line but more fractal, curved in distance...

Yes, have 4D. The 4D concept is time and space is not physic. Is the relation of movement between time and space.
When you are talking about 6D is 3D with 6 faces. 3D is based in perspective, isometric, bla.. bla.. (look the red lines).
Your 3D object can be in any position in space in the second 1 and in second 10 is in another place.
I dont know any thing about 'physic' 4D.
May be what the 5th dimension is unknown

WIKIPEDIA:
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions.
Then 4D is the movement in space:

5D is more like as 3D space + 2D space = unknow picture !!

Yeah 4D nobody has a picture of that, I think 4D is a space time as "fractured" and curved so more complicate than you may think

However your second 10 I don't understand it your thought, you mean 10D ?

minimy wrote: Sat Jan 03, 2026 1:18 pm WIKIPEDIA:
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions.
Then 4D is the movement in space:

Yeah something more like this but not sure if it is a 4D as movement space... Because 3D is volume so 4D is volume+time that make unique space time than 3D

Maybe something like this :

https://fr.wikipedia.org/wiki/Espace_%C ... 0-cell.gif

more complex than Cube

threedslider wrote: Sat Jan 03, 2026 12:37 pm

STARGÅTE wrote: Sat Jan 03, 2026 12:24 pm No, you can not extrude the 4th dimension into a direction (dimension) you already did an extrusion.

Why not ? 4D is not a cube, it is more complicate than the 3D (cube, the very low approximation), i mean 4D is as double of 3D so it is 6D, this extra dimension adding the sub of 3D and more and more extra dimension it looks like spherical higher dimension
However I would like to know your version of 4D, what is meaning for you ?

Your line is an extrusion of a point in x-direction (1st dimension).
Your square is an extrusion of a line in y-direction (2st dimension).
Your cube is an extrusion of a square in z-direction (3st dimension).
Logically, then a hyper cube can't be an extrusion of a cube in x-, y- or z-direction.
It must be an extrusion into a 4th dimension, but your program has not such an axis.

If you want to create a hyper cube (a four dimensional object), first you need a coordinate system with four axis, e.g. x,y,z,w.
Then you have to define a projection matrix to map this hyper space (4D) into your view plane (2D).
Then we can talk about, how the projection could look like.

And please keep in mind that in general 4D do not mean 3D+time, because time is no spatial dimension.

STARGÅTE wrote: Sat Jan 03, 2026 2:04 pm Your line is an extrusion of a point in x-direction (1st dimension).
Your square is an extrusion of a line in y-direction (2st dimension).
Your cube is an extrusion of a square in z-direction (3st dimension).
Logically, then a hyper cube can't be an extrusion of a cube in x-, y- or z-direction.
It must be an extrusion into a 4th dimension, but your program has not such an axis.

Ok but 4D are everthing of extrusion of 1D,2D and 3D into the new dimension because the rule of extrusion is an adding line not something hypothesis of 4D without line (see the extrusion from 1D2D3D are sum of all dimension in 4D), if we respect of adding lines so the sub of 3D in 4D are here, I show the extrusion of lines in 4D because line is straight distance, in 4D are splitting lines into more complex ... It is more euclidean distance to make a "line", "square", "cube", "extra cube", so on and by adding more lines are more face form and adding to extra cube are more complicate of face form.

STARGÅTE wrote: Sat Jan 03, 2026 2:04 pm If you want to create a hyper cube (a four dimensional object), first you need a coordinate system with four axis, e.g. x,y,z,w.
Then you have to define a projection matrix to map this hyper space (4D) into your view plane (2D).
Then we can talk about, how the projection could look like.

Sorry we cannot say of matrix 4D into 2D space, because 4D is a unique space time, we can show maybe in something in 2D because it is a "cut" of dimension... For example 1D, 2D and 3d are well established in space, 4D is logically to 3D + 1D, 5D to 3D + 2D, and 6D to 3D + 3D, so on.... Because all dimension are independent.

STARGÅTE wrote: Sat Jan 03, 2026 2:04 pm And please keep in mind that in general 4D do not mean 3D+time, because time is no spatial dimension.

Sure but for me the 4D is a time spatial as well to fusion of 3D space, cause 4D is a 3D + 1D (1D is a line space) and not otherwise, 3D is space and 1D is a line space, so what does it mean? It means to 3D is everywhere in space and adding to 1D into 4D means more likely a 3D time space, as you see 1D is left or right, it can be past or futur if you see 3D as three number like x,y,z and adding 1D is x system but we need to not confuse double of "x" so we call t as time, thus x,y,z + t, and if you add the line t into 3d space mean t is curved time over space ... the more dimension the more complex to understand it... very difficult to explain this

If you think 4D is not a extrusion then we need to invent a new system for 4D space, because from now 3D or 2D is a euclidean idea, so for that we need to make different from euclidean system....