IF YOU DONT ALREADY KNOW ALL ABOUT DIFFERENT PROJECTIONS GTFO
NO BRAINLETS ALLOWED, Of course I can't enforce that so the criteria I'm specifying is just at least have basic understanding of what 4D space is and how it works. I don't want this thread clogged up with spoonfeeding about basic brainlet shit.
Now, my mission. I want to visualize in 4D. I want to get my internal imagination to actually understand what an axis perpendicular to x/y/z actually is on an intuitive level. I already can understand the basic idea of course, but I feel like a 2D creature reasoning about cubes, but only able to imagine lines.
So far I think my best bet at gaining this intuition is examining how 3D cubes rotate in 4D space. It seems this should come far easier than jumping to hypercubes right away. While we are pretty good at visualizing 3D from 2D projections..attempting to visualize 4D from 2D projections is kinda absurd. Luckily many apps for examining 4D objects allow stereoscopic views. Unfortunately I haven't found any app which has just a 3D cube in 4D space, instead they're all 4D hypercubes. Cool to look at and help understand the basic idea, not as useful for trying to actually give yourself a new perception.
Pic related, its a 3D cube rotating on XW axis in 4D space. I fucking hate how simple it is, ffs...its so obvious, when its getting 'smaller' its actually just getting farther away in 4D space, however I just can't seem to perceive what that really means. It still looks like a 3D cube turning inside out. I want to REALLY SEE what its actually doing
Does anyone have a visualization of a 2D plane rotating in 4D space...I think that may help.
Tyler Bailey
IT HAS TO BE POSSIBLE
SCI HELP ME
Camden Perry
I hate how I'm so fucking close but just can't quite get it.
I totally get how it works and all but I don't ///get/// it. I keep watching the gif but it just looks like a 3D cube being deformed, I can't seem to actually 'see' the smaller face as not smaller but 'farther away'
Josiah Russell
You're FREAKING OUT MAN 4D is nothing interesting. It's simply the way in which the universe or any other body of space is wrapped around itself. There are no outer edges of the universe. You can go in any direction you want and what is behind you wraps around in all directions such that you would return to the same spot if you were to travel far enough. Smoke a ton of weed or take edibles n you'll understand
Grayson Barnes
I know what it IS, I know HOW it works, but I can't SEE it. I want to perceive it. Look at the 2D plane rotating in 3D space. You can switch back and forth from seeing it as what it is, a square rotating in 3D space, or what the image is, a square deformed into a trapezoid, going through itself and becoming a square again.
I know the 3D cube in 4D is the same thing but I just can't seem to make the perceptual 'pop' into 4D space.
Christian Gray
also that's incorrect, you're talking about hyperbolic space, not 4D
Tyler Rogers
Wait so what do you see in the op picture? Cuz I see it moving inside itself on the left and then wrapping around on the right
Isaac Campbell
yes, but thats not what actually is happening, its actually not being deformed at all. You are seeing a deformed 3D cube, but that is a projection of its 4D position. one face stays stationary, just as one side stays stationary with the 2D square rotating in 3D.
I thought I said no fucking brainlets. this is exactly the kind of basic shit I'm already long past.
Colton Cooper
Thinking in terms of a heat map can get the job done.
You can already visualize 3D space.
A heat map would ascribe a color (from a 1D gradient) to each point of this 3D space (functions from R^3 to R do this). Note: This method is deficient for arbitrary 4D configurations (think vertical line test)
Now for arbitrary 4D configurations, it would not be just one color ascribed to each point in R^3, but instead, an entire set of colors assigned to each point of R^3.
Every rotation in 2D fixes a 0D point Every rotation in 3D fixes a 1D line Every rotation in 4D fixes a 2D plane
If your fixed plane of the 4D rotation is parallel to the "color axis" you will see no change of the colors. These types of rotations would look like ordinary rotations of the heat map in 3D.
Now If your fixed plane of the 4D rotation is not parallel to the "color axis" you will see change of the colors through the rotation and the heat map will rotate elliptically in 3D (or just linearly oscillate if the "color axis" is perpendicular to the fixed plane). You can understand the elliptical rotation if you imagine a tilted circle in 3D projected orthogonally to a plane.
I encourage you to try the same heat map technique in 2D to try to represent the familiar 3D rotations.
It also might help if you discretize the space using lattice points so you can see what is going on better.
