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Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped

Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too. edit: found this: https://youtu.be/S-yRYmdsnGs?t=252 https://youtu.be/S-yRYmdsnGs?t=252 even better: https://youtu.be/dy_MUfBuq2I https://youtu.be/dy_MUfBuq2I (turn on subtitles)

chiasmic 8y ago
I am by no means an expert, but I have thought about trying to visualise the fourth dimension. The issue is that we don’t really see 3D. While in 2D we can view every pixel simultaneously, when we view in 3D we have the issue of aspect and concealed voxels. You can’t visualise simultaneously all voxels of a cube, as most are under others or otherwise obscured. This therefore limits how much we can use 3D to mimic 4D. Perhaps if we were to spend more time with semitransparent objects our brains could learn to visualise 3D better and then maybe 4D.
- sarreph 8y ago
  What an interesting idea! Have you ever produced anything for a representation of 4D with translucent 3D? I'd be very interested to see it...
  - gitgud 8y ago
    I'm not sure that could practically work. The problem, is that translucency would allow only a partial view of concealed voxels. As more voxels cover something, the translucent effect compounds. Additionally, most voxels would appear different with different view perspectives. Due to more or less voxels covering them. The problem is that in 4D all voxels are visible to the viewer. So viewing a 4D apple would allow you to see the apple from all possible view points simultaneously, including interior views. To me it just doesn't seem possible to replicate this concept in 3D VR.
Udik 8y ago
Of course you can, and it would be different from the cross-sections seen in this video. I doubt it would ever become intuitive though, I suspect our brains are hard-wired for a 3d world. Here's a video of a rotating 4d hypercube in a 3d perspective: https://www.youtube.com/watch?v=t-WyreE9ZkI https://www.youtube.com/watch?v=t-WyreE9ZkI It's called a tesseract, and as each face of a 3d cube is a 2d cube (a square), each face of a 4d cube is a normal 3d cube, that we see skewed by the perspective.
- anotheryou 8y ago
  I'd say our brain is anything but hardwired. Sense-substitution works beautifully too and even a tool like a hammer or a mouse becomes one with your body through frequent use. Your linked video maps the 4th dimension to time, it doesn't project to 3D. Projecting through time (especially non-interactively) lacks the immediate feedback needed for the brain to grasp it as intuition.
  - Udik 8y ago
    > Your linked video maps the 4th dimension to time, it doesn't project to 3D No, it projects it to 3d. The movements you see are rotations, not movements of an intersection plane. You can clearly see at any point in time each of the 8 identical cubes making up the tesseract, skewed and resized by projection to a 3d perspective.
arketyp 8y ago
What would be the benefits of the 3D VR? There will always be a 2D bottleneck on your eyes' retina. The most important perspective clue I would say is temporal sampling. For dynamical systems, Takens theorem says that a high dimensional topology can be restituted by the sequential sampling of a single variable alone. It seems likely to me that our perception generally works by this principle. That being said, I think we are quite heavily hardwired to 3D perception. I suspect these circuits cannot be wholly overridden.
- anotheryou 8y ago
  I'd say we have two eyes and compile to something 3D, which is mostly possible because of that and nothing is hardwired, just takes a lot of responsive feedback to rewire itself.
  - Sharlin 8y ago
    We see a 2D projection and infer some 3D information from stereo parallax and other depth cues. But it’s still a 2D projection in the end. A real 3D ”vision” would not have a ”viewpoint”, no perspective, no foreshortening. It’s difficult to even imagine what it would be like to perceive that.
    - jonbarker 8y ago
      Stereo parallax, great term. In other words how cross-eyed we are.
- matte_black 8y ago
  What would a 3D eye even be like? Is it something like having independent depth perception per eye?
  - arketyp 8y ago
    Photons travel in 3D space and may only be occluded by 2D surfaces. There is no getting around that fundamental aspect of reality. In this universe.
h2j24 8y ago
The reason one can represent 3D "quite comfortably" on a 2D monitor can best be explained using linear algebra. The 3D space in the video is "projected" (linearly) onto a 2D space the same way a single one of our eyes project 3D space onto a 2D space. This is just one choice of projection though. For instance, when he shows the 2D beings perspective, he's chosen a different projection from 3D -> 2D and it looks quite foreign to us. The reason you feel comfortable with the normal projection is because your eyes do it all the time. Your eyes don't however, project 4D -> 3D so you don't feel it as natural.
corysama 8y ago
Just like how 3D objects make a 2D shadow (or a 2D projection on a screen), you can make a 3D shadow of a 4D object. https://www.fourthdimensionapp.com https://www.fourthdimensionapp.com walks you through this.

chiasmic 8y ago

I am by no means an expert, but I have thought about trying to visualise the fourth dimension. The issue is that we don’t really see 3D. While in 2D we can view every pixel simultaneously, when we view in 3D we have the issue of aspect and concealed voxels. You can’t visualise simultaneously all voxels of a cube, as most are under others or otherwise obscured. This therefore limits how much we can use 3D to mimic 4D. Perhaps if we were to spend more time with semitransparent objects our brains could learn to visualise 3D better and then maybe 4D.

sarreph 8y ago
What an interesting idea! Have you ever produced anything for a representation of 4D with translucent 3D? I'd be very interested to see it...
- gitgud 8y ago
  I'm not sure that could practically work. The problem, is that translucency would allow only a partial view of concealed voxels. As more voxels cover something, the translucent effect compounds. Additionally, most voxels would appear different with different view perspectives. Due to more or less voxels covering them. The problem is that in 4D all voxels are visible to the viewer. So viewing a 4D apple would allow you to see the apple from all possible view points simultaneously, including interior views. To me it just doesn't seem possible to replicate this concept in 3D VR.

Udik 8y ago

Of course you can, and it would be different from the cross-sections seen in this video. I doubt it would ever become intuitive though, I suspect our brains are hard-wired for a 3d world. Here's a video of a rotating 4d hypercube in a 3d perspective: https://www.youtube.com/watch?v=t-WyreE9ZkI https://www.youtube.com/watch?v=t-WyreE9ZkI It's called a tesseract, and as each face of a 3d cube is a 2d cube (a square), each face of a 4d cube is a normal 3d cube, that we see skewed by the perspective.

anotheryou 8y ago
I'd say our brain is anything but hardwired. Sense-substitution works beautifully too and even a tool like a hammer or a mouse becomes one with your body through frequent use. Your linked video maps the 4th dimension to time, it doesn't project to 3D. Projecting through time (especially non-interactively) lacks the immediate feedback needed for the brain to grasp it as intuition.
- Udik 8y ago
  > Your linked video maps the 4th dimension to time, it doesn't project to 3D No, it projects it to 3d. The movements you see are rotations, not movements of an intersection plane. You can clearly see at any point in time each of the 8 identical cubes making up the tesseract, skewed and resized by projection to a 3d perspective.

arketyp 8y ago

What would be the benefits of the 3D VR? There will always be a 2D bottleneck on your eyes' retina. The most important perspective clue I would say is temporal sampling. For dynamical systems, Takens theorem says that a high dimensional topology can be restituted by the sequential sampling of a single variable alone. It seems likely to me that our perception generally works by this principle. That being said, I think we are quite heavily hardwired to 3D perception. I suspect these circuits cannot be wholly overridden.

anotheryou 8y ago
I'd say we have two eyes and compile to something 3D, which is mostly possible because of that and nothing is hardwired, just takes a lot of responsive feedback to rewire itself.
- Sharlin 8y ago
  We see a 2D projection and infer some 3D information from stereo parallax and other depth cues. But it’s still a 2D projection in the end. A real 3D ”vision” would not have a ”viewpoint”, no perspective, no foreshortening. It’s difficult to even imagine what it would be like to perceive that.
  - jonbarker 8y ago
    Stereo parallax, great term. In other words how cross-eyed we are.
matte_black 8y ago
What would a 3D eye even be like? Is it something like having independent depth perception per eye?
- arketyp 8y ago
  Photons travel in 3D space and may only be occluded by 2D surfaces. There is no getting around that fundamental aspect of reality. In this universe.

h2j24 8y ago

The reason one can represent 3D "quite comfortably" on a 2D monitor can best be explained using linear algebra. The 3D space in the video is "projected" (linearly) onto a 2D space the same way a single one of our eyes project 3D space onto a 2D space. This is just one choice of projection though. For instance, when he shows the 2D beings perspective, he's chosen a different projection from 3D -> 2D and it looks quite foreign to us. The reason you feel comfortable with the normal projection is because your eyes do it all the time. Your eyes don't however, project 4D -> 3D so you don't feel it as natural.

corysama 8y ago

Just like how 3D objects make a 2D shadow (or a 2D projection on a screen), you can make a 3D shadow of a 4D object. https://www.fourthdimensionapp.com https://www.fourthdimensionapp.com walks you through this.