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What would the 4th dimension coordinate of your models even represent, though? I'm having trouble wrapping my head around it.

by viewer5 12y ago

sp332 12y ago
Mathematically, they're identical to any other dimension. You can move a little bit into a fourth dimension just like moving a little bit left-to-right. Or you can rotate things around the fourth axis just like turning something clockwise. In the case of this game, he only shows a 2D projection of a 3D cross-section of a 4D world, so that might be adding to the confusion. What you see in the video is only 3D "slices" of a 4D object rotating.
- 0x0 12y ago
  Would something like an Oculus Rift VR help reduce the number of projections from being "4D->2D" to be "4D->3D"?
  - cosarara97 12y ago
    No, Oculus Rift's screens are still 2D surfaces.
    - 0x0 12y ago
      Sure, but at least you get stereo vision and headtracking that makes it less obvious you're just looking at a flat screen showing a mono projection?
      - sp332 12y ago
        It might help mentally, but it won't reduce the number of projections. You'd have to be able to see every point in the whole 3D volume, not just the surface.
- raimondious 12y ago
  One of the axes introduced by the fourth dimension. There are 3 in 3D, 6 in 4D. XYZ space has axes perpenicular to the planes xy, xz, yz. WXYZ space has axes perpendicular to the planes xy, xz, xw, yz, yw, zw.
  - NickPollard 12y ago
    No. There are only 4 axes in 4-dimensional space - every point is described as a 4d vector, i.e scalar positions along each axis: (x,y,z,w). xy, xz, etc. are not planes in 4d space - they are 3d-hyperplanes, and perpendicular to them are planes, not axes. Imagine this: you have a 4d vector and you hold x and y constant. You still have 2 degrees of freedom: a plane, not a line.
dedward 12y ago
It's naturally confusing, because a 4th spatial dimension isn't something we naturally experience. We can't really say what it represents because it's not real... it's not a model of reality. We see in 2 dimensions and we infer the third from various cues. (The quote that we are "dimly aware of a fourth", which you may have heard, refers to time and is a different issue than a fourth spatial dimension.) We have three dimensions, all orthogonal to each other. We can translate, rotate, and project things in between them. So all we can do is apply those same principles and see what comes out - we shouldn't expect it to match anything recognizeable though.

What would the 4th dimension coordinate of your models even represent, though? I'm having trouble wrapping my head around it.

by viewer5 12y ago

What would the 4th dimension coordinate of your models even represent, though? I'm having trouble wrapping my head around it.

sp332 12y ago

Mathematically, they're identical to any other dimension. You can move a little bit into a fourth dimension just like moving a little bit left-to-right. Or you can rotate things around the fourth axis just like turning something clockwise. In the case of this game, he only shows a 2D projection of a 3D cross-section of a 4D world, so that might be adding to the confusion. What you see in the video is only 3D "slices" of a 4D object rotating.

0x0 12y ago
Would something like an Oculus Rift VR help reduce the number of projections from being "4D->2D" to be "4D->3D"?
- cosarara97 12y ago
  No, Oculus Rift's screens are still 2D surfaces.
  - 0x0 12y ago
    Sure, but at least you get stereo vision and headtracking that makes it less obvious you're just looking at a flat screen showing a mono projection?
    - sp332 12y ago
      It might help mentally, but it won't reduce the number of projections. You'd have to be able to see every point in the whole 3D volume, not just the surface.
raimondious 12y ago
One of the axes introduced by the fourth dimension. There are 3 in 3D, 6 in 4D. XYZ space has axes perpenicular to the planes xy, xz, yz. WXYZ space has axes perpendicular to the planes xy, xz, xw, yz, yw, zw.
- NickPollard 12y ago
  No. There are only 4 axes in 4-dimensional space - every point is described as a 4d vector, i.e scalar positions along each axis: (x,y,z,w). xy, xz, etc. are not planes in 4d space - they are 3d-hyperplanes, and perpendicular to them are planes, not axes. Imagine this: you have a 4d vector and you hold x and y constant. You still have 2 degrees of freedom: a plane, not a line.

dedward 12y ago

It's naturally confusing, because a 4th spatial dimension isn't something we naturally experience. We can't really say what it represents because it's not real... it's not a model of reality. We see in 2 dimensions and we infer the third from various cues. (The quote that we are "dimly aware of a fourth", which you may have heard, refers to time and is a different issue than a fourth spatial dimension.) We have three dimensions, all orthogonal to each other. We can translate, rotate, and project things in between them. So all we can do is apply those same principles and see what comes out - we shouldn't expect it to match anything recognizeable though.