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The game looks fascinating. I'm still trying to get my had around the analogies, but get the feeling that playing the game for real will bring a level of intuit

The game looks fascinating. I'm still trying to get my had around the analogies, but get the feeling that playing the game for real will bring a level of intuition to the experience. In the meanwhile, can anyone help me out? In the 2D->3D example, you have one shared axis (Z -- vertical), and an alternating pair for the second axis (X and Y -- horizontal). In effect, from the 2D character's point of view, 'jumping' into the third dimension is just swapping your horizontal axis. Your previous horizontal axis is a vertical section through your current one, and vice versa. As such, when swapping axes, you would expect one 1D line (ie. a 1-pixel-wide vertical band) to be the same before and after the swap. When going 3D-> 4D, you have 2 shared axes. Your third axis alternates, as before. When switching between your 'third' axes, then, you would expect one entire 2D plane of your perceived world-view to remain the same[1]. This doesn't seem to be the case. What am I missing? [1] EDIT: This plane is likely to be a section through some concrete objects, so you won't necessarily have 'seen' it before, though it will have been there.

DougWebb 12y ago
In the first case, the 1D vertical line is the same, but it's "seen" from a different angle. It looks the same because it's 1D and it doesn't happen to change because of the rotation. For the second case, maybe it's the ground plane that's the same; it certainly has some of the initial texture in it, but it's been rotated and it's now seen from a different angle. But now we can tell the different because it varies along the dimensions it rotated around. Or maybe I just can't visualize the rotation through the fourth dimension... I'm not sure.
roywiggins 12y ago
This is exactly right: when rotating in 4D, you can rotate "around" a plane, leaving it in place. You can also rotate around a line (permuting the other three axes). So, in the video. The Z axis doesn't change (up and down) so that's one axis. The other one that doesn't change is at a 45 degree angle from lower left to upper right. Watch the tree: it is just as wide along this axis as it was before. Everything else sort of smoooshes around but that plane stays the same. I suggest interested people check out adanaxis, a 4D space shooter. It's not particularly playable, but it is true four-dimensional space with four-dimensional spaceships zipping around.
tomerico 12y ago
The plane exists - it is passing through the character body (perpendicular to the ground) and parallel to the desert, grass border in the example video. You can see when the 4D rotation occurs there, that in that plane, everything stays constant (e.g. rocks stay there, trees, etc.) You just look at the objects from different angles as it rotates. Edit: Link to the relevant point in the video - https://www.youtube.com/watch?v=9yW--eQaA2I#t=148 https://www.youtube.com/watch?v=9yW--eQaA2I#t=148

DougWebb 12y ago

In the first case, the 1D vertical line is the same, but it's "seen" from a different angle. It looks the same because it's 1D and it doesn't happen to change because of the rotation. For the second case, maybe it's the ground plane that's the same; it certainly has some of the initial texture in it, but it's been rotated and it's now seen from a different angle. But now we can tell the different because it varies along the dimensions it rotated around. Or maybe I just can't visualize the rotation through the fourth dimension... I'm not sure.

roywiggins 12y ago

This is exactly right: when rotating in 4D, you can rotate "around" a plane, leaving it in place. You can also rotate around a line (permuting the other three axes). So, in the video. The Z axis doesn't change (up and down) so that's one axis. The other one that doesn't change is at a 45 degree angle from lower left to upper right. Watch the tree: it is just as wide along this axis as it was before. Everything else sort of smoooshes around but that plane stays the same. I suggest interested people check out adanaxis, a 4D space shooter. It's not particularly playable, but it is true four-dimensional space with four-dimensional spaceships zipping around.

tomerico 12y ago

The plane exists - it is passing through the character body (perpendicular to the ground) and parallel to the desert, grass border in the example video. You can see when the 4D rotation occurs there, that in that plane, everything stays constant (e.g. rocks stay there, trees, etc.) You just look at the objects from different angles as it rotates. Edit: Link to the relevant point in the video - https://www.youtube.com/watch?v=9yW--eQaA2I#t=148 https://www.youtube.com/watch?v=9yW--eQaA2I#t=148