I saw the video and it just looked like turning "no clip" on for a piece of the puzzle and moving it where it's supposed to be. I'm probably missing something about how this is supposed to work..
So, what's going on, is that one of the dimensions in the game world is getting switched out for a fourth dimension. The visual transformation that you see isn't very clear about what's going on, and I guess it's basically not possible to be clear about this in a rectilinear coordinate system.
I'll try to explain. At 0:12, the game world has 3 axis, aligned with the sides of the blocks. By convention, let's say the vertical axis is the Z-axis, that the one going up and to the right (on the screen) is the X-axis, and the one going up and to the left is the Y axis. There's also a "hidden" axis, which I'll call the W-axis, which can't be displayed (for obvious reasons).
At 0:13, the player switches out the Y-axis for the W-axis. We can no longer see the extent of objects in the Y direction. However, we can now see the extent of objects in the W-axis direction. For example, in the XY-plane, the ground was all green, but in the XW-plane it looks stripped with green and brown. This means there are a series of XY-planes sitting "next to" each other in W-space, alternating in colors. The character was originally sitting on one of the green ones. Now that the Y-axis was switched for the X-axis, we see X-axis "slices" of these XY-planes, arranged along the W-axis.
Note that the big rock structure is located on the W-axis only in the XYZ 3-D "slice" that the character originally occupied. The character then proceeds to move the wooden ring along the W-axis to a different XZ-slice, where the rock structure isn't in the way.
At 0:18, he switches axes back to the XYZ plane, although this isn't strictly necessary. You'll notice he's now on an XYZ slice that, in W-space, has brown ground. The rock structure isn't in the way because it's on a different location on W-axis than everything on-screen (it's displayed as transparent, for reference). He moves the structure along the X-axis, past the rock obstruction. He then switches back to XWZ-space, moves the wooden thing back along the W-axis again, and switches back to the original coordinate system.
Thanks for taking the time to explain. I think I get it better now, but it's probably one of these things that I'll have to try for myself to really understand.
The Cartesian plane is in ℝ^2. Any point can be expressed as a combination of (x,y) where both x,y ∈ ℝ. That means that both x and y are members of the set of real numbers.
A 3D graph is in ℝ^3. Any point can be expressed as (x,y,z), where x,y,z ∈ ℝ.
A 4D graph is in ℝ^4. Any point can be expressed as a combination of (x,y,z,w), where x,y,z,w ∈ ℝ.
Unfortunately, human vision is limited to three dimensions, so only four different perspectives are available (4 choose 3): (x,y,z), (x,y,w), (y,z,w), and (x,z,w). Moreover, the 3D must be collapsed into a 2D for presentation on the screen.
I had a similar feeling but I can't imagine the game would get so much hype if that was really all there was to it. Maybe different locations on the 4th dimensional plane have different obstacles which would make you need to keep a tally of each landscape in your head? That could get very tough depending on the situation.
I watched people playing this for about 15 minutes at GDC. Didn't try it myself and I didn't know at the time that it was 4D, thought it was just some weird xform of the world.
Looked amazing but was completely unintuitive to me. I didn't get it at all but if playing for a while helps me learn to visualize 4D space then I really want to try it.
I don't know if you'll find this helpful or not, but there is one deceptive aspect in the video. Visually, you see a world composed of cubes, but geometrically that is not what is actually happening. In fact the "cubes" are actually points being represented as cubes on the screen. The game world is actually 10x4x6x4 in a discrete grid of points. (The 6 for height is an estimate.)
When the first dimensional swap is done, if the world was literally as it appeared, the big ring would become a two-dimensional square ring as you swapped out its depth for the 0 it has in the fourth dimension. Instead, since it is really just a structure composed of 12 points represented by 12 cubes, the points remain in your 3D space and it seems untouched. That is because it was 2D in the first place, despite being drawn as 3D, and swapping around the two dimensions it didn't exist in in the first place leaves it untouched.
So to some extent it is cheating a bit with the fourth dimension, in the sense that you aren't actually dealing with a continuous world, you're dealing with a very coarse-grained discrete one that is being represented as if it continuous. (I am not objecting. There is no practical other choice. I am just pointing out that if you are already confused, this unavoidable deception may make it more difficult to understand what is going on.)
I will be intrigued to see how well the puzzle designers learn to cope with 4D. I was initially excited, but I'll want to see more than what they showed. I want to rotate the fourth in on the other height axis. (Now, that's a sentence I don't have the chance to write very often.) Keeping gravity constant would require that the height dimension be held constant, and that would probably be an acceptable compromise, vs. freely rotating in all directions. But we've seen a mere minute of a game, so who knows. (The number of people in other discussions I've seen about this video that implicitly assume the interlocking ring thing is somehow the only puzzle that could be given is driving me nuts.)
If you want to go the other direction dimensionally and technologically, you can get 'Flatland, a romance of many dimensions' off project Gutenberg.
http://www.gutenberg.org/etext/97
