In all that time, the core concept of solving puzzles in a four-dimensional world never made much sense to me, but this video is on the right track, I think. It's starting to click for me!
That 2D/3D section shown in the video is actually a playable part of Miegakure and if you've made it through Fez, it should be easy enough to wrap your head around.
The next step? Getting my hands on this at PAX Prime. It's part of the Indie Megabooth.
New Trailer: How to walk through walls using the 4th Dimension [Marc Ten Bosch]