[Philip Lelyveld comment: the mind-stretching 4D concept is explained in a 1 minute video on the link and in the last paragraph below.]

[Kotaku.com]

Miegakure is a video game set in four spatial dimensions: specifically, the dimension that goes out to the sides, like your keyboard; the one that goes up, like a tree; the one that goes out deep, like a dog fetching a stick… and that other dimension, the one you can’t point to unless you’ve got 4D fingers.

Think of it another way. This is like the Mario from Super Mario Bros., who lives in a flat 2D world, being told that the 3D Super Mario 64 exists and being told he can play it…. one 2D slice at a time. Except you’re Mario. You’re 3D. And the “Super Mario 64” we’re talking about is 4D. …

It’s been two years since designer Marc Ten Bosch first showed me Miegakure and convinced me that a game set in four spatial dimensions is possible. The math allows it… all you have to do is take any point in our three-dimensional understanding of space (x,y,z) and add a fourth coordinate to locate its position in a fourth dimension. And if the math allows it, a computer can plot it. If a computer can plot it, we can run through it. And if we can run through it… voila! Video game.  …

See the full story and the video here: http://kotaku.com/5901016/forget-3d-im-ready-to-play-this-4d-video-game