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.
Speaking of Mario, this game's a platformer. You're jumping around, pushing blocks, exploring a world.
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.
Marc shows us a simple level of the game in the video here, which we shot at PAX East. He also showed us a tougher level, but asked that we not show it off, head-hurtingly interesting as it was. He only wants you to see the game at its most polished. So, enjoy the one level we've got for you.
Miegakure will be out "when it's done" on PC (Steam, probably) and a console.
UPDATE: Since a number of readers are clearly hungering for more explanation about how a spatially-4D game world works in a game that is displayed in three dimensions, I'm adding the following from ten Bosch's own description of the game:
Think about a two-dimensional character living on a horizontal, flat two-dimensional plane. To this character, height would be a foreign concept. A number of actions we three-dimensional beings take for granted feel like absolute magic to this two-dimensional character.
For example, if there is a wall in the shape of a circle around an object in 2D, it is essentially closed-off, since to reach it one would have to leave the 2D plane. It is also impossible for an outsider to know what is inside.
But us 3D beings can see the object from above, and also simply lift it off the ground to move it outside, essentially teleporting it. Now by analogy a four-dimensional being could perform many similar miracles to us living in only three-dimensions. This game allows you to perform these "miracles."