Videogame architecture allows us to visualize the impossible

This article is part of a collaboration with iQ by Intel.

As far as the dimensions go, the fourth is pretty mysterious. Part of the problem is that we can’t even see it. For that to happen humans would need to evolve into a radically different species than what they are today. “A fourth-dimensional creature would have eyes with three-dimensional surfaces,” says Marc ten Bosch, developer of Miegakure, a 4D puzzle game which simulates an imperceivable world of geometry. Those shiny multifaceted irises would allow a hopefully friendly inter-dimensional traveler to see “a volume of space,” he tells me—“a three-dimensional grid where every point is filled”—rather than the ordinary dimensions of length, width, and depth we are used to. “As far as how many eyes it has… I don’t know,” he says. “It would probably need a third.”

Miegakure may be the closest we can get to accessing our otherworldly neighboring dimension. 

Short of growing an additional, diamond-shaped eyeball, Miegakure may be the closest we can get to accessing our otherworldly neighboring dimension. Of course, Bosch’s game can’t just magically display astonishing 4D structures. That’s impossible, and, besides, even if it were doable, we couldn’t make sense of it. So, the game does the next best thing: it chops up the fourth dimension into recognizable 3D slices. This is kind of like taking photographs of your house from all sides, which makes sense of a 3D structure using 2D images. Miegakure does that, but one dimensional step up. Bosch thinks of these as “parallel universes” that the player hops back and forth between by pressing a key.

The results look amazing. Stone slabs vanish, distort, and reappear in new arrangements—it’s perfect fodder for a puzzle game. What’s even more amazing, however, is how a puzzle game allows us to grope in the dark, feeling the edges of a hidden dimension that may or may not actually exist outside the realm of pure theoretical possibility. If there’s a truth underlying Miegakure’s koi ponds, it’s that games have this strange capacity to build impossible spaces. “[Humans] invented mathematics to describe the world that we know, but it actually describes more than that,” Bosch says. Computers help us visualize exactly what that “more” is.

This is something of a scientific achievement. Even before the German mathematician Möbius published some findings on the fourth dimension in his early 19th century manuscript Der barycentrische Calcul, the best minds struggled to make heads or tails of it. Dostoevsky in Brothers Karamazov analogized the fourth dimension to the unknowable presence of God. Edwin Abbott Abbott’s Flatland did him one better: It told the story of a square who has an out-of-body experience in the world of cubes. Still, the concept remained ungraspable, vague.

The beauty of Miegakure is that it lets you futz around with mind-bending mathematical discoveries previously best spoken of in analogy, even if you’re math-averse. Soon you’ll realize all sorts of counterintuitive fourth-dimensional realities, such as the fact that our office buildings and houses are totally vulnerable to intruders from higher dimensions. An early puzzle in the game tasks you with entering a locked house, but because 4D structures require six walls instead of four, this is a piece of cake for the player who can simply step over into the next dimension and go in.

What’s miraculous to a 3D person is mostly trivial for a person in 4D. 

“To a fourth dimensional person, it’s like, ‘you forgot two walls to your house,’” Bosch says. As for the hypothetical third-dimensional homeowner who witnessed this, she’d probably faint. “She wouldn’t see someone walking through the wall. She’d see them on one side of the wall. Then, they’d disappear. Then, they’d reappear on the other side,” he tells me.

This is a recurring theme in Miegakure. What’s miraculous to a 3D person is mostly trivial for a person in 4D. If you were facing one direction and turned around, for instance, your heart and internal organs would flip to the other side of your body. If you had two rings made of a solid material, you could bind them and unbind them without breaking them, because—viola!—the fourth dimension. Not to mention there’s all kinds of physical matter you cannot see because it’s tucked away in invisible space. “That’s the really interesting thing about games,” he says. “They make you think about why we only have two eyes.”