Still, most of us are no closer to fundamentally comprehending the fourth dimension than we were when Riemann first conceived it. People have written papers, drawn diagrams, taken psychedelics, but what we really want to do is witness it. Mathematician Rudy Rucker wrote that he had spent 15 years trying to imagine 4-D space and been granted for his labors “perhaps 15 minutes' worth of direct vision” of it.

But for the past five years, ten Bosch has been trying to take us directly into it, in the form of a videogame called Miegakure. The game, essentially a series of puzzles, augments the usual arsenal of in-game movement by allowing the player's avatar, with the press of a button, to travel along the fourth spatial dimension. Building something so ambitious has consumed ten Bosch's life. Chris Hecker, a friend and fellow game designer, marvels that ten Bosch “can't even see the game he's making.” Ten Bosch, who is 30, describes his daily schedule as “wake up, work on the game, go get lunch somewhere, work on the game, go to sleep.” Even after toiling for half a decade, he is still only about 75 percent done.

1 xkcd creator Randall Munroe even devoted a comic strip to Miegakure.

But among the tight-knit community of indie game developers, Miegakure is a hotly anticipated title. The select few who have played it have showered it with praise. 1 Ten Bosch has twice been invited to preview it at the prestigious Experimental Gameplay Workshop at the annual Game Developers Conference in San Francisco. He won the “amazing game” award at IndieCade, the biggest annual showcase of independent games.

Miegakure has the potential to be “one of the great puzzle games of all time,” writes Jonathan Blow, a friend of ten Bosch and the designer of Braid, a game in which players manipulate time to solve puzzles. “Games that are truly mind-expanding are very rare and very difficult to make, but this is one of them.”

If Miegakure can live up to ten Bosch's ambitions, it will be more than just another brainy diversion—it will be the realization of a century-long intellectual quest. Miegakure does not visualize 4-D space or analogize it to something more familiar. Rather, the game attempts to evoke the experience of an actual, explorable world that includes one additional spatial dimension.

“There certainly isn't a fourth dimension in the way there is in the game,” ten Bosch says. We can't rotate objects so that they appear out of nowhere in the real world or disappear in front of our eyes. But he wants the game to give people the intuition that a fourth spatial dimension might exist. The easiest way to wrap our minds around such a slippery concept, he thinks, is to reach out and touch it.