Dan Winters
There's a row of books on a shelf in Marc ten Bosch's living room that contains a crash course in higher dimensions. Titles like Flatland. Einstein, Picasso: Space, Time and the Beauty That Causes Havoc. The Fourth Dimension and Non-Euclidean Geometry in Modern Art. A young-adult novel called The Boy Who Reversed Himself. They're all devoted to helping our brains break out of the three dimensions in which we exist, to aid our understanding of a universe that extends beyond our perception.
This is not just a hypothetical pursuit. Most of us think of time as the fourth dimension, but modern physics theorizes that there is a fourth spatial dimension as well—not width, height, or length but something else that we can't experience through our physical senses. From this fourth dimension, we would be able to see every angle of the three-dimensional world at once, much as we three-dimensional beings can take in the entirety of a two-dimensional plane. Mathematician Bernhard Riemann came up with the concept in the 19th century, and physicists, artists, and philosophers have struggled with it ever since. Writers from Wilde to Proust, Dostoevsky to Conrad invoked the fourth dimension in their work. H. G. Wells' Invisible Man disappeared by discovering a way to travel along it. Cubism was in part an attempt by Picasso and others to visualize what fourth-dimensional creatures might see.
Miegakure creator Marc ten Bosch walks (and talks) viewers through the process of navigating 4-D space.
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.
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.
At the advent of videogaming, we existed digitally as two-dimensional beings. Poor 2-D Mario couldn't step sideways to dodge a barrel hurled by Donkey Kong; viewed from above, Pac Man could not leap to avoid a pincer engagement by Inky, Blinky, Pinky, or Clyde. And because gamers feel a magical and mysterious connection between our physical selves and the virtual characters we control (we use the word “I” to describe them both), in a very real sense we couldn't do those things either.
Dan Winters
There were hints, even in those early days of gaming, that a third dimension might exist, a z axis along which our avatars might wander, if only we knew where to look. Soon, Moore's law enabled us to find it: In the 1990s, 3-D games like Doom and Super Mario 64 opened up new vistas for electronic exploration, turning players into digital Magellans navigating truly round worlds. Later, titles like Portal, Fez, and Blow's Braid allowed players to interact with and manipulate space and time. In Portal, players used a gun to open tunnels in space; in Fez, the player's 2-D avatar could swivel his world like a 3-D cube to change the surface he walks on. Braid was in part a response to Alan Lightman's novel Einstein's Dreams, which asks: What if we experienced time and space as being intricately connected in new and strange ways?
Miegakure picks up these themes and extends them along a strange and previously unknowable axis. You control a small, seemingly Japanese man who lives in a cubic landscape dotted with trees and rocks and Torii gates, the kind you see at Shinto shrines to mark, in ten Bosch's words, “the separation between the sacred and the normal.” Although Miegakure is built upon the math of four-dimensional space, the game is also infused with the ethos of Japanese gardens. 2 The game's title is a reference to that tradition, an aesthetic principle that means “hide and reveal.”
“You can never see the whole garden at once,” ten Bosch says. “So you're always imagining the parts you can't see. It makes the garden feel larger than it really is and maybe more intriguing than it really is.”
That's also been a hallmark of game design—think of the secret worlds and warp portals hiding within Super Mario Bros.' pipes and bricks. Miegakure is even more concerned with the mysteries of the unseen. At a fundamental level, the true shape of reality is invisible to us, thanks to our utter inability to visualize another spatial dimension. We perceive Miegakure as 3-D slices of 4-D worlds, the way a 2-D creature would understand a book as just a series of pages.
But our inability to see all the dimensions of a 4-D world doesn't mean that we can't navigate it, that we can't reach out and feel it with our digital fingertips. What makes Miegakure extraordinary is that it allows our species, for the first time in its history, to enter a four-dimensional space and manipulate it, like blind scientists patting a hyper-elephant. “I think that's one of the magical things about interactivity,” Hecker says. “You can understand it in a way that's not purely conscious.”
The interactions in Miegakure are basic: You can move the character, you can make him jump, you can press a button to enter one of the Torii gates (most of which lead to a puzzle). And you can press another button to travel along the unseeable fourth dimension. When you press it, the world appears to morph and fold in on itself, revealing colored slices to walk on. These slices look like parallel worlds; they're even visually distinct so that players can distinguish them as separate realms. One looks like desert, another like grass, another like ice. Walking onto each slice and then pressing the button seems to transport you into each new universe.
But here's the thing: They're not new universes. They're 3-D cross-sections—“hyperslices,” maybe?—of a 4-D shape. The “morph” button, which appears to make the world around you swirl and the objects within it disappear, does not in fact move your character even a millimeter. You're not teleporting. You're just changing perspective—except you're not looking left or right, not up or down or forward or back. You're looking into the unseeable fourth dimension and only then traveling along it.
Over time, the game nudges you toward an understanding of this by including 3-D objects that move in more than one “universe” when your character pushes them. You find maps that help to illustrate how the spaces intersect. And soon you're performing the miracles that mathematicians say a 4-D being could perform in three-dimensional space: walking through walls, making blocks seem to float in the air, disappearing and reappearing, and interlocking two seemingly impenetrable rings. The math is solid—every shape in the game is defined by four coordinates instead of three—but just as when an illusionist performs that same ring trick, it feels like magic.
For all the attention Miegakure has received, its designer is far from a videogame star. Ten Bosch moved to the United States from Nice, France, more than a decade ago to go to DigiPen Institute of Technology, a for-profit college in Redmond, Washington, known for training students to work at the megacorporations that produce the industry's biggest, most expensive hits, like Call of Duty and Madden NFL. After school, ten Bosch landed a four-month internship at Electronic Arts in Southern California.
The company offered him a job, he says, but he turned it down, swept up in the excitement surrounding a burgeoning indie games scene: Blow's Braid was just hitting Xbox 360s. Ten Bosch also wanted to create a game that mattered, so in late 2008 he set out to build a prototype from a thought experiment: Normally you use three numbers to create digital spaces, but what if there were four?
I finally have the chance to play the result of that question one afternoon in September. Ten Bosch shines a projector onto a wall in his spartan apartment and hands me a controller. The game begins with an epitaph from Oliver Wendell Holmes: “Man's mind, once stretched by a new idea, never regains its original dimensions.”
Even among string theorists, there's a debate around the margins of the theory of higher spatial dimensions: Why can't we see them? Maybe they're too small to measure, or maybe space is warped in such a way that they remain hidden from us. Maybe we live on a three-dimensional membrane that is floating in 11-dimensional space, 3 making us something like water droplets that can't escape from the shower curtain we're attached to. Maybe our universe of four-dimensional spacetime split from a smaller six-dimensional universe at the moment of the Big Bang and our only hope to escape the heat-death of this universe is to find a way to get inside the other one.
Miegakure makes no efforts to explore these existential questions. Instead, it guides players to an intuitive, if incomplete, grasp of the geometry involved. It's a little like shooting a free throw in a game of four-dimensional basketball: You don't know how to calculate the curve the ball must follow or even how to imagine the line it draws through space as it falls through the net, but you can somehow make the shot.
These are, for now, ineffable concepts. But after several hours inside Miegakure, 4-D space has become somehow a bit more … effable. Faced with a level in which I had to appear atop a floating box on another cross-section of the hyperworld—on the other side of the screen—I found that I knew where to stand in 4-D space to pull it off. I couldn't tell you why I should stand in a particular spot, nor could I visualize the space that I was skillfully navigating. Ten Bosch insists that I shouldn't worry about it.
“I think you have the instinct,” he says, looking pleased. “I think you get it.”
No comments:
Post a Comment