Marc ten Bosch is the only man I have ever treated as if he had a super-power. Not super-strength. Not heat vision. Something better.
I believed, because it is sort of true, that he can see the fourth dimension.
That would make him a special class of person. Depending on your perspective, it could make him a human being with a sense I don't have, or a god, or a ghost, or a good mathematician.
What Marc ten Bosch really is, however, is a man who sculpts in 4D. His chisel is programming code. The statue emerging from his block of marble is a video game called Miegakure. It is a game that might accomplish a task other than the ones people think games are capable.
Could it make us laugh or cry?
Would it allow us to have fun or entertain our basest desires?
How about this: It could teach us how to think and move in the fourth dimension.
Ten Bosch's game, Miegakure, plays across four spatial dimensions: the good old horizontal axis, the vertical one, the z axis of depth and, well, whatever the fourth one would be that is at right angles to all of that.
That fourth dimension is the one jutting out of our three-dimensional world into space we can't reach.
That's the space into which I had hoped Marc could see, a space that might also be where god lives.
Testing The Super-Power
I met Marc in the spring in Boston at a video game convention. He was showcasing his game in the indie section of PAX East, a three-day event swarmed with gamers. Ten Bosch's table was set up not far from an elaborate walled showcase of Rockstar Games' Red Dead Redemption and EA's Dante's Inferno. Ten Bosch ran Miegakure on a computer set on a humble table. He used to work in big video game development, having put in some time on EA's Command & Conquer. At 25, he's now trying to survive making his four-dimensional video game.
I pulled him away from a computer that was running his game, leaving it to be comprehended by showgoers without ten Bosch's oversight. We walked to a table off to the side, pulled up two chairs and, soon enough I was asking him to survey the room and tell me what it looked like in four dimensions. This moment was slightly similar to the scene in the first Superman movie, when Lois Lane tests the Man of Steel's powers by asking him to use his X-ray vision to determine the color of her underwear.
Ten Bosch did not pause. He did not squint. He simply let me down. "I don't know what the fourth dimension part of the room this is." He couldn't see it. The room looked the same to him as it did to me.
Ten Bosch is a mere mortal, of course. But if you consider what he is building, the way making Miegakure must make him see things, it was reasonable for me to expect that he could eyeball a room and know how it would look in four dimensions.
Such a power would be similar to the ability you or I have to look a flat piece of paper and know what it would look like if turned on its edge.
If you had this power to know a dimension greater than the one you breathed in, you could be a flat 2D person — let's say Super Mario — and would be able to turn your head 90 degrees to the right and see the world outside. Even if you could never get out there and walk through it
My assumption when I met ten Bosch was that he too could turn his head that 90 or so degrees to the right and know what is out there in the fourth dimension beyond a Boston convention center. I hoped he could know the shape of the space that extends outside of the 3D world we live in. After all, that is exactly what he made a video game about.
Miegakure, his game, had made my head hurt by the time I met ten Bosch. But it had made me assume great things of the man. " You're like a super-hero to me," I told him. "You can see the fourth dimension."
He was patient with me because I didn't really get it. "Everybody who plays the game enough will be able to as well," he said. "That's kind of the idea of it."
The 4D Video Game
Ten Bosch is in some ways unexceptional, just one of a crowd. There are many men and women who can think about things in 4D, many men and women who digitally construct things in 4D.
They render things like the four-dimensional cube, which is called a hypercube and looks sort of like this:
Professor Tom Banchoff of Brown University has played a demo version of Miegakure. He said it checks out. He would know. He is a mathematics professor and a geometer who has studied the fourth dimension for decades. "My job is tell you what it will look like if we ever go there or if we are visited by somebody [who has been]," he said. "If you tell me how it looked I can say, well it probably came from the fourth dimension. I know how things from the fourth dimension go because I can instruct a computer to show me what it would look like … if it were projected or sliced or somehow visited our world."
Banchoff would describe to me many facets of the fourth dimension. He's been thinking about it and teaching it for a long time.
Marc is unusual among his fellow 4D thinkers and sculptors in that he has made a 4D video game. He has made 4D interactive by constructing a virtual landscape that follows the rules of the fourth dimension. We can play his game and explore what it would be like to travel up, through, and around in a 4D space.
At its most basic, Miegakure is a puzzle-platformer. Its name is Japanese for "hidden from sight." You control a man who stands on a landscape of cubes and can sometimes pull them, push them or climb them as he approaches whichever part of his level is his goal. If this game didn't have a fourth-dimension, it would be a very basic Mario-style 3D game.
Ten Bosch's game Miegakure, which is still in development and not available to the public yet, offers a not-very-shallow wade into 4D depth. The 4D concept that ten Bosch uses is called slicing. His game shows slivers of the fourth dimension, one at a time. The slivers are 3D — 3D cuts from a 4D world.
This makes sense, I am sure of it. Miegakure demonstrates it to be the case.
If you have a 3D object, say, a cube, you have something that you can slice. If you cut a horizontal slice into it, you have, essentially, defined a flat square, a 2D plane that exists within the cube. The Miegakure game presents the player with a key trick early on. Imagine that cube and that slice cut through it. Now imagine that cut being rotated inside the cube, rotated so that it no longer defines a horizontal cut but a vertical cut. The new slice and the original slice would have one intersecting line of substance in common.
Let's say that the first horizontal slice of the cube was the first world of Super Mario Bros. And let's say that, as Mario ran through the slice, the player could, at any moment, press a button that would rotate the cut through this cube. Mario's next step would not be on his Super Mario Bros horizontal slice; it would be up the new vertical slice. Mario would have smoothly jogged from one lovely 2D view of the world to one that cut into that view of the world at a right angle. Poor, flat Mario would never be able to zoom out and see the cube containing his worlds, but he would be able to explore its 3D space by running from one 2D cut of the world to the next.
Miegakure is all of that, but with the player's character exploring 3D slices of 4D.
The game's world is a 4D piece of terrain that we can only glimpse part of at any moment. At just about any moment, though, the player can press a button and the current visible 3D slice of the world ten Bosch has created will be rotated on, a new 3D slice showing up instead. Just as one line is shared by two 2D cuts that intersect each other in a cube, in Miegakure, one line of 3D space is retained as you shift from one 3D cut to the next.
Playing this game hurts my head, but it all makes sense to ten Bosch.
"There's the subtle parts of what the fourth dimension is which I guess I understand more than others," he told me, "But when I actually make a level I just think about all the different slices of the fourth dimension and I make all the slices. If something is hard even for me to understand, then I can just play the level and see what happens."
This is the special thing about Miegakure, the thing that proves that games are sometimes superior to the written word or headache-inducing thought. When you are playing Miegakure, you aren't trying to imagine 4D. You are moving a little man through 4D. You are experiencing it.
Professor Banchoff, a man whose cranium does not ache when he plays Miegakure, sees the game's presentation of moving from one 3D slice of a bigger world to another as an elegant achievement. "It's really not too much different than being in a building trying to find your way around and deciding at a certain stage to take an elevator. You get into this box and after a while you get out of this box and you're someplace else."
It's all math. Ten Bosch studied advanced math and he understands it. On paper, the fourth dimension is just another variable, one more letter added to the X, Y and Z. You could just as easily add one more dimension, ten Bosch told me. "I knew I could do four or five or however many that I wanted. And I knew I could also do collision detection. Collision detection is actually really generizable into any number of dimensions."
Rolling the Four-Dimensional Dice
These people who understand 4D are calm about this whole other dimension, which is odd because they are talking about something that is literally bigger than all of us, something that is out there. Still, they speak with nonchalance.
You get the feeling when talking to these guys that the fourth dimension is no big deal. "I know what happens when cubes rotate in three dimensions of space and what they look like on a screen," Professor Banchoff said. "And by long years of experience I know what a cube looks like in four dimensional space when it rotates. You see different faces of it one after another."
That's the Hypercube again, which is a vague enough concept to seem neat but comfortably disengaged enough from the real world to not hurt a reporter's head. The Hypercube can keep on doing its thing. Miegakure, a puzzle game that begs to be solved, stresses me more; it asks that we don't merely comprehend the fourth dimension but that we engage it.
For me, the fourth dimension is intimidating. For ten Bosch or Banchoff, it doesn't seem to be.
"Some people have actually played games with four-dimensional dice," Banchoff said matter-of-factly before I screeched him to a stop and asked for an explanation.
The 4D die thing comes from Andrew Hanson, a physics professor at Indiana University. Banchoff tried to explain it to me.
"We already know that if you have a die and put six numbers on it you can see three of those numbers at once, when you look at the die from a certain point of view. Maybe one if you look at it straight on. You can do that with four dimensions as well… You'd have eight [sides] and you'd see four of them at a time...
"When you look at a traditional die, you see three parallelograms meeting at a point," he continued. "What you have in three dimensional space would be four sort-of-deformed cubes meeting at a point. Those could have numbers on them, floating around in the middle of them, and as you rotate it in four dimensional space, one of these cubes would sort of flatten out and another would appear on the same side. That would be the same thing as rotating a die and seeing one face flatten out and it disappears as its opposite number shows up. Things like that are what you get when you rotate objects in four dimensions."
Naturally, our 3D eyeballs can't ever see a 4D die or the full world of Miegakure all at once.
Is 4D Another Name For God?
In Boston, ten Bosch and I talked about heaven. The Biblical home of angels and God fits the description of the non-visible parts of Miegakure or Andrew Hanson's 4D die. It is a place connected to our 3D world but unseen by those of us on Earth.
If there was someone who could see 4D, who could travel from 3D slice to 3D slice, they could be in this world with us and then, from our perspective, be out of it. They could be "above" our world in a fourth direction, always near enough to drop in for a visit, but beyond our 3D grasp.
"I've totally thought of that," ten Bosch said. "I thought about how heaven and hell could actually be in the fourth dimension. Heaven could be just like our world, just slightly shifted to the fourth dimension. It's like a parallel universe."
Ten Bosch doesn't believe in God, but he likes the notion that things we think of as spiritual could have this physical 4D connection.
"When people started to think about the fourth dimension a lot of spiritual people tried to explain things by grabbing onto the mathematical aspects of it. They said maybe ghosts are actually slightly inside the fourth dimension, like displaced into the fourth dimension."
The 19th century book Flatland of which ten Bosch and Banchoff are both aficionados demonstrates this potentially divine state of existing in the dimension higher than the subjects of the flatter world below.
The man who lives on a line and can see only forward, not up or down, will see the swoop of a sine wave traveling along his line land as a dot that appears here and there, farther and farther ahead.
The man who lives on a flat plane and can look only around him — but not elevate high so that he can look down below — will view a line drawn in front of him as an insurmountable barrier; the omniscient spectator above will know both that the line could be hurdled and will know of all the other lines in the neighborhood of this man's world with the same glance you'd pay to a street map.
If I had believed that Marc ten Bosch could see the fourth dimension, then I could believe he could see how the slice of the 4D world that was the big room in which we sat in Boston could be rotated into a new 3D cut of the 4D world. He could imagine that our bodies extend into four dimensions, not in the sense that some see the fourth dimension as time, but in the sense that he could tell me if I have a third arm sticking out into the fourth direction.
These are not the skills ten Bosch yet possessed. He can't see Heaven, though he can dream in 4D. "I actually dreamed in the mechanic of my game not too long ago, this shifting thing that happens," he told me. "I think I was looking for something, honestly and the way I was moving was that mechanic of switching [slices]."
Oh, that we could all at least dream in 4D.
Taking Us To The Fourth Dimension
Neither ten Bosch nor Banchoff will say that they believe the fourth dimension exists. Banchoff boots the question. Ten Bosch protests that he's not a physicist. He said he just doesn't know.
"My goal in making the game is, 'If there was a fourth dimension, what would it look like so that it makes sense in the world we are in now?'"
Miegakure is a work in progress. (Keep an eye on the official Miegakure site.) Ten Bosch hopes it can be released as a downloadable game for computers and maybe a game console. I'm sure he wants people to have fun with it, but the game's potential is exciting for more than just the prospect of pleasure. The game's potential is what it could do to our brains, how it could help to make us think a little more like Prof. Banchoff or ten Bosch.
"When we are born there's nothing inside our brain that knows about three dimensions," ten Bosch said to me in Boston. "We sort of learn. We play around and just touch the world and see what happens. I think a video game really has the power to give you that and extend it to other things we cannot experience in the real world — and just being able to play it and experience it long enough begins to build it into your brain."
We're 3D infants and Marc ten Bosch wants us to play with some 4D blocks. He doesn't have superpowers, but maybe we can learn one from his game.