Marc ten Bosch is creating Miegakure, a puzzle platformer in the fourth dimension. He took the time to talk with Cat about how that works, what it’s like designing a game in 4D, and the implications of exploring the fourth dimension.
CAT: Miegakure is a game of the fourth dimension - you better explain that! How did you arrive at the game concept? How exactly does that *work*?
MARC: When you program a 3D game every object’s position is represented using three numbers (x,y,z). Each number represents how far the object is along one of three directions. However, the computer doesn't care how many numbers there are. So in this game every position is represented with four numbers. That's how I came up with the idea of making a 4D game.
As far as we know the universe is 3D, though. So our solution is to display only three dimensions at a time, and the player can swap which three by pressing a button. What does it mean to only see three dimensions out of four? We can get a feel for it by thinking about what it would be like to only see two dimensions out of the usual three. Basically we could only see inside a flat 2D plane, like taking a 2D slice of a 3D world. For example if you could only see a 2D plane and a 3D sphere crossed the plane, you would see a circle that grows until the sphere is halfway into the plane, at which point the circle would start to shrink, until it is completely gone.
Like in this picture from the 1884 novella called Flatland: http://1.bp.blogspot.com/_X...
So basically you are taking cross-sections of the sphere, like slicing an apple into a thin slices. It turns out you can do the same thing, in one higher dimension, where you take 3D cross-sections of 4D objects. This is what the game does.
CAT: I remember when I first played feeling like there was a disconnect between what Miegakure *is* and how I played the game. Can you talk about the relationship between explaining the 4th dimension and playing in it?
MARC: Yeah that's a very important point, and I think the game's greatest accomplishment is that it finds a way to set up the 4D world so that it maps to concepts we are familiar with.
If you have a 3D world, you can take a bunch of 2D cross-sections of it. Each cross-section looks like a 2D world. These 2D worlds are literally parallel universes, because they are literately parallel planes. You can think a 3D world as being lots of 2D worlds stacked on top of each other. Similarly, one can think of a 4D world as being lots of 3D worlds stacked on top of each other. That's a metaphor that Miegakure employs often. You start in some 3D world, and you can move to different parallel 3D worlds. But the way you move across worlds is by switching your perspective so that you can see many slivers of 3D worlds at once. So in a way it's a generalization of "Zelda: A Link to the Past" to more than two worlds, with a special view that allows to move between worlds, and with a proper mathematical formulation (which brings a lot of crazy new things!).
But that's still a bit hard to explain with words, and I don't want to have a heavy-handed tutorial... but we humans are really good at learning logical systems by just playing with them.
An example I use often is that of a toy ball. By playing with a toy ball as a kid you intuitively learn about how gravity works. You can adjust the throwing angle and force and see the different paths the ball takes. You learn about parabolas without even knowing the word for them. This is very different from knowing the second-order differential equations of motion under the force of gravity. Clearly you don't need to understand a lot of Math to know how to throw a ball.
In the same way, Miegakure doesn't explain anything explicitly about the fourth dimension, it just lets you be inside of a 4D world. If someone wants to learn the mathematical theory, however, it can be built upon stronger instincts.
CAT: What is level design like, in the fourth dimension?
MARC: The idea of building things out of 3D worlds helps a lot. Designing the levels first and foremost involves placing 4D tiles (Minecraft has 3D tiles, and this games has 4D tiles).
Since there are no tricks or hacks in our engine, we are building what a 4D world would be like, in many ways. This creates a space were puzzles happen naturally: they are just simple consequences of 4D space. More traditional puzzle games very carefully set up situations, and the behaviour is limited to what the designer has intended (for example you need to input the right code to open the door, and the code is written down somewhere hidden). Because what we are building is so general, I might not know all the solutions to a particular puzzle... or I might discover a lot of puzzles by just setting up random situations and playing and seeing what happens. If something surprising and interesting happens, I will make it into its own puzzle.
People have also been thinking about the fourth dimension for more than a century, trying to come up with cool things you could do if you could move in 4D. Things like being able to "walk through" walls, binding two solid rings without breaking them, being able to enter closed buildings by going around their walls in the fourth dimension, etc... A lot of the levels are about letting you perform these "miracles" of the fourth dimension.
CAT: What engine are you using?
MARC: I have developed our engine from scratch. It's a real R&D project to develop all this technology, and a ton of fun! Making a 4D engine involved questioning every element of a 3D game we take for granted: what sort of objects can we put in a 4D world, how does the player interact with them, how do we program them, how do we make them look good, how does that relate to understanding the 4D? For example, in 3D games 3D models have a two-dimensional surface generally made up of triangles, but 4D models have a three-dimensional surface (made up of tetrahedra)!
CAT: What are the limits on possibility here? Are there any?
MARC: The limits keep getting pushed back as I figure out each feature! So yeah, there aren't many limits right now, we can build any shape we want (as long as it is not too complex, since it is slower to render). One thing that's a limit of the fourth dimension is that it takes exponentially more stuff to fill a space as you increase its dimension. It's a lot more work to make a 3D game than a 2D game, and even more work to make a 4D game! One way we solve that is by condensing the gameplay into relatively small environments.
CAT: What does it mean that we can now, if not physically, at least mathematically, explore the 4th dimension?
MARC: I think it's fascinating that there is this other type of exploration that video games open up. We've been exploring physical space for a long time (discovering new continents, going to the moon, building microscopes...), and now we can simulate and explore worlds that make sense mathematically, but do not exist in our physical universe (as far as we know).
Continue reading with Part Two of the Interview You can read Part One of the interview here: http://n4g.com/user/blogpos...
Day 14 | Marc ten Bosch