Marc ten Bosch and the mathematical mysteries of his 4D videogame

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The mantis shrimp is said to have the most complex eyes in all of the animal kingdom (including humans). These ancient crustaceans can move their segmented eyes independently and each is capable of depth perception all on its own. Additionally, the mantis shrimp’s eyes contain more than five times the number of color receptors as the human eye, meaning they can see colors that are imperceptible to you and me, including several bands of ultraviolet light. We know these types of colors exist because we have special instruments that allow us to bear witness to them, if only through data readouts or other visual abstractions. But to the mantis shrimp, ultraviolet light is nothing special; it’s just an expected facet of the visual world like any other hue.

Marc ten Bosch doesn’t have mantis shrimp eyes or any kind of superhuman abilities, but in his game Miegakure he does one better—he gives players the power to traverse the fourth dimension. The same way that a cubist Picasso painting grants viewers a way of experiencing a three-dimensional portrait on a flat plane, ten Bosch manages to carve four-dimensional slices into three-dimensional spaces (represented via two-dimensional computer monitor). At first glance, Miegakure doesn’t appear more complicated than any other isometric puzzle game. You move a character around a small square of land floating on a plane above a dynamic background wallpaper. You can jump and push things to traverse the zen garden-like space, but ultimately you’ll run into a dead end where the only option will be swapping one dimension for another. At once your static square morphs into an elongated rectangle, and what was a stone wall has been replaced by a flat, sandy surface. It’s a head-spinning feat, made possible through a merging of artistic ideas and mathematical practice—an intersection that’s at the heart of all videogames, but approached here by ten Bosch with a pioneering spirit that sets it apart.

Marc ten Bosch math

You might be surprised to know that IRL Marc ten Bosch is relegated to a regular three-dimensional Earth-bound existence just like everyone else. In fact, though there’s such complex systems at work in ten Bosch’s game, the way he speaks about it is somewhat nonchalant. “I had to invent some new types of math for this,” he tossed out as part of a longer response. Yeah, he just invented some new math. No big deal, right? Though ten Bosch has enlisted outside work for modeling, animation, and music, developing Miegakure is largely a solo affair. He builds his four-dimensional worlds on a simple laptop after sketching them out with basic pencil and paper.

I asked ten Bosch if his 4D virtual world ever starts blurring with the real one, to which he chuckled, “Not really.” He went on. “This process of taking the world we know and trying to make it independent of dimension is actually very enlightening, but not in a ‘what if this room was 4D’ sense. More like, ‘Oh, I understand what turning an object means regardless of how many dimensions it has.’” It’s an elaborate way of understanding a simple action very deeply, an ethos that seems ingrained into Miegakure’s design and ten Bosch’s creative process.

Ten Bosch has been working on Miegakure for over seven years now, and it’s an enveloping project for a one-person team, but he’s careful to prevent the game from becoming too much of a self-portrait. “I’m the one who’s presenting [the game] to you, so clearly I’m a part of the process, but I’m trying to disconnect myself from the concept because it’s beautiful [on its own], and I don’t need to be in there.” In fact, he’d rather not dictate the meaning behind the game at all, answering questions with more questions like, “What if the universe had all these things that you didn’t know?” and “What if it’s only presenting you with a specific part of it, and at some point you could suddenly see what was always hidden to you?”

the art of building a space to the point that it’s almost therapeutic

“Miegakure” translates to “hide and reveal,” and is used in reference to Japanese gardens. It embodies the concept that to truly understand and appreciate the garden, one must experience it firsthand, witnessing all manner of purposefully designed and naturally occurring phenomena. As part of the development of Miegakure, ten Bosch made a trip to Japan, where he visited some of the country’s renowned imperial gardens. “When you see a Japanese garden, it makes you feel amazing just to be next to it, and I didn’t expect that from just pictures,” he said. “It’s the art of building a space to the point that it’s almost therapeutic.” The zen garden and temple aesthetics of Miegakure hit this point of reference explicitly, but ten Bosch is quick to note that he’s not intent on making some direct comment on Japanese gardens or their surrounding culture. “The influences from Japan on this game are, for me, mostly intuitive,” he said. “It’s all connected but not in a way that you can pick apart.” Not that saying as much will stop players from trying.

There’s also a certain degree of “hide and reveal” in game programming, where the underlying frameworks are rarely seen by players, but intricate and emotive characters and worlds are borne out of layers of code. Perhaps one of the most stunning elements of Miegakure is that its fourth-dimensionality has not been faked. Remember when I described a wall disappearing into sand earlier? Well, ten Bosch’s fourth dimension is not just some parallel universe that the game transports you to when you step through a portal. No, four dimensions are built into the architecture of the game world at the code level. There’s no fudging the details to make it look like something spectacular is happening when one spatial dimension is swapped with another. Something spectacular is in fact happening. The wall and the sand exist at the same time. The difference is in what you can see. “Having applications is what brings anything forward,” ten Bosch told me. And this is where that whole “new math” bit comes in. “There’s a lot of math that exists to cover [these concepts], but once you actually try and apply it to something, then you bring up these problems and questions that wouldn’t necessarily come up when you’re just manipulating symbols for no reason. Which is the same in any kind of science.”

Marc Ten Bosch

And that’s the tricky thing with working on an artistic concept that is so contingent on its science: how do you maintain its personal expressiveness? “The process is mathematical, but the output is beautiful images,” said ten Bosch. Neither art nor science exists without the other, and ten Bosch uses the inherent mystery of 4D objects to seed artistic intrigue. “[An ordinary object] suddenly becomes beautiful because you can’t see all of it.“ For all the actualization of 4D space, ten Bosch’s greatest success might be in stirring players’ imaginations. The difference between what is real and what we can or cannot see just got a whole lot more complicated. Luckily, you don’t have to be a mantis shrimp to see it.

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