Why Non-Euclidean Games Are the Trend of the Future

Non-Euclidean games may hold the key to the future of gaming. But what exactly are they, and why do they matter? Slowly rising in popularity in recent years, these titles allow for experiences we could never hope outside of the medium.

Why Non-Euclidean Games Are the Trend of the Future

Playing games is perhaps the greatest form of escapism. For a moment, we’re able to step into another world, live someone else’s life, and experience things we never could in reality. Almost all games give us at least one of those options as a way to escape our mundane world. While great stories and worlds to explore have become very common, the idea of bending reality is just beginning to reach its greatest heights. non-Euclidean games have been gaining popularity and may hold the key to the evolution of gaming.

Non-Euclidean Worlds Engine

What is Non-Euclidean Gaming?

So what exactly does “non-Euclidean” mean? To explain that, we first need to establish what ‘Euclidean’ means. Remember taking Geometry in school? That class may have neglected to tell you that you were only learning one of several forms of geometry. In school, they teach Euclidean geometry. The word refers to the type of rules you’ll encounter in that form of the subject. You probably remember the basics, such as the rule that parallel lines will never meet. But non-Euclidean geometry follows different rules.

Euclidean geometry is easier to study because it’s based on a two-dimensional plane. But we don’t live in a two-dimensional world. If you draw two parallel lines on a piece of paper, then map it onto a sphere, you’ll find that as the lines keep going, they’ll eventually meet at the poles. non-Euclidean geometry is full of different surprises like that. So you can imagine if we transition from geometry to physics, those surprises become even more complex.

Structures like this could never exist in our world, but with non-Euclidean physics, it becomes possible

Structures like this could never exist in our world, but with non-Euclidean physics, it becomes possible

So a non-Euclidean game would be one where you experience non-Euclidean physics. In Euclidean geometry, the shortest path between two points will always be a straight line. But physics doesn’t allow that concept to work in a spherical, three-dimensional world. A straight line becomes impossible without puncturing the surface of the sphere. Think of it like tunneling through the earth to reach the other side. Even if it were possible, it’s just not practical. But in a game, we can simulate non-Euclidean physics. Suddenly the shortest path from point A to point B may not be a straight line. These are the kind of experiences we can only have in these types of titles.

Why Does This Matter?

It allows us to step into another reality. So how is that different from any other game? The nature of non-Euclidean physics is something we can only really experience in a digital world. One of the best things a game can do is allow us to experience the impossible. Non-Euclidean games not only do that, but they showcase the fun that can be had by breaking free of the physical rules we’re constrained by. If that’s not enough, these ideas may help shape the future of games as we know them.

Virtual reality is an evolving form of gaming. There are various reasons it hasn’t entirely taken off yet, and one is the space needed to properly experience it. Few people can set aside a full room of their home for VR gaming. Even if they can, without being able to see the room you’re in, it can quickly become dangerous to move while wearing the headset. But what if we agree on a certain area of physical space for games to take place in? Say all developers agree to use a 10’ by 10’ square area of free space for any VR game.

This is just some of the gear required for the PlayStation VR setup

This is just some of the gear required for the PlayStation VR setup

By using non-Euclidean physics, developers could squeeze an entire building into that space. Then you could fully move and explore the real world without the danger of running into anything. Digitally breaking the laws of physics has the power to help conserve physical space in the real world. This is just one example of the doors that can be opened when we begin to realize that games don’t have to conform to the laws of physics we know in the real world.

Examples of Non-Euclidean Games

Probably the most famous example of non-Euclidean rules being applied to gaming is in the Portal series. Placing portals bridges two distant points together. That allows us to get from A to B faster by means that aren’t normally possible. By punching holes in the reality we know, the portal gun effectively breaks Euclidean physics. That theoretic principle is easy enough to understand once you get into the right mindset. But it only scratches the surface of what non-Euclidean gaming can achieve.

The first game that allowed us to experience a fully non-Euclidean world is Antichamber. The game is known for its first puzzle involving two staircases, one going up and one going down. No matter which one you take, you end up returning to the two staircases. The solution is to go back the way you came, where you’ll find a completely different room from the one you left moments ago.

The game is almost entirely about traversal in this space where the laws of physics aren’t the ones we’re familiar with. You can encounter hallways that take 6 right turns without doubling back on themselves and clear boxes with different scenes visible on each side. Antichamber gives us a glimpse into a fully non-Euclidean world, and it’s staggering the first time you experience it.

This is how I felt for most of my time playing Antichamber, in a good way

This is how I felt for most of my time playing Antichamber, in a good way

Manifold Garden is presented in a world similar to Antichamber. It also showcases strange rules of physics that can be classified as non-Euclidean. Most notable are its gravity puzzles. Some rooms allow you to walk on the walls and ceiling, while others contain cubes that control gravity. Another game that shows non-Euclidean puzzle-solving is Superliminal. This one explores the idea of forced perspective. It exists in a reality where your forced perspective actually changes the size of different objects. As something impossible in the Euclidean world we know, this can also be classified as non-Euclidean.

So, as you can see, several games, mostly in the puzzle genre, have already adopted non-Euclidean elements. The majority of them have received positive responses from their audience as well. Because of that, it wouldn’t be much of a surprise to see non-Euclidean mechanics begin popping up in other genres as well. Games like The Stanley Parable have experimented with using these mechanics to tell intriguing stories. The application is only slight there, but exploring a non-Euclidean world could have a drastic effect on the stories that might be told there.

It would also be interesting to see how multiplayer games could adopt these changes. Arena shooters or racing games seem like prime opportunities for experimentation of people exploring these environments together. We’re only scratching the surface of what a non-Euclidean game may become. With that in mind, we can be optimistic about the future of the gaming landscape.

(Video by CodeParade.)


1 Comment

  1. That’s a fascinating subject! There are lots of inaccuracies in this article, though:

    1. What is “non-Euclidean physics”?? Euclid was not a physicist, he was a mathematician/geometer. Non-Euclidean is a property of geometry, not physics.
    2. “The shortest path between two points will always be a straight line” — this is misleading, because it is basically true both in Euclidean and non-Euclidean geometry.
    3. “The first game that allowed us to experience a fully non-Euclidean world is Antichamber.” — nah, it is just the game which has started the unfortunate trend of calling games taking places in weirdly-structured worlds “non-Euclidean”. Games were experimenting with weird structure of the world, or weird physics since forever. Pacman and Asteroids had wrapping space (like Manifold Garden but in 2D and without gravity changing). Basically any platformer where you can adjust your position while jumping is not based on real physics.
    4. Non-Euclidean geometry is one of the most celebrated discoveries in mathematics, and crucial for understanding the modern physics. Scientists are crazy about it, so some people are abusing this by calling various things non-Euclidean and thinking it will bring them more audience. While games are a great way to learn about non-Euclidean geometry, the games mentioned in the article have NOTHING to do with it! Portals and stuff change the *topology* of the world, but its geometry remains Euclidean. They are fun, sure, but actual non-Euclidean geometry is even better!

    Really, non-Euclidean geometry in games is a fascinating subject that needs more good articles about it!


Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>