Have you ever read Flatland by Edwin Abbott Abbott?

I did as a kid (nerd). Each group in literature class got to choose a novel to study and we picked Flatland. One day, two-dimensional creature A. Square gets a visit from a three-dimensional creature and gets a glimpse of a new dimension beyond his world’s two. The novel ends something like this:

“So are there more dimensions beyond the third?”

“Nah,” said Sphere.

Anyway, let’s go golfing!

Sphere was wrong and 4D Golf is the proof. I got it on the recent sale and just started it and it’s just about what I expected.

It’s really a straightforward game. You play mini-golf, but the course spans the space of four dimensions instead of three. However, you, the player, are still a 3D creature and can only see a slice of the 4D space. That means the part of the challenge is just to figure out where you actually need to face to get the ball into the hole.

As a bit of aid, the game gives you several tools to help you visualize and navigate the course. You have the ability to spin around the 4th axis and you can see ghost images of what’s perpendicular to you in the fourth axis so you get a better idea of what’s around you.

You can also switch to a “volume view”, which lets you see and explore the floor plan of the level. Like how a floor plan is two-dimensional for a 3D area, it’s three-dimensional in 4D, so you fly around with six degrees of freedom in the floor plan mode.

After playing a handful of levels, I think I’ve built up enough of an intuition to orient myself properly. I’m getting a hang of this internal mental shorthand of the level changing around the ball as it moves.

The first few levels also deliver a quick tutorial on understanding 4D space, with the classic explanation for the topic. It starts by talking about how a 2D creature would perceive 3D space, then extends the analogy to a 3D creature in 4D space. It really is quick, so I’m not sure how helpful it could be for anyone who isn’t already slightly familiar with 4D.

I’m slightly familiar with 4D

Yeah, Flatland got young me fascinated in this kind of funky geometry stuff. I was finding sites to learn about exotic geometries. Four dimensions was only the start.

Well, I clearly wasn’t the only person who was fascinated by this stuff. 4D Golf is essentially developer CodeParade’s followup to their previous game, Hyperbolica, which was set in a three-dimensional world where the rules of geometry were different. Parallel lines never stayed parallel and five squares could share a corner, not four.

I’m glad I get to enjoy multiple extremely nerdy geometry games.

Bonus: discover more funky geometry-related stuff

Novels

• Flatland by Edwin Abbott Abbott — A. Square lives in a two-dimensional society and discovers the third dimension. It’s in the public domain, so it’s free to read online!
• The Planiverse by A. K. Dewdney — A class in a computer lab accidentally makes contact with a two-dimensional universe. It’s a more rational, “hard” take on how a two-dimensional universe would work.

Online resources

• http://hi.gher.space/ — 2003-era site with an introduction to four-dimensional space and an exploration of how a world like that would work.
• Outside In AKA “turning a sphere inside out” — An old-school YouTube upload of an even older-school animated presentation about math research on the topic. Here’s the 1996 official site!
• Portals to Non-Euclidean Geometries — In this YouTube video, the host takes you through portals to spaces where the rules of geometry are weird and different.

More games

• Hyperbolica — By the same guy as 4D Golf. A light-hearted walking simulator in a world with hyperbolic geometry.
• Miegakure — A 4D puzzle game that’s been perpetually in development since like 2007. It still shows up on YouTube, at conferences, and in the solo dev’s blog posts from time to time.