I’ve been fascinated by the fourth spatial dimension since a long time. First time I heard about that I was in high school and I tried to visualize it in my mind in every way, but couldn’t find a proper one. I asked my math teacher and he said to me “Time is the fourth dimension. Think about what happens in physics, you have 3 spatial components and 1 temporal one”, but this didn’t satisfy me… time is something different… I wanted to see things in 4D! I wanted to imagine 4 physical dimensions, the 4D space.

The best way I did find to imagine that was drawing a cube on a piece of paper and then imagine the 4th dimension as the one perpendicular to the sheet. It was something, but not good enough. My struggle ended today, when I tried 4D Toys, by Marc Ten Bosh.

4D Toys is a little toybox that Marc Ten Bosh has made in preparation for its upcoming 4D game Miegakure. As the same author says on his website

Near the beginning of Miegakure’s development, someone joked I should make a 4D physics engine. Then a few years ago I had gathered enough knowledge that it was a possibility. So I made one for fun, and kept working on it on the side. I had a ton of fun inventing the math for it.

I was only planning to use 4D physics a little bit for Miegakure as a purely aesthetic component, but I started thinking about making a stand-alone toy to play with 4D objects, to take full advantage of the physics. At first it was going to a simple dice simulation but I kept adding new shapes… and it got out of hand.

(OMG, I think that my mind would melt while developing a physics system in 4D!)

I discovered this game because I read an article about it on Road To VR: as soon as I read about a 4D game for VR, I made everything possible to try it. I’ve downloaded it on Steam and launched it with a lot of curiosity.

When 4D Toys starts, you are immediately presented with some 4D hypercubes falling from the ceiling and having some weird results. Because yes, seeing 4D cubes falling one over the other produces a really WTF result. Judge it by yourself.

If you’re asking yourself “what the hell is happening”, well, welcome to the fourth dimension. As 3-dimensional beings we can’t understand a 4D space… it would like trying to explain Super Mario what is a cube… he lives in a 2D world, can’t understand it. So while the above behavior has perfectly sense in 4D, for us humble 3D beings it’s just a mind-blowing experience.

After this intro, an automatic little tutorial starts and it teaches you how to interact with the experience: basically you can grab objects with your controller trigger (the index trigger on Touch) and then do with them whatever you want (like throwing them in the air, etc…); you can move in 3 dimensions with room scale and move in the 4th dimension using the thumbstick on your controllers. Because yes, this is the ingenious way the author has found to make you move in 4D: you have a slider on your controller that makes you see the 4th coordinate you’re in beside the one of the other objects in the scene (you see a coloured tag on the slider showing you where in 4D is every object in the scene). Moving that slider using your thumbstick is a trippy experience because makes you move in the 4th dimension… and other mind blowing things happen.

If you hold an object while you move in the 4th dimension, that objects move with you and this is useful to move objects along this coordinate.

After the tutorial, you see a storyboard that tells you the story behind the game… basically, a guy finds a box full of toys sent from the fourth dimension. Bah, in my opinion this little story is useless for this application, even because it is present only there and there’s not an evolution of the plot while you play. Maybe it is there as a teaser for Miegakure? Who Knows.

After the storyboard, you find in a white environment that is the menu with all the possible experiences that you can try in this game. You can select them with your controllers: clicking one time you can see the name of the experience and a little animation; if you click again, you’re teleported there.

All the experiences happen in a gray environment where you can move inside a cube-shaped area. In this cube, there are your 4D toys and you can play with them. The first experience I tried, I just grabbed objects and threw one against the other, or threw them in the air. The experience was super trippy, because cubes transform in ehm, abnormal 3D shapes, while spheres change dimensions when colliding. It’s interesting… it’s super-trippy.

If inside an experience you find the “?” sign, you can select it with your controller and have a nice explanation of what is happening there and what you’re supposed to learn. For instance, thanks to these writings I discovered that a 4D cube can be called a “Tesseract”.

Every experience is so just a little sandbox where you have some objects that interact one with the other: usually, an initial basic interaction occurs (e.g. the 5 cubes that drop one on the other) and then you’re free to play around with the shapes in the scene. After having played a bit by throwing objects one on the others in the first experiment, I went trying the other ones. Throwing objects was nice and the odd behaviors are intriguing. But I still felt something was missing.

Then I found that one of these sandboxes is actually a tutorial to explain the 4th dimension. You can find it in the middle of the experiments menu. I opened that and… WOW. This tutorial is worth the whole experience in my opinion! Starting from the 1-dimensional space (a line), the tutorial guides you through the 4D world in an interactive way explaining what are all those strange 3d shapes that you see when a cube moves in the fourth dimension. It explains to you why you see the spheres becoming bigger and littler when you launch them inside the game. I think he managed to find a way to explain 4D to our 3D beings in a very effective way. I won’t tell you how he does that (you have to try the game by yourself!), but he helped me a lot in understanding what I missed all these years. Thank you, Mark, really.

After the tutorial, things got a bit clearer to me. My mind still blew after each experiment, but it was a less powerful explosion.

After I tried some of the experiences, new ones appeared. Some of these are very cool. For instance, in one of them I found 2 rings, one inside the other and moving one on the fourth dimension I was able to free it…

In another one I made a whatever-it-was to roll and to change shape and colors

Then I played domino in 4D… and also bowling! Don’t know if I made a strike, though…

I also launched a 4-dimensional dice: the 3D shape onto which it falls upon determines the number of the dice. Guess what number will come out!

15 sir! Who bet on that number has won…

Then there are the spirals in 3 and 4 dimensions and a lot of other cool stuff!

As you can see, I enjoyed a lot trying this mathematical experience. But I also think it has a big issue and this is durability. After a while, all experiments seems too similar one to the other and the more you play, the less “WOW” moments you have. And the lack of a purpose is a killer: this experience is just a big 4D toy box… you don’t have tasks you have to perform; you don’t have time constraints; you don’t have a story to follow. You just take stuff and launch it in the air. Very interesting, but doesn’t last for long. This is the reason why I think that the price of $14.99 on Steam is a bit too high for this experience (should be half IMHO). That money is clearly deserved by the developer for his amazing job, but the game after some hours of fun has no more meaning for the user.

In the end, I think that durability issues apart, this is an amazing experience. The idea is damn original and the development of this idea into a 4D physics engine is, well… I’ll let Shia LeBoeuf express that for me.

If you like math, you can only love this little crazy experiment. The tutorial part really got me and the rest of game is a continuous interesting experimentation. I see this program very useful in math classes. There’s a lot talking about educational applications of VR and this can be one of them… if my math teachers had made me try this experience, it would have opened me new horizons.

To increment the durability, the author could develop a 4D world creation… it would be really interesting. Instead of having multiple pre-determined sandboxes, he should let the user create its own 4D experiments in its own 4D world. Everyone says that VR is great to teleport us in another world… but what about another dimension, too? Hope that the game Miegakure would make this possible. The game is also available for standard screen, but I think that VR is its natural environment, since it makes you really feel as you are there, in a crazy 4-dimensional world. All those things happen in front of your eyes, all around you. This is amazing.

In the end, I can say that if you have a passion for maths, physics and other nerdy stuff, you MUST try this game. You can find it on Steam, if you’re interested. Don’t let your mind blow too much…

(Header image and various GIFs by Marc ten Bosh)

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