Crazy VR game lets you explore a world made from 4D mathematical models

4D Toys also works on iOS devices, was borne from upcoming puzzle game Miegakure.

I'm hesitant to describe a virtual reality experience as a "killer app" ever again, but I'm oh so tempted once more. I just emerged from a glimpse into the fourth dimension by way of a VR experience, and I'm still amazed and perplexed by what I played with.

My extra-dimensional leap came courtesy of 4D Toys, which went live on Friday on the iOS App Store ($6 here) and the SteamVR Marketplace. If you can pull it off, I strongly urge you to opt for the $15 VR version.

This immersive dive into the mathematical systems of a fourth dimension is actually a byproduct of a long-in-development video game called Miegakure. The ambitious game demands that players figure out puzzles by moving a character through four dimensions of space, all viewed within the confines of a three-dimensional perspective.

Unsurprisingly, this concept has taken a while to arrive as a complete, playable game. So its creator Marc Ten Bosch decided to try something weird in the meantime: letting people freely experiment in a freeform 4D playpen.

"4D Toys doesn't take you through carefully constructed, successively harder challenges the way Miegakure does," Bosch writes at his development blog. "It's just 4D shapes, as if you were a very young kid again and given a box of wooden toys. Since the toys are 4D, that's sort of true: you have no experience playing with 4D shapes."

The interactive app was borne out of tests to add a robust "physics" system to the Miegakure game, which Bosch said would apply more to the game's aesthetics than to actual puzzle play (since bouncing and moving objects would complicate the puzzles he's already building).

"Surprisingly, it is possible to generalize physical laws that describe our universe, such as Newton's Laws of Motion, to any number of dimensions," Bosch writes on the app's official site. "To do this we had to come up with new mathematics. For example, forces are four-dimensional vectors, and objects rotate around planes instead of axes."

https://youtu.be/0t4aKJuKP0Q

After a trippy comic strip introduction plays out, users must move objects through the fourth dimension by picking them up, then sliding a finger on a touch surface (like your iOS device's screen or the HTC Vive's touchpad) to move back and forth in 4D space. App users are then presented with a giant floor of colorful toys, along with a formally written tutorial. You can watch an alternate version of the 4D tutorial in the above embedded video, but 4D Toys presents these lessons in a fully interactive manner. Instructional text appears and reacts to your every grab of objects and swipe through four-dimensional space.

I squealed when I warped through the fourth dimension to follow that ball on its sliding journey.

In short: Think of how an MRI scan looks. Thanks to your knowledge and perception, you know it's a 2D slice of a much larger and dimensionally varying 3D object (a brain). If you want to perceive the full bounds of that 3D object, but can only perceive two dimensions, you have to look at a zillion flat MRI images to mentally estimate its full 3D shape. In the same way, a fourth dimension is made up of an infinite number of 3D images. Since you cannot perceive a fourth dimension, you can only approximate it by stitching together the 3D shapes that you can perceive.

Still confused? Watch the video. You'll appreciate the visual aids. But the VR version is even cooler. The tutorial inside of 4D Toys set off one of the brightest light-bulb explosions my brain has ever felt. As I actively defined and modified the fourth dimensional coordinates of my playfield, I began to finally understand what about it I could and couldn't perceive.

With the tutorial complete, I sat down in real life so I could get my hands all over the app's densely lined floor of toys. I've snapped some screens of what I discovered, though they don't quite do their in-game counterparts justice. As you glide across the fourth dimension via a finger swipe, the three-dimensional objects in your field of view transform, since you can only see a single slice of their full 4D form at any given time. Some of the toys let you grab and fling things within the dimension that you perceive, but they are still able to move and transform through other dimensions. Once I realized this, and flung a ball over a toy-like string, I squealed when I warped through the fourth dimension to follow that ball on its sliding journey.

I am not sure that I've ever seen a more compelling "show-don't-tell" educational tool than 4D Toys. I'm already imagining the world's burgeoning math wizards playing inside of 4D Toys' robust playsets and discovering the coolest answer to the age-old question, "why should I care about math?" And if my time with the app is any indication, its helpful text and open-ended zaniness should lead adults through similar fits of childlike wonder.