4D Toys is a toy box filled with four-dimensional toys. By four-dimensional I mean that they exist in a world with four of dimensions of space and one dimension of time. instead of three dimensions of space and one dimension of time. It turns out that the rules of how objects bounce, slide and roll around can be generalized to higher dimensions, and this unique toy lets you experience what that would look like. So I thought I would show it to you and in the process explain what the fourth dimension is. So here’s a stack of 4D hypercubes. To us, a 4D hypercube kind of looks like a regular 3D cube sometimes because even though these toys are 4D, our universe is only 3D so we can only see three dimensions out of four. I’ll explain soon, but first I am going to grab this one and throw it. I knocked down that pile and some of the cubes even got knocked into the fourth dimension, so I can’t see them anymore. Here’s a ball pit filled with 200 hyperspheres. I can move along the fourth dimension and see all of the hyperspheres that I couldn’t see before. Let’s see… I can grab this 4D shape called a 120Cell and I can roll it around. It’s gone into the fourth dimension so I will move along the fourth dimension to find it. I can also look at different 3D cross-sections of it. So it’s fun to simply play around with these, but we can try to understand what’s going on a little bit more by looking at a version in one less dimension. So let’s do that before I show some more stuff. So say that you are a 2D character, and you can only see two dimensions: up-down and left-right. But what if the world was actually 3D and you were just a flat 2D character stuck on a 2D plane? This is what the world actually looks like, and these 2D shapes were actually 2D cross-sections Of 3D shapes. I can move this sphere back and forth in the third dimension and see how its intersection with the 2D plane gets smaller or larger. But a 2D character can can only see two dimensions out of three, so let’s go back to their perspective, from inside the 2D plane. We do keep the 3D view in the bottom-left corner though. So, these 2D shapes don’t behave like a 2D character would expect 2D objects to behave. For example, this red circle seems to mysteriously float in mid-air… but we know it’s actually just the cross-section of the red sphere. The slice does not go through the center of the sphere, which is why the circle looks like it is floating. If I the red sphere hits another sphere, it might bounce into the third dimension and disappear from our slice. After bouncing, the square shape seems to mysteriously change how many sides it has, And gets smaller and disappears. But we know that’s because it’s a cube, and it moved into the third dimension. It’s still hard to predict exactly how the shape changes though. And now, let’s move the 2D plane we are standing on along the third dimension. The circles shrink and grow and the squares morph because we are changing which slice we are taking. It might look weird to a 2D character, but for us 3D beings it makes sense: it’s kind of like a taking an MRI. Each 2D circle we see is only a part of a 3D sphere. Ok now back to 4D Toys. In 4D toys, instead of a 2D being living in a 3D world, we are a 3D being living in a 4D world. So we can only see three dimensions out of four, instead of two out three. And instead of seeing a 2D cross section of a 3D world, we see a 3D cross section of a 4D world. But otherwise many of the same things happen, just in one higher dimension. These 3D shapes don’t behave like a 3D being would expect 3D objects to behave. This sphere floating in mid-air is actually just a 3D cross section of a 4D hypersphere. The slice does not go through the center of the hypersphere, which is why the sphere looks like it is floating. If the red hypersphere hits another sphere, it might bounce into the fourth dimension And disappear from our slice. After bouncing, the cube shape seems to mysteriously change how many faces it has, and gets smaller and disappears. But that’s because it’s actually a 4D hypercube, and it moved into the fourth dimension.. It’s still hard to predict exactly how the shape changes though, even harder than in 2D. If I move the 3D plane along the fourth dimension, the spheres grow and shrink, and the cubes change shape, but what is happening is only that we are taking different 3D cross sections of the actual 4D objects. Each 3D sphere we see is only a part of a 4D hypersphere. However unlike last time, when we could pull out the camera to see the entire 3D world, here we can’t see the entire 4D world, because our universe is only three-dimensional. Ok let me show you some more stuff. These two rings that can be unbound not by breaking them, but only using the fourth dimension. This is a 4D shape with 24 faces that you can use as a fair die, there are others with 5, 8, 16, 120 and 600 faces… Here is the four-dimensional version of a familiar kid’s toy. Oh and you can try fitting this hypercube into this hyperhole. You’re basically a kid playing with toy blocks again, they are just 4D toy blocks… Video Information
This video, titled ‘4D Toys: a box of four-dimensional toys, and how objects bounce and roll in 4D’, was uploaded by [mtbdesignworks {Miegakure, 4D Toys}] on 2017-06-02 17:43:29. It has garnered views and [vid_likes] likes. The duration of the video is or seconds.
Showing 4D Toys and an explanation of how 4D objects would look like and bounce around from the perspective of a 3D being.