When you look at the Dali painting, Corpus Hypercubus, what comes to your mind? Weird, bizarre structure? Eerie feeling? What is the secret behind the cubes arranged together in the shape of a cross?
The answer may shock you: It is a hidden picture of a 4D cube.
Huh, I heard you sneer. We don’t even know what a 4D cube look like, how can one draw one on a 2D plane, and how can you understand it?
Well, the best way to imagine a higher dimension is to think of the relationship between our dimension and a lower dimension, and then picture that relationship onto a higher dimension and our dimension. This is what we’ll do a lot in the understanding of the fourth dimension. Take a 3D cube first. We all know what a cube looks like, right? It looks like this:
The cube sonsists of 6 sides which are 6 identical 2D squares, with 2 squares opposite each other. And similarly, “cube” in 2D space, a square, consists of 4 identical sides of 1 dimension. Therefore we can imagine that a 4D cube should have been consisted of 3D cubes with two 3D cubes facing each other on opposite sides. Grab a piece of paper, and draw down 2 3D cubes slightly apart, then we have the two opposite sides of the 4D cube. Now we connect the vertices together, we get a very curious picture below:
Now this is what a 4D cube look like from a 3D perspective. It consists of 8 cubes (count it yourself!). The cubes are a little deformed because they are connected in the 4D space, and we cannot draw that connection out in the Euclid Geometry. In the picture below, the orange part marked out by the marker is another cube that is created by connecting two 2D sides of the opposite cubes.
Now that we’ve pictured what a 4D cube looks like in out 3D vision, let’s try to change the cube into a 3D model that could very well represent the cube in 4D. Let’s get back to the relationship between 3D and 2D: what happens when we cut a 3D cube up into a 2D picture? We take a paper cube and cut it up along the edges. We get the picture on the left. If we print it out on a piece of paper and then cut it out, we can fold it up into a 3D cube.
Now, if we cut the 4D cube up, we get a 3D model. In order to visualize it better, I drew a different version of a 4D cube. The difference between this 4D cube and the 4D cube I drew before would be explained in Part 2.
Anyways if we take this cube, and cut it up along the edges, we can get a model in 3D that can be folded up into a 4D shape. What does this model look like? Wait for it…
Did you get it right? And, hey, that really look kind of similar! That’s the cross in Dali’s painting!
Secret revealed! The surreal artist used a 3D model painted on the 2D canvas to demonstrate a 4D cube. He is telling us that God and the divine powers are a form of energy in higher dimensions that we cannot perceive. We can only glimpse their power and glory from a fraction of 3D perspective. Dalí’s inspiration for Corpus Hypercubus came from his change in artistic style during the 1940s and 1950s. Around that time, his interest in traditional surrealism diminished and he became fascinated with nuclear science. Sparked by science, his imagination takes him to explore concepts of a higher dimension, and thus born this interesting picture.
So in Part 1, we explained the shape and form of a 4D cube, imagined in a 3D perspective, and hopefully gave you some understanding of 4D geometry. But we have this weird and mythical picture in front of us, does it actually mean anything? How can we understand the nature of the fourth dimension through a cube? Is there any other way of picturing a 4D cube? All this and more, we will explain in the next part!
The next part will be posted on the 15th of January. Before then, follow us!!
-Ian
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