Before starting, I would like to clarify that this article is just a small portion of the Fourth Dimension, an introduction to immerse you in a new dimension we call the fourth dimension. In this article, we will not delve deeply into the fourth dimension but rather talk more about what dimensions are and how to transition between them.
I would like you to make suggestions as the series of articles progresses about inexplicable things that could be solved by 4D, or things closely related to 4D, so I can investigate, explain, and even represent them.
What are dimensions?
Imagine a 2D game, yes, one of those Scratch Platformer-type games where a cube has to go through a parkour, or one of those mazes from kids’ menus at Foster’s, or even simpler, a word search puzzle you always find in English books. All of that is in 2D, meaning you can only move in one direction x (horizontal) or y (vertical), as there is no other direction.
In the Platformer game, you can only move left-right and jump (up-down), more or less the same happens with the maze, you can move left-right and up-down, and even if you say you can move vertically, you are still in the same 2D plane.
Now imagine a line with a ball that will be our player. The ball can only move along the line 1D, meaning it can only move left-right, not up or down, that is, it can only move in the x (horizontal) direction. If we took the ball to a 2D game (x, y) and we could only see in 1D (x), if the ball moves in the x or -x direction, we could see it, but if it moves in the y or -y direction, we would stop seeing the ball because it is in a different plane than ours.
Now imagine a game like Minecraft, Planet Coaster… a 3D game, 3 dimensions. In that game, we could move left-right, which we already knew from 1D, up-down, which we already knew from 2D, but we could also move forward and backward, this is known as the third dimension, denoted by the letter z (depth). Now, just like before, if we place a 3D object in a 1D or 2D view and move it in the z direction, the object would eventually disappear, just like in the previous example.
Transitioning between dimensions?
In the world of dimensions, we can transition between dimensions by connecting vertices. For example, to go from 1D to 2D, we need 2 lines (1D), each with 2 vertices, one at each end of the line. If we place one line above the other and connect their vertices vertically (y), we will form a square or rectangle made in 2D.
The same happens to go from 2D to 3D. Two squares, each with four vertices placed at their respective corners, we place one square in front of the other and connect the corners in the z direction.
The Fourth Dimension, Hypercubes
As in the previous examples, we already know that each dimension brings a new direction (1D x, 2D y, 3D z). The fourth dimension brings the direction w, a direction we cannot see since we are in the third dimension, just as someone in 1D cannot see 2D (y).
A Hypercube is the main figure of 4D, and it is formed from two cubes, each with eight vertices at their respective corners. One is placed inside the other, and the vertices are connected.
Conclusion
- Dimensions can be said to define the number of directions you can go in that dimension.
- If we move an object in one dimension and view it from a lower dimension, the object will eventually disappear for us.
- To transition between dimensions, we need to connect vertices in the direction of the new dimension.
- The fourth dimension brings the direction w.
