Tyler

This is a great gif I found on Wikipedia while researching hypercubes. It’s a Tesseract— a 3-dimensional representation of the 4th dimension (“Duration” or “Time”). The movement of the center box as it shifts around itself is meant (to my understanding) to represent the constant value of space, but the moving value of time. It is the line that can be drawn between, say, the beginning of the universe, and its end. The next dimension up, the fifth dimension, is to the 4th dimension what the square is to the line, a broadening of it. On the fifth dimension, time branches off into an imagined X axis in a way that any fan of science fiction will instantly recognize as alternate histories, with each moment in time creating its own little branch on this fifth-dimensional space.

In much the same way that we can fold a piece of paper (a 2-dimensional plane) into a tube (a 3-dimensional object), so it must also be that this fifth-dimensional plane can be folded into a 6th-dimensional “solid”. And just like folding allows you to draw a line off one edge of the paper and onto another, so too must you be able to draw a line off of one “edge” of this folded 5th dimension, and onto another. This is another way of saying “Time Travel.”

And this is why the 3D model is so interesting to me: A hypercube is a cube surrounded by cubes. The next dimension up must then be a hypercube surrounded by hypercubes (not the easiest thing to draw, let me tell you). Then the next dimension is this “ultracube” surrounded by yet more ultracubes. Within this model, you will have multiple representations of Time (the 4-dimensional object represented above) and Space (a simple cube). However, our model of the 6th dimension is able to move just like the model above, with cubes and tesseracts changing places without ultimately altering the shape of the overall structure! It would be a representation of a theoretical proof of time travel! 

Okay, science soapbox moment over. Go back to your lives, citizens. Pictures of cats to follow.

This morning, I’ve been messing around with drawing dimensions past the fifth dimension. I’m a shitty artist compared to a lot of Tumblr, but this is freaking cool. Think about this: 

1. A Line is a Dot extended in any direction. 
2. A Square is made when you move that Line one unit length perpendicular to itself. 
3. If you move that Square one unit length perpendicular to the plane that it’s drawn on, it becomes a Cube. Now you’re playing with the Third Dimension. 
4. Now if you take that Cube and move it one unit length into the Fourth Dimension (Not quite perpendicular to the Third Dimension), you create a Four-Dimensional unit called a Hypercube. 
5. With the Hypercube, you can continue this pattern (using math!) to demonstrate an infinite number of dimensions. 

So in theory, you should be able to (given a fine enough pencil and a large enough piece of paper) draw a unit on the twelfth dimension (a “dodekeract”) on a two-dimensional plane. So that’s one of the things that blows my mind, but here’s the other thing:

A Dot is a Hypercube representation of the 0th dimension. A Line is a Hypercube of the 1st Dimension, a Square of the 2nd, etc.

So you can go to all of this effort to stretch your mind into drawing a hypercube and representing the 4th Dimension, but if you’re thinking about it terms of dimensions, all of these shapes are actually the same shape. I don’t care how into math you are, that’s frakking awesome.