Understanding the fourth dimension (And some other stuff thrown in just for fun)

Visual representation of the 4th dimension

Howdy, Imgur!

So, yesterday I came across this post http://imgur.com/gallery/lwTEC which claimed to explain how the fourth, fifth, sixth etc dimensions work. (There are eleven, by the way). It was a very interesting post- however, it was incorrect. I made a comment saying so, and I got an overwhelming amount of people in the comments and even in private messages asking me to explain how it DOES work**, if that wasn't it. I agreed, saying I'd post it today. I love physics, so with so many people asking me to, I couldn't refuse!

Okay, so the first thing you need to understand before understanding the fourth dimension is the first three, the ones we're familiar with. The good old X, Y and Z axis. Well, those and the Zero-th dimension. So let's get started.

So we'll start with the zero-th dimension. Yes, it exists. Think of it as a dot that's infinitely small. It has no size, no up or down, no anything, but it exists. (If you're familiar with the Big Bang theory, the universe was zero dimensions before the big bang happened). With me so far? Okay,

Now, the first dimension. The first dimension is a line, just a line that extends on forever. The line has no width or thickness, only length. And this first-dimensional line is made up of an infinite number of zero-dimensional points lined up side by side.

Now, the second dimension. You're probably familiar with how this one works- Think "Tetris" or "Super Mario Bros". The pieces and characters on the screen can move left and right, up and down, but that's it. They cannot move towards or away from us. If the third dimension is made up of an X, Y and Z axis, then the second dimension only has an X and a Y. This is the second dimension, and it is a "Plane" made up of an infinite number of one-dimensional lines stacked up on top of each other.

Before I go on to the third dimension, I'd like to throw in a little bit of extra info on the second dimension, a sort of disclaimer if you will. If you've ever read or seen "Flatland", you may think that a theoretical two-dimensional being can only see the "Edge" of objects in front of it, like a line segment. This is NOT true! A two-dimensional being cannot see anything, because there exists no "Edge" for it to see. Remember, this objects aren't just extremely thin, they are INFINITELY thin. There IS no thickness!

Alright, moving on. Three dimensions. I should hope you're familiar with this one, it's the one you live in! As stated earlier, the third dimension has three axis, an X, Y and a Z. If you can move left and right, and then forward and back, and then up and down- Congratulations! You're a three-dimensional being (or higher)! This third dimension is made up of an infinite number of two-dimensional planes stacked up on top of each other- Anyone noticing a pattern yet? I hope so, because understanding the relationship between the dimensions I've described so far will help you wrap your mind around the ones coming up... kind of.

So before I begin explaining the fourth dimension, I've got to say... the fourth dimension is NOT time. Say it with me. The fourth dimension is not time. The fourth dimension is not time. THE FOURTH DIMENSION IS NOT TIME. Got it? Good. So then, where did that idea come from? Why do people think the fourth dimension is time? Well, in 1908, a man named Hermann Minkowski presented a paper suggesting the idea that time could act as the fourth dimension of spacetime (Which I might do a post about later on). However, the geometry of spacetime is profoundly different from this idea. Like I said, I might get into it in a later post, but all you need to remember for now is that this guy was wrong.

Now, a square is two dimensions. A cube is the three-dimensional version of a square. But what is the fourth dimensional equivalent? It's called a hypercube, or a tesseract, and it's that thing in the gif at the top of this post- well, kind of. It's more the "Shadow" that a fourth-dimensional cube (or Hypercube) would leave, similar to how http://i.imgur.com/JsOAyod.jpg is like the shadow that a three-dimensional cube would leave.

If two dimensions is a plane, then three dimensions is a "Space". Now, space is made up of infinite planes- so think of fourth-dimensional space being made up of infinite "Space", stacked on top of each other just like all of the previous ones. Kind of hard to picture, but stay with me. Fourth-dimensional space would be made up of a W, X, Y and Z axis. That's all it is. You can name ANY point in three dimensions by quoting a X, Y and a Z. In order to pinpoint a spot in four-dimensional space, you'd need to quote a W, X, Y and a Z.

There's a fifth dimension, as well. Think V, W, X, Y and Z. If we lived in a fifth-dimensional space and you asked me for coordinates that told you where I was, I'd need to give you five numbers, just like how if we were in one-dimensional space I'd need to give you one number (Think: Number line), or if we were in two-dimensional space I'd need to give you two numbers (Think: Graph).

Imgur user @Preincarnage left this gif in the comments, I thought it was worth sharing:
http://i.imgur.com/1AVySho.gif

So how many dimensions are there, then? There are eleven, according to string theorists (String theory is another topic I might do a post on, if you guys end up liking this one). Each one is created the same way, by taking an infinite amount of whatever the previous dimension was made up of and stacking them on top of each other, and adding an axis (So an 11-dimensional space would have a P, Q, R, S, T, U, V, W, X, Y and Z axis). Hopefully this post has helped out a bit if you were struggling to picture the fourth dimension. Anyhow, that's about all I've got to say on the matter. Cheers, Imgur!

**Disclaimer: While I DO have a pretty decent understanding of the fourth+ dimensions, the reader should bear in mind I am only 18 years old and far from a genius. If somebody qualified (Say, a physics professor or somebody with a degree in physics) notices that I have made an error, and I'll edit my post to fix it. Cheers!

Oh, and for those of you who are interested, here's a fourth-dimensional Rubik's cube you can download! http://superliminal.com/cube/cube.htm