It’s likely that everyone has encountered a work of fiction involving an extra dimension at some point. Be it time travel or trans dimensional beings, “extra dimensions” is a very popular topic. But what does it actually mean?

## The Basics

If I was asked the question “What is a dimension?” I would say “A place for a number to go in a coordinate”. That is, if I was to give a coordinate of a point in a particular space, for each dimension that space has, I would need to specify one number. In a one dimensional space (think an infinitely long line), to specify any point, I need only one number, and that will tell you how far along the line my point is. In a two dimensional space (Super Mario), I can move (say) up/down and left/right, so I need to specify two numbers. Similarly, to specify a point in three dimensional space, I need three numbers. Imagine a space where you would need four numbers to specify a point. It’s very easy to imagine spaces with up to three dimensions, but due to the nature of our universe, we are not accustomed to go any higher than that.

## What about time?

Time can be considered a dimension, and it’s possibly the easiest way to imagine a fourth dimension. To specify a point in the universe at a particular time, we need three numbers to specify the point (as it is a 3D space) and a fourth number to specify the time. Thinking of time as a dimension is a convenient way to help understand a fourth geometric dimension, by thinking of a three dimensional space inside the four dimensional space changing as the fourth axis is traversed. That last sentence was a bit intense, but should become clearer to you in the course of, well, time.

## Analogy Time!

Imagine a pen, with an infinitely small point. If you draw an infinitely small dot on a page, we could say that the dot has zero dimensions. Now, with the pen, draw a straight horizontal line on the page. The line has one dimension. Now imagine grabbing the line and pulling it down the page, forming a square. Now take the square, and pull it up, out of the page, and you get a cube. Now what? We can go no further in a three dimensional space. So what does the cube become?

Imagine living in a two dimensional world. Suppose we inhabited a large sheet of flat paper. Three dimensional beings might take a cube, and push it through our world. Initially, there would be just some empty space. Then, depending on how they push the cube, we might suddenly see a square appear, or a rectangle, or a triangle. We would continue to see a two dimensional cross section of the cube until it completely passed through our world and vanished. If four dimensional beings want to push a four dimensional shape through our three dimensional universe, we would only be able to see a single three dimensional cross section at a time.

If you get a whole bunch of cut-out square pieces of paper and stack them together, you can make a cube. You are creating a 3D shape by stacking 2D shapes in a third dimension. Now say you had a whole bunch of cubes. You can’t stack these like you did the squares to enter a new dimension, but you can “stack” them through a fourth dimension. At any point, you can only see one of them. Think of our 3D universe as a cross section of a 4D universe containing our “stack” of cubes. We can re-position our universe on the stack (as you could re-position a 2D plane making a cross section with a cube to obtain a non-square cross section). At each new position, we might see a cube. If we went too far in the new dimension, we would go “off the edge” and see nothing. If we rotated our universe (as you might tilt the paper to get a rectangle or triangle), you would see *something else*.

One more. You learn to draw prisms by drawing a 2D shape and projecting lines off its vertices to create a 3D shape. If you draw a square and project lines from each corner, you can draw a cube. At the end of each line is a vertex of a second square, located in a different 2D plane of the 3D space. Although you’re drawing on a two dimensional surface, you imagine these lines as being projected in a third dimension to create an image of a 3D shape. So take a cube, and from each vertex, project a line through a new, fourth dimension. At the end of each line is a vertex of a second cube, located in a different 3D space of the 4D “hyperspace”.