This is going to be quite a long post, so I may cut it short and come back to expand it later.
One night, when I was in the shower, I was frustrated about how the 4th dimension was so different compared to the first three. Keep in mind the fact that I have Asperger's Syndrome. I suddenly had a moment of inspiration. "What if they aren't so different? What if they follow the same pattern? What if the difference between dimensions two and three are the same as between three and four?" I then started scribbling in a notebook for the next few hours. This is what I got:
The 0th dimension is a dot. No length, no width, no height. Zero dimensions.
The 1st dimension is a line. This single dimension is usually called length.
The 2nd dimension is like a square. They have two dimensions, which are titled two of the three following: length, width, and height.
The 3rd dimension is like a cube. It has three dimensions, being length, width, and height.
It follows the pattern:
The 4th dimension is like a cube, stretched out through a timeline. It has four dimensions, being length, width, height, and time!
The 5th dimension is like a cube, stretched out through multiple timelines. It has five dimensions, being length, width, height, time, and what is probably an unnamed measurement whatchamacallit.
Here is another pattern, that really makes light-bulbs go off in people's heads:
The 0th dimension is a dot.
The 1st dimension is a line. A line is made of an infinite number of dots strung together.
The 2nd dimension is like a square, which is made of an infinite number of lines strung together.
The 3rd dimension is like a cube, which is made of an infinite number of squares strung together.
The 4th dimension is like a cube stretched out through a timeline, which is made of an infinite number of squares strung together.
Because of this pattern, there are an infinite number of dimensions. Given the fact that there are infinite dimensions, separations between dimensions are an illusion we created by giving them a name. A dimension is just a way of classifying a part of something that is already there, but everything has infinite dimensions. Paper still has thickness. Paper still moves through time. The paper still exists in alternate timelines. Et cetera.
I've also used these patterns to show how time flows, how time travel would work, etc., but I'm short on time. I'll come back and edit this post within the next few days.