2. The Second Dimension – A Split
If we now take our first dimensional line and draw a second line crossing the first, we’ve entered the second dimension. The object we’re representing now has a length and a width, but no depth. To help us with imagining the higher dimensions, we’re going to represent our second dimensional object as being created using a second line which branches off from the first.

Now, let’s imagine a race of two-dimensional creatures called “Flatlanders”. What would it be like to be a Flatlander living in their two-dimensional world? A two-dimensional creature would have only length and width, as if they were the royalty on an impossibly flat playing card. Picture this: a Flatlander couldn’t possibly have a digestive tract, because the pipe from their mouth to their bottom would divide them into two pieces! And a Flatlander trying to view our three-dimensional world would only be able to perceive shapes in two-dimensional cross-sections. A balloon passing through the Flatlander’s world, for instance, would start as a tiny dot, become a hollow circle which inexplicably grows to a certain size, then shrinks back to a dot before popping out of existence. And we three-dimensional human beings would seem very strange indeed to a Flatlander.

1. The first dimension – a line
A second point, then, can be used to indicate a different position, but it, too, is of indeterminate size. To create the first dimension, all we need is a line joining any two points. A first dimensional object has length only, no width or depth.

0. A point (no dimension)
We start with a point. Like the “point” we know from geometry, it has no size, no dimension. It’s just an imaginary idea that indicates a position in a system.