Dimensions #2

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.

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