What is the first dimension? A single line going to infinity in both directions, how do you split it in half? A single point.

What is the second dimension? A plane streaching to infinity in all directions. How do you split it in half? A single line (1D object).

What is the third dimension? A cube streaching to infinity in all directions.
How do you split it in half? A plane (2D object).

So what is the fourth dimension? Something that could be split in half by an infinitley large three dimensional object.