Learn your lines and the hyperplane will follow i

Take an empty [rectangular] space (A4 paper in landscape)

Blank! Isn't it?

Take a line. Yes, call it that.

Divide the space vertically, and equally, in two. 

Do this again but horizontally.

You can call these lines, partitions if you wish?

Or, as per adopted convention here, axes.

Now, there are four empty spaces.

These spaces can be called quadrants, planes, or domains. The latter term usually adopted here.

Labels can be decided, and assigned to the axes and the resulting domains.

Given a purpose, in practice (initially) the 'empty' spaces have the ability to assign significance to what may be placed within them.

Such decisions are non-trivial, in the sense that context and situation determine what follows, influenced by objective and subjective considerations.

The domains can contain concepts, or keywords with decisions driven by categorical reasoning.

The content of the domains can also be viewed as classes and sub-classes.

ii to follow (with revision here?)