Brought to you by the Number 1

What numbers are these?

Perhaps it hasn't occured to you that we can draw pictures of numbers. We can, and here are several examples.

In each of these examples we are portraying the number, not the name of the number or the numeral but the number itself. Like every good portaitist we want our pictures to communicate the essence of what the number is in itself.

The number zero	The number one	The number two	The number three
Nothing. No thing, no relationship.	One thing. But no relationship.	More than one thing. And one relationship.	Three things. Three relationships.

How far can we keep this going? Already with the number 4 we can find questions about what the picture should look like.

The number four	The number four
Is this the number four? Four things and four relationships but just one shape.	Or is this the number four? Four things and four triangular shapes but six relationships. On the left, one of the triangles is overlaid by the other 3; you might think of it as a top-down view of a tetrahedron. On the right the tetrahedron is seen in perspective from the side.

Which is more true to the number four? Not enough shapes or too many relationships?

We aren't going to resolve the question of how to draw the numbers 4, 5, or 72. What we will do is look at some ways to make structures like these.