The lines in which we write mathematical symbols impose constraints upon mathematical thinking.

A simple space of representation is proposed that does not enforce the linear concepts of associativity, commutativity, duplicity of representation, and binary scope. The properties of this simple space are discussed in the foundational case when the space is empty and in the self-referential case when the space contains only representations of itself.

Concepts that evolve from this discussion include representational incompleteness, functional spaces, boundary objects, representational unity of object and process, and two kinds of void. The implications of a representational space without linear properties are explored for propositional calculus. A graph notation is proposed as a simplification of the traditional linear notation for logic.