  We present a new proof that $O_2$ is a multiple context-free language. It
contrasts with a recent proof by Salvati (2015) in its avoidance of concepts
that seem specific to two-dimensional geometry, such as the complex exponential
function. Our simple proof creates realistic prospects of widening the results
to higher dimensions. This finding is of central importance to the relation
between extreme free word order and classes of grammars used to describe the
syntax of natural language.
