  We study the medial axis of a set $K$ in Euclidean space (the set of points
in space with more than one closest point in $K$) from a "coarse" and
"quantitative" perspective. We show that on "most" balls $B(x,r)$ in the
complement of $K$, the set of almost-closest points to $x$ in $K$ takes up a
small angle as seen from $x$. In other words, most locations and scales in the
complement of $K$ "appear" to fall outside the medial axis if one looks with
only a certain finite resolution. The word "most" involves a Carleson packing
condition, and our bounds are independent of the set $K$.
