  In this paper we are proving the following fact. Let P be an arbitrary simple
polygon, and let S be an arbitrary set of 15 points inside P. Then there exists
a subset T of S that is not "visually discernible", that is, T is not equal to
the intersection of S with the visibility region vis(v) of any point v in P. In
other words, the VC-dimension d of visibility regions in a simple polygon
cannot exceed 14. Since Valtr proved in 1998 that d \in [6,23] holds, no
progress has been made on this bound. By epsilon-net theorems our reduction
immediately implies a smaller upper bound to the number of guards needed to
cover P.
