  An oblivious point on a translation surface is a point with no closed
geodesic passing through it. Nguyen, Pan, and Su (2017) showed that there are
at most finitely many oblivious points on any given translation surface and
constructed a family of surfaces with exactly one oblivious point. We construct
new families of translation surfaces with arbitrarily many oblivious points and
prove that there is a translation surface in every genus $\ge3$ with an
oblivious point.
