In everyday language, "zero" and "nothing" are generally synonyms if not interchangeable. In physics, however, these two terms are quite distinct. Zero often refers to a number and nothing often refers to the vacuum state. Furthermore, the number zero has a variety of different meanings, among which physics teachers shift flexibly and effortlessly. This article informally describes some of the difficulties associated with the choice of zero in the context of gravitational potential energy, and relates an instructional approach that facilitates students' understanding.