According to the Newtonian formula for a simple pendulum, the period of a pendulum is inversely proportional to the square root of "g", the gravitational field strength. Einstein's theory of general relativity leads to the result that time slows down where gravity is intense. The two claims look contradictory and can muddle student and teacher alike. There is, however, no real paradox. This article, which aims to clarify the conceptual issues, identifies two sources of confusion. One is a failure to distinguish a pendulum from a pendulum clock. The other is a failure to distinguish between two distinct gravitational fields.