In popular accounts of the time dilation effect in Einstein's special relativity, one often encounters the statement that moving clocks run slow. For instance, in the acclaimed PBS program "NOVA," Professor Brian Greene says, "[I]f I walk toward that guy... he'll perceive my watch ticking slower." Also in his earlier piece for The New York Times, he writes that "if from your perspective someone is moving, you will see time elapsing slower for him than it does for you. Everything he does ... will appear in slow motion." We need to be care- ful with this kind of description, because sometimes authors neglect to consider the finite time of signal exchange between the two individuals when they observe each other. This article points out that when two individuals approach each other, everything will actually appear in fast motion--a manifestation of the relativistic Doppler effect. (Contains 1 figure.)