As the Ithaca Journal recently noted (August 22, 2000), a computer based on strictly quantum mechanical principles can profoundly alter the nature of computation. In this colloquium, a somewhat tardy advertisement for my Fall 2000 course CS483-Phys481 (Tuesday and Thursday, 1:25-2:15, Rockefeller 122), I will attempt to do something as amazing as a quantum computation: explain in one hour to people who know no quantum mechanics how a quantum computer executes the simplest of its miraculous tricks.