A strange loop arises when, by moving up or down through a hierarchical system, one finds oneself back where one started.
An example: the endless apprenticeship of University life, i.e. how when, after years of drudgery as an ignorant slave to an all-knowing master or masters, you take a step (by dint of many tiny steps) up the ladder, only to find yourself ignorant slave to another all-knowing master or masters. Commonly known as the academic smackdown.
There are more productive strange loops like the Shepard tone, named after Roger Shepard is a sound consisting of a superposition of sine waves separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower (see example).
See also M. C. Escher's Ascending and Descending.