As an example of Self-Reference and Strange Loops, in 1988, children’s performer Shari Lewis released a video of her show Lamb Chop’s Sing-Along, Play-Along, which included the musical track “The Song that Doesn’t End.” The song contained a single verse that could be looped infinitely with the last line of the lyrics leading directly back to the first line. Lewis’s song illustrates Hofstadter’s core theme in Gödel, Escher, Bach: An Eternal Golden Braid. “The Song that Doesn’t End” utilizes self-reference, a concept describing something referring to itself or pointing back to itself, like a snake eating its tail. Shari Lewis’s song uses self-reference in the opening line by referring to itself: “This is the song that never ends.” A strange loop is formed with the last line of the song engaging in self-reference to the first: “You’ll continue singing it forever just because...”

Strange loops are more than just recursive or self-referential: They take a unique shape and move along hierarchies, always returning to the beginning. Many of Escher’s drawings and lithographs visually exemplify the notions of self-reference and strange loops. Sky Castle by M.C. Escher shows a mountainous castle hovering above an ocean where it is reflected.