Gödel, Escher, Bach by Douglas R. Hofstadter

Bach uses a similar idea in a variation in The Musical Offering. The sound is looped but the frequencies are cleverly chosen to given an illusion of the pitch continually climbing. An illusion called a Shepard tone consists of notes that seem to get higher and higher in pitch yet never seem to go beyond audible frequencies. There are interesting examples of strange loops in sound. One strand of our triptych at the Barbican explores visual feedback in an interactive installation created by the artist Ben Kreukniet. Thus Escher is there to help the reader see the concept of a strange loop. Hofstadter realised he had had Escher’s images in his mind as he wrote about loops that climb yet return to the beginning. But when his father read the first draft he complained that there were no pictures. Hofstadter admitted, when I interviewed him for the Barbican project, that the book was going to have an academic title about the human brain that did not refer to Escher or Bach. And yet the image confuses us because we can’t work out which is the primary layer.

An image of a hand drawing a hand seems to imply the first hand is in a world above the drawn hand. Or the image of two hands each drawing the other. Think about the famous Escher image of the monks climbing a quadrangle of squares that seem to keep climbing and yet, at full circle the monks step on to the stair they started from. Circular proposition … the Dutch artist Maurits Cornelis Escher.

Gödel, Escher, Bach by Douglas R. Hofstadter