Gödel, Escher, Bach: An Eternal Golden Braid

Hofstadter’s introduction highlights each of the three featured figures in the work’s title: Johann Sebastian Bach, Maurits Cornelis Escher, and Kurt Gödel. Hofstadter begins by analyzing Bach’s Musical Offering to Frederick the Great, King of Prussia. Bach inscribed the fugues—short melodies or musical phrases that are repeated and interwoven into the rest of the piece—with the word “ricercar,” meaning “to seek.” Fugues and canons use a self-referential structure, which Hofstadter presents as the foundation of his understanding of consciousness:

“The ‘Strange Loop’ phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started” (10).

M.C. Escher captured strange loops in his art by blending drawing and math. Hofstadter provides a few examples of Escher’s works, including Waterfall and Ascending and Descending, each revealing a strange loop. By following the path of the structures in Escher’s paintings, such as the staircase of a castle in Ascending and Descending, the trail forms an infinite spiral that always returns to beginning. Hofstadter explains that infinity is a key component of strange loops.

The conflict between the infinite nature of a strange loop and the finite nature of human understanding creates a