A Strange Loop is a concept created by Douglas R. Hofstadter in his book, Godel, Escher, Bach: An Eternal Braid. The 'Strange Loop' is a continuous cycle of feedback in a system that allows it to 'perceive itself', to talk about itself, to become 'self-aware'." Hofstadter's Inspiration for writing GEB, first published in 1979, was his long-held conviction that his strange loop notion "holds the key to unraveling the mystery that we conscious beings call 'being' or 'consciousness'." Also called an "isomorphism", Hofstadter sees Strange Loops as an analogy for the way human language tracks reality "through the [complex] organic processes taking place inside the brains of carbon based life forms." In Mathematics, the Strange Loop is an "endless mathematical system that perceives itself through 'meaningless' symbols that use patterns to accurately track, or mirror, various phenomena in the world [such as a computer program]." Implicit in Hofstadter's definition of Strange Loops is the concept of infinity - a way of representing an endless process in a finite way.
In GEB, Hofstadter extends his Strange Loop analogy to mathematics, art and music, giving examples of this phenomena discovered by mathematician Kurt Godel (Incompleteness Theorem in Mathematical Logic - a mathematical proof that connects self-referential statements to number theory); intellectually stimulating lithographs and woodcuts by Dutch Graphic artist M.C. Escher; and complex Canons and Fugues by Eighteenth Century musician, J.S. Bach, (specifically, Musical Offering, representing one of Bach's supreme accomplishments in musical counterpoint.) It is Hofstadter's insight on Bach's musical work that I want to discuss here.
Hofstadter explains that on May 7, 1747, Bach first played his Fugue, Musical Offering, extemporaneously for Frederick the Great, King of Prussia, who played the flute and enjoyed evening concerts of chamber music. The King wanted Bach to try out his large collection of pianos, and summoned him to his palace. He asked the King to give him a subject (musical idea) for a Fugue. The King did, and expressed a wish to hear the Fugue based on his idea with six Obligato (accompaniment) parts! To the King's astonishment, Bach was able to perform it. When Bach returned home to Leipzig, he composed it in three and six parts, including ten of the most sophisticated canons he ever wrote, had it engraved under the title of "Musikalisches Opfer" (Musical Offering) and humbly dedicated it to the King.
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