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A Strange Loop is a concept created by Douglas R. Hofstadter in his book, Godel, Escher, Bach: an eternal braid. The “weird loop” is a continuous cycle of feedback in a system that allows it to “perceive itself”, speak for itself, become “self-aware”. Hofstadter’s Inspiration for writing GEB, first published in 1979, was his long-held belief that his bizarre notion of a loop “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 of how human language follows reality “through the [complex] organic processes taking place inside the brain of carbon-based life forms. “In mathematics, the weird loop is an ‘endless mathematical system that perceives itself through’ meaningless’ symbols that use patterns to accurately track, or reflect, various phenomena around the world [such as a computer program]“The concept of infinity is implicit in Hofstadter’s definition of Strange Loops – 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 phenomenon discovered by the mathematician Kurt Godel (Theorem of incompleteness in mathematical logic – a mathematical proof that connects the self-referential statements to number theory); intellectually stimulating lithographs and woodcuts by Dutch graphic designer MC Escher; and the intricate canons and fugues of eighteenth-century musician JS Bach, (in particular, Musical offering, representing one of Bach’s supreme accomplishments in musical counterpoint.) It is Hofstadter’s insight into Bach’s musical work that I want to discuss here.
Hofstadter explains that on May 7, 1747, Bach played his fugue for the first time, Musical offering, extemporaneously for Frederick the Great, King of Prussia, who played the flute and enjoyed evening chamber music concerts. 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 made, and expressed the wish to hear the Fugue based on his idea with six Obligato parts (accompaniment)! To the king’s surprise, 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 had ever written, had it engraved under the title of “Musikalisches Opfer” (Musical Offering) and humbly dedicated it. to the king.
Hofstadter’s discussion of the endless and growing nature of Bach’s isomorph Strange Loop is both fascinating and accessible.
“The idea of a canon is that only one theme is played against itself. This is done by having ‘copies’ of the theme played by the different participating voices. But there are many ways to do this. simpler of all guns is the trick, like “Three Blind Mice”, Row, Row, Row Your Boat “, or” Frere Jacques “. Here the theme enters the first voice and after a fixed delay a “copy” of it enters, precisely in the same key. After the same fixed delay in the second voice, the third voice enters carrying the same theme, and so on. Most themes will not harmonize with themselves this way. For a theme to function as a canon theme, each of its notes must be able to play a double (or triple or quadruple) role: it must first be part of a melody, and secondly it must be part of a melody. ‘harmonization. of the same melody. When there are three canonical voices, for example, each note in the theme should act in two distinct harmonic ways, as well as melodically. Thus, each note of a canon has more than one musical meaning; the listener’s ear and brain automatically find the appropriate meaning, referring to the context.
The gun can then continue to gain in complexity …
The first escalation of complexity occurs when the “copies” of the theme are shifted not only in time, but also in height; thus, the first voice could sing the theme starting with C, and the second voice, overlapping the first voice, could sing the identical theme starting five notes higher, on G. A third voice, starting with D, but five notes higher , can overlap the first two, and so on. The next escalation in complexity occurs when the speeds of different voices are not equal; thus, the second voice could sing twice as fast, or twice as slowly, as the first voice. The first is called decrease, the second increase (since the chart seems to be narrowing or expanding.)
Wait, there’s more …
The next step of complexity in a canon construction is to invert the theme, which means making a melody that jumps down every time the original theme jumps, and by exactly the same number of semitones. It’s a pretty weird melodic transformation, but when you’ve heard a lot of reverse themes, it starts to sound pretty natural. Bach was particularly fond of inversions, and they appear often in his work – and the Musical Offering is no exception.
Not finished yet…
Finally, the most esoteric of “copies” is the retrograde copy – where the theme is played backwards in time. A cannon that uses this trick is affectionately called a crab cannon, due to the peculiarities of crab locomotion. Bach included a crab cannon in the Musical Offering.
Hofstadter explains that since each type of Bach’s “ copy ” Musical offering “preserves all the information of the original theme, in the sense that the theme is fully retrievable from any of the copies”, this can be called an isomorphism, or a weird loop. He suggests that pianists try to compose their own Canon to the tune of the good King Wenceslas. A fan of Bach’s music, I was reading GEB over the Christmas holidays a few years ago and couldn’t resist exploring this musical puzzle on the piano. It was very fun! This musical process is very similar, as Hofstadter describes it, to “A Cannon on the Endless Rise”.
JS Bach had an extraordinary gift for producing the most beautifully intelligent and invigorating music – a mirror of his great musical soul. If nothing else, Hofstadter’s analogy between Bach’s work and his own concept of Strange Loops which reflect what it means to be “to be,” offers an inspiring glimpse into the human drive and its ability to innovate. Especially when the choice is –
Be … or DO NOT be……..Most humble and obedient servant of Your Majesty!
Don’t wait to start piano lessons!
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Source by Cynthia VanLandingham
