Strange Loops & Musical Puzzles - Complex Patterns That Mirror the Soul

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.

Hofstadter's discussion of the infinite, escalating nature of Bach's isomorphic, Strange Loop is both fascinating and accessible.

"The idea of a canon is that one single theme is played against itself. This is done by having "copies" of the theme played by the various participating voices. But there are many ways to do this. The most straightforward of all canons is the round, such as "Three Blind Mice", Row, Row, Row Your Boat", or "Frere Jacques". Here the theme enters the first voice and after a fixed time-delay, a "copy" of it enters, in precisely the same key. After the same fixed time-delay in the second voice, the third voice enters carrying the same theme, and so on. Most themes will not harmonize with themselves in this way. In order for a theme to work as a canon theme, each of its notes must be able to serve in a dual (or triple or quadruple) role: it must firstly be part of a melody, and secondly it must be part of a harmonization of the same melody. When there are three canonical voices, for instance, each note of the theme must act in two distinct harmonic ways, as well as melodically. Thus, each note in a canon has more than one musical meaning; the listener's ear and brain automatically figure out the appropriate meaning, by referring to context.

The cannon can then continue to grow in complexity...

The first escalation in complexity comes when the "copies" of the theme are staggered not only in time, but also in pitch; thus, the first voice might sing the theme starting on C, and the second voice, overlapping with the first voice, might sing the identical theme starting five notes higher, on G. A third voice, starting on D, yet five notes higher, might overlap with the first two, and so on. The next escalation in complexity comes when the speeds of the different voices are not equal; thus, the second voice might sing twice as quickly, or twice as slowly, as the first voice. The former is called diminution, the latter augmentation (since the theme seems to shrink or expand.)

Wait, there's more...

The next stage of complexity in a canon construction is to invert the theme, which means to make a melody which jumps down whenever the original theme jumps up, and by exactly the same number of semitones. This is a rather weird melodic transformation, but when one has heard many themes inverted, it begins to seem quite natural. Bach was especially fond of inversions, and they show up often in his work-and the Musical Offering is no exception.

Not done yet...

Finally the most esoteric of "copies" is the retrograde copy- where the theme is played backwards in time. A canon which uses this trick is affectionately known as a crab canon, because of the peculiarities of crab locomotion. Bach included a crab canon in the Musical Offering.

Hofstadter reasons that since every type of 'copy' in Bach's Musical Offering "preserves all the information in the original theme, in the sense that the theme is fully recoverable from any of the copies," it can be called an isomorphism, or a Strange Loop. He suggests pianists try composing a Canon of their own to the tune of Good King Wenceslas. A fan of Bach's music, I was reading GEB around the Christmas holidays a couple of years ago, and couldn't resist exploring this musical puzzle on the piano. It was great fun! This musical process is much like, as Hofstadter describes it - "An Endlessly Rising Canon."

J. S. Bach had an extraordinary gift for producing the most beautifully intelligent, life-giving music - a mirror of his great musical soul. If nothing else, Hofstadter's analogy of Bach's work to his own concept of Strange Loops that mirror what it is to "be", offers inspiring insight into the human drive and ability to innovate. Especially when the choice is -

To be....or NOT be........Your Majesty's most humble and obedient servant!

Don't Wait to Begin Piano Lessons!

complex models that reflect the soul - Strange Loop & Puzzles Musical

A Strange Loop is a concept by Douglas R. Hofstadter in his book "Godel, Escher, Bach has created. Eternal Braid The" Strange Loop "is a continuous cycle of feedback in a system that can" see themselves "to talk about themselves," self-conscious " . Hofstadter inspiration for writing the ERC, first published in 1979 was allowed, his conviction that his long-standing concept of a strange loop "holds the key to solving the puzzle that we are conscious beings call 'being' or 'conscience'. " Evencalled "isomorphism," Strange Loop Hofstadter sees it as an analogy for how human language actually tracks "by the [complex] biological processes within the brain of carbon-based life forms." In mathematics, a Strange Loop "infinite mathematical system that is perceived to be" useless "symbols using models to follow closely, or mirrors, various phenomena of the world [such as a computer program]." Implicit in the definition of Hofstadter's Strange Loopthe concept of infinity - a way of presenting an endless process in a way over.

In GEB extends Strange Loop Hofstadter analogy to mathematics, art and music, with examples of these phenomena) have found mathematician Kurt Gödel (incompleteness theorem of mathematical logic - a mathematical proof that the connection of self-referential statements about number theory, intellectually stimulating, lithographs and woodcuts by the Dutch graphic artist MC Escher, and canons complexJoints of the musician of the eighteenth century, JS Bach, (especially Musical Offering, which is a high performance of the musical counterpoint of Bach.) Hofstadter There is access to the work of Bach's music that I want to discuss here.

Hofstadter explains that May 7, 1747, first played the Bach Fugue, Musical Offering, on the arm of Frederick the Great, King of Prussia, who played the flute and enjoyed the evening concerts of chamber music. The king wanted to Bach, groped thelarge collection of pianos and summoned him to his palace. He asked the king to his theme (musical ideas) for a family member. The king has done, and hear expressed the hope that idea on its flight with six Obligato (solo) part in bed! To the amazement of the King, Bach was able to run it. When he returned home to Bach in Leipzig, he had three to six parties, including ten of the most modern weapons, which he has ever written, this is engraved with the title "Musical Offering" (MusicalBid) and humble devotion to the king.

Hofstadter's discussion of the infinite escalation, the nature of Bach isomorphic Strange Loop is fascinating and the Internet.

"The idea of a fee to a single theme is played against itself. This is done by listening to the" copies "of the theme by the various participating voices won. But there are many ways to do this. The gun is easier every turn, like "Three Blind Mice", Row, Row, Row Your Boat "or"Frere Jacques". Here, the idea with the voice before and after a fixed time, a "copy" of it is, is exactly the same key. According to the same period of time specified in the second vote, the third entry with the same subject, and so on. Most people are not in harmony with itself in this way. To work on a topic such as cannons, each of its notes may serve in a dual (or triple or quadruple) Role: First, it must be part of a melody, and secondly, it must bePart of harmonizing the same melody. When there are three canonical voices, for example, each note of the issue must act in two separate harmonically and melodically. So each note has a fee on more than one musical importance listener ear and out the brain automatically have the corresponding meaning, with reference to the context.

The gun can then continue to grow in complexity ...

The first escalation of complexity arises if the "copy" of the subjectstaggered not only in time but also in pitch, which is the first voice could sing the theme from C, and the rumor, overlaps with the first voice, could sing the same theme of five notes higher than G. A third item from the D, five tones higher, may overlap with the first two, and so on. The subsequent escalation of the complexity comes when the speeds of the various items are not equal, so that the second voice singing twice as fast, or twice as slow as thefirst voice. The former is called diminution, the latter augmentation (since the theme seems to shrink or expand.)

Wait, there's more...

The next stage of complexity in a canon construction is to invert the theme, which means to make a melody which jumps down whenever the original theme jumps up, and by exactly the same number of semitones. This is a rather weird melodic transformation, but when one has heard many themes inverted, it begins to seem quite natural. Bach was especially as inversions, and often appear in his work and offer musical is no exception.

Not yet ready ...

Finally, the most esoteric of "copies" is the copy protection retrograde, where the theme played backwards in time. A canon that this trick is used affectionately known as a crab canon called the special characteristics of crab locomotion. Including a Bach Musical Offering Canon crab.

Hofstadter reasons, since any kind of 'copy' in Bach's Musical Offering preserved "all information in the original theme, in the sense that the problem is entirely the responsibility of one of the copies, "you can is an isomorphism, or a series of strange looks. suggests that the pianists try to write a Canon right in the height of Good King Wenceslas. A fan of music by Bach, I read GEB near the Christmas holidays a few years, and could not resist exploring this enigma music on the piano. 'was great fun! This musical is very similar, as Hofstadterdescribes it - "a fee increase to infinity."

JS Bach had an extraordinary gift to make the music more intelligent, who gives his life - the mirror of his great soul music. If nothing else, the analogy of the work of Bach Hofstadter offers his concept of Strange Loop, what does "being" is a reflection, in-depth and inspiring in the reader the human capacity for innovation. Especially if the choice -

For .... or not ........ Your Majesty's most humble and obedientServo!

Wait, do not you start with piano lessons!