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 item. The first is reduced, increasing the latter (since the theme seems to reduce or expand).
Wait, there's more ...
The next level of complexity in a canon of construction is to reverse the subject of half-tones, many of which funds the sum back when the original topic on jumps, and exactly the same thing. This is a transformation rather strange melodic, but has reversed many of the issues, they begin to behave naturally. Bach wasespecially fond of reversals, 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" of Bach's Musical Offering"Keep all information in the original theme, in the sense that the subject of a full cost of the copies is, can only be an isomorphism, or an odd cycle. Suggests that the pianists try to write just a Canon in the amount of Good King Wenceslas . A fan of the music of Bach, I was reading GEB near the Christmas holidays a few years ago and could not resist exploring this enigma music on the piano. It '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!
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