Stumble It!
Wonderful! Bach was, after all, the greatest jazz musician ever to have lived...T
The most impressive of Johann Sebastian Bach’s pieces, musicophiles may have told you, will knock you over with their ingeniousness, or at least their sheer complexity. Indeed, the music of Bach has, over the past two and a half centuries, provided meat and drink to both professional and amateur students of the relationship between ingeniousness and complexity. It’s no mistake, for instance, that the composer has offered such a rich source of intellectual inspiration to Gödel, Escher, Bach author Douglas R. Hofstadter, well beyond having given him a word to fill out the book’s title. Listen to the first canon from Bach’s Musical Offering, and you’ll hear what sounds like a simple beginning develop into what sounds like quite a complex middle. You may hear it and instinctively understand what’s going on; you may hear it and have no idea what’s going on beyond your suspicion that something is happening.
If you process things more visually than you do aurally, pay attention to the video above, a visualization of the piece by mathematical image-maker Jos Leys. You can follow the score, note for note, and then watch as the piece reverses itself, running back across the staff in the other direction. So far, so easy, but another layer appears: Bach wrote the piece to then be played simultaneously backwards as well as forwards. But prepare yourself for the mind-blowing coup de grâce when Leys shows us at a stroke just what the impossible shape of the Möbius strip has to do with the form of this “crab canon,” meaning a canon made of two complementary, reversed musical lines. Hofstadter had a great deal of fun with that term in Gödel, Escher, Bach, but then, he has one of those brains — you’ll notice many Bach enthusiasts do — that explodes with connections, transpositions, and permutations, even in its unaltered state. Alternatively, if you consider yourself a consciousness-bending psychonaut, feel free get into your preferred frame of mind, watch Bach’s crab canon visualized, and call me in the morning.
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Related content:
A Big Bach Download: All of Bach’s Organ Works for Free
The Open Goldberg Variations: J.S. Bach’s Masterpiece Free to Download
Glenn Gould Explains the Genius of Johann Sebastian Bach (1962)
Wednesday, July 09, 2014
The Genius of J.S. Bach's "Crab Canon" Visualized on a Möbius Strip | Open Culture
Friday, July 04, 2014
Free to Choose
The greatest economic mind of the 20th century, Milton Friedman. Here is his entire TV series on PBS, "Free to Choose", taken from his book of the same name, that became the intellectual foundations of the Reagan ( and Jack Kemp) Tax cut bill that saved our nation in the early 80's. Without Mr. Friedman, it is questionable that there would even have BEEN a Reagan presidency. God bless him! Watch them all via the link below...T
http://miltonfriedman.blogspot.com/
Here's one sample. Please watch them all!...T
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