Crab Canon from Gödel, Escher, Bach
http://www.youtube.com/watch?v=36ykl2tJwZM
The above is a video of the score of Canon 1 a 2 voci: Canon Cancrizans (Crab Canon). Crabs mark the spot on the score and its corresponding opposite. The title of the piece, which is from Bach’s Musical Offering, a leitmotif of Douglas Hofstadter’s magnum opus, “Gödel, Escher, Bach: an Eternal Golden Braid”, means “crab canon”, and is a reference to the incredible game of form and content played by a true master of the two. Johann Sebastian Bach successfully composed a canon in which one voice plays the inverse of the other voice, making the song palindromic and really, really cool.
Douglas Hofstadter, a more contemporary form-content aficionado as well as a Bach fanatic like myself, weaves together elements of the form of Bach’s Crab Canon, an M.C. Escher print which Hofstadter liberally dubs “Crab Canon” (it features a tessellation of crabs, in which the negative space of some crabs provide the positive space of others. It is particularly impressive because the crabs face opposite directions… not so different from the bass clef of a score forming the treble clef at the other end of the song), and his own literary “crab canon” form. You will see what I mean if you read the dialogue below. The characters from the dialogue are borrowed from Lewis Carroll, who wrote a dialogue between a Tortoise and Achilles for the purposes of demonstrating a mathematical idea. He borrowed the same two characters from the Greek philosopher Zeno, whose paradoxes of motion are fascinating and worth an essay unto themselves. He also introduces a third character, the Crab, whose contribution to the form of the dialogue is an all-important midpoint to serve as a fulcrum for the dialogue.
If the image refuses to post, as my audio clip of the Bach canon from my personal library failed, and my embedding of the youtube video failed as well, here is a link to the Escher print.
http://www.iescarrus.com/edumat/imagenes/baul/curiosidades/Bach_02.jpg
Dialogue, typed word for word by myself:
Crab Canon
Achilles and the Tortoise happen upon each other in teh park one day while strolling.
Tortoise: Good day, Mr. A
Achilles: Why, same to you.
Tortoise: So nice to run into you.
Achilles: That echoes my thoughts.
Tortoise: And it’s a perfect day for a walk. I think I’ll be walking home soon.
Achilles: Oh really? I guess there’s nothing better for you than walking.
Tortoise: Incidentally, you’re looking in very fine fettle these days, I must say.
Achilles: Thank you very much.
Tortoise: Not at all. Here, care for one of my cigars?
Achilles: Oh, you are such a philistine. In this area, the Dutch contributions are of markedly inferior taste, don’t you think?
Tortoise: I disagree, in this case. But speaking of taste, I finally saw that Crab Canon by your favorite artist, M. C. Escher, in a gallery the other day, and I fully appreciate the beauty and ingenuity with which he made one single theme mesh with itself going both backwards and forwards. But I am afraid I will always feel Bach is superior to Escher.
Achilles: I don’t know. But one thing for certain is that I don’t worry about arguments of taste. De gustibus non est disputandum.
Tortoise: Tell me, what’s it like to be your age? Is it true that one has no worries at all?
Achilles: To be precise, one has no frets.
Tortoise: Oh well, it’s all the same to me.
Achilles: Fiddle. It makes a big difference, you know.
Tortoise: Say, don’t you play the guitar?
Achilles: That’s my good friend. He often plays, the fool. But I myself wouldn’t touch a guitar with a ten- foot pole!
(Suddenly, the Crab, appearing from otu of nowhere, wanders up excitedly, pointing to a rather prominent black eye)
Crab: Hallo! Hulloo! What’s up? What’s new? You see this bump, this lump? Given to me by a grump. Ho! And on such a fine day. You see, I was just idly loafing about the park when up lumbers this giant fellow from Warsaw– a colossal bear of a man– playing a lute. He was three meters tall, if I’m a day. I mosey on up to the chap, reach skyward and manage to tap him on the knee, saying , “Pardon me, sir, but you are Pole-luting our park with your mazurkas.” But WOW! he had no sense of humor– not a bit, not a wit– and POW!– he lets loose and belts me one, smack in the eye! Were it in my nature, I would crab up a storm, but in the time-honored tradition of my species, I backed off. After all, when we walk forwards, we move backwards. It’s in our genes, you know, turning round and round. That reminds me– I’ve always wondered, “Which came first– the Crab, or the Gene?” That is to say, “Which came last– the Gene, or the Crab?” I’m always turning thigns round and round, you know. It’s in our genes, after all. When we walk backwards, we move forwards. Ah me, oh my! I must lope along on my merry way– so off I go on such a fine day. Sing “ho!” for the life of a Crab! TATA! ¡Olé!
(and he disappears as suddenly as he arrived.)
Tortoise: That’s my good friend. He often plays the fool. But I myself wouldn’t touch a ten-foot Pole with a guitar!
Achilles: Say, don’t you play the guitar?
Tortoise: Fiddle. It makes a big difference, you know.
Achilles: Oh, well, it’s all teh same to me.
Tortoise: To be precise, one has no frets.
Achilles: Tell me, what’s it like to be your age? Is it true that one has no worries at all?
Tortoise: I don’t know. But one thing for certain is that I don’t worry about arguments of taste. Disputandum non est de gustibus.
Achilles: I disagree, in this case. But speaking of taste, I finally heard that Crab Canon by your favorite composer, J.S. Bach, in a concert hte other day, and I fully appreciate the beauty and ingenuity with which he made one single theme mesh with itself going both backwards and forwards. But I’m afraid I will always feel Escher is superior to Bach.
Tortoise: Oh, you are such a philistine. In this area, the Dutch contributions are of markedly inferior taste, don’t you think?
Achilles: Not at all. Here, care for one of my cigars?
Tortoise: Thank you very much.
Achilles: Incidentally, you’re looking in very fine fettle these days, I must say.
Tortoise: Oh, really? I guess tehres’ nothing better for you than walking.
Achilles: And it’s a perfect day for a walk. I think I’ll be walking home soon.
Tortoise: That echoes my thoughts.
Achilles: So nice to run into you.
Tortoise: Why, same to you.
Achilles: Good day, Mr. T.
As you’ve noticed, the author builds a dialogue COMPLETELY out of form. the content, though often hilarious, and highly informative, is mainly built based on its compatibility with the strict form. Good day is used as both greeting and farewell. Even the word “frets” is used both to describe the wedges on the fingerboard of a guitar, and a synonym for worries, all for the purposes of strict adherence to crab-canon form. The amusing game played with the latin aphorism “On taste, there is no argument” (Hebrew speakers may recognize על טעם וריח אין מה להתוכח) switches it, in the context of the Tortoise’s age, into “Arguments are not about taste”, that is, the Tortoise’s taste buds are old. Not touching a guitar with a ten foot pole, becomes not touching a ten foot Pole (that is, a lute-playing fellow from Warsaw who is three meters tall) with a guitar. The crab’s own “Hallo”! is switched phonetically into ¡Olé!
The dialogue, clever in its own right, closely parallels the structure of Bach’s Canon Cancrizans. Just as the statements of one character become those of the other by the end, Bach’s left-hand and right-hand clefs switch at the midpoint (represented by the crab). He may have named this canon based on the somewhat odd concept that crabs “walk backwards”. A modern day analogy, which Hofstadter makes extensive use of, is the interesting fact that crab DNA is palindromic. That is, the strings of nucleotides when reversed can form double helixes with themselves. That is why Hofstadter cleverly worked in the farewell “tata” and capitalized it. The crab was subtly (in spite of his boorish demeanor) hinting to the Adenine-Thymine bonds in DNA. In the book, illustrations of crab DNA, as well as the score of the canon and the M.C. Escher print, accompany the dialogue. The reason he chose these two in particular corresponds to our characters. Mr. A, and Mr. T, Achilles and the Tortoise, happen to have names initialed by the same letters as that very purine (adenine) and that very pyrimidine (Thymine).
Conclusions: Bach rules. Escher rules. Hofstadter rules. Lewis Caroll rules. Molecular biology rules (I’ll consider that a major work of the Divine Composer, who Rules with a capital “R”). I highly recommend Gödel Escher Bach: An Eternal Golden Braid. I suggest as many people as possible buy it (though it’s kind of pricey. A secondhand might be worth considering. Also kind of dense, and long, and I know of no secondhand that saves money AND time. But it’s very worth the time, and honestly, is anyone in college that busy?). As one reviewer put it, it contains “a complete humanistic education”. My personal review: Greatest Book Ever.
Liz Wolff performance
Liz Wolff will preform on the 18th in the Green salon as part of environmental discussion forum.
Check it out.
http://www.global-changefoundation.com/content/green-salon
“To please, educate and enlighten”
Tuesday November 18, 2008
5:00–7:30 PM
Program Begins at 5:30
Klavierhaus, 211 West 58th Street, New York City
Learn more about The Green Salon
Eco-Art: Join us for the second gathering of The Green Salon. Artists, environmentalists and supporters are invited to participate in formal and informal conversation on green issues, energy, the environment and global warming. This early evening gathering enhances that slice of time between work and dinner.
* Elizabeth Wolff, Concert Pianist.
* John Nettleton, Senior Lecturer and Executive Director of Cornell Urban Scholars Program, City & Regional Planning. John share his insights on Advanced Biofuels.
* Peter Fusaro, energy, environment, carbon expert, and author of NY Times best seller What Went Wrong at Enron will host and moderate.
To register for this seminar, visit the event page now.
This Thursday Nov.6th -10:30
We are meeting on 65th and Amsterdam Ave. at the Lincoln Center Media library entrance to watch a screening of Musical theater. Bring your pass. Tanisha Johns will escort us to the media room. We must pass through security, so come a little early.
see you there
Hassam’s New York - Arielle Algarin
I chose to visit the Broad Street location of Hassam’s painting for this assignment because it looked so different from the Wall Street area I am familiar with. My aunt worked in this area for quite a while and I spent a lot of time around Wall Street. The painting portrays the Financial District with such light and natural colors that it seemed almost foreign to me except for the recognizable stock exchange building. When I was able to visit this area for this project, unfortunately it was at a much different time of day then when Hassam created this work. The painting seems to be during the early day, with the sun almost impossibly bright. My photograph is from twilight, at the end of the day and the area surrounding Wall and Broad street has had so much development that hardly any light reaches the street. It is so dark on the street that the street lamps are already turned on, despite the sun clearly still being out. It would be almost impossible to recreate the perspective that Hassam has without being on top of another building at the exact same angle. But the same hustle of people still exists on Broad street, but I feel as if the painting and the photo are depicting two very different energies, Hassam painted what seems like a much more “relaxed” Wall/Broad street. The two pictures represent very different time periods and almost seem to be different places, but the famous buildings and groups of people tie the two depictions together.
Union Square 2- Mya Marshall
I chose to replicate Union Square 2 by Hassam.
I decided that I wanted to choose a painting of Union Square since I have so many memories there, and at one point in my life I regarded it as somewhat my second home. Considering my long history with the park, I figured that it would be easier for me to figure out where exactly the painting was created, whereas it would have been a lot more difficult in a place unfamiliar to me.
I found the picture a little harder to replicate than I had expected. It seems that Hassam was at a higher angle than I was while painting his picture, as his painting depicts a more bird’s eye view of the park. I could only get as high as the top floor in Filene’s Basement across the street. Also, looking at the perspective and vantage point of the painting, I noticed that the painting was at an off-center angle, while my photograph is at a more centered angle. In addition, the park has gone through so many changes and renovations over the years, causing it to look very different from today. The patches of grass are in different areas and broken up at different spots. It is difficult to see the patches of grass in my photograph, because of the density of the trees, and the increased number of them.
At first I thought that Hassam’s painting was done a little later in the year, as the foliage on the trees is sparse, while in my photograph the trees are still full of leaves, but still having the shades of fall. Then I realized that the color of the grass and remaining leaves on the trees seems more like the color of new growth in spring. The time of day appears to be the same, but my photograph appears to have been taken on a rainier day, as the lighting in Hassam’s painting is bright and sunnier, as opposed to my picture, which is a lot grayer.
bethesda fountain-steve chu
For some reason or another, this link :http://www.mcny.org/shop/76/202/7865/bethesda-fountain-central-park.html
was posted among the other pictures with the Hassam assignment. Not knowing any better and figuring it was the closest thing to school, I attempted to take a photo of the Bethesda Fountain in Central Park in the same position that this original photo was taken. The original photograph was taken by H.L. Wittemann during the 1930s. I attempted to be in the exact position that he must’ve taken the photo but was unable to for several reasons. The first being my use of my laptop as a camera and the difficulty in trying to take a picture simply by holding my computer in my hands so i set it down on a part of the terrace facing the fountain. I also found the ideal point obstructed by a high reaching peace of the terrace. I would’ve liked to back up for a better angle but would’ve found myself in the middle of the road,or even further which would’ve placed me on a hill, so i settled for the terrace. The view of the two buildings in the upper left corner is quite clear in the original but due to the high reachign trees of the present as well as the poor lighting condition i found that day, they simply appear as white streaks in my replication. There was also my inability to see the view through the lenses without being in the grass, where i was not supposed to be. I did my best in attempting to replicate this picture, and at the very least my version has color and beautiful fall leaves.
Shawn Jean-Louis—- Review of South Pacific: EXTRA CREDIT
South Pacific is an energetic musical by Rogers and Hammerstein that is set during World War II with two romantic love stories at its heart. The original Broadway Production ran from April 7, 1949 to January 16, 1954 with 1,925 performances being put on. There were even two movie versions of the play made, one was the 1958 cinematic version and the other was a heavily criticized made for television film which came out in 2001. The romance of nurse Nellie Forbush and rich Frenchman Emile Debecque as well as that of Lt. Joe Cable and native girl Liat are simply captivating. The way they intertwine cohesively with the war setting, yet neither the war nor the romance detract from the other’s significance is marvelous. Lively musical scores such as “Honey Bun”, “There is Nothing Like a Dame”, and “I’m gonna wash that man rite outta my hair” as well as the graceful “Some Enchanted Evening” and “I’m in Love with a Wonderful Guy” help to make the show quite the spectacle. The Lincoln Center revival I saw was quite fascinating and brought the script to life in a way that I thought was riveting and entertaining.
The audience in the proscenium watching South Pacific that evening was great. They laughed when they were supposed to, were touched when they were supposed 2 be, and cheered loudly after every musical score. They really gave the actors a mood to work with that undoubtedly made their job on stage easier to an extent. It takes a load off of an actor’s shoulders when the audience is responding positively to what is going on onstage. My attendance at Lincoln Center on October 6 was only the second time I had experienced a live production as an audience member and I am very happy with the way it turned out. I was totally in sync with everybody in attendance, it was clear they were enjoying the show and so was I. As I sat there and watched the show, although everybody there was a stranger to me, I got a sense of family for the three hours the show was going on. That sense of togetherness regarding what was going on onstage was just that strong
I was amazed by both the acting and directing of the show I went to see. The casting for the show was obviously very good, the casting directors made some great choices. The actors onstage were absolutely phenomenal, one of the reasons I was so enthralled by the show was because they made their characters so real and believable. The traditional American way of acting was executed to its fullest potential that night. I think the highlights of the evening were the singing of “Some enchanted Evening” by Paulo Szot (Emile DeBecque) and the hilarity of Danny Burstein (Luther Billis). I even recognized one of the actors from television, which was a nice surprise; I wasn’t expecting that to occur. All of the performers were very energetic, which kept the audience alive and interested. However, the great acting in the show was definitely partially due to the high quality directing. A good director is crucial to an actor’s work, they help the actors develop their character and makes sure they get the best work out the performers. The show was definitely interesting because of the cohesive nature with which it was put together and that can only come from good direction.
Having read the script and actually performed the play myself, I thought I had I general idea of what I was going to see on the night of the show. However, despite that fact, I was still blown away by the performance. The text was executed masterfully onstage and far surpassed any expectations I had. As for the set design, it was definitely in sync with show all night. The environment the actors were in matched and worked with what they were doing and mood of every scene. This is a key factor because even if the acting is superb if the set design is poor it can take the audiences attention away from the performers and detract immensely from the quality of the show. However, there was no such problem in South Pacific.
As you can see I have nothing but praise for the revival of South Pacific at Lincoln Center, it is a great show. The only thing I would have changed would probably be to make the chorus a little bigger just to get more of a military feeling, I also feel a bigger chorus would have added to the scene when the soldiers are sitting around a stage themselves watching a performance (when “Honey Bun” is sang). Other than that I definitely give the show two thumbs up, it’s a peck of fun!!!!!!!!!
Funerary Art: Public Displays of Private Sentiment
Funerary art takes the loss of a dear loved one and shows it with a
piece of art which can be viewed by the entire community.
Most of us have been through the awful experience of losing someone
dear. It is a part of life that all of us will have to deal with at
some point. One way in which we deal with our grief is through
mourning with others at a funeral, and it is usually at this point
that we erect some type of monument to the departed. If the family is
rich this monument could be an elaborate obelisk, statue or mausoleum
complete with stained glass windows. If the family is not it is often
more simple, but no less powerful. Often the monument depicts some
aspect of that persons life that the family or community thinks is
most worthy of remembrance.
This picture is of an approximately life size statue of a father and daughter sitting
in a chair, with the simple haunting inscription “Motherless”. This
bronze statue sits in front of a crypt for the Mellon family, so we
know that they were very wealthy. Yet seeing this does not conjure
the common feeling of difference that display of class often does.
One simply sees the misfortune of a father and husband and his
daughter. It is a representation of an intensely private moment, put
out in a sunny field for all the world (or at least those who climb
the hill in this cemetery) to see.
Sometimes this type of art makes its way out of the graveyard to the
streets, becoming even more intensely public. The ghost bikes you can
find all over the city are a sobering reminder of mortality.
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Cultural Map
"The Original Topography of Manhattan Island from the Battery to 155th Street" From Report on the Social Statistics of Cities, Compiled by George E. Waring, Jr., United States. Census Office, Part I, 1886. (Perry-Castañeda Library Map Collection, University of Texas-Austin)
