Tool: Lateralus. Form and Content in Progressive Metal
http://www.youtube.com/watch?v=wS7CZIJVxFY
I was first excited to find the video above, then dismayed to find that it said much of what I wanted to say. But by no means all of it, and there is some to correct. But I’m getting ahead of myself.
So there I was, listening to Lateralus for about the thirtieth time, remarking to myself once more how funky Maynard James Keenan’s (the name’s a sobriquet, I imagine it’s a play from his actual name James Herbert Keenan to John Maynard Keynes, the greatest economist of the last century) rhythms were in this song. And so I tapped my fingers across my laptop case, in the familiar sequence.
Black
Then
White are
All I see
In my infancy
Red and yellow then came to be….
WHAAAAAT?????? IS THAT FIBONACCI???? Obviously my first instinct was to panic. How the hell did I miss the Fibonacci sequence? I’m a confirmed pseudomath nerd. I read books about math written for the mathematically mediocre all the time! This’d be like being hit with Fermat’s Last Theorem and not recognizing it. I had to check Wikipedia to confirm my findings (not that I was in any doubt. I just wanted to say what else Tool fans, among the more lyrically and musically sophisticated losers on the interwebs, had contributed to the collective understanding of this song). Here’s what I found:
“ounting between pauses, the syllables in Maynard James Keenan’s vocals during the verses form the first few Fibonacci numbers, ascending and descending:”
“The Fibonacci sequence shares a relationship with spirals, which are mentioned several times later in the lyrics.” (that was actually added this week… it was NOT there when I checked, and I wanted to add it!)
“Additionally, Keenan begins singing at 1:37 into the song. 1 minute 37 seconds, or 97 seconds, is approximately 1.618 of a full minute. This happens to be the golden ratio, which is closely related to the Fibonacci sequence.” (specifically, and I may add this to the wiki-page or at least put in a link to the Golden Ratio/Phi page, the ratio of a step in the sequence to its preceding term approaches Phi [1.618...] as you approach infinity)
“The time signatures of the chorus change from 9/8 to 8/8 to 7/8; as drummer Danny Carey says, “It was originally titled 9-8-7. For the time signatures. Then it turned out that 987 was the 17th step of the Fibonacci sequence. So that was cool.” (I had long since noticed the changes in time signature, but had not been aware of its history or Fibonacci significance.)
“In a 2001 interview, Keenan commented on the lyric mentioning black, white, red and yellow: “I use the archetype stories of North American aboriginals and the themes or colours which appear over and over again in the oral stories handed down through generations. Black, white, red, and yellow play very heavily in aboriginal stories of creation.” (This is a common theme for Tool)
If you guys aren’t impressed yet, then obviously you didn’t watch the video. The fan was obviously a bit on the gushy side, but his interpretation isn’t far off. Tool’s message, “Spiral out. Keep going, going…”, is repeated at the end (I wish I could make something of their decision to make the song exactly 9:24. they rarely do anything without a reason. I just did some quick calculations and could find no relationship to Phi, Pi, e, or any other sexy math). But that’s a very primitive formulation of their message. They say it several ways. The full lyrics are here:
Black then white are all I see in my infancy.
red and yellow then came to be, reaching out to me.
lets me see.
As below, so above and beyond, I imagine
drawn beyond the lines of reason.
Push the envelope. Watch it bend.
Over thinking, over analyzing separates the body from the mind.
Withering my intuition, missing opportunities and I must
Feed my will to feel my moment drawing way outside the lines.
Black then white are all I see in my infancy.
red and yellow then came to be, reaching out to me.
lets me see there is so much more
and beckons me to look through to these infinite possibilities.
As below, so above and beyond, I imagine
drawn outside the lines of reason.
Push the envelope. Watch it bend.
Over thinking, over analyzing separates the body from the mind.
Withering my intuition leaving all these opportunities behind.
Feed my will to feel this moment urging me to cross the line.
Reaching out to embrace the random.
Reaching out to embrace whatever may come.
I embrace my desire to
feel the rhythm, to feel connected
enough to step aside and weep like a widow
to feel inspired, to fathom the power,
to witness the beauty, to bathe in the fountain,
to swing on the spiral
of our divinity and still be a human.
With my feet upon the ground I lose myself
between the sounds and open wide to suck it in,
I feel it move across my skin.
I’m reaching up and reaching out,
I’m reaching for the random or what ever will bewilder me.
And following our will and wind we may just go where no one’s been.
We’ll ride the spiral to the end and may just go where no one’s been.
Spiral out. Keep going, going…
Observe the many references to the form of the song, within its content. “Swing on a spiral”. The song swings on a spiral, because the form of its verse is 1-1-2-3-5-8-13 (fulcrum)-8-5-3-2-1-1 . “urging me to cross this line”, one of several geometric metaphors pertinent to spirals (and Phi, and Fibonacci…). “Reaching out”, which he mentions multiple times, is exactly the act of a spiral, constantly expanding, reaching for new horizons. “Drawn outside the lines of reason”, a statement about their goal: to push their fans (and themselves) to cease thinking linearly and begin thinking laterally (Lateralus… is it coming together yet?). “Push the envelope… watch it bend”, a nice rhetorical flourish, indicating a desire not only to expand the borders of what’s allowed, but to break those rules as well.
An oblique reference to Phi outside the context of spirals comes at the end: “Witness the beauty” may as well have been written with a capital B, because he refers to the Capitalized Essence known as Beauty. Greek mathematicians, whose mystical approach towards numbers has been legendary since Pythagoras, considered Phi the Golden Ratio because of its application in rectangles. An “aesthetically pleasing” rectangle has a ratio of Phi between its long and short side. The amazing thing is that when a square whose side equals the short side is removed from such a rectangle, the result is a similar rectangle, that is, one whose dimensions maintain that golden ratio! “Beauty” and Phi have a historical connection. Similarly, a statement about what “connects us all” may well be a subtle hint to all the literature (much of it, but by no means all, apocryphal) about the Golden Ratio in nature. A classmate pointed out to me this week that the spiral of a nautilus’ shell follows this proportion (I have yet to decide whether or not this information is admissible, as it may have come from “The Da Vinci Code”). The proportion can be found all over our bodies as well (for debunking of extraordinary claims to this effect, though, see http://www.straightdope.com/columns/read/2513/is-phi-a-mystical-number-as-claimed-in-em-the-da-vinci-code-em ).
Does the song (and interpretation of the video artist, who did a decent but not great job) not speak for itself in a form-content discussion? The first instance I know of music built upon the Golden Ratio (though it would not at all surprise me to learn that it was used far earlier… heck, this is right up Bach’s alley), the song actually takes the very idea of spirals to make its point. Break the rules. Grow outward. Do not be bound by linear thinking, think Laterally. Feel the Beauty, the Divine pattern that connects us all (a particularly religious math teacher of mine considers Phi God’s magic number. He also, when asked who discovered Euler’s equation [e^iπ+1=0], replied with a straight face “God”, and proceeded to clarify that it was Leonhard Euler who “wrote it down”).
The content is similar. Black then white, the most primitive of colors, give way to red and yellow, the first primary colors (garnered from Native American creation myths, which in itself is a concept relevant to growth), finally giving way to the power of imagination. Imagination, as Einstein and Maynard James Keenan inform us, is far superior to any overthinking, overanalyzing.
I’d be remiss in my responsibility as a Tool fan not to point out, again, the funky rhythm. The drums are lively and pretty cool, though not as technically impressive as in many of their other songs. Rhythm has always been the musical arena in which Tool has pushed, and bent, the envelope.
Conclusions: Math is cool. Tool are freakin’ smart. A self-respecting metalhead has the attention span to listen to 9 minute songs (though we cannot tolerate top 40 for a duration exceeding 1.618 seconds. It is hardwired into us… God’s magic number, you know). Odd-time signatures are pretty fun to nod your head to. And 2:45 A.M. is the only time to write a progmetal review.
Michael Elka - Reviews
About three weeks ago I saw “La Traviata” by Verdi at the Metropolitan Opera. I had seen the opera once before, in Italy, and it was fantastic. This rendition was just as good, and the set design was fabulous. Act One had a particularly great set design, leaving very little of the Parisian salon up to the imagination. Everything was really spectacular, except for something I usually gripe about: the libretto. I grew up speaking Italian with my grandparents, and I know for certain that a great deal of what is said, or sung, rather, in the opera is very colloquial. This colloquial use of the language was not reflected in the translation provided on the monitors; the translation was highly formalized. Opera was originally meant for the elite, but by the time Baroque opera came around, such things as the “opera season” had been introduced in Venice, providing entertainment for everyday people. Personally, I think this was a good thing; it allowed the medium to grow and gain popularity. The excessively formal translations of today, however, take away from that original sentiment of familiarity and universality. Overly poetic translations seem to put opera high up on a pedestal, accessible only to the highly refined. While it is a good thing that performers and composers of opera are revered for the talent, skill, and musicianship involved in producing such work, opera in and of itself should not be held so loftily. A newcomer to opera might read the excessively formal translations of today and be scared away from the genre, and that is sad. While musically and theatrically opera should be held in high esteem, it should still be intimate and familiar, allowing the viewer to actually be comfortable being involved in such a production.
This past Saturday, I saw a production called “Le Sept Plages de la Ruse” (The Seven Boards of Skill) at the Brooklyn Academy of Music. This production consisted of roughly twenty dancers and a large, flat, three-dimensional black wooden box. The box itself was comprised of seven smaller shapes, like triangles and trapezoids. At times, to give an idea of setting, a string instrument was played using pentatonic scales, which give off an Asian vibe and let the viewer know that the work is evocative of China. The dancers used dance, martial arts, and acrobatics throughout the production to move and manipulate the seven pieces of the wooden box, transforming it from its flat state, to one evocative of mountains, plains, cities, etc. At times the dancers would solely be involved in placement of these shapes, while at other times, the shapes would stay stationary and the dancers would “settle” the scene, performing acrobatics. The entire production was evocative of the different landscapes of China and the different cultures that develop because of different geography. For example, when the shapes were flat on the ground, it was clear that the setting was farmland; when sticking in the air, it was clear that the shapes were evoking a mountain range or a city. Each movement of the piece consisted of the dancers “inhabiting” their area, which, again, was symbolized through acrobatics and dance. Each change in scenery, in which the large shapes were moved around, signaled a change in the direction of the production, or a new movement. Overall the production was fantastic, sending a clear message that the people of China, or of any people, both influence and are influenced by their surroundings, in the past, present, and future. I highly recommend it!
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.
Heather’s Review of Jeff Koons on the Roof- Extra Credit Assignment
It was silly and ridiculous, but quite delightful. The exhibition was made up of three sculptures: a larger-than-life balloon dog, a heart wrapped up for the taking and an illegible mass of color depicting a cartoon character. Set against the backdrop of the New York skyline, these items take on an even more surreal quality than would be experienced inside of the museum, where whimsy and color are expected.
From a purely aesthetic point of view, the details of the wrinkled paper on the heart were impressive and appreciated, through the “Coloring Book” sculpture, nothing but a mass of color, seemed odd and out of place next to the other two definitive symbols.
On a deeper level, and connecting it to the concept of Symbolism, I’m not sure I got the deeper meaning behind the sculptures. The “Sacred Heart (Red/Gold)” was obviously about the commercialization of emotions and “love” in our society. And once I was informed of the identity of “Coloring Book” I was able to ascertain an odd message of hero worship and celebrity, even of a character of infantile fiction. Obviously, I’m still an amateur art critic, so I missed the hypersexual message behind the balloon dog I was supposed to catch. The exhibit really did point out how touch-and-go symbolism can be sometimes. People often discredit artistic symbolism because of the argument “How do we know that’s actually what the artist intended?” I take the opposite view. For example, I may have been able to understand a meaning for the balloon dog all my own if it weren’t for the fact that I was “supposed” to see a sexual concept. Symbols are about the story being told and I believe that story is a collaborative effort by both the artist and the viewer. Simply because my interpretation was not the original meaning doesn’t mean it isn’t still a valid way of viewing the piece- it’s simply how it relates to my unique point of view and experiences.
As for advanced critics, they all seemed to dislike the exhibition. They felt it was dwarfed by the outer elements and was generally kitschy, clichéd and silly.
I would recommend you see for yourself- at the very least it’s interesting to look at.
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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)
