Posts Tagged ‘fractals’

What is art? Why do I enjoy Bartok’s Concerto for Orchestra, yet my 12-year old son thinks it is wretched? Why are the first three Song of Ice and Fire books great, but the last two are mediocre at best?

I’m sure that there’s a long history of the philosophy of art, and I’d love to quote it here to give you some insight. Unfortunately, this is a subject that I know nothing about. Nothing. Literally. I haven’t even googled “philosophy of art” to see what comes up.

That’s because I already have my own theory. I share it now because I have enough hubris to think that it may speak to you, too.

In a nutshell: with art we want to see patterns, but also be surprised and have our expectations subverted.

Now, art has more purpose then what I’ve just described. Art can educate, or enlighten, or convey some specific emotion (Pain? Love?) But I’m concerned with what I see as the primary function of art: to entertain. I don’t listen to Mozart to learn anything; I don’t read Brandon Sanderson to gain insight into my own soul. And I certainly won’t pay $15 to go to an art museum for any purpose other than to entertain myself for an afternoon.

But what about non-fiction books, you say? Didn’t you read a three-volume biography of Winston Churchill last year?

Yes, I did. I read that biography as a form of entertainment. I find learning entertaining. I found the story fascinating. I wasn’t trying to educate myself, except tangentially; I have no pressing reason to know anything about the former prime minister.

But as for art, as entertainment: I think humans are biologically predisposed to enjoy patterns, but I also think we enjoy being surprised. It is in the confluence of these two (sometimes competing) factors that art resides.


There is a kind of sweet-spot here: if patterns are too obvious they’re boring; if patterns are too complicated (or even non-existent) then that’s boring too. For every person there is an ideal pattern complexity for a given artistic medium, and it’s fascinating that these ideals seldom overlap.

Take patterns in novels. Novels exist on a spectrum of complexity:

Dr. Seuss Nancy Drew A Wrinkle in Time The Da Vinci Code Harry Potter The Foundation Series Dune The Brothers Karamazov Gravity’s Rainbow Ulysses


You may disagree with the exact ordering but that’s not the point (it’s subjective anyway). To me, the ideal novel is somewhere around level 7 (Dune). I will almost always read something in the 6-8 range. I didn’t enjoy the Harry Potter series because it was too simple; likewise I found James Joyce’s Ulysses incomprehensible.

But other people disagree. An awful lot of people find the complexity level of the Da Vinci Code to be just right. And that’s great: I don’t mean to imply that my preference for more complexity is somehow better. And if you can “read” Ulysses for more than five minutes without laughing, then more power to you.


I don’t see it.

We are hard-wired by evolution to see patterns in everything, even if the patterns are spurious. We see faces on Mars. We see Jesus in cheese toast. People see meaning (even if it’s unintended) in Finnegan’s Wake. The thing is, our abilities are not the same. Where I see pattern, you see noise; where I see banality, you see complexity. That’s why our tastes differ. And our ability to see patterns depends on two things: raw processing ability, and content knowledge.

There’s a great scene in the movie Defending Your Life where an “unenlightened” soul tries food that a more “enlightened” person is eating. (The “enlightened” people use a lot more of their brain, you see.)

Albert Brooks: What are you eating?

Rip Torn: You wouldn’t like this.

Brooks: What is it? What does it taste like?

Torn: You’re curious, aren’t you? Good, I like that about you. Want to try?

Brooks: Yeah. Looks so weird. Oh, my God!

Torn: A little like horseshit, huh? As you get smarter, you begin to manipulate your senses. This tastes much different to me than it does to you.

Brooks: This is what smart people eat?

Now, I don’t think it’s controversial to declare that pattern-recognition ability differs from one entity to another. For example, I doubt that a ladybug can detect the difference between white noise and Metallica (sometimes I can’t, either). In my experience dogs don’t seem to respond much to music (others do think they might have a musical sense). I will go out on a limb and say that I can enjoy Dune whereas an eleven-year-old will not, because I have more ability to hold the patterns of such a book in my mind.

But wait. I don’t want this to be an elitist manifesto; I’m not better than the Joneses. So I will add that content knowledge and context are more important than raw processor speed. Dune is an adult book, with topics and themes that resonate with people who have more experience in the world. I was a smart eleven-year-old, and I read Dune back in 1980, but I didn’t get much out of it because a lot of it didn’t make much sense to me. It wasn’t a matter of complexity, but of experience.

Consider music. If you study music theory, you’ll be able to hear patterns and structures that others cannot; you may enjoy certain music when others do not. It has less to do with processing ability and more to do with content knowledge.

For example, I find much of modern music boring. Why? Because the chord progressions are banal (I-IV-V-I) and the rhythms unvarying (drum machine, anyone?) But obviously, a lot of people like such music, and in part it’s because of the simplicity. The chord progression I-IV-V-I is common enough that even the untrained ear can pick it out; it is a pattern that people recognize.

This also explains why certain music “grows on you”. The first time I listened to Bela Bartok’s Concerto for Orchestra, in a laundry mat in Torrejón, Spain, I found the music off-putting and bizarre. But I listened to it again and again, probably because I was stubborn enough to think that eventually I would understand it. And I did. I find it today the single greatest piece of music ever written, in part because it is so familiar to me now that I hear its patterns and complexities almost instinctually. I daresay I have the whole thing memorized, and when I listen to it, it is almost as if I am recalling it in real time. The experience is sublime.

To you, it may taste like horseshit.

At the premiere of Beethoven’s String Quartet No. 13 (Op. 130), the audience did not demand an encore of the final movement (the so-called Große Fuge). “Beethoven, enraged, was reported to have growled, ‘And why didn’t they encore the Fugue? That alone should have been repeated! Cattle! Asses!’”  The fugue itself was dismissed at the time as being repellent and incomprehensible. Did Beethoven have the ability to imagine complexities that were too complex for the average listener?

[Note: listen to this five times over five days. I guarantee that your experience the fifth time will be vastly different then the first.]

I have focused unduly on music, but the same ideas apply to other arts as well. For example, the appeal of paintings by Jackson Pollock may have something to do with fractal dimension (a measure of complexity).  Pollock knew nothing about fractals, but he instinctively splattered paint in a way that is “pleasing” in some mathematical sense. His paintings had quantifiable complexity, and that complexity fell in the range that humans find appealing. His paintings only appear random at first glance.


Untitled, ca. 1948–49 ( Jackson Pollock) © 2011 The Pollock–Krasner Foundation / Artists Rights Society (ARS), New York

There is obviously room for experiment here. Is there a quantifiable difference in complexity between Bartok and Lady Gaga, or between Ulysses and Harry Potter? Do a person’s tastes in music (or art, or literature) settle onto a single uniform “complexity level”? For example, if I enjoy Bartok, then would I tend to prefer a jazz piece that has a similar level of complexity? Am I just whistling Dixie, here?

Subverting Expectations

But art also, ideally, involves something else. It involves


which is to say, breaking the rules, breaking the obvious patterns

into patterns of a different kind.

I don’t just want to see patterns in my literature or artwork or music, but I want to see novel patterns, a herd of horses of a different color. I want to be surprised. And the best kind of surprise is when you realize that there was a pattern there all along, but you just didn’t notice it. It’s humbling, and marvelous. It’s like—

—when George Taylor falls to his knees in front of the half-submerged Statue of Liberty, cursing humanity—

—when you discover exactly who murdered Roger Ackroyd—

—when in the glorious 9th three instrumental themes are recounted and discarded, and then the human voice breaks free, because instruments alone cannot do justice to the final ode—

—when you notice the tiny legs of Icarus in the water, and the indifference of the wide world—

—when the chorus of demons judges the singer, and finds him wanting, with a devil put aside for him—


Bohemian Rhapsody is a comic-horror-opera grafted onto a Styx-style power love ballad, and that makes all the difference.

These are patterns turned upside-down, subverted in the best possible way. It is the subversion of the plot twist, the delight of the unexpected, the imp of the perverse, that turn art from mere pattern-production into something more profound.

But how do you truly surprise someone in art? Context makes all the difference.

When the movie Psycho first appeared in 1960, audiences were shocked. After all, Janet Leigh was billed as the star…and she dies 30 minutes into the film! Can you do that? Is that allowed?

The movie doesn’t really impact viewers today (I’ve never met someone born after 1980 who liked the film). I think that’s because people have been jaded by movies like Friday the 13th and Halloween…once you let a certain amount of gore out of the box, you can’t put it back in. To scare audiences today, you need to keep upping the ante…and of course you also have to know who Janet Leigh is.

Context makes all the difference.

People were said to have rioted at the premiere of Stravinsky’s “Right of Spring”. This would be unfathomable today…

Context makes all the difference.

When The Sixth Sense first came out, people loved the movie because of its twist ending. Ironically, the twist that made the director M. Night Shyamalan famous also guaranteed that he’d never have a good movie again. Why? Because we are all looking for a twist now. This meta-knowledge ruins the experience; it can’t really be a twist unless you’re not expecting it to happen. I thought The Village was awful because, knowing who the director was, I was looking to figure out what “the twist” was from the very first moments…

Context makes all the difference.

Here’s how you make good art: you layer your work with different patterns, of differing complexities. This is called “having something for everyone!” A complex story can have simple themes; a complex symphony can have the I-IV-V-I chord progression. Then, on top of the patterns and complexities, you need to have something new, something unexpected. Basically, you need to throw the Red Wedding in there somewhere. Which brings me to the question: Why are the first three Song of Ice and Fire books great, but the last two are mediocre at best?


Answer: no Red Wedding. Here’s a minor spoiler: in A Feast for Crows, nothing really happens. The entire book can be skipped without anyone losing any plot threads. (Seriously.) A Dance with Dragons is marginally better, and there are a few shockers towards the end, but the sense that the series has an overall pattern is diminishing. Major spoiler alert. Take Daenerys’ story arc. At the end of A Dance with Dragons she is basically in the exact same position as she was three books earlier: no followers, no kingdom, no armies, no clue. It’s as if nothing happened. The plot of the series has ground to a halt, and the reader doesn’t really have confidence (after the A Feast for Crows debacle) that the writer’s-block inflicted author can ever get back on track. We’ll see.

Hey, George: subvert our expectations. Write a book in less than five years!

In fact, I’ve changed my mind. Art is 99% perspiration. I need to get back to the book that I’m writing:


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