Order and Chaos and the Clash of the Titans of Modern Art and Science
"Broadway Boogie-Woogie" by Piet Mondrian, 1942-
Image courtesy Metopolitan Museum of Modern Art.
Entropy means that things fall apart, and order does not hold. Which reminds me of a conversation Piet Mondrian and Peggy Guggenheim had while looking at a painting by Jackson Pollock in a group show of young American artists in New York in 1942. “That’s not painting, is it?” the patroness of modern art asked the exalter of geometrical order. “There’s absolutely no discipline at all. That man has serious problems.”
“I’m not so sure,” said the great Dutch modernist. “I think this is the most interesting work I’ve yet seen in America. You must watch this man.”
“You can’t be serious!” exclaimed the founding patron of American modernism. “You can’t compare this to the way you paint.”
“The way I paint and the way I think are two different things,” Mondrian smiled.
He must have seen that Pollock too was after some universal quality underlying all things. The fact that to the uninitiated the painting looked like visual noise might confirm that Pollock had learned to see an order in chaos no one had previously been able to catch.
The supreme compliment we can give a work of art is that it may change the way we see the world. Mondrian did it with his celebration of lines and squares and broad swaths of rectilinear color. These images enraged people in its day as looking cold and calculated. Yet as he wrote about his work in the book Natural Reality and Abstract Reality, his words are lush and alluring, with a mix of humility and the pull of the grand quest: “Nature is perfect, but man doesn’t need to represent perfect nature in art, precisely because nature is already so perfect. What he does need to represent is the inward. We have to transform natural appearance, precisely in order to see nature more perfectly.” Art must turn away from nature because it is a sin of pride to imagine we can represent it better than it is. Inside human thought likes line, shape, and pure form. When we have got that all figured out though, we will be able to see nature all the better. So don’t paint what you see, but paint whatever tools you need to see the world as precisely as you can.
This picture of art is one great claim of why abstraction was supposed to matter so much—that it would change the way we see the world. And this is the function, much more so than the idea that it socially could change the world, that is most helpful to my vision of showing how the arts and sciences aid and promote each other. Mondrian’s ideas, expressed in this strange and Galileo-like three part conversation first published in Dutch in 1919, seem very much about purely visual issues, not claiming too much for what the picture can do for us. Even Mondrian’s most famous work of geometric grids is called “Broadway Boogie-Woogie,” and is always put forth as an example of how an abstract grid is actually an image of an exciting New Yawkish world of jazz and swing, traffic lights, noise, and sweat. The exciting color splash of modernity in a man-made machinish world.
It is tempting to use art as a sign of its times. But if one tries to strip all you think you know about a piece and just look at it, the value of seeing might truly come clear. Geometry is not art, math is not appearing beautiful in a meaningful, formal way. Mondrian does want to make the world more human and less natural, pushing us further into the grid which seems so alien to the rest of the evolved world. His approach has made an impact, as the forms he so eloquenty painted and suggested to us are now the stuff of architecture, graphic, and electronic design. We are so used to them we easily forget how one man pushed them to their limits, going beyond his simple notion that straight is better than curved and making real art about these ideas by using form, composition, color, the classic techniques of visual design.
Still, it is worth noting that Mondrian thought abstract art was the most “concrete” art that could be. What did he mean by this sleight-of-words? “The new man will learn to see plastically, and bend the curved to the straight. The external will be an image of the internal.” Diagrams of the workings of the mind? Today’s more complete consciousness demands a different representation, but we are indebted to Mondrian’s rectilinear dreams, and his efforts to describe them. The work is always more than the essence, and the visual should still be the strongest argument an artist has to bear.
"Number 31" by Jackson Pollock, 1950.
Image courtesy Metopolitan Museum of Modern Art.
Mondrian knew that Pollock wasn’t bluffing, that the American upstart too was in on the perceivable music of the visual world, that once you start admiring his works of all nature might have a new kind of beauty. Chaos is its own kind of order, and only after a generation came to applaud Pollock’s way of seeing as also art did we generate a whole mathematics of chaos, expanding our scientific notion of what order can be.
How does the viewer grasp the organization of the swirls and drips in a Pollock painting? Is there really something natural about them? Do they reveal some new kind of order in nature? The mathematician Richard Taylor, in 1999, felt strongly that there ought to be a way to prove that Pollock’s work reveals something fundamental in nature. By the end of the 20th century, Pollocks’ paintings easily appeared brilliant, important, but also somehow real to many who saw them. To Taylor this meant there was something specific about the way they approached an aesthetic of nature. Was there a way to mathematically prove this?
Taylor and his colleagues were able to demonstrate through mathematical analysis that the form of Pollock’s layers of lines on the canvas was akin to nature’s own patterns of snow on the forest floor, trees in a forest seen from the air, or lichen growing on rocks: unplanned, but not random, ordered and designed according to a mathematics of chaos derived from the fractal equations of the famous Mandelbrot set.
It is fractal mathematics that allows computer games to spew out convincing mountain ranges and landscapes with fairly simple equations, showing how order can be found in what at first seems random. Break down a broccoli head into smaller headlets, and they all have the same basic shapes. Take a river and stare down at it from the sky, or gaze at the rivulets that stream down a tiny muddy bank, they all have the same kind of branching structure, never exactly symmetrical, but looking similar and vastly different nested levels of scale.
Physicists have dripped paint from swinging pendulums that oscillate in several dimensions, and they soon approximate the kind of drip-stroke that Pollock made as he swung his arms back and forth over the canvas on the floor, going for the same kind of chaotic motion that in the end, Taylor believes he has proven that Pollock mimics, either implicitly or explicitly, the way nature works. This is why when you gaze long enough at a Pollock painting until you feel like you are inside it, you get the same feeling of running fast through a thick forest or tangled wood.
The artist grasped the importance of fractal geometry before it was even discovered. Instead of representing nature, he intuitively adopted its own undiscovered language to make abstract works infinitely more real than anything before him. A fragment of the painting inside a frame has as much happening as the whole thing, as Ornette Coleman discovered when he chose a piece of a Pollock for his album cover for his album Free Jazz. It’s like a complex bird song slowed down that only becomes more complex the more it’s stretched out, with layers of intricacy like an infinite coastline.
"Geinrust Farm in Watery Landscape" by Piet
Image courtesy Frans Hals Museum in Haarlem, Netherlands.
E.O. Wilson has this to say in Consilience about how to make good art. “Imitate, make it geometrical, intensify: That’s not a bad three-part formula for the driving pulse of the arts as a whole. Somehow innovators know how it all is to be done.” Wilson only likes Mondrian’s most early work, from 1905, where in “Geinrust Farm in Watery Landscape” the young Piet drew a row of very thin trees in front of a dark shadowy house in charcoal, all in an arrangement of spacing and proportion that Wilson says follow a pattern that modern brain image would conclude is the most arousing to the human mind.
Later, Mondrian abstracts this technique to weaving, flowing branches, still intuitively coming up with an arrangement which science can today conclude is the most pleasing, and then abstracting toward a cubist direction, and then to bold rectilinear colors and patterns into the style we most expect from him. Yet there is something of the Pollock-like wildness in this early piece. Is it really true that in the best artwork we can find those proportions that science can calculate as being the most amenable to human perception and enjoyment? He figured out on his own the best possible ratios and appearances.
Can science really calculate such things? Wilson is impressed that already in the 1970s Belgian psychologist Gerda Smets concluded that people prefer 20 percent redundancy when it comes to evaluating abstract designs. She concluded this was something innate, not something culturally learned. We always knew we need a balance between sameness and difference. Now a scientist has quantified it. Wilson is impressed; he found the same thing in Mondrian. Why don’t artists like this method, or the simplicity of its conclusion?
We feel it robs our thunder, applying numbers to our hunt for genius. We know advertisers think this way, and that there are computer programs out there trying to create the next hit song. We want to believe movies are created by auteurs, that writers create their novels alone, and that focus groups don’t lead to movies with better endings. “If there’s one thing you can’t steal, it’s that feel.”Here the tensions come out between art and science, here is where I want scientists to admit they too can learn from art, rather than believe they can explain it. Otherwise it’s still the case of one approach to the world claiming it’s better than another.
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