[Originally posted at our new home at Scientific American.]
What is it about painter Jackson Pollock that physicists find so entrancing? His notorious drip paintings have earned the artist as many naysayers as admirers over the years, but within today's art community his genius is largely undisputed. A genuine Pollock canvas is worth millions. And now a couple of physicists have published an intriguing article in the June issue of Physics Today on Pollock's seemingly intuitive grasp of the mathematical connection between viscosity and flow rate of a fluid (in Pollock's case, paint).
Pollock's technique was pretty unique for his era: he used a stick or a trowel to drip paint on the canvas, or fling it to form his signature splatter, or make elaborate coils with the liquid paint. The seemingly haphazard way he went about this caused more than one person to comment that surely even a trained chimpanzee could produce a canvas that looked like a Pollock -- certainly a chimp like Congo, who produced a series of paintings in the mid 1950s and was often held up as a way to ridicule Pollock's work. (Congo's oeuvre came up for auction in 2005, and the chimp seems to have also accrued value in death: the lot sold for £12,000. The same article reports that Salvador Dali is said to have quipped, "The hand of the chimpanzee is quasi-human; the hand of Jackson Pollock is totally animal.")
According to Andrzej Herczynski, a physicist at Boston College, and Harvard mathematician Lakshminarayanan Mahadevan, along with Boston College art historian Claude Cernuschi, the hand of Jackson Pollock was also the hand of a brilliantly intuitive physicist of sorts.
"His particular painting technique essentially lets physics be a player in the creative process," Herczynski told Wired. "To the degree that he lets physics take a role in painting process, he is inviting physics to be a coauthor of his pieces." (Full disclosure: Herczynski is a friend of some years' standing; we used to joke that if you combined all the letters in our respective names -- his is heavy on consonants, mine on vowels -- you'd almost get the complete alphabet. <*waves*> Hi Andrzej!)
So, what's the specific physics we're talking about here? It's a phenomenon in fluid dynamics known as "coiling instability," first described in physics papers in the late 1950s. Anyone who has ever played with the syrup on their morning pancakes -- and who among us has not? -- knows what this is. It's a mathematical way of describing the way in which a thick, viscous liquid folds onto itself like a coiling rope.
Herczynski and Mahadevan measured the thickness of lines and the radius of the coils in one of Pollock's paintings where this effect occurs, and used those measurements to estimate the flow rate of the paint Pollock used as he moved his hand across the canvas. Recent fluid dynamics studies demonstrate that the kinds of patterns fluids form as they fall depends on two factors: how thick they are (viscosity), and the speed at which they are moving. For instance, a thick fluid will form a straight line when it's moving rapidly (say, paint across a canvas), but when it's poured slowly, it will form various loops and squiggles and figure eights. You see just that in Pollock's "Untitled 1948-49" (for all his genius, Pollock kind of sucked at catchy titles).
It's well known that Pollock deliberately played with the texture and viscosity of his paints, mixing them with solvents to make them thicker or thinner, depending on the effect he was looking to achieve. He was able to control the degree to which this coiling effect showed up in the final painting by moving his arm at different speeds, combined with using paints of different viscosities. In fact, while many art historians previously believed Pollock created the coiling effect by "wiggling his hand in a sinusoidal way," Herczynski et al maintain he did with simple gravity.
"When Pollock was doing that, when he mixed his paints and diluted them and chose paints of similar density and different viscosity and so on, in a way he was doing experiments in fluid dynamics," Herczynski told Wired-- and he did so before physicists themselves had established fluid dynamics as a separate field. Pollock wasn't consciously conducting physics experiments, of course, but perhaps the best evidence in favor of this analysis can be found in a 1950 video of Pollock at work (see end of post), in which the splatter master asserts in the voice-over, "I can control the flow of paint. There is no accident."
This isn't the first time Pollock has piqued the interest of physicists. Several years ago, I wrote a feature article for Discover (and then a blog post) on the work of physicist Richard Taylor, who used the same analysis techniques he applied in his laboratory to study several paintings by the splatter master (affectionately known to Jen-Luc Piquant as "Jack the Dripper"). He found very clear fractal patterns in the seemingly random drip patterns Pollock splayed across his giant canvases.
Thanks to the enormous popularity of Jurassic Park, many people now realize that "chaos" -- a word that typically denotes utter randomness -- has a different meaning in the context of math and science. It applies to systems that only appear to be random on the surface; underneath is a hidden order.
The stock market is a chaotic system, for example: a slight blip can be amplified many times over until the system "goes critical" and the market crashes. It's known as the "butterfly effect" (not to be confused with the 2004 Ashton Kutcher film by the same name, although the movie certainly plays with the implications of the concept): a butterfly flaps its wings in Brazil, and the air disturbance amplifies over time and distance, eventually causing a tornado in Texas (along with loads of other equally unpredictable changes everywhere else, of varying severity).
Fractal patterns are the mathematical offspring of chaos theory, the remnant of chaotic motion -- wreckage strewn in the wake of a hurricane, for example. Something might appear to be haphazard on the surface, but look closer and one might realize that there is, in fact, a single geometric pattern repeated thousands of times over at different size scales, just like those nested Russian dolls. That telltale pattern is known as "self-similarity."
I've always liked the concept of chaos. So I was chuffed to learn that fractal patterns pop up not just in art, but in music and literature as well. I love it when two widely divergent disciplines -- science and art, in this instance -- somehow manage to find common ground. Taylor's work particularly fascinated me because he explored not just whether such patterns occurred in Pollock's paintings, but why they might be there in the first place. When he analyzed archival film footage of Pollock in the act of creating those canvases -- shot in 1950 by Hans Namuth -- Taylor found that Pollock actually moved around the canvases in chaotic motions. So there was nothing random about Pollock's work at all, at least to Taylor's way of thinking.
Nearly five years after that, Taylor (who had since moved to the University of Oregon) was back in the news, having been asked to analyze several small paintings that were recently discovered, and appear to be original Pollocks. His findings, published in the British journal Nature, indicated that they might not be authentic. They didn't exhibit those telltale fractal patterns that Taylor had found to typify Pollock's greatest work. In fact, there were "significant differences" in the drip patterns -- so significant that Taylor concluded the new paintings were either due to one artist whose style was extremely varied, or to several different artists.
Naturally, the owner of the paintings, one Alex Matter, was less than thrilled with this news. Pollock's work typically fetches millions of dollars at auctions, so Matter's cache of canvases, collectively, would be equivalent to winning the lottery -- if they were genuine.
Some contended that the paintings were more likely to be a pale imitation of Pollock's signature technique on the part of Matter's mother, Mercedes, an artist in her own right, as well as an art teacher, and also an "F.O.J." ("friend of Jack").
These naysayers pointed to Taylor's analysis as hard, empirical evidence that the foundling canvases couldn't be genuine. Matter's supporters insisted that fractal analysis is far from a proven commodity when applied to the field of art authentication, which by its nature is fairly subjective, and usually comes down to a consensus judgment call.
"Irrespective of whatever determination is ultimately made on the authenticity of the... Matter paintings, fractal analysis should not be considered a foolproof technique for authenticating works by Pollock," Case Western Reserve University art historian Ellen Landau told Nature in 2006. After all, how could a mere computer program possibly be capable of analyzing all the complexities of the human creative process?
There's something to that criticism. The presence of fractal patterns in some of Pollock's painting is interesting, to be sure, especially since this shows up in the canvases considered to be his greatest work. But artists change and refine their techniques over time; and even Pollock had his off days, producing lesser works. What are the odds that every single Pollock canvas is fractal, if the secret to the splatter master's aesthetic appeal is that telltale self-similarity? Using that argument, the Matter paintings could still be genuine, since the absence of the expected scaling behavior in the paintings may be attributable to the fact that they were executed by Pollock at a different period from that of the paintings that Taylor had analyzed earlier.
Of Fractals and Photoshop
At least a couple of physicists agreed with Landau's assessment. Shortly after the 2006 Nature article appeared, Case University physicists Katherine Jones-Smith and Harsh Mathur published the results of their own analysis, claiming that Taylor's work was "seriously flawed" and "lacked the range of scales needed to be considered fractal." See, that whole self-similarity aspect of fractals isn't always visible to the eye; there is a computational technique known as box-counting to detect fractal patterns down to size scales beyond the limits of the human eye. Using that method, Pollock's paintings do not meet the criteria for "fractal," Jones-Smith and Mathur argue -- because the smallest marks of paint found in a Pollock canvas are "only a thousand times smaller than the entire canvas."
To prove her point, Jones-Smith created her own version of a fractal painting -- based on the criteria Taylor has made public so far -- in about five minutes using Photoshop, called "Untitled 5" (see photo at right). As you can see, it looks nothing like a Jackson Pollock, nor would anyone ever mistake it for such. Hell, even Congo could have done better. Still, Jones-Smith and Mathur maintain it meets Taylor's public fractal "criteria," and Mathur jokingly told Science News, "Either Taylor is wrong or Kate's drawings are worth $40 million. We'd be happy either way."
Oh, snap! It's a clever comeback, but also a bit disingenuous: there is a lot more to the value of a Pollock painting than its fractal (or non-fractal) nature, and Jones-Smith and Mathur most certainly know it. This illustrates the downside when physicists try to tackle art and apply rigorous quantitative analysis to assess aesthetic value. Our responses to art are highly subjective and vary with the individual.
That inherent subjectivity is why Taylor himself didn't claim his technique was "foolproof" for authentication. Indeed, he has been careful to insist that his analysis shouldn't be the final word on the subject, just one tool among many, telling the New York Times that his findings "should be integrated with all the known facts -- including provenance, visual inspection, and materials analysis." In other words, any objective, scientific data should be considered in light of the traditional, more subjective criteria typically employed by art historians.
Arguing that there can't be fractal patterns in a Pollock painting because the paint blobs aren't small enough strikes the average non-scientist as pointless nitpicking -- and even some bona fide scientists. The late Benoit ("father of fractals") Mandelbrot himself defended Taylor's work, telling Science News back in 2006, "I do believe Pollocks are fractal." And Taylor pointed out that his use of "fractal" is perfectly consistent with how it has been defined by the research community, adding that by "dismissing Pollock's fractals because of their limited magnification rage, [they] would also dismiss half the published investigations of physical fractals."
There is one criticism offered by Jones-Smith and Mathur that strikes me as a valid point: as of 2006, at least, Taylor had only analyzed 17 of Pollock's more than 180 drip paintings, a sample too statistically insignificant to draw substantial conclusions. I'm waiting for the first person to step forward and level the same criticism at Herczynski and Mahadevan, who focused their analysis mostly on a single painting.
Oh, you know it's coming; folks are passionate about Pollock, and physicists are no exception. I'm sure the scientists will respond with admirably convincing counter-arguments. Indeed, they seem to have anticipated something of that nature, since Herczynski observed that it's possible the coils may be present in other paintings but are obscured because Pollock favored canvases with course surfaces. The authors also acknowledge this was an effect Pollock used rather sparingly in his work because he didn't like "relinquishing too much control" in his paintings. See above re: how artists' techniques change and evolve over time.
That kind of spirited back and forth is exactly how science works. Thus far, Herczynski and his collaborators seem to have the support of a few folks in the art community, which is encouraging, and even have the support of Mathur, one of the physicists who led the charge against Taylor's work.
As for me, I'll continue to savor these kinds of art/science collaborations; they only enhance both my appreciation of the masters, and of the wonder of science. It's nice to see the growing body of evidence that Pollock really did know what he was doing, even if was due to intuitive artistic instinct. Besides, as Landau told Science in response to this latest paper, "What Pollock produced without a specific scientific knowledge base seems a quintessential illustration of the fact that art and science are not such emphatically different side-of-the-brain activities as so many believe." Speak it, sister.