Tag Archives: Jackson Pollock

The physics of Jackson Pollock’s painting technique

I long ago stumbled across the fascination that Jackson Pollock’s art work exerts over physicists but this work from Brown University adds some colours to the picture (wordplay intended).

One: Number 31, 1950. Jackson Pollock (American, 1912–1956). 1950. Oil and enamel paint on canvas, 8′ 10″ x 17′ 5 5/8″ (269.5 x 530.8 cm) Courtesy: Museum of Modern Art (MOMA) [downloaded from: https://www.moma.org/learn/moma_learning/jackson-pollock-one-number-31-1950-1950/]

From an October 30, 2019 Brown University news release (also on EurekAlert),

The celebrated painter Jackson Pollock created his most iconic works not with a brush, but by pouring paint onto the canvas from above, weaving sinuous filaments of color into abstract masterpieces. A team of researchers analyzing the physics of Pollock’s technique has shown that the artist had a keen understanding of a classic phenomenon in fluid dynamics — whether he was aware of it or not.

In a paper published in the journal PLOS ONE, the researchers show that Pollock’s technique seems to intentionally avoid what’s known as coiling instability — the tendency of a viscous fluid to form curls and coils when poured on a surface.

“Like most painters, Jackson Pollock went through a long process of experimentation in order to perfect his technique,” said Roberto Zenit, a professor in Brown’s School of Engineering and senior author on the paper. “What we were trying to do with this research is figure out what conclusions Pollock reached in order to execute his paintings the way he wanted. Our main finding in this paper was that Pollock’s movements and the properties of his paints were such he avoided this coiling instability.”

Pollock’s technique typically involved pouring paint straight from a can or along a stick onto a canvas lying horizontally on the floor. It’s often referred to as the “drip technique,” but that’s a bit of a misnomer in the parlance of fluid mechanics, Zenit says. In fluid mechanics, “dripping” would be dispensing the fluid in a way that makes discrete droplets on the canvas. Pollock largely avoided droplets, in favor of unbroken filaments of paint stretching across the canvas.

In order to understand exactly how the technique worked, Zenit and colleagues from the Universidad Nacional Autonoma de Mexico analyzed extensive video of Pollock at work, taking careful measure of how fast he moved and how far from the canvas he poured his paints. Having gathered data on how Pollock worked, the researchers used an experimental setup to recreate his technique. Using the setup, the researchers could deposit paint using a syringe mounted at varying heights onto a canvas moving at varying speeds. The experiments helped to zero in on the most important aspects of what Pollock was doing.

“We can vary one thing at a time so we can decipher the key elements of the technique,” Zenit said. “For example, we could vary the height from which the paint is poured and keep the speed constant to see how that changes things.”

The researchers found that the combination of Pollock’s hand speed, the distance he maintained from the canvas and the viscosity of his paint seem to be aimed at avoiding coiling instability. Anyone who’s ever poured a viscous fluid — perhaps some honey on toast — has likely seen some coiling instability. When a small amount of a viscous fluid is poured, it tends to stack up like a coil of rope before oozing across the surface.

In the context of Pollock’s technique, the instability can result in paint filaments making pigtail-like curls when poured from the can. Some prior research had concluded that that the curved lines in Pollock’s paintings were a result of this instability, but this latest research shows the opposite.

“What we found is that he moved his hand at a sufficiently high speed and a sufficiently short height such that this coiling would not occur,” Zenit said.

Zenit says the findings could be useful in authenticating Pollock’s works. Too many tight curls might suggest that a drip-style painting is not a Pollock. The work could also inform other settings in which viscous fluids are stretched into filaments, such as the manufacture of fiber optics. But Zenit says his main interest in the work is that it’s simply a fascinating way to explore interesting questions in fluid mechanics.

“I consider myself to be a fluid mechanics messenger,” he said. “This is my excuse to talk science. It’s fascinating to see that painters are really fluid mechanicians, even though they may not know it.”

Here’s a link to and a citation for the paper,

Pollock avoided hydrodynamic instabilities to paint with his dripping technique by Bernardo Palacios, Alfonso Rosario, Monica M. Wilhelmus, Sandra Zetina, Roberto Zenit. PLOS ONE DOI: https://doi.org/10.1371/journal.pone.0223706 Published: October 30, 2019

This paper is open access.

I could not find any videos related to this research that I know how to embed but Palacios, Zetina, and Zenit have investigated Polock’s ‘physics’ before,

If you want to see Pollock dripping his painting in action, there’s a 10 min. 13 secs. film made in 1950 (Note: Links have been removed from text; link to 10 min. film is below),

In the summer of 1950, Hans Namuth approached Jackson Pollock and asked the abstract expressionist painter if he could photograph him in his studio, working with his “drip” technique of painting. When Namuth arrived, he found:

“A dripping wet canvas covered the entire floor. Blinding shafts of sunlight hit the wet canvas, making its surface hard to see. There was complete silence…. Pollock looked at the painting. Then unexpectedly, he picked up can and paintbrush and started to move around the canvas. It was as if he suddenly realized the painting was not finished. His movements, slow at first, gradually became faster and more dancelike as he flung black, white and rust-colored paint onto the canvas.”

The images from this shoot “helped transform Pollock from a talented, cranky loner into the first media-driven superstar of American contemporary art, the jeans-clad, chain-smoking poster boy of abstract expressionism,” one critic later wrote in The Washington Post.

You can find the film and accompanying Open Culture text intact with links here.

Paint to Programming: exploring the role of algorithms in SciArt; a Dec. 4, 2018 ArtSci Salon event in Toronto, Canada

Here’s the latest from a November 20, 2018 ArtSci Salon announcement received via email,

Paint to Programming: exploring the role of algorithms in SciArt

Description

What is the role of programming in artwork creation? is programming preliminary a Medium to be hidden to an audience more interested in the interface rather than in its algorithmic content ? or is it both medium and content, revealing the inner working, the politics, and the tactical/strategic uses of code and algorithmic complexity in a culture increasingly withdrawn from its crucial implications?

Thanks to a collaboration between Art the Science and ArtSci Salon, this event is meant to initiate a conversation to understand the many uses of algorithms in artistic and scientific research, from ways to solve problems in fluid mechanics by drawing inspiration from the dripping technique of Jackson Pollock, to exploring and making visible the complex dynamics of the blockchain, to using algorithms to process and display data for science communication.

Join ArtSci Salon and Art the Science at Fields for an evening of presentation and discussion with:

Julia Krolik : Exploring algorithms in SciArt
Owen Fernley: Creative coding
Sarah Friend: Software as a medium
Bernardo Palacios Muñiz: Modern painting: A fluid mechanics perspective

Moderator: Roberta Buiani

December 4th | 6pm-8pm

The Fields Institute for Research in Mathematical Sciences
222 College Street | Room 230
Toronto ON | M5T 3J1
Please, RSVP here 

Bios

Julia Krolik is the founder and Chief Executive Officer of Art the Science, an organization dedicated to uniting and empowering artists and scientists to collectively advance scientific knowledge. As an exhibiting artist, focusing on science, art and new media, Julia has created works for CBC, the Ontario Science Centre, the Toronto Urban Film Festival and the Scotia Bank Photography Festival. 

Owen Fernley is an engineer and experimentalist. He has experience programming computational engines in Fortran and C and is currently building front-end web tools in javascript to aid in exploration geology.He co-created Decomposing Pianos, an experimental music collective focusing on projects related to art, science, experimental music and new media. 

Sarah Friend is an artist and software engineer working at a large blockchain development studio. When not doing that, she creates games and other interactive experiences. Her practice investigates murky dichotomies – like those between privacy and transparency, centralization and decentralization, and the environment and technology – with playfulness and absurdist humour.

Bernardo Palacios Muñiz is a mechanical engineer and a researcher from Mexico City. His thesis at UNAM “Descifrando a Pollock: Arte y Mecánica de Fluidos” explored the technique inplemented by Jackson POllock through the perspective of fluid mechanics

Like so many of the events from the ArtSci salon, this is very timely. On a somewhat related note, there’s an art/AI emergence mentioned in my August 31, 2018 posting (scroll down about 70% of the way to this subhead ‘Artworks generated by an AI system are to be sold at Christie’s auction house’).

I’ve also mentioned ArtSci Salon’s presentation partner, Art the Science, in an October 23, 2017 posting. Amongst other programmes, they advertise and promote artist  residencies. I notice that their events are held exclusively in Ontario and the descriptions for participants in their 2018 online gallery exhibit feature a preponderance of Ontario-based artists. I’m sure they’d like to get more participation from across the country but that takes extra time and effort and volunteer organizations such as this one don’t have much of either to spare. Their three year life (they were founded in 2015) is quite an accomplishment.

As for a more national art/sci or sciart network, maybe it’s time to organize something, eh?

Did artists lead the way in mathematics?

There is no way to definitively answer the question of whether artists have led the way in mathematics but the question does provide interesting fodder for an essay (h/t April 28, 2017 news item on phys.org) by Henry Adams, professor of Art History at Case Western Reserve University , in his April 28, 2017 essay for TheConversation.com,

Mathematics and art are generally viewed as very different disciplines – one devoted to abstract thought, the other to feeling. But sometimes the parallels between the two are uncanny.

From Islamic tiling to the chaotic patterns of Jackson Pollock, we can see remarkable similarities between art and the mathematical research that follows it. The two modes of thinking are not exactly the same, but, in interesting ways, often one seems to foreshadow the other.

Does art sometimes spur mathematical discovery? There’s no simple answer to this question, but in some instances it seems very likely.

Patterns in the Alhambra

Consider Islamic ornament, such as that found in the Alhambra in Granada, Spain.

In the 14th and 15th centuries, the Alhambra served as the palace and harem of the Berber monarchs. For many visitors, it’s a setting as close to paradise as anything on earth: a series of open courtyards with fountains, surrounded by arcades that provide shelter and shade. The ceilings are molded in elaborate geometric patterns that resemble stalactites. The crowning glory is the ornament in colorful tile on the surrounding walls, which dazzles the eye in a hypnotic way that’s strangely blissful. In a fashion akin to music, the patterns lift the onlooker into an almost out-of-body state, a sort of heavenly rapture.

It’s a triumph of art – and of mathematical reasoning. The ornament explores a branch of mathematics known as tiling, which seeks to fill a space completely with regular geometric patterns. Math shows that a flat surface can be regularly covered by symmetric shapes with three, four and six sides, but not with shapes of five sides.

It’s also possible to combine different shapes, using triangular, square and hexagonal tiles to fill a space completely. The Alhambra revels in elaborate combinations of this sort, which are hard to see as stable rather than in motion. They seem to spin before our eyes. They trigger our brain into action and, as we look, we arrange and rearrange their patterns in different configurations.

An emotional experience? Very much so. But what’s fascinating about such Islamic tilings is that the work of anonymous artists and craftsmen also displays a near-perfect mastery of mathematical logic. Mathematicians have identified 17 types of symmetry: bilateral symmetry, rotational symmetry and so forth. At least 16 appear in the tilework of the Alhambra, almost as if they were textbook diagrams.

The patterns are not merely beautiful, but mathematically rigorous as well. They explore the fundamental characteristics of symmetry in a surprisingly complete way. Mathematicians, however, did not come up with their analysis of the principles of symmetry until several centuries after the tiles of the Alhambra had been set in place.

Tiles at the Alhambra. Credit: Wikimedia Commons, CC BY-SA

Quasicrystalline tiles

Stunning as they are, the decorations of the Alhambra may have been surpassed by a masterpiece in Persia. There, in 1453, anonymous craftsmen at the Darbi-I Imam shrine in Isfahan discovered quasicrystalline patterns. These patterns have complex and mysterious mathematical properties that were not analyzed by mathematicians until the discovery of Penrose tilings in the 1970s.

Such patterns fill a space completely with regular shapes, but in a configuration which never repeats itself – indeed, is infinitely nonrepeated – although the mathematical constant known as the Golden Section occurs over and over again.

Daniel Schectman won the 2001 Nobel Prize [Schechtman was awarded the Nobel Prize for Chemistry in 2011 as per his Wikipedia entry] or the discovery of quasicrystals, which obey this law of organization. This breakthrough forced scientists to reconsider their conception of the very nature of matter.

In 2005, Harvard physicist Peter James Lu showed that it’s possible to generate such quasicrystalline patterns relatively easily using girih tiles. Girih tiles combine several pure geometric shapes into five patterns: a regular decagon, an irregular hexagon, a bow tie, a rhombus and a regular pentagon.

Whatever the method, it’s clear that the quasicrystalline patterns at Darbi-I Imam were created by craftsmen without advanced training in mathematics. It took several more centuries for mathematicians to analyze and articulate what they were doing. In other words, intuition preceded full understanding.

It’s a fascinating essay and, if you have the time and the interest, it’s definitely a worthwhile read (Henry’s April 28, 2017 essay ).

Fractal imagery (from nature or from art or from mathematics) soothes

Jackson Pollock’s work is often cited when fractal art is discussed. I think it’s largely because he likely produced the art without knowing about the concept.

No. 5, 1948 (Jackson Pollock, downloaded from Wikipedia essay about No. 5, 1948)

Richard Taylor, a professor of physics at the University of Oregon, provides more information about how fractals affect us and how this is relevant to his work with retinal implants in a March 30, 2017 essay for The Conversation (h/t Mar. 31, 2017 news item on phys.org), Note: Links have been removed),

Humans are visual creatures. Objects we call “beautiful” or “aesthetic” are a crucial part of our humanity. Even the oldest known examples of rock and cave art served aesthetic rather than utilitarian roles. Although aesthetics is often regarded as an ill-defined vague quality, research groups like mine are using sophisticated techniques to quantify it – and its impact on the observer.

We’re finding that aesthetic images can induce staggering changes to the body, including radical reductions in the observer’s stress levels. Job stress alone is estimated to cost American businesses many billions of dollars annually, so studying aesthetics holds a huge potential benefit to society.

Researchers are untangling just what makes particular works of art or natural scenes visually appealing and stress-relieving – and one crucial factor is the presence of the repetitive patterns called fractals.

When it comes to aesthetics, who better to study than famous artists? They are, after all, the visual experts. My research group took this approach with Jackson Pollock, who rose to the peak of modern art in the late 1940s by pouring paint directly from a can onto horizontal canvases laid across his studio floor. Although battles raged among Pollock scholars regarding the meaning of his splattered patterns, many agreed they had an organic, natural feel to them.

My scientific curiosity was stirred when I learned that many of nature’s objects are fractal, featuring patterns that repeat at increasingly fine magnifications. For example, think of a tree. First you see the big branches growing out of the trunk. Then you see smaller versions growing out of each big branch. As you keep zooming in, finer and finer branches appear, all the way down to the smallest twigs. Other examples of nature’s fractals include clouds, rivers, coastlines and mountains.

In 1999, my group used computer pattern analysis techniques to show that Pollock’s paintings are as fractal as patterns found in natural scenery. Since then, more than 10 different groups have performed various forms of fractal analysis on his paintings. Pollock’s ability to express nature’s fractal aesthetics helps explain the enduring popularity of his work.

The impact of nature’s aesthetics is surprisingly powerful. In the 1980s, architects found that patients recovered more quickly from surgery when given hospital rooms with windows looking out on nature. Other studies since then have demonstrated that just looking at pictures of natural scenes can change the way a person’s autonomic nervous system responds to stress.

Are fractals the secret to some soothing natural scenes? Ronan, CC BY-NC-ND

For me, this raises the same question I’d asked of Pollock: Are fractals responsible? Collaborating with psychologists and neuroscientists, we measured people’s responses to fractals found in nature (using photos of natural scenes), art (Pollock’s paintings) and mathematics (computer generated images) and discovered a universal effect we labeled “fractal fluency.”

Through exposure to nature’s fractal scenery, people’s visual systems have adapted to efficiently process fractals with ease. We found that this adaptation occurs at many stages of the visual system, from the way our eyes move to which regions of the brain get activated. This fluency puts us in a comfort zone and so we enjoy looking at fractals. Crucially, we used EEG to record the brain’s electrical activity and skin conductance techniques to show that this aesthetic experience is accompanied by stress reduction of 60 percent – a surprisingly large effect for a nonmedicinal treatment. This physiological change even accelerates post-surgical recovery rates.

Pollock’s motivation for continually increasing the complexity of his fractal patterns became apparent recently when I studied the fractal properties of Rorschach inkblots. These abstract blots are famous because people see imaginary forms (figures and animals) in them. I explained this process in terms of the fractal fluency effect, which enhances people’s pattern recognition processes. The low complexity fractal inkblots made this process trigger-happy, fooling observers into seeing images that aren’t there.

Pollock disliked the idea that viewers of his paintings were distracted by such imaginary figures, which he called “extra cargo.” He intuitively increased the complexity of his works to prevent this phenomenon.

Pollock’s abstract expressionist colleague, Willem De Kooning, also painted fractals. When he was diagnosed with dementia, some art scholars called for his retirement amid concerns that that it would reduce the nurture component of his work. Yet, although they predicted a deterioration in his paintings, his later works conveyed a peacefulness missing from his earlier pieces. Recently, the fractal complexity of his paintings was shown to drop steadily as he slipped into dementia. The study focused on seven artists with different neurological conditions and highlighted the potential of using art works as a new tool for studying these diseases. To me, the most inspiring message is that, when fighting these diseases, artists can still create beautiful artworks.

Recognizing how looking at fractals reduces stress means it’s possible to create retinal implants that mimic the mechanism. Nautilus image via www.shutterstock.com.

My main research focuses on developing retinal implants to restore vision to victims of retinal diseases. At first glance, this goal seems a long way from Pollock’s art. Yet, it was his work that gave me the first clue to fractal fluency and the role nature’s fractals can play in keeping people’s stress levels in check. To make sure my bio-inspired implants induce the same stress reduction when looking at nature’s fractals as normal eyes do, they closely mimic the retina’s design.

When I started my Pollock research, I never imagined it would inform artificial eye designs. This, though, is the power of interdisciplinary endeavors – thinking “out of the box” leads to unexpected but potentially revolutionary ideas.

Fabulous essay, eh?

I have previously featured Jackson Pollock in a June 30, 2011 posting titled: Jackson Pollock’s physics and and briefly mentioned him in a May 11, 2010 visual arts commentary titled: Rennie Collection’s latest: Richard Jackson, Georges Seurat & Jackson Pollock, guns, the act of painting, and women (scroll down about 45% of the way).

Art (Lawren Harris and the Group of Seven), science (Raman spectroscopic examinations), and other collisions at the 2014 Canadian Chemistry Conference (part 2 of 4)

Testing the sample and Raman fingerprints

The first stage of the June 3, 2010 test of David Robertson’s Autumn Harbour, required taking a tiny sample from the painting,. These samples are usually a fleck of a few microns (millionths of an inch), which can then be tested to ensure the lasers are set at the correct level assuring no danger of damage to the painting. (Robertson extracted the sample himself prior to arriving at the conference. He did not allow anyone else to touch his purported Harris before, during, or after the test.)

Here’s how ProSpect* Scientific describes the ‘rehearsal’ test on the paint chip,

Tests on this chip were done simply to ensure we knew what power levels were safe for use on the painting.  While David R stated he believed the painting was oil on canvas without lacquer, we were not entirely certain of that.  Lacquer tends to be easier to burn than oil pigments and so we wanted to work with this chip just to be entirely certain there was no risk to the painting itself.

The preliminary (rehearsal) test resulted in a line graph that showed the frequencies of the various pigments in the test sample. Titanium dioxide, for example, was detected and its frequency (spectra) reflected on the graph.

I found this example of a line graph representing the spectra (fingerprint) for a molecule of an ultramarine (blue) pigment along with a general explanation of a Raman ‘fingerprint’. There is no indication as to where the ultramarine pigment was obtained. From the  WebExhibits.org website featuring a section on Pigments through the Ages and a webpage on Spectroscopy,

raman-ArtPigment

Ultramarine [downloaded from http://www.webexhibits.org/pigments/intro/spectroscopy.html]

Raman spectra consist of sharp bands whose position and height are characteristic of the specific molecule in the sample. Each line of the spectrum corresponds to a specific vibrational mode of the chemical bonds in the molecule. Since each type of molecule has its own Raman spectrum, this can be used to characterize molecular structure and identify chemical compounds.

Most people don’t realize that the chemical signature (spectra) for pigment can change over time with new pigments being introduced. Finding a pigment that was on the market from 1970 onwards in a painting by Jackson Pollock who died in 1956 suggests strongly that the painting couldn’t have come from Pollock’s hand. (See Michael Shnayerson’s May 2012 article, A Question of Provenance, in Vanity Fair for more about the Pollock painting. The article details the fall of a fabled New York art gallery that had been in business prior to the US Civil War.)

The ability to identify a pigment’s molecular fingerprint means that an examination by Raman spectroscopy can be part of an authentication, a restoration, or a conservation process. Here is how a representative from ProSpect Scientific describes the process,

Raman spectroscopy is non-destructive (when conducted at the proper power levels) and identifies the molecular components in the pigments, allowing characterization of the pigments for proper restoration or validation by comparison with other pigments of the same place/time. It is valuable to art institutions and conservators because it can do this.  In most cases of authentication Raman spectroscopy is one of many tools used and not the first in line. A painting would be first viewed by art experts for technique, format etc, then most often analysed with IR or X-Ray, then perhaps Raman spectroscopy. It is impossible to use Raman spectroscopy to prove authenticity as paint pigments are usually not unique to any particular painter.  Most often Raman spectroscopy is used by conservators to determine proper pigments for appropriate restoration.  Sometimes Raman will tell us that the pigment isn’t from the time/era the painting is purported to be from (anachronisms).

Autumn Harbour test

Getting back to the June 3, 2014 tests, once the levels were set then it was time to examine Autumn Harbour itself to determine the spectra for the various pigments.  ProSpect Scientific has provided an explanation of the process,

This spectrometer was equipped with an extension that allowed delivery of the laser and collection of the scattered light at a point other than directly under the microscope. We could also have used a flexible fibre optic probe for this, but this device is slightly more efficient. This allowed us to position the delivery/collection point for the light just above the painting at the spot we wished to test. For this test, we don’t sweep across the surface, we test a small pinpoint that we feel is a pigment of the target colour.

We only use one laser at a time. The system is built so we can easily select one laser or another, depending on what we wish to look at. Some researchers have 3 or 4 lasers in their system because different lasers provide a better/worse raman spectrum depending on the nature of the sample. In this case we principally used the 785nm laser as it is better for samples that exhibit fluorescence at visible wavelengths. 532nm is a visible wavelength.  For samples that didn’t produce good signal we tried the 532nm laser as it produces better signal to noise than 785nm, generally speaking. I believe the usable results in our case were obtained with the 785nm laser.

The graphed Raman spectra shows peaks for the frequency of scattered light that we collect from the laser-illuminated sample (when shining a laser on a sample the vast majority of light is scattered in the same frequency of the laser, but a very small amount is scattered at different frequencies unique to the molecules in the sample). Those frequencies correspond to and identify molecules in the sample. We use a database (on the computer attached to the spectrometer) to pattern match the spectra to identify the constituents.

One would have thought ‘game over’ at this point. According to some informal sources, Canada has a very small (almost nonexistent) data bank of information about pigments used in its important paintings. For example, the federal government’s Canadian Conservation Institute (CCI) has a very small database of pigments and nothing from Lawren Harris paintings [See the CCI’s response in this addendum], so the chances that David Robertson would have been able to find a record of pigments used by Lawren Harris roughly in the same time period that Autumn Harbour seems to have been painted are not good.

Everything changes

In a stunning turn of events and despite the lack of enthusiasm from Vancouver Art Gallery (VAG) curator, Ian Thom, on Wednesday, June 4, 2014 the owner of the authenticated Harris, Hurdy Gurdy, relented and brought the painting in for tests.

Here’s what the folks from ProSpect Scientific had to say about the comparison,

Many pigments were evaluated. Good spectra were obtained for blue and white. The blue pigment matched on both paintings, the white didn’t match. We didn’t get useful Raman spectra from other pigments. We had limited time, with more time we might fine tune and get more data.

One might be tempted to say that the results were 50/50 with one matching and the other not, The response from the representative of ProSpect Scientific is more measured,

We noted that the mineral used in the pigment was the same.  Beyond that is interpretation:  Richard offered the view that lapis-lazuli was a typical and characteristic component for blue in that time period (early 1900’s).   We saw different molecules in the whites used in the two paintings, and Richard offered that both were characteristic of the early 1900’s.

Part 1

Part 3

Part 4

* ‘ProsPect’ changed to ‘ProSpect’ on June 30, 2014.

ETA July 14, 2014 at 1300 hours PDT: There is now an addendum to this series, which features a reply from the Canadian Conservation Institute to a query about art pigments used by Canadian artists and access to a database of information about them.

Lawren Harris (Group of Seven), art authentication, and the Canadian Conservation Insitute (addendum to four-part series)

 

The Code; a preview of the BBC documentary being released in Canada and the US

The three episodes (Numbers, Shapes, and Prediction)  of The Code, a BBC (British Broadcasting Corporation) documentary featuring Professor Marcus du Sautoy, focus on a ‘code’ that according to du Sautoy unlocks the secrets to the laws governing the universe.

During the weekend (June 16 & 17, 2012) I had the pleasure of viewing the two-disc DVD set which is to be released tomorrow, June 19, 2012, in the US and Canada.  It’s a beautiful and, in its way, exuberant exploration of patterns that recur throughout nature and throughout human endeavours. In the first episode, Numbers, du Sautoy relates the architecture of the Chartres Cathedral (France) , St. Augustine‘s (a Roman Catholic theologian born in an area we now call Algeria) sacred numbers, the life cycle of the periodic cicada in Alabama, US and more to number patterns. Here’s an excerpt of du Sautoy in Alabama with Dr. John Cooley discussing the cicadas’ qualities as pets and their remarkable 13 year life cycle,

In the second episode, Shapes,  du Sautoy covers beehive construction (engineering marvels), bird migrations and their distinct shapes (anyone who’s ever seen a big flock of birds move as one has likely marveled at the shapes the flock takes as it moves from area to another), computer animation, soap bubbles and more, explaining how these shapes can be derived from the principle of simplicity or as du Sautoy notes, ‘nature is lazy’. The question being, how do you make the most efficient structure to achieve your ends, i.e., structure a bird flock so it moves efficiently when thousands and thousands are migrating huge distances, build the best beehive while conserving your worker bees’ energies and extracting the most honey possible, create stunning animated movies with tiny algorithms, etc.?

Here’s du Sautoy with ‘soap bubbleologist’ Tom Noddy who’s demonstrating geometry in action,

For the final episode, Prediction, du Sautoy brings the numbers and geometry together demonstrating repeating patterns such as fractals which dominate our landscape, our biology, and our universe. du Sautoy visits a Rock Paper Scissors tournament in New York City trying to discern why some folks can ‘win’ while others cannot (individuals who can read other people’s patterns while breaking their own are more successful), discusses geographic profiling with criminal geographic profiler Prof. Kim Rossmo, Jackson Pollock’s paintings and his fractals, amongst other intriguing patterns.

I paid special to the Rossmo segment as he created and developed his geographic profiling techniques when he worked for the Vancouver (Canada) Police Department (VPD) and studied at a nearby university. As this groundbreaking work was done in my neck of the woods and Rossmo was treated badly by the VPD, I felt a special interest. There’s more about Rossmo’s work and the VPD issues in the Wikipedia essay (Note: I have removed links from the excerpt.),

D. Kim Rossmo is a Canadian criminologist specializing in geographic profiling. He joined the Vancouver Police Department as a civilian employee in 1978 and became a sworn officer in 1980. In 1987 he received a Master’s degree in criminology from Simon Fraser University and in 1995 became the first police officer in Canada to obtain a doctorate in criminology. His dissertation research resulted in a new criminal investigative methodology called geographic profiling, based on Rossmo’s formula.

In 1995, he was promoted to detective inspector and founded a geographic profiling section within the Vancouver Police Department. In 1998, his analysis of cases of missing sex trade workers determined that a serial killer was at work, a conclusion ultimately vindicated by the arrest and conviction of Robert Pickton in 2002. A retired Vancouver police staff sergeant has claimed that animosity toward Rossmo delayed the arrest of Pickton, leaving him free to carry out additional murders. His analytic results were not accepted at the time and after a falling out with senior members of the department he left in 2001. His unsuccessful lawsuit against the Vancouver Police Board for wrongful dismissal exposed considerable apparent dysfunction within that department.

… he moved to Texas State University where he currently holds the Endowed Chair in Criminology and is director of the Center for Geospatial Intelligence and Investigation. …

Within what appeared to be chaos, Rossmo found order. Somehow Jackson Pollock did the same thing to achieve entirely different ends, a new form of art. Here’s a video clip of du Sautoy with artist and physicist, Richard Taylor,

Intuitively, Pollock dripped paint onto his canvases creating fractals decades before mathematician, Benoit Mandelbrot, coined the phrase and established the theory.  (I wrote previously about Jackson Pollock [and fluid dynamics] in my June 30, 2011 posting.)

I gather that du Sautoy’s ‘code’ will offer a unified theory drawing together numbers, patterns, and shapes as they are found throughout the universe in nature  and in our technologies and sciences.

The DVDs offer three extras (4 mins. each): Phi’s the Limit (beauty and the golden ratio or Phi), Go Forth and Multiply (a base 2 system developed by Ethiopian traders predating binary computer codes by millenia) and Imagining the Impossible: The Mathematical Art of M. C. Escher  (Dutch artist’s [Escher] experiments with tessellation/tiling).

I quite enjoyed the episodes although I was glad to have read James Gleick‘s book, Chaos (years ago) before viewing the third episode, Prediction and I was a little puzzled by du Sautoy’s comment in the first episode, Numbers, that atoms are not divisible. As I recall, you create an atomic bomb when you split an atom but it may have been one of those comments that didn’t come out as intended or I misunderstood.

You can find out more about The Code DVDs at Athena Learning. The suggested retail cost is $39.99 US or $52.99 CAD (which seems a little steep for Canadian purchasers since the Canadian dollar is close to par these days and, I believe, has been for some time).

In sum, this is a very engaging look at numbers and mathematics.

Jackson Pollock’s physics

Take a mathematician (L. Mahadevan), a physicist (Andrzej Herczynski), and an art historian (Claude Cernuschi) and you’re liable to get a different perspective on Jackson Pollock*, a major figure in abstract expressionism, art. (I’m pretty sure there’s a joke in there of the: “There was mathematician and a physicist in a bar when an art historian came in …” ilk. I just can’t come up with it. If you can, please do leave it in the comments.)

Let’s start with a picture (image downloaded from the Wikipedia essay about Jackson Pollock’s No. 5, 1948),

No. 5, 1948 (Jackson Pollock, downloaded from Wikipedia essay about No. 5, 1948)

In a recent paper published in Physics Today (Painting with drops, jets, and sheets, which is behind a paywall), Mahadevan, Herczynski, and Cernuschi speculate about Pollock’s intuitive understanding of physics, in this case, fluid dynamics. From the June 28, 2011 news item on physorg.com,

A quantitative analysis of Pollock’s streams, drips, and coils, by Harvard mathematician L. Mahadevan and collaborators at Boston College, reveals, however, that the artist had to be slow—he had to be deliberate—to exploit fluid dynamics in the way that he did.

The finding, published in Physics Today, represents a rare collision between mathematics, physics, and art history, providing new insight into the artist’s method and techniques—as well as his appreciation for the beauty of natural phenomena.

“My own interest,” says Mahadevan, “is in the tension between the medium—the dynamics of the fluid, and the way it is applied (written, brushed, poured…)—and the message. While the latter will eventually transcend the former, the medium can be sometimes limiting and sometimes liberating.”

Pollock’s signature style involved laying a canvas on the floor and pouring paint onto it in continuous, curving streams. Rather than pouring straight from the can, he applied paint from a stick or a trowel, waving his hand back and forth above the canvas and adjusting the height and angle of the trowel to make the stream of paint wider or thinner.

Simultaneously restricted and inspired by the laws of nature, Pollock took on the role of experimentalist, ceding a certain amount of control to physics in order to create new aesthetic effects.

The artist, of course, must have discovered the effects he could create through experimentation with various motions and types of paint, and perhaps some intuition and luck. But that, says Mahadevan, is the essence of science: “We are all students of nature, and so was Pollock. Often, artists and artisans are far ahead, as they push boundaries in ways that are quite similar to, and yet different from, how scientists and engineers do the same.”

There’s more about this study on the physorg.com site including a video illustrating fluid dynamics. You can also find a June 29, 2011 news item on Science Daily and a June 29, 2011 article in Harvard Magazine about the study. From the Harvard news article,

MODERN ART WAS NEVER more famously lampooned than when Tom Stoppard [playwright and screenwriter] said, “Skill without imagination is craftsmanship and gives us many useful objects such as wickerwork picnic baskets. Imagination without skill gives us modern art.”

The article by expanding on Mahadevan’s research gives the lie to Stoppard’s quote. (I wonder if Stoppard will write a play about physics and art in the light of this new thinking about Pollock’s work?)

This all brought to mind, Richard Jackson’s work which was featured in 2010 at the Rennie Collection in Vancouver (my most substantive comments about Jackson’s work are in my May 11, 2010 posting). Trained as both an artist and an engineer, he too works with paint and its vicosity. I still remember the piece in the gallery basement that featured three (as I recall) cans of paint apparently caught in the act of being poured. In retrospect, one of the things I liked best about the show is that a lot of Jackson’s work is very much about the physical act of painting and the physicality of the materials.

One final note, the L. in Mahadevan’s name stands for Lakshinarayan.

*’Pollock’s’ corrected to Pollock on April 27, 2017.