Zoë Shulman

Professor Katharine Kindervater

Complexity Theory

9 December 2012

A Discourse on Artistic Process and Complexity

Whenever I search for a topic of investigation in my practice, I always look for contrast in nature.  It is these differences of values that signal the occurrence of movement and, ultimately, change.  As an artist, I conceptualize and quantify contrasts through geometric compositions in order to create the visual experience of change.

Coming into my recent work, I developed a keen interest in the paradigm shift toward postmodernism with regard to the increasing role that subjectivity is playing in creating a more complex world.  In the search for a topic, I found that my postmodern concerns were greatly illuminated by this year’s election.  The heat and friction surrounding the debates on economic policy, civil rights and national identity caused a great cultural uplift in which marginalized communities rose to the surface and fought for equality.  Being a part of America’s changing landscape inspired me to question the relationship between contrast, hierarchy and subjectivity:  How does contrast work to create movement and change within a hierarchy?  What is the nature of that movement and how is it influenced by subjectivity?

These inquiries lead me to create a small series of wood panel paintings called Postmodern Landscapes:

Postmodern Landscapes, acrylic and resin on wood panel, 1’ X 1’ (each), 2012

            My first step consisted of conceptualizing a geometric composition that could describe the emergence of the postmodern paradigm.  To start, I drew a Cartesian grid on the surface of my wood panels.  I strategically divided the surface into thirteen units (a “Fibonacci number”) in order to carve golden rectangles into the grid (see fig. 1).  In previous works, I have used the golden rectangle to describe complex movements and decided to apply the motif to achieve a contrast of form within the grid’s linear structure.  This contrast served as the metaphor for the paradigm shift from modern linearity to postmodern complexity.

Figure 1

In aesthetic design, the golden rectangle is defined as a fractal that employs unity of shape and variety of proportion to form an infinite progression of self-similar parts.  As a result of self-similarity, the rectangle balances between order and chaos through the perpetual organization of disproportionate causality.  According to the fine artist and designer, Maitland Graves, “the rectangle is used to organize proportion in relation to the surface division of two-dimensional spaces (231).  The conception of size or measure is relative, because it is impossible to comprehend one magnitude except in comparison with another” (232). 

The relative magnitude of proportion within the golden rectangle is similar to the complexity of behavioral patterns in groups.  One of the key characteristics of complexity is emergence, a process in which groups organize themselves according to a set of simple rules that have complex results.  This organizational process occurs from a bottom-to-top hierarchy that causes all members of the group to follow rules relative to their neighbors.  Examples of emergence can be seen in schools of fish, flocks of birds and even crowds of people.  Altogether, the behavior of the whole is beyond the sum of its parts (Larter, “Emergence: Complexity from Simplicity”). 

This complex group dynamic depicted the type of movement that I experienced during the election.  Watching communities coming together on all levels and merging various subjectivities into a greater, more inclusive whole allowed me to picture a complex hierarchy in which top and bottom were in constant motion due to the relationship between different magnitudes of proportion.

After carving out the surface of each panel, I could see the elements of unitary measurement and complex form coming together to create a territorialized, topological surface (see fig. 2).   The juxtaposition of the grid with complex interlocking forms created a subtle bending that pushed each unit into a flux of concavity.  Akin to sculpture, this effect increased with the varying degrees of perspective from which one viewed the surface, particularly when the paintings were presented face-up on the floor.  I imagined myself as René Descartes draping a gridded handkerchief over one of Mandelbrot’s fractals and watching a vast terrain of complex levels shift through space.  

Figure 2

Although the planar excavations had provided a complex movement via a metaphorical contrast, the sense of hierarchy was still yet to be defined as a transitory relation of territories.  To show uplift, I needed to ascribe quantities of color to the territories.   Having studied the color field painters of the 1940s and 50s, I knew that certain relationships of colors had the qualitative effect of “pushing and pulling” illusionistic space.  Therefore, I could pull the deepest excavations into the foreground, while pushing the most immediate surfaces into the background.  The play between illusionistic and visible space created the “optical flicker” that was necessary to form a paradoxical fluidity within the prescribed hierarchy and thus depict change. 

My final decision was to present the pieces face-up on a floor pedestal.  In Elizabeth Grosz’s Chaos: Cosmos, Territory, Architecture, she defines the floor as a primeval architectural plane in which the earth becomes foundationally organized by horizontal demarcations of territory that explore the expressions of movement under gravity (14).  In applying this concept to my work, I have challenged the notion that a painting exists authoritatively on the wall – that in fact, it can function on any plane to address flatness within every spatial paradigm.  I approach flatness the same way that Benoît Mandelbrot understands the second dimension: that in essence it is an illusion created by distance and a lack of perspective (Gleick 97).  Essentially, I argue that every painting has a sculpted surface – it is merely a matter of visible thickness within the layers of paint.  Carved substrates simply exploit the surface to push the paint into visible dimensions of “roughness”.

My Postmodern Landscapes specifically address the hierarchical (top/bottom) movement of territory interwoven within the paintings’ depth that is experienced on the floor plane.  Further, the paintings’ sculptural surfaces create topological shifts that change with the angle from which the works are viewed.  This, in turn, changes all the relativities of contrast within the painting, placing emphasis on the viewer’s subjectivity as the means through which the world is experienced.

Ultimately, I am pleased that my work has embraced a more flexible approach to empirical knowledge.  As long as the world is alive, moves and changes, the concrete will always be in a state of question.  I believe formal method can only smooth the surface until uplift unleashes fractures of complexity that both obscure and elaborate on the nature of the whole. 

Works Cited

Gleick, James.  Chaos: Making a New Science.  New York: Penguin, 1987. 

Print.

Graves, Maitland.  The Art of Color and Design.  New York: McGraw-Hill Book

Company, 1951.  Print.

Green, Thomas.  Vector.  contracosta.edu.  Thomas M. Green.  30 Apr. 2010.  Web.  10

Dec. 2012.

Grosz, Elizabeth.  Chaos, Territory, Art: Deleuze and the Framing of the Earth.  New

York: Columbia University Press, 2008.  Print.  

Larter, Raima.  “Emergence: Complexity from Simplicity.”  raimalarter.blogspot.com. 

Raima Larter.  6 Feb. 2012.  Web.  10 Dec. 2012. 

Zoe Shulman

Professor Katharine Kindervater

Linear Perspectives

7 May 2012

A Discourse on Artistic Process and Linearity

In Discourse on the Method for Conducting One’s Reason Well and Seeking the Truth in the Sciences, René Descartes wrote about the importance of learning through travel:

As to false doctrines, I thought I already knew well enough what they were worth, so as not to be liable to be deceived either by the promises of an alchemist, the predictions of an astrologer, the tricks of a magician, or the ruses or boasts of any of those who profess to know more than they do… That is why, as soon as age permitted me to emerge from the supervision of my teachers, I completely abandoned the study of letters.  And resolving to search for no knowledge other than what could be found within myself, or else in the great book of the world, I spent the rest of my youth traveling. (5)

Last semester, I packed my bags and left for Burren, Ireland to study by myself.  Upon my arrival, I was both mystified and overwhelmed by the frequent ecological contrasts that I observed within the landscape.  Turbulent weather transitions of rain, wind, hail and mist perpetuated the mystery of immense stone hills, vast green pastures and churning seas.  In a rush of excitement, I became inspired to explore the obscurity within this unfamiliar world.

My first endeavor was to gain my bearings within the environment by investigating the Burren’s unique sense of time.  With all the fluctuating rates of change in the weather, it was difficult to see things with any degree of consistency.  Therefore, I set out to understand these fluctuations by going on a hike and trying to map out my experience in some measure of intervals.  My hike took me to the top of Mullaghmore Mountain in the Burren National Park.  Taking pictures along the way, I was able to stop time and notice the angular transitions of the sun in relation to the sinking horizon through a progression of frames.  At the summit, I reclined in a patch of grass and felt the stillness of the sun beaming directly above me.  A blissful duration of present tense set me at ease, and for a moment, life seemed to pause.  After my descent, I studied my photographs and drew Perceptual Lapse.         

Perceptual Lapse, Graphite, 8” X 4.5’, 2011

Using geometry, I ordered my experience into a progression of linear elements.  Like a filmstrip, the composition divides the ascent and descent into units of squares that describe a passage of time.  Using angles, transparency and value contrasts, I conveyed time as an inconsistent variable in relation to the perceptual experience.  At the summit, time became cairological as I gazed out at the ethereal horizon.  In creating this drawing, I balanced myself to a more flexible rhythm that could unify the junctions of different times. 

As Michel Serres said in Method:

Just as in space we situate ourselves at the center, at the navel of the things in the universe, so for time, through progress, we never cease to be at the summit, on the cutting edge, at the state-of-the-art of development.  It follows that we are always right, for the simple, banal, and naïve reason that we are living in the present moment.  The curve traced by the idea of progress thus seems to me to sketch or project into time the vanity and fatuousness expressed spatially by that central position.  Instead of inhabiting the heart or the middle of the world, we are sojourning at the summit, the height, the best of truth. (48)

As blissful as the present tense was, I did not remain at the summit.  I drifted through times, converging with prehistoric glacial erratics and 6,000 year old tombs.  I learned of the natural ecology and began to understand the gestalt behind its interconnected balance of changing elements.  For example, I observed how underground networks of turloughs fed ground water to various valleys at different times, causing plant and animal migration.  From this, I imagined the external world as a dialectical whole in which a relationship of order and chaos was occurring throughout the micro and macro that could not be defined by a static summation of parts.  In reflecting on this inquiry, I have come to realize that I was noticing complexity in nature. 

An excerpt from Stuart Kauffman in From Grid to Network discusses complexity: “For what can the teeming molecules that hustled themselves into self-reproducing metabolisms, the cells coordinating their behaviors to form multi-celled organisms, the ecosystems and even economic and political systems have in common?  The wonderful possibility… is that on many fronts, life evolves toward a regime that is poised between order and chaos” (qtd. in Taylor 7).  I was excited that my newfound trust in geometric structure had allowed me to organize and make sense of contrasting relationships.  I wanted to continue my inquiry by looking at the functions of various geometries.  What structure could I use to describe this phenomenally complex movement of time and matter? 

With some research, I discovered a fractal called the golden rectangle (see fig. 1).  In aesthetic design, the golden rectangle is defined as a unity of shape and variety of proportion, meaning that it can be divided into an infinite progression of self-similar parts.  As a result of self-similarity, the rectangle balances between order and chaos through the perpetual organization of disproportionate causality.  The rectangle’s numeric pattern, known as the Fibonacci sequence, can be found in nature.  Complex systems like the nautilus shell, sunflowers, human bodily proportions, tree limbs, snowflakes, cloud formations, heartbeats, forest growth patterns…etc. all share the Fibonacci sequence.  I had a thought: If all these natural complexities correlate with this sequence, then is it possible that the rectangle could describe complexity?

Figure 1

Historically, the golden rectangle has been used as a tool of divine measurement since the Ancient Egyptians.  From the Great Pyramids of Giza to Leonardo Da Vinci’s Vitruvian Man, the rectangle has been used to describe humankind’s sacred connection to perfection and the infinite (Graves 231).  It wasn’t until the modern era that the rectangle departed from cultural formalism in search of a more objective meaning.  In modern art, scientific advancements in the understanding of movement, space, light and color led to a more quantified method for applying design and color theory.  According to the modern fine artist and designer, Maitland Graves, “the rectangle is used to organize proportion in relation to the surface division of two-dimensional spaces (231).  The conception of size or measure is relative, because it is impossible to comprehend one magnitude except in comparison with another” (232). 

The relative magnitude of proportion within the golden rectangle is similar to the complexity of behavioral patterns in groups.  One of the key characteristics of complexity is emergence, a process in which groups organize themselves according to a set of simple rules that have complex results.  This organizational process occurs from a bottom-to-top hierarchy that causes all members of the group to follow rules relative to their neighbors.  Examples of emergence can be seen in schools of fish, flocks of birds and even crowds of people.  Altogether, the behavior of the whole is beyond the sum of its parts (Larter, “Emergence: Complexity from Simplicity”).

With this knowledge, I used the golden rectangle as a compositional structure for the Tabula Rasa paintings.  From bottom layer to top layer, I began to chaotically define and relate various proportions of contrasts within the rectangle, each decision influencing the next to create a dialectical whole.  Aesthetically, the complex interplay of polarities within the paint began to create a sense of unexpected balance – complimentary colors, wild and conservative strokes, organic and geometric shapes, rugged and shiny textures all layered together in a topography of organized chaos. 

The Tabula Rasa Series, 1’ X 1’ (each), Mixed media, 2011

Departing from complexity, I returned to linearity and began to wonder how order and chaos could function in relation to the bodily space within the external world.  In my final project, (In)Decision Within the Perimeters of Order and Chaos, I approached my inquiry through the medium of interactive performance, bringing it into real time and space.  Shelving the golden rectangle, I decided to change my compositional structure and isolate the most basic forms of order and chaos into a linear design.  Using two squares, I created a simple (linear) maze and a void.  The maze presented a structure of order that dictated the decisions made within the space, while the void presented a structure of chaos, leaving the viewer to make decisions within the realm of nothingness.  To create these spaces, I taped out the demarcation of the maze and void on the floor.  As the performer, I nonverbally moderated the relationship between the viewer and the spaces by using a flag as a destination marker to blur the line of authority within the decision making process.

My work does not claim to show empirical data of human behavior, as it was a performance and not an experiment.  However, the power of performance is that it explores the possibilities our concepts have in relation to the external world.  In looking back on my video documentations of the event, I couldn’t help but recognize how the illusion of rules affected the viewer’s perception of authority.  I noticed a correlation of obedience occurring within the simple maze and hierarchal conflict occurring within the void.  In some cases, the viewer obeyed the rules and walked perfectly within the boundaries of the maze to the destination marker.  In other cases, the viewer played capture the flag and fought for dominance.  Overall, there was an overwhelming presence of order within both spaces.  Even within the void, a conflict of dominance created an establishment of hierarchy and order.  

(In)Decision Within the Perimeters of Order and Chaos, Performance, 2011

“[The Panopticon] is a type of location of bodies in space, of distribution of individuals in relation to one another, of hierarchal organization, of disposition of centres and channels of power, of definition of the instruments and modes of intervention of power…”  (Foucault 205).  Like the Panopticon, my linear design presents an illusionistic arrangement of space that influences the ways in which the viewer responds to authority.  Without physical boundaries, however, the responsibility of creating order rests in the actions of the viewer.

Altogether, my artistic process demonstrates a range of different interpretations of linearity and their consequences.  Working through these concepts has brought me into a rich intellectual and personal experience of the mechanics of the external world.  By quantifying what is relative to my perspective of reality, I have been able to measure myself against time, complexity, order, and chaos.

Works Cited

Descartes, René.  Discourse on Method.  Indianapolis: Hackett Publishing Company,

Inc., 1998.  Print.

Foucault, Michel.  Discipline and Punish: The Birth of the Prison.  New York: Random

House, Inc., 1995.  Print.

Graves, Maitland.  The Art of Color and Design.  New York: McGraw-Hill Book

Company, 1951.  Print.

Larter, Raima.  “Emergence: Complexity from Simplicity.”  raimalarter.blogspot.com. 

Raima Larter.  6 Feb. 2012.  Web.  7 May 2012.

Serres, Michel.  Conversations on Science, Culture, and Time.  Michigan: University of

Michigan Press, 1995.  Print.

Taylor, Mark.  The Moment of Complexity.  Chicago: The University of Chicago Press,

2001.  Print.

Images

Green, Thomas.  Vector.  contracosta.edu.  Thomas M. Green.  30 Apr. 2010.  Web.  7

May 2012.

Please note: All images of artwork were taken by the author.