Donovan Barfield
Complexity from Simplicity
Symmetry is ubiquitous in nature. From the spiral arrays found in flowering plants to the very molecules composing the air we breathe, this phenomenon pervades almost everything - often with deep implications that tend to be overlooked in many core science classes. Over the course of my experience in TSR, I have looked deeply into this mathematical property and learned a great deal about how symmetry can be used to establish parameters for chemical bonding. As a biological chemist interested in synthesis and drug design, I have found this study to be an extremely valuable complement to the knowledge I have gathered in the chemistry curriculum and the hands-on experience I have gained through lab research. Equally valuable, however, is the chance I have been given to communicate some of this newfound knowledge through the universally accessible medium of art. I feel too often some of the most powerful insights into nature are hidden behind the veil of numbers and equations, and thus many people turn away from valuable mathematical discussions due to apparent surface complexity. By packaging this mathematical language into the visual medium of time-lapse photography, I sought to show how complex symmetries (integral to the understanding of molecular point groups) can be generated from a very small set of linear transformations. This, in essence, became the heart of my project (piloted under the banner Complexity from Simplicity), and I chose the artistic medium of string art to accomplish my goal. I began working on the project in January 2012, and after well over 100 hours of planning and construction, was able to produce the final product. In the following discussion, I reflect on the process of building this large-scale sculpture from scratch with attention to successes, shortcomings, and advice, so that others interested in this medium may have a foundation on which to expand this engaging form of visual art and think about the creation of beautiful symmetries.
Choice of Geometry – The Limitations of String and Wood
To begin, allow me to describe how the inner-geometric figure was created by only a few simple matrix transformations. Tying a single string from one node to its opposite partner, I defined the angle and length of a line segment in 3D space. By fixing a point in the center of the segment and applying a series of rotation operations along a square base, the familiar figure of an hourglass was made along one axis. Repetition of these operations along mutually orthogonal axes led to the complex figure seen in the display.
This choice of geometry was deliberate and only settled upon after hours of experimenting with at least ten different patterns. When I was first deciding which geometric figure I wanted to string for the project, I did all my prototypes on paper, and therefore ran into a problem when I began to translate the art into a 3D medium. The difference between line segments drawn on paper and line segments defined by string is (what now seems obvious) that string cannot run through other strings, contrary to the infinite number of intersections that can be drawn by hand. The medium itself creates a physical barrier, thus creating an upper boundary on the types of figures that can be created in three dimensions. A good illustration of this principle is the “knot” present at the intersection of the six square pyramidal lobes. On paper, this would appear as lines collapsing perfectly into a singularity, whereas in reality, the bundles of red, black, and yellow string had to rest intertwined in a trifold twist. The figure I wanted to put on display needed to minimize these bundles, and in choosing the square pyramidal motif, I could keep this overlap to a single case that would not be distracting to viewers.
Secondly, I also had to consider I was working with wood as my frame – a highly rigid medium that limited the number of conformations into which I could shape the outer boundaries of the display. Circular patterns became nearly impossible to craft from linear segments of wood, and higher degree polygons (pentagons, hexagons, etc.) also became difficult due to the structural instability caused by not having the wood meet at orthogonal angles. I quickly settled on the fact that frame I was going to build would need to have all segments of wood meeting at right angles. To provide the proper orientation of nodes for the square pyramidal motif, I constructed “window panes” within each face of the cube. This structure proved a prudent choice, as the structural support beams on the panes added rigidity to the twelve beams comprising the outer edges of the cube. Because the dimensions of the cube measured 4’x4’x4’, the outward-pointing force vectors of the window pane beams helped maintain the cubic configuration and ultimately were necessary to minimize slant motions of the frame during construction.
The Agony and the Ecstasy – Transforming 64 Cubic Feet
As pattern-seeking mammals, humans are capable of picking up small changes that interrupt otherwise fluid designs. This fact, combined with the high degree of symmetry in the final project, meant that I would have to be extremely careful with every string and screw I placed into the design. With over 1,500 screws, 3,000 feet of string, and a picture that had to be taken for each string placed in the design (for the time lapse video), this amounted to long hours of meticulous work and thinking through problems not immediately apparent at the onset of the project. In the discussion below, I highlight two of these problems that required special attention to detail.
When I began working on stringing the corner pattern of the cube, I encountered an issue that had not arisen while crafting the center geometric figure. Because each triangular section of the corner was strung using a single red thread (as opposed to individual threads for each node-to-node step of the center design), the rotational orientation of the thread around each screw became important. This means that I could not just wrap the thread around each screw clockwise or counterclockwise, but had to make a choice to keep the pattern consistent. For example, when working on the triangular corner motif, the top row of screws had to be wrapped clockwise and the vertical column of screws wrapped counterclockwise (or vice versa), otherwise the width of the screw would split each line into two non-overlapping lines. By maintaining this pattern of opposite pairing, the string would overlap itself, thus giving the appearance of a single thread for each node-to-node function.
Another issue, and probably the most difficult task of the project, was the attempt to keep the height of the screw constant when placing the nodes for the points of string attachment. Because screw placement in all took around 40 hours, the power output of the drill was not constant as its battery life diminished, and thus I had to use sight approximation from node-to-node to keep height constant. Unfortunately, this is not quite as easy it might sound, and the placement of 48 screws in a row (one screw per inch over four feet), proved to be taxing to get all points equal height from the wood. Throughout the work, I strove to keep the point of string attachment at a height of one inch from the wood for all screws placed in the project in order to maintain the greatest possible degree of symmetry. Looking back on the work, one idea I might have tried would have been to vary the height of paired corners, making the height of each partner corner (across the hypotenuse) different. This would have led to a greater variance in 3D shape along the frame of the display and might have resulted in some visually stimulating patterns that I did not explore.
Learning to Adapt – Experimentation with Music
Perhaps the most important lesson I have learned in my undergraduate experience at Stanford is to be able to adapt to change, even when the cost is high. The original plan for this project vs. the final product indeed pays homage to this maxim. When I started making the time lapse video for this project, my plan was to explore the theme of complexity from simplicity both through sight and sound, by pairing the visual aspects described in the above discussion with the musical style of chorale and variations. A chorale and variations is a musical form in which one begins with a simple melody and then grows the tune through runs and variations to a piece of full classical complexity – seemingly the perfect style for the intended goal of my project. Having played classical piano for sixteen years, I began with this part of the work and decided I would pair the visual aspects with my music later on during the project.
The amount of time I spent on the music is not calculated into the total number of hours I spent on the project, otherwise the number would be quite large. During winter break, I spent hours each day composing a piece that I envisioned would fit well with the pictures I would later take as I constructed the 3D string art sculpture. I cannot stress enough how much I wish I had reversed the order in my creative process. After I had all the images I needed for my video, the pairing of my composed music was out of place with the images. The white cloud-like setting in which the project was constructed fit much better with peaceful, soft tones than the driving sounds of the variations I had built into my chorale and variations. To see what I mean firsthand, I suggest you view the final time-lapse video in the first link below, and then listen to my composed piece in the second link.
Final Time Lapse Video:
http://www.youtube.com/watch?v=qkV3uCtwbEo&list=UUcGDy3bIa6sqZTPWkMOkC3g&index=1&feature=plcp
Original Composition for Time Lapse Video:
http://www.youtube.com/watch?v=ZCH20tSjqts&list=UUcGDy3bIa6sqZTPWkMOkC3g&index=3&feature=plcp
Thus, I was faced with a choice – abandon the hours of work I had poured into my music for a more complete final product, or stay with the original composition to have every last detail of the work be my own. While the second option was more appealing to my pride, I ultimately decided to consider the time I had invested in the music sunk costs and to search for more appropriate music for my video (ultimately choosing Yann Tiersenn’s version of Comptine D'un Autre été). Decisions like this are difficult to make, but in the end I was satisfied with the result and proud of my ability to adapt to the situation.
Future of the Project (and Me)
As I am preparing to graduate from Stanford next week, I am looking for a place on campus to leave the project. As a double major in chemistry and biology, I would like to donate the project to either of the departments (depending on which has more space) to give back for a truly outstanding education in the sciences. Given the large size of the project and limited space in the offices, however, I would also be willing to donate the sculpture to the Art Gallery or Cantor Arts Museum and allow the administrators to decide the most appropriate location.
To close, I will leave a note about what I am planning to do in the future and how this project on symmetry is relevant to my career. For the next four years, I will be studying medicine at the University of California, San Francisco School of Medicine with the intent of specializing in neurosurgery. My research interests are in drug design for neurodegenerative disease, and an understanding of molecular symmetry is critical to designing efficient syntheses. Just to give one case example, by designing molecules with a symmetric core, branching syntheses can be carried out quickly, and by integrating this approach on a solid support, asymmetry (and thus differential reactivity) can be introduced in the final steps.
This project has thus given me a lot of time to think deeply about symmetry and has helped put me in a frame of mind to work, iterate, make difficult choices, and adapt. These are the critical skills required to be a good physician and an efficient researcher and will serve me well in the next chapter of my life.