Midterm Statement
My research inquiry is; how can math and science be used to influence aesthetics and enhance art and design? For my case study, the visual representation I chose is The Great Wave off Kanagawa by Hokusai (Fig. 1). I selected this piece because it is an extraordinarily famous piece of art with several hidden mathematical concepts you might not see at first, therefore it perfectly relates to my research inquiry.
The first mathematical concept that Hokusai was exploring in his work is fractal patterns. Fractals are defined as objects that “possess self-similarity -- that is , the fractal is composed of smaller copies of itself”. Fractals can be seen in many different places in nature, tree branch structures, vein structures, plants and flowers, etc. all exhibit fractal patterns. Hokusai is relating this mathematical concept back to nature and using it to enhance his art making. The wave itself is an example of a fractal. You can see the wave is made up of smaller waves or “the fractal is composed of smaller copies of itself”. Fig. 2 is a detail of the wave in which the fractal structure is clearly shown. The second mathematical concept Hokusai utilizes in this piece is the golden ratio. The golden ratio has been a subject of study for countless artists. Similar to fractals, the golden ratio can be found in many different places in the natural world. The golden ratio is “a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron”. The golden ratio is also a representation of the Fibonacci sequence. The golden rectangle is a rectangle derived from the golden ratio. That rectangle can also be split infinitely and connected with an arc. The relationships between the golden rectangle and spiral have been explored by many artists, including Hokusai. Hokusai used the golden ratio to construct the proportions of the wave (Fig. 3). Hokusai is using mathematical concepts that describe systems in nature to influence his aesthetics and make his art more beautiful. He is also commenting on the fact that simple mathematical concepts can be applied to something so random and chaotic appearing, such as nature.
Irit Rogoff states in her piece, Studying Visual Culture, that “spectatorship as an investigative field understands that what the eye purportedly ‘sees’ is dictated to it by an entire set of beliefs and desires and by a set of coded languages and generic apparatuses”.This image, however, represents a more universal fear. It depicts a group of sailors encountering a huge, crashing wave. Spectators viewing this image will most likely have a similar reaction no matter what their social and cultural contexts are. I think most people will see this as a representation of a natural disaster or rough seas which represent danger to the sailors. The wave is very large in comparison to Mount Fuji in the background, showing that certain things are inescapable. Perhaps, it’s a representation of the inevitability of death in that case. Most people might feel a sense of awe and terror at the force of nature, a feeling of sublime while looking at this piece. The meaning and feeling this piece gives spectators is a universal feeling most anyone can relate to, however cultural and societal context can still influence how a spectator views this image. For example, people familiar with Eastern cultures will recognize the tradition of Japanese woodblock printing and how this piece relates to that tradition. People in Eastern cultures who are more familiar with the concept of Yin and Yang might also recognize the subtle representation of the Yin and Yang symbol in the composition.
When analyzing this piece, I used the principle of Power from Duncum’s Seven Principles for Visual Culture Education. Power, according to Duncum, is all about who has power and how they exercise that power. But in Hokusai’s piece I see a different kind of power. It’s not about humans exerting power over each other, rather it’s about nature being the ultimate power and how it often dwarfs human’s power and some things are out of our control. This concept also relates to Rogoff’s idea of how cultural context changes the meaning because this idea is important in our Western imperialist/ capitalist context because nature should be seen as something to be respected and to coexist with rather than something to be “tamed” or “dominated”.
This piece relates to my inquiry because it shows how math and science can be used to enhance art and design. For my piece, I created an art object (Fig. 4) that looks like an abstract piece but is actually based on a mathematical equation. The equation I explored is Euler’s characteristic. Euler’s characteristic is a formula that can be applied to polyhedrons as well as lines. The equation is as such: V - E + F = 2 (euler). V corresponds to the vertices, E is edges and F is faces. I used a cube as my art object because it perfectly fits this equation. A cube has 8 vertices (or corners), 12 edges, and 6 faces. 8 - 12 + 6 = 2. On each of the sides of the cube, there are lines that look like doodles, these doodles also follow the Euler characteristic. A line that intersects itself at least once in a closed rectangle will always follow this formula (Fig. 5). This applies to all ‘doodles’, even if they are more complex (Fig. 6). The drawings on the sides of the cubes, therefore, all follow this formula. Similar to Hokusai’s piece, my piece is about how things might appear complex and chaotic but they can be described with simple mathematical equations. At first, this just looks like an abstract piece of art but it’s based on a single equation. This relates back to my research inquiry because I am showing how math and science can influence aesthetics and be used to enhance art and design.
References:
Duncum, Paul. "SEVEN PRINCIPLES for Visual Culture Education." Art Education 63, no. 1 (2010): 6-10. Accessed October 19, 2020. doi:10.2307/20694807.
Larry Riddle. "Creating Symmetric Fractals." Math Horizons 24, no. 2 (2016): 18-21. Accessed October 19, 2020. doi:10.4169/mathhorizons.24.2.18.
Rogoff, Irit. “Studying Visual Culture.” In The Visual Culture Reader, edited by Nicholas Mirzoeff, 2nd ed., 24–36. London: Routledge, 2002.
Vogt, Isabel. “An Introduction to the Euler Characteristic.” Accessed October 19, 2020. http://web.stanford.edu/~vogti/EulerChar_PrimesTalk.pdf.
Weisstein, Eric W. "Golden Ratio." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GoldenRatio.html