Week 1_Origami, Golden Ratio, and Art-Science Coexistence by Cheng-Kuang Liu

Indeed the bias between “the two cultures” as described by C.P. Snow still exists in the society today. Stereotypically, scientists’ and engineers’ works are deemed “useful” and “practical,” while those of writers and artists are considered “romantic,” with the connotation, “unrealistic.” (I may have spoken with the scientific bias, since I study engineering) These two fields seem to separate like oil and water, with neither hope nor intention to mingle with one another. Despite all the misunderstanding, art and science can and do coexist harmoniously.

Since childhood, I have always been fascinated with origami, a Japanese paper-folding art. Throughout my academic pursuit, it grew increasingly evident that I will devote to the field of science and engineering, but my passion for origami never diminished. In fact, in this world of folding paper squares, I find a wondrous universe of mathematical and scientific principles—angles, dimensions, strength. This also laid a foundation for my interest in geometry.

Through the internet, I found websites of many who share the same interest as I. One of the most impressive artists is Brian Chan (note 1), a Mechanical-Engineering student at Massachusetts Institute of Technology. He employs his technical expertise and robust physical intuition to create astonishing designs that readily blow traditional origami away. More over, he insists on using “single uncut square,” which is the Holy Grail of what many conservative origami purists consider “true origami” and is much more challenging than its alternatives. From a plain square sheet, origami artists like Brian Chan create unfathomable galaxies of wonder—simple yet extremely complex, static yet dynamic, rigid yet elegant (http://blog.makezine.com/upload/2008/04/080414_origami.jpg, http://neatorama.cachefly.net/images/2006-02/gabriel-origami.jpg, http://chosetec.darkclan.net/origami/cannabis/).

Interestingly, while the nature of origami is mechanical, with straight lines and rigid angles, most origami designs revolve around nature, where there are hardly any straight lines. Some artists do fold vehicles and instruments, but most artists I encounter make animals, plants, and even mystical creatures. Perhaps intuitively these artists realize the true beauty that lies within the vast creation, and they instinctively attempt to imitate it. On the other hand, while it appears to be an art with nothing to do with technology, origami finds practical engineering applications, the grandest of which may be the folding pattern of the reflective plate on a satellite (note 2).

As an extension of my interest in geometry, another topic appears to tickle my fancy: golden ratio. It is a magic ratio ubiquitous in nature and pervasive in many significant art works, including “Mona Lisa” and the Egyptian pyramids. Some people even go so far as saying that this ratio defines beauty. To me, the charm of this ratio originates from the infinity encased within this simple yet mysterious shell: its exact mathematical form is 2 : 1 + (5)^(1/2), which can be obtained from a continued fraction form or a continued square root form, both of which forms are infinitely repeating. The golden ratio constructs the golden rectangle, a shape that can be infinitely reproduced by repeatedly removing square portions. This infinite self-replication of a golden rectangle helps construct an infinite spiral, which bears stunning resemblance to the cross section of a conch (http://personal.denison.edu/~karian/goldensection/images/GoldenM.jpg). A manga (Japanese comic) even incorporates the concept of infinite spiral into its plot, expanding the idea with remarkable imagination. Strikingly, something defined mathematically finds its place in the most elemental form of art and fantasy.

Art and science, science and art, these two seemingly opposite sectors of society can actually be reconciled in a harmonious union. Whether it is art applied in science or science applied in art, it just illustrates that art and science are not mutually exclusive, but alternative manifestations of human intellect. There needs not be more segregation and misunderstanding from one to the other, but there needs be embracing and integrating of the two for their fullest development.

Note 1: http://chosetec.darkclan.net/origami/

Note 2: http://web-japan.org/trends/08_sci-tech/sci080303.html

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