Week 2: Math + Art

As a senior majoring in applied mathematics, I am more sensitive and experienced than others in the connection of mathematics and other subjects, and because of imbuing in mathematics for years, I know math well as art for a long time. Being well known by me, things like Babylonian sexagesimal number system and the golden ratio had became common sense through my math study and daily exercise. However, what exited me today is a new insight beyond the application of mathematics knowledge as a tool, but that art can be driven by mathematics through some ideology or concept directly.

"Composition No. 10" (1939–42), oil on canvas. Fellow De Stijl artist
Theo van Doesburg suggested a link between non-representational

works of art and ideals of peace and spirituality.

Just as professor Victoria shows us how “Piet Mondrian believed in mathematic, simple geometrical shapes, and primary colors that could be used to express reality and nature and logic,” this revolutionary point of view exemplifies that mathematics bridges new ideology in artists’ minds. The analysis of the art progression from the fourth dimensions by Henderson gives me a more thorough walk through the development or “update” of modern art ideology: with artists’ improvement in their understanding of the new mathematical concept and its function to help to build people’s deeper or newer knowledge of the world, new doctrines alternates the old. Also, the interesting work flatland insinuates the hierarchy of Victorian culture with the aid of geometry knowledge: the properties of different geometrical shapes clearly and effectively transits the humanity and social nature, and successfully endows the artwork with not only artistic charm but also political significance. For all mentioned above, I found a common straightforward transition of mathematical ideology to artistic ideology. As M.C. Escher suggests, the mathematical theory is not exclusively mathematics question. "[Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it." But artists can see through the gate, the mathematics, and enjoy the further view of the garden, the art.

The Interstellar bookcase in three dimensions (top)
and then represented spatially in five dimensions (lower).

Similarly, the development of integration of art and mathematics ideology is still evolving. From the classical space view of three-dimensional space, Einstein’s relativity is established on the four-dimensional space consisting of classical space and one more dimension of time, which had inspired artists’ expression of the world through art of new doctrines. Nowadays, artists like Christopher Nolan had already integrated the knowledge of five-dimensional space into his artistic creation. As Nolan explained the reason he showed the five-dimensional space, “Why five? Because if we can get our heads around the idea that time is just a fourth dimension... it should be possible, which lets us imagine a complete understanding of our four-dimensional existence rendered instantly by our new, higher-dimensional perspective. Many of the people and ideas springing from these pages push so hard in this direction (a direction we know exists but cannot visualize) that the limits of our world start to seem a tiny bit more porous than they did.” This is truly the brilliant artistic creation that explains the time reversible paradox, through the mathematical ideology, because it offers us an illustration of the reasonability of time reversibility in a higher-dimension. Just as the two-dimensional moving forward on a three-dimensional Mobius strip seems to be infinite, higher-dimension containing infinite three-dimensional space contains infinite possibilities as well. Therefore, Nolan is great for visualizing the mathematical ideology of higher-dimension to explore our universe with his movie art.

Möbius Strip II (Red Ants) by M.C. Escher; woodcut, 1963

In conclusion, I think mathematics exists and develops as the natural philosophy, and art is just being created and innovated in the pursuit of the same philosophy. For this reason, art and mathematics will and must have the perfect integration, which is how and why I would juxtapose them together with the same origin.

Citations:

Vesna, Victoria. Mathematics, Perspective, Time, Space. 2012.

web. <https://www.youtube.com/watch?v=mMmq5B1LKDg>

Henderson, Dalrymple. "The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion."

Leonardo, Vol. 17.1984. Print.

Abbott, Edwin A. Flatland: A Romance of Many Dimensions. 1884. Print.

Smith, B. Sidney. "The Mathematical Art of M.C. Escher." Platonic Realms Minitexts. Platonic Realms, 13 Mar 2014. Web. 13 Mar 2014. <http://platonicrealms.com/>

Nolan, Christopher. "Space. Time. Dimension. Let's Leap Beyond the Limits of Our World."Wired. 1 Nov. 2014.

Web. <http://www.wired.com/2014/11/christopher-nolan-wired-editor/>.