Week 2 - Math + Art

Although art is perhaps one of the most diverse things ever invented by human beings, many branches of it try to present a precise view of the real or imagination world of artists to people. To reach such precision, artists must conform to patterns and rules by which human eyes perceive the world. Mathematics is designed exactly for this reason – to precisely describe patterns, rules and relationships of things in the world. Among all the tools developed and adopted, the technique of perspective is truly a milestone in the history of art. Proposed by Muslin mathematician Alhazen, perspective formulates how three-dimension objects should be put on the canvas according to their relative position and size. (Vesna, “Lecture …”) It is the perspective rules that makes drawings look “real”.

While artists create precise drawings of objects using tools like perspective, they also like to jump out of the box and think of something abstract or innovative. For example, the fourth dimension is a popular concept that artists extend. Although inspired by the idea in math and physics, artists tend not to replicate mathematicians’ and physicists’ interpretation exactly. Instead, they add flavors to it. To some of the artists like Duchamp, the fourth dimension is a lever for him to jump across the bar set by the real world to create abstract artworks. (Henderson, “The Fourth …”) Another artist in 1970s, Tony Robbin, also makes a similar points when he says

Artist who are interested in four dimensional space are not motivated by a desire to solve mathematical problems. We are motivated by a desire to complete our subjective experience by inventing new aesthetic and conceptual capabilities. (Robbin, "The New ...")

Figure 1: Drawing Hands by Escher

https://upload.wikimedia.org/wikipedia/en/b/ba/DrawingHands.jpg

Figure 2: "GEB" Book

http://ecx.images-amazon.com/images/

I/4193iI6WHqL._SY344_BO1,204,203,200_.jpg

This creates an interesting relationship between science and art. Art uses scientific methods as a tool, but is not limited by science. Usually, art shows innovative representations of scientific ideas. My favorite artist, Escher, perhaps many computer scientists’ favorite as well, created many drawings in close relation to concepts in logic and computer science. The drawing Drawing Hands visualizes the idea of mutual recursion; the left hand is drawing the right hand while the right hand is drawing the left hand. This idea can also be represented in code. Consider the following C code, if someone calls either of the two, the program will not terminate. This concept, named Strange Loop by Douglas Hofstadter, is explained in detail in his Pulitzer-awarded book Gödel, Escher, Bach: An Eternal Golden Braid. I recommend this book to all of you.

void draw_left_hand() {
    do_draw_left_hand();
    draw_right_hand();
}

void draw_right_hand() {
    do_draw_right_hand;
    draw_left_hand();
}

Listing 2: Mutual recursive functions

Gödel, Escher, Bach: An Eternal Golden Braid is a perfect illustration of the juxtaposition of art and science. In the book, the author discusses one conceptual pattern – iteration and recursion – with different realizations in different subjects. We have seen Escher’s work. Hofstadter also covers the techniques of round and canon in music, the problem of self-reference in mathematics, and program language parsing in computer science. For me, it is rewarding to examine an abstract idea in different ways. This intellectual diversity constructs the beauty of the cosmos.

Bibliography

D. Hofstadter. Gödel, Escher, Bach: An Eternal Golden Braid. 1979. Print.

Robbin. "The New Art of 4-Dimensional Space." 1977. Print.

L. D. Henderson. "The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion." 1984. Print.

V. Vesna. DESMA 9 Lectures on Math + Art. 2016. Video. Accessed 04/08/2016.