Sunday, June 26, 2016

Week 1 (Unit 2): Math + Art

In this set of lectures, I've been reintroduced to what happens when mathematics and art collaborate in both nature and human creations.

According to Wolfram MathWorld, the golden ratio, one of many examples of the prominence of mathematics in nature, is a "number often encountered when taking the ratios of distances in simple geometric figures". In art and in nature, the golden ratio embodies the 'perfect' proportions of an image. For example, in nature, the ideal positioning of flower petals to absorb the most sunlight is a factor of the golden ratio, and the number of petals is always a Fibonacci number. Similarly, artists commonly use this mathematical concept to create an aesthetic appeal in their pieces. Michelangelo applied this over a dozen times in the Sistine Chapel. Along with other aspects of the paintings, the hands of figures are pointing directly at golden ratio points. Thus, Michelangelo's use of the golden ratio in various parts of the paintings allowed him to subtly create an image that visually draws in viewers.

An example of the golden ratio in Michelangelo's "Drunkenness of Noah" painting of the Sistine Chapel

What is it about classical music that makes it so soothing to listen to? The use of mathematics in music creates an arrangement of tones and harmonies that appeals to listeners. Several composers have used numbers to create musical masterpieces that have endured to this day. German composer Ludwig van Beethoven laced many of his pieces with numerical patterns and symmetry. In music, three notes played as a third is called a 'harmonic triad'. The YouTube video below demonstrates how Beethoven applies this concept to create the soothing melody of one of his most famous pieces, "Moonlight Sonata".

Video that demonstrates mathematics in Beethoven's "Moonlight Sonata"

I find the idea of perspective to be the most intriguing combination of mathematics and art. Italian Renaissance artist and architect Leon Battisti Alberti describes an image as "the intersection of a visual pyramid at a given distance with a fixed centre and a defined position of light"; in other words, art may require the use of geometric methods to create a realistic visual effect. That intersection, also known as the vanishing point, was introduced during the Renaissance by Filippo Brunelleschi and still continues to dominate art today. In modern art, this concept can be applied to create a three-dimensional effect. One impressive example is a trend known as '3D Street Art'. Artists attempt to create the illusion of more than just an asphalt surface. Similar to the paintings of the Renaissance, objects closer to the viewer seem larger while images farther away seem to disappear into a point in the horizon.

Left: Artist Edgar Mueller draws lines that converge towards a point at the bottom of the image
Right: "The Crevasse" is a massive 3D street painting that looks like a large opening into the ground.
Bottom: This video is a time-lapse of the creation of the painting.

Overall, this unit has revived my interest in the combination of art and mathematics. It has compelled me to more closely analyze the details of paintings and music and find out what makes them so visually and auditorily appealing. Through the recommended readings, I have discovered several more instances of mathematics and art that I had not noticed before. Put simply, the balance that mathematics and art creates is absolutely mind-blowing.


Frantz, Marc. Lesson 3: Vanishing Points and Looking at Art (2000): 2-11. University of Central Florida College of Engineering and Computer Science, 2000. Web. Accessed 25 June 2016.

Meisner, Gary. "Golden Ratio in Art Composition and Design." PhiPoint Solutions, LLC, 2014. Web. Accessed 25 June 2016.

Mueller, Edgar. The Crevasse. 2008. Ireland. Edgar Mueller. Web. Accessed 25 June 2016.

Sautoy, Marcus Du. "How Composers from Mozart to Bach Made Their Music Add up." The Guardian. Guardian News and Media, 2013. Web. Accessed 25 June 2016.

St. Clair, Natalya. "Music and Math: The Genius of Beethoven." TED-Ed. TED CONFERENCES, LLC, 2014. Web. Accessed 25 June 2016.

Vesna, Victoria. DESMA 9 Lectures on Math + Art. 2016. Video. Accessed 24 June 2016.

Weisstein, Eric W. "Golden Ratio." MathWorld. Wolfram Research, Inc., n.d. Web. Accessed 24 June 2016.

Friday, June 24, 2016

Week 1 (Unit 1): Two Cultures

The idea of two cultures has been prominent in both my academic life and my personal life.  I am from a traditional Chinese family; though my parents encourage artistic ventures, such as piano and art, ultimately, they prefer that my career choice be based in some technological field.  My academic life has revolved around math and science, which contributed to my decision to become a computer science major.  However, being in this major has also opened new opportunities to explore the artistic world as well.

This week's topic has encouraged me to look deeper into the relationship between art and science.  In my opinion, computer science serves as an intersecting point between the two disciplines in modern society.  In a TedxTalk, Cole Wiley, an artist and a software engineer, claims he did not start "making real strides in either until I started mixing them together."  He describes several of his projects, including "new media art and interactive installations" (Wiley).  I believe this type of work is a clear example of the rising 'third culture', a term coined by C.P. Snow and described in John Brockman's The Third Culture.

TedxTalk - Cole Wiley on "The creative interface: connecting art and computer science"

I am especially interested in the video game industry.  The founders of Blizzard Entertainment, home to many major online games such as World of Warcraft, were all engineering majors at UCLA.  Their work in computer science and electrical engineering led to the creation of entire virtual worlds with elaborate character and background design.  Some may say this is the result of scientists working with art while others may say this is from artists working with technology.  Overall, this reflects the type of work that has resulted in "freedom to reinforce the delicate bridge" between art and science (Vesna 122).

2015 'Legion' expansion of the World of Warcraft game

As mentioned in Professor Vesna's lecture, the idea of art and science as two separate areas is relatively novel.  However, though people's mindsets are changing to accept the two disciplines as one again, the merge is made difficult by existing stereotypes, hence the analogy of a "delicate bridge" (Vesna 122).  C.P. Snow makes note of such stereotypes, claiming "they have a curious distorted image of each other" (Snow 4).  From a young age, children are already engrained with the contrasting images of the 'scientist' and the 'artist'.  This mentality will influence them in their academic lives and future careers by dictating how they view the choices for their future.  From personal experience, I find this mindset to be very dangerous to the development of their later interests and ambitions.  Therefore, I believe that the modern education system is in dire need of some reformation.

A depiction of the stereotype of scientists being left-brained and artists being right-brained


Graham-Rowe, Duncan. "John Brockman: Matchmaking with Science and Art." WIRED UK. 2011. Web. Accessed 22 June 2016.

Snow, Charles Percy. Two Cultures and the Scientific Revolution. 1964. Print.

Takahashi, Dean. "Blizzard CEO Mike Morhaime on the Last 25 Years of Games — and the Next 25." VentureBeat. 2016. Web. Accessed 22 June 2016.

Vesna, Victoria. "Toward a Third Culture: Being In Between." 2001. Web. Accessed 22 June 2016.

Vesna, Victoria. DESMA 9 Lectures on Two Cultures. 2016. Video. Accessed 20 June 2016.