Order and Chaos: Cage, Rothko, Newman, and Kolkov's Golden Ratio

P.S. I don't know what category to put this in

Recently, I came across a series of paintings made by the composer John Cage. Although he is most famous for his musical works–“the silent song” under the official title 4’33”, and the composition As Slow As Possible that lasts for 639 years–his visual art deserves plenty of recognition, not only because of its unique nature, but because it opens up a larger conversation about harmony and connects back to one of my favorite academic works ever published.

The Sight of Silence was an exhibition of watercolor paintings by John Cage, which he created with a nearly complete reliance on chance. This is a technique he has used to create his music as well, like his composition Music of Changes, in which he left it up to the algorithm to pick the time signatures and chords. Almost every aspect of the paintings was left up to chance. There were many variables–the rocks, which were separated by approximate size and numbers, feathers, which Cage used as paintbrushes, the colors themselves, the space on the canvas–and all of them were randomized by mathematics, a pre-made algorithm that rid the pieces of Human. Except, of course, for the movement of Cage’s hand. As said by Cage himself, “I have to accept what I do.” 

I was shown this video of him creating the paintings in class, and the first thing that was said by my teacher by its end is that this approach to creating art may seem nihilistic. Leaving everything up to chance strips the artwork from the emotional meaning it's made to embody. If there is no human mind making the decisions that lead to the ultimate creation of an art piece, could it even be considered as such? 

This question is more relevant than ever with the presence of A.I. generated artwork (as much as I, truthfully, dislike the subject). While I recognize the validity of the nihilistic perspective, John Cage’s artworks have made the opposite impression on me. Many of his works, musical or otherwise, seem to revolve around the in-betweens of artwork, the beauty of them. Writing a composition where the music is silence highlights the life present between the sounds made by a single musician or an orchestra. Performances of 4’33” in an audience with a coughing viewer or a shattering glass are the most exciting for that exact reason. No moment is ever truly silent. As Slow As Possible also contains a lot of silence due to the nature of how slow it is. A sound is played every couple of months, years even, and the silence in between is the longest “sound” in the composition, containing all the life of society's day-to-day before the next chord chimes. It is no accident that these visual works are called The Sight of Silence and bear a similar message. What this title means is that we are seeing the silence of the artist on a canvas. Every single decision is randomized; an inhuman, automated algorithm with no emotion or experience to draw upon determined the look of these pieces. But every line is made by hand. Every predetermined rock is picked up by Cage’s fingers and placed on the predetermined spot on the paper, with his hand moving the predetermined feather brush to place the predetermined paint on the clean surface. Everything is predetermined aside from the fulfillment of artificial orders by a real human hand. The result is the sight of the artist’s silence.

To me, this is what makes the artwork beautiful. It shows that no matter how automated an art piece gets, there is a human part of it that will always remain. Of course, Cage was working on these paintings by hand–a clear difference from the nearly complete automation of A.I. artworks. However, consider the fact that A.I. cannot be compelled to make art by itself. It does not have the feelings or desires that motivate it to create art. There is always a human hand typing out the prompt, a human voice dictating directions, a pair of fingers creating the code needed for the A.I. to “create” and exist in the first place. There will always be a human element to art. An incredibly hopeful thought.

But another work that The Sight of Silence has reminded me of (and I was not the only person to think this) was the academic work of A.I. Kolkov titled “Harmony and Art.” When discussing The Sight of Silence with my mother, she brought up the paper before I ever mentioned it. Despite the lack of eyes on it, I have never read anything more captivating; Kolkov described his and his team’s process of developing a formula that shows how every self-regulating system, when synthesized, nears a single constant number: 0.380. Kolkov calls this number “The Golden Ratio,” although it does not relate to Fibonacci’s sequence. It is the average of every measure of relative entropy belonging to every aspect of a given system. For example, languages, all of which are self-regulating systems, near the Golden Ratio when considered in their entirety. Languages from completely different families, unrelated in all possible ways, get close to the same index of relative entropy. The same can be seen in nature. Every natural structure, whether that be a tree leaf, a bush, or a drop of water, nears that Golden Ratio. It is the natural harmony of the world. What this means is that a system is most effective not when it is at its most ordered or disordered, but at a certain ratio of order and chaos; and this rule can be applied to absolutely anything in the world. 

Just how beauty and harmony are not created by complete order or complete chaos, art needs to be balanced. Or, rather, a part of it will always be balanced, as it regulates itself through the involvement of a human mind. Knowing this, however, harmony can also be offset to create a truly impactful artwork. Cage has done this job well. In The Sight of Silence, everything seems to be orderly. Those paintings are created with perfect calculation, with an algorithm that obeys the rules of science and pre-made rules instead of human judgement and feeling, and yet there is some chaos–some human nature–in them. Art will always have chaos in some capacity. Although math led the actions of the artist, the stones he traced were provided by a riverside, his brushes were provided by birds and their naturally grown feathers, and his paints were provided from naturally occurring chemicals, his paper by the harmony of trees. That is what makes it so beautiful.

Another two artists that come to mind when I think about the impact of order and chaos in art are Rothko and Newman. There is not a lot of traditional artistic order in their paintings. It’s all shapes and colors with no characters or structure. Despite the seeming simplicity of the paintings, many of them have elicited surprisingly emotional reactions from the viewers, the most striking of which is unease and anger. Newman’s “Who’s Afraid of Red, Yellow and Blue”  elicited a plethora of outraged letters sent to the museum that hosted it, imploring the exhibition curators to take it down due to the feelings it evoked, some of which were even physical–some reported feeling nausea at its sight. Rothko’s work has also been the center of controversy for similar reasons. But why would simple shapes and colors evoke such strong reactions? 

Once again, the ratio of order and chaos comes into play; however, compared to Cage’s artworks, Rothko’s and Newman's paintings show the impact of how evident the lack of order is. Disorder and chaos aren't always large amounts of small details and clashing colors and loud noises. Sometimes, it is a lack of structure seen in Rothko’s work. There is no subject, no scenery, and the colors chosen tend to be either incredibly “loud,” with many of his paintings including red and orange, or very somber and deep, like black or dark blue. All these factors make the viewer lost. There is nothing for the eye to catch onto aside from color and shape, something primal and basic, and nothing for the mind to occupy itself with. No wonder such freedom of interpretation makes people uneasy.

In direct reference to Kolkov’s “Organization and Harmony,” another paper of his that explains the intricacies of this concept, these artists can be compared to the arctic tundra. With his formula, he calculated the relative entropy of the arctic tundra as a stand-alone ecosystem. It’s important to note that, in its complete entirety, the ecosystem will still be near Kolkov’s Golden Ratio, and the average of all relative entropy indexes of all existing ecosystems calculated by Kolkov results in the exact value of 0.380; but its own index of relative entropy taken from this paper is very high, meaning that there is more chaos than there is order. The arctic tundra is brutal, and the organisms there are few and highly specialized. But chaos and arctic tundra do not go together well. Disorder is always associated with something loud, confusing, disorienting. The arctic tundra, however, is quiet. It’s cold and empty, not exactly fitting for “chaos.” However, when examined more closely, it truly is chaotic: cold weather, little food, little community. Everything kills. That’s real chaos.

A human mind is chaos. Thoughts aren’t controlled, and thus the experience of viewing a Rothko painting could be compared to the intricacies and disorder of the aforementioned ecosystem. There is too little to cling onto and too much happening inside one’s own head, creating a perfect recipe for distress, confusion, and existential dread. This is the exact reason the Rothko Chapel is an effective place to practice mindfulness. It is a space for the mind to wander, because the black of the surrounding walls is a reflection of one’s mind, not a scenery or portrait to analyze. An emptiness that’s filled by the viewer themselves. A stark contrast to the mathematics of The Sight of Silence and the quietness of its human parts, its emphasis on order.

Kolkov’s papers are exceptional. The concept of everything in the world being united by his Golden Ratio is a beautiful thought that has stuck with me for months, and many artworks remind me of it; Rothko, Newman and Cage stand out the most. They are similar in nature–chaos and order coexist together–but their impacts are created by the offset of the balance between the two. Chaos over order (Rothko and Newman) swallows the viewer, gives too much space and forces us to face our own mind, trying to savor the quiet in the storm of a mind, the constants in the ever-flowing of thought; order over chaos (Cage) shows the beauty of the in-between, the silence, the disorder present in the order of mathematics. Opposing sides of the spectrum of entropy, and yet not extremes. 

I’m unsure of what conclusion to draw from this. It’s a fact of art, it’s a fact of all life, and I think it’s beautiful. There is no lesson to learn–perhaps how to make more impactful, thought-provoking art. It is simply a wonderful fact of life that opens a whole new world of new information that could explain thousands of occurrences, from soup cans thrown at a Van Gogh painting to excessive jokes made in a friendly conversation. In the end, it is all about finding a balance, about loss and gain, about order and chaos.