Science

Randomness vs Structure: John Cage vs Prospect Theory

“Our intention is to affirm this life, not to bring order out of chaos, nor to suggest improvements in creation, but simply to wake up to the very life we’re living, which is so excellent once one gets one’s mind and desires out of its way and lets it act of it’s own accord.” – John Cage

Why is randomness beautiful? Many modern artists introduce randomness to their creative process. Jackson Pollock’s drip paintings are probably the most famous example. John Cage is another interesting one – he is best known for his experimental music composition, but his use of randomness in art is also very intriguing.

When I first watched his performance of the silent music piece 4’33” on YouTube, I thought it was experimental in the sense that it separated the visual and audio components of music performance. But maybe I missed his point. The quote above made me realize that the focus of 4’33” is on the sounds in the ambience environment. Listening to everyday noises in the surroundings is a way to “wake up to the very life we’re living”. The same spirit is in Aoki Emiko (青木 恵美子)’s mirror displays, where the reflection of the surroundings is part of her artwork. John Cage embraces chaos and randomness because that is the truth in the life that we are living.

If the idea of silent music in 4’33” seems too experimental, you might like John Cage’s Music of Changes better. Music of Changes is an indeterminate piano solo composed by randomized decision rules on sounds, durations, and tempo according to I-Ching, a classical Chinese text. I-Ching means “Book of Changes” in Chinese, hence the name Music of Changes. I’m not sure how much of the music pattern is actually from I-Ching, and I speculate he was more using the eight trigrams in I-Ching as a system of exotic symbols to help him think outside the box. The picture below, Fontana Mix, is an example of John Cage’s “graphical score”.

(Side note: Somewhat curiously, Herman Hesse was also obsessed with I-Ching in The Glass Bead Game, but my impression is that he associated I-Ching more with structure rather than randomness, since he compared I-Ching to Bach’s music.)

graphic scores john cage

John Cage, Fontana Mix, 1958

john cage

John Cage, Strings 1-20, 1980

 

To answer the question “why is randomness beautiful?“, we need to ask ourselves “what is beauty?” first. To me, beauty is perhaps best described as a feeling of pleasure. One psychological explanation of beauty is that beauty originates in our childhood desire for security. Here’s one example from Rothko’s essay: the child’s notion of security is connected to the form of his mother, and therefore the curves and tactile planes in the human body are considered beautiful. Thinking along this line, it’s strange that randomness would be pleasing to the eye, since it’s the opposite of security.

Our instinctive desire for security is confirmed experimentally by Kahneman and Tversky’s Prospect Theory in behavioral economics. Prospect Theory is different from expected utility theory in that the utilities of outcomes are not only weighted by their probabilities. The Certainty Effect in Prospect Theory states that people overweight outcomes that are considered certain in decision making, relative to outcomes which are merely probable.

If we favor certainty, why do we consider randomness beautiful? This seems contradictory, but in fact, our cognitive bias towards certainty helps with our artistic appreciation of randomness: our cognitive system tends to over-interpret randomly composed pictures and add imaginary structures. That’s why when we see, for example, the above painting Strings 1-20, the first thing that crosses our mind is not “this is a random sample drawn from a probability distribution”. Instead, we relate the curves and forms to familiar images in our memory. (This top-down visual perception mechanism is explained much better in detail in Kandel’s book.)

The dynamic sense of movement may be another reason why randomness is beautiful. I can’t speak for other people, but at least personally when I look at a structured classical painting, I tend to look from left to right and from top to bottom. However, when I look at John Cage or Jackson Pollock, something very quickly catches the focus of my eyes, and my sight drifts around according to the random lines and curves. The unstable trajectory of eye movement might explain why randomness looks more dynamic.

To end this post, I want to show once again John Cage’s quote. Isn’t it nice to think that the purpose of life is to affirm this very life?

“Our intention is to affirm this life, not to bring order out of chaos, nor to suggest improvements in creation, but simply to wake up to the very life we’re living, which is so excellent once one gets one’s mind and desires out of its way and lets it act of it’s own accord.” – John Cage

 

Sources:

Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision under Risk

Mark Rothko, The Artist’s Reality: Philosophies of Art

Eric Kandel, Reductionism in Art and Brain Science

Matilde Marcolli, “Structures of Randomness

Favorite Non-fiction of the Year: “Reductionism in Art and Brain Science”

This book is by Eric Kandel, a Nobel Prize winner in Physiology or Medicine. I haven’t finished reading the book yet, but it’s already my favorite non-fiction of the year. To be more precise, it was published in 2016, so I should say favorite non-fiction that I read this year.

Things that I learned from the book:

  1. There are two parallel visual pathways in the brain, one that deals with what an image is about and one that deals with where it is located in the world. The what pathway is the only one that leads to hippocampus, which deals with the explicit memory of people, places, and objects. The where pathway is concerned with motion, depth, and spatial information. The pathways can exchange information, but they are distinct and separated. Art exploits the fact that seemingly inseparable information is actually processed in separate pathways.
  2. Occipital cortex responds to both sight and the sense of touch. The texture of an object activates cells in the medial occipital cortex regardless of whether the object is perceived by the eye or by the hand.  (This explains how I ‘feel’ the textures of Raku tea bowls or Franz Kline’s paintings.)
  3. Aplysia (large sea snail) has about 20,000 neurons. Its neural circuit is wired in a fixed way, but learning changes the strength of the connections among neurons.
  4. Each nerve cell in the primary visual cortex responds to simple lines and edges with a specific orientation, and that’w how we assemble contours and geometric shapes.
  5. Mating and fighting are mediated by the same population of neurons, and the difference is only on the intensity of the stimulus.
  6. The prefrontal cortex responds to categorized figurative images, whereas the superior parietal cortex is activated by any visual image, meaningful or not.

Some random art facts:

  1. Kandinsky discovered his abstract painting style from listening to Schoenberg’s Second String Quartet and Three Piano Pieces Op 11.
  2. Legend has it that upon viewing a sunset painted by Turner, a young women remarked, “I never saw a sunset like that, Mr. Turner,” to which Turner replied, “Don’t you wish you could, madam?”
  3. Klimt shows women’s teeth in his paintings, such as in Judith and Woman I.

 

 

Conservation Laws and Symmetry (Noether’s Theorem)

Today, when I was studying a mechanics textbook, I found something interesting. It was mentioned that symmetries and conservation laws are closely related. As an example, energy conservation corresponds to the time-translation symmetry in time (which means the laws of physics do not change according to time). The conservation of momentum corresponds to the space-translation symmetry, while the conservation of angular momentum has the rotational symmetry as its corresponding symmetry.

For detailed explanation of Noether’s Theorem, you might want to look at this post: http://gravityandlevity.wordpress.com/2011/01/20/problems-you-can-solve-just-by-looking-at-them-the-meaning-of-noethers-theorem/

Emmy Noether was a female German mathematician Emmy Noether, and her life story is quite interesting. Here is a New York Times article about Emmy Noether: http://www.nytimes.com/2012/03/27/science/emmy-noether-the-most-significant-mathematician-youve-never-heard-of.html