"When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have the answer to the first." - Werner Heisenberg
The starry night, the luminescence of the sky outside of Van Gogh's mental hospital spoke to him on a night of insanity. A mind severed from reality as we perceive it, conveys to us the turbulence of the world though its paintings. The spinning and swirling of moonlight into the night sky, moonlight flying in controlled chaos, spiraling and circling. Through Van Gogh's insane, disconnected, and chaotic mind, he described the world's turbulence with mysteriously high mathematical accuracy. The accuracy was in the presentation of the turbulence, how it behaved similar to turbulence in fluid systems. Van Gogh was no mathematician, knew little arithmetic and certainly nothing about fluid dynamics. It should be noted that the mathematical precision in Van Gogh's works were highest at the times of his mental lapses, his 'insanity'. What do we make of this, and what can this tell about the nature of the mind.
The chaos that builds in our abstract thought processes is in my opinion structured how the world works, or for the selfish among us, the inverse of such a process is true. The world, evolution, nature, God, all of the above shape the mind into an appropriate mode of functionality for the world. Beauty comes from exploration of our thoughts at different levels. For the artists among us, we bring out patterns from the world through music, paintings, and writing. We can see there is a correlation between how things sound and their mathematical properties, consonance and dissonance, melody and harmonics. What we cannot measure and study however is how the mind brings out beauty from the chaos so well. It is hard to see mathematically how music sounds good. What is known: consonance is when the oscillations, vibrations, of notes line up neatly with each other, and dissonance is where they do not. Consonance sounds good, dissonance alone sounds bad. How can vibrations in the air that can be described mathematically elicit such feeling of emotion and beauty in humans, there is surely beauty in the creation of such works.
Is it safe to assume that we project ourselves and learned things onto the environment around us? Seeing shapes in clouds, a face on the moon, or hearing some hidden message in music. This phenomenon is known as pareidolia. We can classify most things we come into an encounter with into their respective, learned, groups in our mind. Just as we do this, we build machines that do this type of classification. I believe that there was something that made Van Gogh, on the most insane of nights, perceive the world as more chaotic and turbulent, which he then reflected in his paintings.
Deep dream, created by google, is an interesting idea which explores the black box of a CNN to a deeper extent. There is a classification neural network who's loss function was computed to maximize the correct classification of objects in a landscape over thousands of different classes. What if instead of maximizing the final layer, output, of the network, we worked to maximize some other neuron. There is a known, important, hierarchical structure of neural networks, not even convolutional ones, where the pieces will come more formed together until it reaches the final layer, resembling whatever the goal was. So from the ground up, we must identify what a cat is among other animals. We start with the first layer of abstraction from the image: lines are identified, curves and such. It is not enough to distinguish animals from one and other, so we must develop a deeper abstraction. Layer two: these lines and curves come together to make circles, and edges, and simple shapes. A few more layers down the line, and there is an effective generalization of what a cat looks like. What deep dream intends to do is to shine a light on what it means for a machine to find patterns, and to show us in an interesting visual way. It can be conceptualized as shining a light through the layers of abstraction and painting a picture of what a generalized phenomenon looks like, and it does it in quite beautiful ways.
So we have our picture of a land scape, and we wanted to pull out, seemly from nothing, the faces of cats. What we would do, is to have a classification algorithm look at the picture and change one or several of the neurons that fire when they see cats, and max out those neurons. What we get in the picture, after 40-80 iteration is a resultant image, psychedelic like, of cats coming out of nowhere. Maximizing a neuron representative of an abstracted, more general, representation of an idea, shines that idea though and ingrains that physical idea throughout the image, becoming more prevalent after every iteration. We define objects in our networks as physical for our intents and purposes, a physical idea of a turtle, or house, or coffee maker. Therefore the only abstraction that occurs in a convolutional network is that of the physical.
If we choose to maximize neurons in a lower level of abstraction (lines and edges), we can see an almost impressionistic art piece after an appropriate number of iterations (usually 40-80). The lines in the artwork become more prevalent, and basic patterns emerge as a consequence of us telling the model to maximize some neurons in a low level. Turbulent flow of any fluid with any viscosity, can be characterized as chaotic. Chaotic being that any small change to an initial condition results in a seemly random result after a period of time, chaos. Is it that in Van Gogh's mind, that there is a hierarchical structure of abstraction of the way he perceives the physical, that builds up on top of itself? Maybe at one of the lowest levels of abstraction there is that of a fundamental understanding of chaos, and built upon that over many levels of abstraction emerges order. Perhaps, these nights of insanity for Van Gogh are somewhat, loosely, analogous to the maximization of a low layer neuron, or neurons, in a convolutional, or any, neural network. A pareidolia of not faces, but the building blocks of the physical or mental, into the mind of Gogh, chaos.