Compressing God into a .txt File
These are some off the cuff thoughts that stem from my reading the paper here: [0812.4360] Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes. The thoughts here are more me spitballing as opposed to well thought out positions, though they are positions I at the moment loosely hold. I may get some amount of terminology here wrong, and if that’s the case, please do correct me.
The above paper convinced me that there’s a link between compression of information and subjective beauty. If you don’t want to go through and read the paper, the thesis of it is that notions of subjective beauty relate to compression and simplicity in information. I want to relate this thesis to some of my personal experiences.
Fractal Art
The picture above looks immensely complicated, but in reality carries very little information and is a simple mathematical object. This fractal is called the Mandelbrot set.
I start with fractal art to create a bridge between the mathematical idea of compression and the more human aspect of subjective beauty. A fractal is, without getting bogged down in mathematics, a self-similar object. If you take the Mandelbrot set and zoom in, you find… the Mandelbrot set again. It’s deceiving since that picture looks complicated and intricately designed, but in fact it’s the same pattern repeating over and over again. The fact that the pattern repeats over and over again suggests that there may not actually be that much to the image, that it’s relatively simple.
We can formalize this notion through the idea of Kolmogorov complexity, which can be roughly described as a minimal description of an object. If you want to see the technical definition, click here. If I wanted to store that image on my computer, it ends up being 68kB. In our modern day, this is nothing in terms of storage, but a simple computer program can recreate that same image and take up far less space. The amount of space the shortest such program would take up is the Kolmogorov complexity of the image, and provides an optimal compression of the image.
With the understanding that the fractal is very simple and that the pattern that we see is repeated ad infinitum as we scale down, the fractal is imbued with an added dimension of “interestingness”. It was already a beautiful object, but the notion of simplicity within the fractal and its compressibility makes it stand out from any other pattern of random colors. There’s a reason this picture above isn’t considered beautiful - because we’re not able to compress any of the information being transmitted through the barrage of colors into some sort of pattern.
This being said, is there something innate to fractals and our perception? The concept of fractal isn’t immediately obvious to most people when verbalized, but I’ve got a hunch that humans have some sort of innate understanding of what fractals are, that it’s biologically inherent to recognize fractals and experience beauty in them. If we model our brains as compression algorithms that take in information from reality and experience the resulting subjective beauty and interestingness from the compressed information, I’d guess that the cognition and compression schemes that our brains use involve fractals somehow. One other clue to this notion is that people on psychedelic drugs often talk about their vision fractalizing. It seems that at lighter doses, things in their visual fields fractalize, and at heavier doses fractals appear out of nowhere. Similarly, thoughts begin to fractalize as people explore the infinitely recursive nature of their thoughts. I’ve heard the sensory complex and the brain referred to as a filter of reality before, and it seems that psychedelics tend to remove filters for reality and normal thought processes, so perhaps the processes that normally run in a sober person are fractal compression algorithms of external senses? These are things I’d like to explore more, ideally with some harder scientific backing to my claims. I’m sure there are neuroscience and psychology articles that could confirm and/or debunk my hunches here.
Maxwell’s Equations
One notable instance of experiencing a massive wave of “interestingness” occurred in the final days of my first semester of college. I’d been taking a class on electromagnetic theory that started off from the formulation of Maxwell’s Equations. These equations, when combined with the Coulomb force law, provide a total picture of electromagnetic theory. From these equations we worked through concepts from optics, radiation, and conservation laws. Here are the Maxwell’s equations below:
These equations provide a first compression of electromagnetic theory when combined with the Coulomb force law. These 5 equations contain the whole theory - this was something I found to be exciting. (Note that while these equations may not make sense, the important thing I want to stress is that, using vector calculus, we were able to compress EM theory into 5 equations.)
The final chapter from that course covered the concepts of relativity within electromagnetic theory and introduced tensor notation and the tensor form of Maxwell’s equations. A very rough description of what tensor notation allowed us to do is that it gave us an avenue to work in a more general and abstract mathematical toolbox than just vectors, which is important because in the relativistic formulation we begin working with mathematical objects called 4-vectors that encode both space and time information. The end result of this development is reformulating Maxwell’s equations into 2 tensor equations:
Once again, these equations may not make any sense, but the emphasis here is on the use of tensor calculus to compress EM theory into 3 equations (there’s also a tensor version of the Coulomb force law which, combined with the above two, provide a full theory of electromagnetism).
I found this simplification of electromagnetism to be satisfying in that we managed to further compress reality by using more abstract mathematical objects. I believe that when people see beauty in mathematics and physics, it was this same feeling that I had in the simplification of Maxwell’s equations that results from the compression of the ineffable into a perceptibly small amount of information.
The program of mathematics and physics (and science in general I guess) is one of information compression through the creation of general theories. In the case of science, this is through the repetitive compression of reality into theories that attempt to hold higher generality as well as fewer laws. In mathematics, it is the process of abstraction of the axioms you are working with to provide a more general framework through which to view reality and to explore the results of these axioms in the form of theorems. This process is infinite (see infinite regress), but each next step in the ladder of the infinite regress provides more subjective beauty due to the increased compression of information and reality.
That is, as long as you don’t quit math/physics because it gets a bit too difficult or abstract. I’m getting pretty close to the point of it being too abstract, so hopefully applied math can provide the same kinds of beauty.
Religion
We often think of religion as a set of moral codes that are used to bind societies together via the power of a divine force or as a remnant of a past where fear of a supernatural force was required to get people to act in a pro-social manner (which of these two, among many other possible views, you hold depends on your individual perspective). However, religion to me is a compression of the post-logical aspects of reality that determine a fundamental moral code as to how humans should exist, this code resulting from the post-logical nature of consciousness. And I think this compression is beautiful and awe inspiring, a sentiment echoed by the many who are enamored by religious and spiritual texts from all around the world.
The most formative religious text I’ve read in my 21 years of life is the Bhagavad Gita, which I read during a time of serious emotional instability. The scripture captures a discourse between the despondent warrior Arjuna, who is tasked with killing old teachers and family members for the purpose of saving his kingdom, and Krishna, who is the incarnation of God. I read this scripture at a ripe time in my life as I was dealing with significant mental health issues, and I feel I can credit it with precipitating my formation of a more stable and healthy mental structure. The text provided me with a set of principles that I could follow, and there were sections of the scripture that brought tears to my eyes. I share with you a quote:
I see Thee without beginning, middle or end, infinite in power, of endless arms, the sun and the moon being Thy eyes, the burning fire Thy mouth, heating the entire universe with Thy radiance.
In the script, Krishna reveals to Arjuna his true form. This discourse details the grand nature of what God means to Arjuna and how all-encompassing the existence of God is asserted to be. In my toils with my personal problems and experiencing slow but steady progress through meditation and psychotherapy, I’d come to question many aspects of reality and found the vast majority of it to be ineffable, thoroughly embedded in the post-logical. But in the reading of this text, I found the closest approximation to textually describing the grand nature of reality that I myself had perceived at times. And that is why I found the Gita beautiful.
This beautiful aspect of religion extends beyond the Gita. I want to discuss two more texts I’ve found to be particularly beautiful, though in their own unique and very different way.
The heavy is the fundamental of the light.
Tranquility is the master of agitation.
Therefore, the saint always conducts himself with the essence of Tao and never departs from It. Although he is surrounded by the splendor of wealth, he remains to live a simple and ordinary life.
How can a ruler govern a nation without recklessness if he indulges in power and desire?
He who acts recklessly shall lose the essence of Tao.
He who is agitated with lust and desires shall lose his true nature.
The Tao Te Ching to me encompasses a compression of the strange loop. If you’re unfamiliar with what strange loops are, click this link. For the purpose of this discussion, we can think of them as infinitely self-referential structures. When I read this text, I’d become aware of some of the paradoxical aspects of human existence and reality. At the time, I was grappling with the idea of the backwards law, as termed by Mark Manson, which describes that sometimes in life, if you want something, you can’t try too hard to get it. I’d seen this non intuitive law apply in many aspects of my life, but to grasp its implications was overwhelming. Luckily, the Tao provided the perfect compression of the idea, delivered through its cryptic yet simple poems.
In contrast to the subtlety of the Tao, Dante Allighieri’s Inferno, which I am in the process of reading at the time of writing this essay, encapsulates the emotional and spiritual devastation of existence in Hell in a clear and illustrative manner. While Inferno and the Divine Comedy are not spiritual texts in the same manner as the Gita or the Bible, its impact and the content of what it attempts to capture motivates me to categorize it similarly. The subjective beauty of Inferno cannot be captured in a quote or verse, as the medium of it being an epic creates the message. However, the engagement I feel as the narrator passes through the circles of Hell, the uncertainty and fear that follows his descent downwards, and the pain he witnesses in the denizens of Hell capture the painful atmosphere in a beautiful manner. The text is flawless in its conveyal of the divine punishment resulting from breaking the rules of the Christian God. I can see why the Divine Comedy has influenced depictions of Christian theology to its immense extent.
Music and Memories
The feeling of nostalgia that often accompanies listening to old music is in reality the decompression of memory that was compressed into music, if we’re to follow the ideas being developed here. I’ve always used music as a lens through which to make sense of complex emotions associated with a series of events. If I try to write about these emotions, I find that the words just don’t do Reality justice.
But calling it nostalgia is not enough. Some music makes me feel nostalgic about inconsequential things, such as the bus ride I used to take during high school. While I do feel nostalgia for these events, the music that brings me back to these moments isn’t something I’d call “beautiful”, and I’d say this is because the memories being compressed and encoded into the music are memories that don’t hold much weight on the narrative of my life. Sitting in the bus every morning to get to school isn’t something I deem very important in making me who I am. It is the emotional valence of the memory that is encoded into the music that makes a certain piece of music more or less beautiful. And by the word beautiful, that isn’t restricted to a pleasant sort of beauty. There have been many moments in my life where events unfolded that were very unpleasant to experience but still have a significant impact on the narrative flow of my life. Perhaps we should use a different word than beauty in this context, but in keeping with the development of the ideas in this piece we will settle for now. We consider these corresponding pieces of music beautiful because the stronger the emotional valence, the more complex the emotions being experienced are and the more information being encoded into the music.
This idea leads to each individual person finding different pieces of music beautiful depending on their life experiences. However, I also want to take a look at culture and genre defining music, music which becomes massively popular and represents an era. Similar to how individual people compress complex emotional states into music that they individually find beautiful, these sorts of “classics” encode cultural atmospheres and compress them into symbolic pieces of music. One example is “Master of Puppets” by Metallica. The 8 minute long song is one of the hallmark songs of thrash metal and is the perfect compression of what the genre is all about. People listen to thrash metal for the aggression and technicality of the music combined with the often transgressive nature of the lyrics, the motivation driven by a rejection of mainstream culture and a desire for something darker. While thrash metal’s popularity has waned in recent years, it was wildly popular in the 80’s, with Metallica being one of the bands to spearhead its growth. In this sense, “Master of Puppets” compresses a complex cultural zeitgeist that simultaneously held mainstream popularity and rejected mainstream tropes, which is why it is held as a genre defining song.
More Questions
While this was an off the cuff essay reflecting on the paper linked, there are a series of questions that I’d like to explore which were hinted at throughout.
Is there a way to relate neural circuits and brain structures to compression algorithms?
Compression algorithms often try to find patterns within information for reconstruction, which makes fractals very easily compressible. Do our cognitions model such compression algorithms?
Can we relate compression and decompression algorithms to notions of intelligence? I already have heard the idea that intelligence is a local entropy decreasing process. This usually has the thermodynamic notion of entropy in mind, but how would we link that to the information theoretic definition of entropy?
If the brain can be modeled as an information compression and decompression mechanism, what happens when we listen to nostalgic music under this framework?
What exactly goes on in the brain when people experience some level of beauty from reading religious texts? Is there any way to relate this to what happens in the brain when somebody is on a psychedelic?
There are probably more that I’m leaving out, but these are a good start. I doubt I’ll get to an answer for any of them but they’re interesting to think about.