Is the world simple, or is it complex?

What does "simple" even look like?

Perhaps the simplest painting is the empty canvas. The simplest number is zero, and the simplest blog post contains no text. A simplest world would then be one with nothing inside. Almost as simple would be a painting that is a single line, a song that is a single pitch. Tic tac toe is a simple game - a functional strategy can be conveyed in a few brief sentences. Things that we can explain in a single sentence are clearly simple. The world is not one of those things.

What of complexity, then?

The most complex things are irreducible in their complexity. A line on a canvas is not complex in such a way, because it can be summarized and transmitted linguistically with less information density than the potential that the canvas can express. Thus, the most complex thing is random noise. The static on a TV screen is incompressible, immemorably complex, and maximally informationally dense. Its entropy is greater than any patterned subset of things displayable on the TV, like peoples' faces, or natural photography. The world is not as such either: something which is so dense in information cannot be meaningfully perceived. There is no way to salvage meaningful information out of true static. But, we can make sense of the world, implying it is not static.

Perception requires a hint of simplicity.

One day I will find the right words, and they will be simple.
- Jack Kerouac

We can think of perception as an organizer of input. Our perceptive mechanisms discard unimportant data, assign value to certain information, and make raw data actionable.

Consider the autoencoder, a specific type of neural network used to convert a large amount of inherently patterned, meaningful data into a small vector which it can then render back onto the original data. Some researchers trained an autoencoder to reduce a black-on-white photo of a person making a pose into about 70 bits from which it could reproduce the original almost perfectly. It can accomplish this because the set of human-pose-photos is governed by an inherent pattern, and is not as highly entropic as the space of all possible black and white images. Had they attempted to perform the same trick on static, it obviously would not have worked, and the result would have been only 35 bits better than random chance. This is great for the autoencoder, but more importantly it tells us something about the set of images it was trained on: that it has structure. Because it was able to be perceived, we know that it has an inherent form.

Consider an agent in the world. In order to act, the agent needs some sort of perceptive structure. An ideal perceptive structure would holistically encapsulate all things in the world. Us humans aren't afforded that luxury: we are bounded by the laws of physics, and can only perceive that which interacts directly with our sensory organs. But, that alone is very powerful! The reduction of an incomprehensible amount of data around us to a very small set of perceivable feelings is still immensely useful in navigating the world. We thus know that our world must be less like static, and more like the set of human poses. It is shaped to a form, and thus is not absolute in its complexity.

We are between simple and complex.

Not only does this paradigm explain the nature of our world, but the nature of computers, humans, and so on.

Although at a physical level a human is infinitely packed with information, we can meaningfully analyze at a chemical, cellular, and anatomical level to the point that the workings of the human body can be communicated to some degree of accuracy in a biology textbook, WAY less information than actually present.

No computer scientist knows what exact wires have what voltages when their program is running, but a decent one can describe a stack of abstracted functionality, each laying upon and interfacing with the prior, to provide a decent picture of the workings of the integrated system as a whole.

Our neurology reflects our environment.

To straddle that fundamental duality is to be balanced: to have one foot firmly planted in order and security, and the other in chaos, possibility, growth and adventure. When life suddenly reveals itself as intense, gripping and meaningful; [...] you are located precisely on the border between order and chaos.
- Jordan Peterson

It is of import that our brains are bifurcated. When the individual can have a unified experience and control the entire body, why should the brain not be completely interconnected? The complete answer to this question is unknown, but we can get a decent idea by observing the lateralization of certain circuitry. In popular culture people are called "right brained" or "left brained", corresponding to a creative and logical personality respectively. This is a bastardization of a real psychological truth: it doesn't seem that the neurotypical individual has a "dominant" side of the brain, however the two sides of the brain do indeed correspond to the supposed mental tasks. The left hemisphere contains specific neurology related to language production, whereas the right does not. They seem to interact with the world in different ways.

When the corpus callosum, enabler of cross-hemisphere communication, is cut, the ways of thinking of each side of the brain seem to be highlighted. Showing the word "face" to the patient's left eye (right brain), the patient can then draw a face with the left hand but not articulate the word. Shown to the right eye, (left brain), the patient articulates the word.

Could it be that the right hemisphere is better at dealing with chaos and complexity, while the left hemisphere deals with the organization of what is already known: the simple?

Perhaps this is why we listen to music. Just like the world surrounding us, it dances on the border between simplicity and complexity. Boundless in potential realizations, but still internally constrained by guiding patterned structure.

The world isn't simple nor complex. What is it?

The space between the sky and the earth, how much is it like large bellows! Empty but endless; just move, and wind is produced.

The world is a chaotic system with many interacting resolutions of mechanics. Quantum, Physical, Chemical, Biological, Psychological, Sociological, and Geopolitical levels of analysis all exist and have import to us. Strikingly, each of these fields of study give birth to similar objects, to the point that they can be described by similar governing equations.

What other thing behaves like this? What is a thing that generates atop it patterned albeit unpredictable behaviors? Consider go. Here is a quote from Dustin Lacewell's blog:

I have heard the question, "Go is more complex than Chess right?" It is a question that comes innocently but misidentifies Go's character. Go doesn't just support more complex gameplay; it is so simply beyond direct articulation that its pedagogy comprises an amalgam of geometric insights, history, metaphor, proverb, strategic principles and a rich zoology of shapes with funny names like Monkey Jump, Elephant Eye and Tiger's Mouth. Each with their own unique tactical properties. None of these things are built into the rules. They just emerge out of them.

A physicist friend of mine with a brilliant understanding of the sciences, but lacking a hint of creative observation, argued why he preferred "Axis and Allies" to Go: "Go doesn't represent anything. Axis and Allies is actually real." He laughed when I claimed with a straight face that the opposite seemed self-evident: In Go can be seen one of the most phenomenal things in reality: the differentiation of identifiable items from a lower-level substrate. It seems uncanny how analogous it is to the abstracted similarities of the many resolutional facets of reality.

This seems to be a property of formal systems in general. Define some set of rules and allow them to play themselves out, and above them forms an entire taxonomy of emergent objects and behaviors. This can be seen among formal systems as simple as cellular automata, and as complex as particle mechanics. It would come as no surprise to me for particle mechanics to be an emergent feature of some lower level, more simple formal system.

And I wouldn't want it any other way.

Whatever it is at the bottom generating this dream of magnificent integrated complexity, this holy reality of differentiated self-similarity, might as well be no more overdefined than a few basic objects and their interactions. You, me, and all of this beauty - this is the radiant dream of some elementary axiomatic system.