Chaos vs Structure (parts 1 & 2)

I started writing on this topic and realized that there is far too much to say that can be expressed in a single post. I will separate this post into multiple parts and even doing so I only begin to scratch the surface of all that can be said. In this first post, I will introduce a general vision of how I think about concepts. In future posts, I will go on to give an interpretation of general human dynamics.

Part 1 - Introduction to chaos

Chaos is defined by the Merriam-Webster as a state of things in which chance is supreme. In other words, chaos is disorder and lack of structure. Chaos can be perceived on different order of magnitudes. For example, we can observe the chaotic behaviour of waterfalls, when the water from the top of the fall impacts on the bottom and all water molecules scatter in an unpredictable manner for which you can never truly observe the same exact event twice or observe chaos that is created by the merging of two neutron stars. We can also see chaos to be a state in which there is confusion. We can find ourselves not being in control of a situation and referring to it as chaotic. Say that you are in a meeting and each person has their own agenda up their sleeve, everyone is talking over each other and you can barely hear and understand what anyone has to say because there is too much information that is being thrown out without any structured direction.

I believe that our universe started in a state of pure chaos in which there were no rules, no implications, no meaning. As space-time started its expansion, structures started to form. We had particles forming atoms which themselves formed molecules and much later formed life. Out of pure chaos, structure emerged as time moved on. After billions of years, here we are as vessels that have high mobility with a brain that contains 100 billion neurons (a vastly complex structure). From this pattern, we can see that the universe is trying to contain chaos as much as possible and trying to give birth to order out of disorder. That is an underlying principle that is very much present in every aspect of our lives.

When we are born, we perceive everything as almost raw sensations in which we later try to give meaning to each one. How we chose to interpret each of these sensations is mostly defined by the emotional weight that we attribute to them. This also ties into the whole concept of good and evil, on why humans feel similar emotions. This concept might be discussed in a future post. We grow up and label objects, experiences and feelings (as discussed in my first article). We do so to be able to use the concepts we create to form new ones. Our bubble of control increases and gives us more freedom to flow in this world.

And so, after millions of years, we learned how to write. Every word was given a meaning which was accepted by the community to properly store information over time and communicate with a sense of clarity. We then tried to describe events of nature using a language that we named mathematics. This language started out in its most basic form as a collection of numbers to quantify a general aspect of things present in society at that time. It evolved like most structures in our universe do and notation was introduced to compact information. Formulae were derived and rederived with different notation giving us more freedom with equations to derive other formulae that regrouped more information than the previous ones (an example of this for the physics people is Maxwell’s equation described by vector calculus notation (4 equations) vs differential geometry notation (2 equations) or even the information contained in Feynman diagrams). This procedure of compacting information to describe more complicated phenomena is a form of evolving structure. It all comes down to classifying this infinite chaos into things that we can understand. This is not only the case with mathematics but with every other subject that there is out there. Each of these subjects analyze specific forms of the chaos which may or may not overlap with each other and evolve in their own separate direction. We expand on our knowledge by building on what is already there. This process can be done by building inwards or by building outwards.

Part 2 – Different types of structures

I define building inwards as a process to reinforce a concept or to explore its implications (what is implied by having defined our concept as we have). Let us consider the concept of a banana (first thing that came to mind). At first we see it as a yellow object with a certain shape. We define it as being mushy with a white interior that has seeds. We then realize we can eat the banana and classify it as a food. Later after having studied the banana more intensively, we see that it exhibits the same properties of something that we defined as being a fruit. After more research we learn that the banana is composed of many nutrients that may be healthy for our body. We can even create myths about the banana. All this reinforces our concept of what a banana is. The word banana contains all that information that I mentioned above (more or less depending on your perception of the banana). We take pre-existing knowledge about something and we add concepts to the structure that was already there. In other words, we build substructures to reinforce our existing concept. There is an infinite number of substructures that can be formed for each structure and another infinite number of substructures that can be formed for each substructure. In our banana example a substructure would be saying that the banana has nutrients. The substructure of that substructure would be to study all the benefits of those nutrients and all the information that comes with the concept of nutrients associated to the banana.

Now this isn’t a straightforward idea since many different concepts can encompass similar substructures or even some of the substructures can encompass the initial structure itself. In our example we can say that bananas contain vitamin C but then when talking about vitamin C, it comes with a lot of different implications and is not necessarily only related to bananas. For example, it can be related to oranges as well. This is what I define as an overlap in substructures and can schematically be represented as follows:

Here I have shown a very simple model of how we conceptualize things. In red are the categories that are the same for both bananas and oranges. They are both a type of food but have different properties. Similarly, they both have nutrients but different ones. Vitamin C is represented in green which characterizes overlaps since all that falls under this substructure is the same (that I know of) for both fruits. There can be an infinite amount of overlaps with some bigger than others and an infinite set of information for each subcategory. This is a very complex system that I can hardly begin to describe.

Notice that we say that banana is a food and not that food is a banana, if both were true then we would have infinite loops while classifying things. Generally, we try to avoid these loops by setting one of the concepts as being the generalized term and associating things under that category. In our society, we find that food is our general group and banana is a subset of the group. This isn’t necessarily true for every concept because reality is chaotic. When we classify information, we try our best to create this type of hierarchical structure to increase our clarity on the subject.

Then, I define building outwards as the process of using concepts to create new ones. We can simply think of it as building blocks in order to achieve the desired structure. This is something that can be conceptualized with more ease by thinking about how we need to build up knowledge in order to become experts in any field. Once we have studied and understood what are field currently is, we can formulate ideas to expand knowledge in our field. You are adding your own blocks of knowledge to the blocks that were already present.

Another way of thinking of building concepts can be represented by this Figure:

We represent the square/rectangular boundaries as concepts. What we are trying to do is fill the space in them with more concepts to get a clearer picture. We fill them with substructures which themselves are concepts. As mentioned previously, some concepts overlap with each other. What is interesting to notice is that each square no matter how small it may appear, contains an infinite space that can be filled with more concepts. This is shown in the right part of the Figure. We are zooming into one of these substructures only to see that it contains a whole world of substructures itself. All that we can do is keep on filling the squares endlessly to improve our understanding of the universe on an infinitely large scale as well as an infinitely small scale. The squares will never be completely full, there will always be an empty layer if we zoom in/out enough. This view represents both building inwards and building outwards. We can conclude that there are different levels of structure and each one of them is relevant in accordance to the other.

Our brain is no different. It learned to classify every form of sensation through evolution. If you think about it all 5 senses (sight, sound, smell, taste and touch) can be represented by a single sense of feeling or contact. You see things because light rays make contact with your eyes and your brain processes that information to produce an image. You hear things because sound waves make contact with your ears which your brain interpreted as sounds. You smell something because molecules of whatever you are smelling are making contact with your nose and irritating in such a way that you can recognize certain patterns and introduce a feeling that you label as a sense of smell. Taste and touch follow the same logic. We think of these senses as being different only because they have each evolved in their own specific direction, leaving behind complex structures such as our eyes, ears, nose, mouth and skin to interpret them.

To add another layer of depth to the subject, we can consider dynamic structures (or structures that evolve through time). Not all our concepts remain set in stone once they have been declared. Most often, we set ideas which we later revisit once we find better ways of expressing them. Sometimes we find that our concepts are wrong with respect to others and to assure a logical continuum, we adjust them to coordinate with each other. We can also completely remodel our way of thinking by destroying previous structures to build new ones. An example would be of a bridge that was built for us to cross from one point to another. At the time, we built the bridge with the only way we knew how to build it which was building a straight platform from point A to point B. We realize that the bridge can only carry a certain amount of weight and we need to find a way to make it support more. We then remodel our bridge to be able to support a truss system across the platform, but to implement it, we need to redesign the platform and build it using a different type of material. So we destroy our old bridge in order to build the new one. This process will keep on repeating since in the future there will be needs for us to construct a new bridge or even find another way from going from point A to point B. It is a slowly evolving process.

Another example can be to think of our law system. When our country was founded, rules were imposed, and many other rules were built to support these founding rules. There are a lot more laws now than there were in 1867. As time passed, we reinforce our concept of what living in this country represents and create laws to increase every civilian’s clarity on their freedoms. These rules change as certain ideologies gather more influence in order to accommodate for them. As grandiose as our perception of the law might be, there is always and there will always be a boundary where a certain set of rules will be ambiguous which we define as the “grey zone”. We can take any concept and keep on asking questions about it: “what, how or why” and we will inevitably hit a wall where we will not be able to explain the concept. We will then find words or substructures to try to explain it and form another law or concept. We can then repeat our questioning process and realize again there will be things that cannot be explained. This is an example of another infinite loop. This is applicable in any type of career. Most jobs objectives are either to develop structure in an organization or to carry out a procedure created from that structure.

There are many more examples which I can expand on that we can derive just by looking at nature itself. All that we can create comes from what is already there and the observation of natural phenomena lead to some of the greatest inventions throughout time. All of this to say that chaos is very present in our world and that we deal with it by trying to gain more control and by forming structures. Now how can all these concepts relate to the world that you are currently experiencing?

To be continued ...