A Sort of Markovian Life

Introduction

I am no expert on math by any means. However, I'd like to introduce others to a world model that I have built, a “philosophy” on how the world works that has helped me in understanding my own life better.

Axioms of Life

Each one of us has an internal belief system that we use when performing day-to-day actions and making decisions. This system allows us to execute actions on a consistent basis with confidence that the actions we perform are correct in some manner.

We can then say that this internal belief system is a set of axioms. We need these axioms so that we can execute actions with ease. Without them, we lose the ability to execute as we do not properly comprehend the current world state. For example, if one is unsure if a business deal will go through or if you made the cut for your sports team, then they will feel lost and not know what actions to take.

On the other hand, if they assume an axiom – that the deal went through, that they made the team – then it is easier for them to take action. And in the case the axiom was incorrect, then they can simply update their beliefs.

The key point of this introduction to the axioms of life is that one needs a strong set of beliefs in their world model to take action. Weak and unknown beliefs cause you to lose the ability to properly execute actions, leading to what many call “analysis paralysis”.

How does one assume these axioms and iterate upon them? Simply have consistent beliefs. Beliefs that you have committed to time and time again. Then, have a level of conviction that you're ready to form new beliefs; that you are open to evaluating the world and adding, removing, or simply updating your set of axioms.

Some examples of life axioms are as such:

• You can arrive at any point in life if you know the exact steps to get there.
• You have control over your life.
• The way you react to external phenomena is all that exists.

I will mainly talk about points one and two in the latter portion of this essay.

Visualizing Life

Visualization is one of the most important tools given to the human species. The ability to produce mental images of a certain scenario allows us to clearly describe what we desire. I believe that visualizing your dream is the beginning to producing a proper world model.

To do this, dream of where you want to be in life after 10, maybe 20, years. What do you see? Who are you surrounded by? Where do you live? How do you feel? Are you satisfied? What do you want to do next? Ask yourself questions, and when you are unable to answer one, do not stray away from it. Think long and hard about what the questions means to you, and what answer you truly wish for. Shake your brain until it spins because these are the questions that reveal your true self. And if you do not know who you are now, how will you ever know who you want to be?

Once you have visualized who you want to be 20 years from now, think of the previous moment you would be in before this point. What kind of state are you in there? What did you do to go from there to your ideal state? Why did you take that action? Is there a better way to achieve this ideal state?

Now do this for every previous state until you reach where you currently are.

Markov

A Markov chain is a process that describes a sequence of possible events where the probability of each event is entirely dependent on the previous state.

We can represent our entire life as a Markov chain. Each moment of our life is some state that can be defined by a list of properties such as where we live, who we're surrounded by, how much money is in our bank account, what point of our career we're in, etc. We can now build on this model by letting each action at any state go to an intermediary node. This node will then have the transitions and probabilities to each next state.

We have essentially created a representation of life, where each state and action pair have a set of possible attainable states. And with the visualization of where we want to be, we have an idea of the path we want to take to progress through.

Obviously, this is not a completely perfect Markov chain. In this representation, we see that at each state, we have a set of actions we can take which lead to intermediary nodes; it is at these nodes where the multiple transition probabilities come to play, and the weights of these transitions depend upon how you performed the action.

If we were omniscient, this representation would be unfathomably large as there are essentially any number of futures we can end up in. However, we are not omniscient and the issue of information has revealed itself.

We only know about so many “ideal terminal” states. Out of those, we care about reaching only a select few, likely one, as well.

On a quick tangent, one's knowledge of the representation and actions needed to progress certain paths boils down to an information problem. We can increase our understanding of the complete Markov chain by learning about more paths in life, mainly by putting ourselves in different experiences and increasing the surface area of our knowledge; in the case we don't care about taking a certain path, we can simply prune it from our current mental model. There is no reason to think about how you will progress through a path of life you have no interest in. Furthermore, the necessary actions to transition from one state to another also require one to know what the correct action to perform is. Performing the action is no simple task either, as one needs to meet the proper skill threshold to complete the action in a manner that allows them to transition states. So advancing through the Markov chain has been shown to be a set of two problems: knowing what path and actions you want to take, and then achieving a suitable level of skill to execute the actions.

Understand that time – and in essence, life – only moves forward. We, as humans, have the ability to reflect upon the past and to think about the future. However, there is inherently no reason for previous time states to affect what actions we take currently and in the future. It is a flaw that we allow our previous experiences to sculpt our current selves.

There are now a few problems to address:

1. How do we detach ourselves from the past so that we can focus on the present?
2. How do we know what the Markov chain looks like? What is the transition matrix?

The first problem can actually be abstracted to a broader issue: How do we detach emotions from the Markov chain, and why is this important to do?

If we think about a properly defined Markov process, we can come to realize that the process is inherently a closed environment. Each state is only accessible through some other state, and the transitions between states are well-defined. Additionally, each state can be described by a list of properties. A properly defined Markov process should have no external influences.

External influences include things such as emotions, mental thoughts, and anything else that can affect your decision making. At the end of the day, this Markov process essentially models your states in life through definable characteristics. Emotions are neither clearly definable nor are they internal to the process. Then, attaching emotion to your Markov chain in any form – be it desire, regret, pride – will affect it and the performance of your actions in relation to this process thereafter.

This does not mean we believe emotions are unnecessary in living; they are simply unnecessary in the part of our world model that we use to progress through certain definable characteristics in life.

It is vital to understand the Markov chain is memoryless, meaning you must also be memoryless, and emotionless, in making your decisions. You can only choose the best decision at your current state, not dependent on previous experiences or emotional outbursts. It is guaranteed to break down the world model that we've built up so far.

Updating the Models

I have talked about having a set of axioms for life and using the Markov model to progress through life. These models are not perfect, and one will need to update them time and time again. In lieu of this, I believe that it is essential to observe and reflect on how these models affect your day-to-day life.

Our axioms are based on what we have seen and believed in. We have established that we assume at least a subset of them, so we must also be open to updating them when necessary.

Likewise, our Markov process is built upon our current knowledge of the world state. If new state information is discovered, it is necessary to recompute our process and also reevaluate what terminal or ideal state we want to reach.

These models, like all other beliefs, should not be set in stone once established. In fact, we encourage you to build upon these models yourself and see how else you can represent your life.

Moving (Forward, hopefully)

Now that we have established this new understanding of our world, the next step is to use it to actually move to a state we want to be in.

There is not much I can provide on this as each person will formulate their own internal representation, so I leave you with the following statement:

Once you understand where you want to be and what you need to do to get there, all that is left is to trust in yourself to execute properly. If you cannot trust yourself to perform up to par, then trust yourself enough to at least try.

Sidenotes

On Desire

What I consider the largest disruptor to the Markov representation of our lives is desire. By not desiring, we are able to get lost in the moment and optimize for the next state rather than fantasizing about a future thousands of states ahead.

Desire will throw you off and additionally make it harder to be steadfast in the things that actually matter to you. Recall that desire is an external variable. Markov chains are inherently a closed environment, meaning desire is a variable not accounted for. To desire, is to then break this model we have created and thus ruins our ability to execute on this model. The way to use desire is to understand what end/intermediary state you wish to arrive at, then executing upon that understanding without desiring any concrete intermediary node.

A naive way of understanding this concept is that you must trust the process – in this case, the Markov process – and not be swayed by intermediary states, positive or negative.

On Competition

Each person has their own model of reality, and thus they have their own unique Markov model. Then, competing with oneself is easy to measure as one simply has to measure the “success”, “freedom”, or any other metric they wish to measure at some state and compare it to their previous state. However, competing with others then becomes inherently incorrect as you are comparing two different models of reality and two different Markov models and transition matrices. The only way for true competition with others then is through a shared reality and Markov model (i.e. economic markets are a simple example).

You have your own context, nobody else is playing the same game as you.