Markov And Life

CS2 is a paper from where there is a lot to gain in terms of knowledge and even life! The topic that I will be taking up is Markov chains. Markov chain is a stochastic process with discrete state space and discrete-time set and it possesses the Markov property. If all of these are satisfied then the process can be modelled as a Markov chain. Let us relate it to life. Possessing discrete state space and time set means in life it is very important for us to do things one at a time and not rush anything, because in this journey of life it is crucial to do things taken up by us with full heart and passion and that can be only done when you do them one at a time. So remember to jump from 1 to 2 and not to 1.5! Now let us look at the Markov property, it states that the future evolutions of the process can be formed by knowing only its current state and all the past of the process is irrelevant. Well, this speaks loads, if a person is not bothered by his past and not be distracted by what has happened, rather concentrating on what he has and using only that he builds his future he will definitely succeed. “The past has no power over us. It doesn’t matter how long we have had a negative pattern. The point of power is in the present moment. What a wonderful thing to realize!” If you are at 4 this year don’t care whether you had been at 3 or 5 in the previous one! But is this all that is needed? No, it is very important to conclude whether the Markov chain will become stationary i.e. will it settle down? There are 3 conditions that must be satisfied for it to become stationary: (i) It must have finite state space. It can be dangerous if we think of the future that is too far-fetched and get a false sense of satisfaction. What can be done best is set short term and distinct goals that can be achieved; deciding things indefinitely in this ever-changing world will become problematic. (ii) It must be irreducible which means it is possible for the the process to move from one state to all other states ultimately. Having the goals set, it must be possible to think and evaluate as to how they can be achieved. How can one move from one goal to another and even come back to the previous one to improve results? (iii) Finally, the chain must be aperiodic which means all states must have period one if a process is irreducible then all states have the same period. If any state has a route back to itself then it has period 1 and given it is irreducible all other states have the same period. Route back to itself! Well, when you are not being able to find a way it is important to sit with yourself and ask questions to yourself rather than questioning others because the best person to help you move forward is none other than you yourself. You just need to come home and trust that the future path passes through your own fine sense of judgment. If the Markov chain satisfies these 3 conditions it will settle down, settling down doesn’t mean that things will be constant it just means that things coming in and the ones going out are setting off each other perfectly and that will give you the balance that is required in the journey of life. Let us learn from the beautiful journey the Markov chain takes with its ultimate aim being to settle down i.e. to be happy and content! I guess the most difficult condition to satisfy is the Markov property, being indifferent to your past. We all in some way carry the burden of the past but what we should actually be carrying is the experience and the positives out of it. Don’t worry if you don’t possess the Markov property currently, go through the goals that you wish to achieve and carefully evaluate on which goal your past is acting as a barrier. Once you realize the critical state maybe then you will be able to split that state into 2 or more states and then you will satisfy the Markov property! WRITTEN BY KARAN KUMAR BINANI


11 July