How about Markov Chain for Human Beings ?
In mathematics, a (discrete-time) Markov chain, named after Andrei Markov, is a discrete-time stochastic process with the Markov property. In such a process, the past is irrelevant for predicting the future given knowledge of the present.A Markov chain is a sequence X1, X2, X3, ... of random variables. The range of these variables, i.e., the set of their possible values, is called the state space, the value of Xn being the state of the process at time n. The conditional probability distribution of Xn+1 on past states is a function of Xn alone,where x is some state of the process. The identity above identifies the Markov property.
A simple way to visualize a specific type of Markov chain is through a finite state machine. If you are at state y at time n, then the probability that you will move on to state x at time n+1 does not depend on n, and only depends on the current state y that you are in. Hence at any time n, a finite Markov chain can be characterized by a matrix of probabilities whose x, y element is given by and is independent of the time index n.
As per the Hindu religion and the philosophy, human mind has six states which are called as Sadripu, six enemies:
1. Kama, pleasure or desire.
2. Lobha, greed.
3. Krodha, anger.
4. Mada, drunk or under influence of strong emotion.
5. Moha, confusion.
6. Matsarya, jealousy.
Now say, we have these six possible states of mind denoted as X1, X2, X3, X4, X5, X6. Given this, we can define the whole life as a combination of these states. Our every reaction to any event is one of these states or combination of two /more.Every single time the state of your mind achieved depends upon the previous state of mind you had. Each of these states have a transition probability (For example, the probability of changing the state anger to confusion, confusion to jealousy..etc.). In short our whole life is a matrix of these state transition probabilities.
If the state space is finite(number of years you live for), the transition probability distribution can be represented as a matrix, called the transition matrix, with the (i, j)'th element equal to Pij = P(Xn+1 =i | Xn =j)
In this formulation, element (i, j) is the probability of a transition from j to i. An equivalent formulation is sometimes given with element (i, j) equal to the probability of a transition from i to j. In that case the transition matrix is just the transpose of the one given here.
For a discrete state space, the integrations in the k-step transition probability are summations, and can be computed as the k'th power of the transition matrix. That is, if P is the one-step transition matrix, then Pk is the transition matrix for the k-step transition.
A Markov chain is characterized by the conditional distribution P(Xn+1 | Xn)
which is called the transition probability of the process. This is sometimes called the "one-step" transition probability. The probability of a transition in two, three, or more steps is derived from the one-step transition probability and the Markov property:
P(Xn+2 | Xn) = Integration{ P(Xn+2,Xn+1 | Xn) dXn+1
= Integration { P(Xn+2 | Xn+1) P(Xn+1 | Xn)}
Likewise,
P(Xn+3 | Xn) =
Integration{ P(Xn+3 | Xn+2) Integration { P(Xn+2 | Xn+1) P(Xn+1 | Xn)dXn+1}dXn+2}
These formulas generalize to arbitrary future times n + k by multiplying the transition probabilities and integrating k times.
So our change of mind state may be one step, two step or more…but the state transition probability for each of this transition can be calculated. We have only six states of mind.Other mind states are just combination of these six states.
The whole life is a matrix of these transition probabilities. Now this matrix is different for all human beings. Its very difficult to calculate these probabilities and that too on what basis?
If such could be accomplished, we can control every single state of our mind. Hindus achieve this control by YOGA with which you discipline your mind to do the things which you want. With the process called “Meditation” you control your mind hence the senses and remain in a state of “bliss” which is altogether a different state than the above six states. Normally for most of the people, their mind has the control over them because of which they can not control the state transition and they remain in state which “they don’t want.”
A simple way to visualize a specific type of Markov chain is through a finite state machine. If you are at state y at time n, then the probability that you will move on to state x at time n+1 does not depend on n, and only depends on the current state y that you are in. Hence at any time n, a finite Markov chain can be characterized by a matrix of probabilities whose x, y element is given by and is independent of the time index n.
As per the Hindu religion and the philosophy, human mind has six states which are called as Sadripu, six enemies:
1. Kama, pleasure or desire.
2. Lobha, greed.
3. Krodha, anger.
4. Mada, drunk or under influence of strong emotion.
5. Moha, confusion.
6. Matsarya, jealousy.
Now say, we have these six possible states of mind denoted as X1, X2, X3, X4, X5, X6. Given this, we can define the whole life as a combination of these states. Our every reaction to any event is one of these states or combination of two /more.Every single time the state of your mind achieved depends upon the previous state of mind you had. Each of these states have a transition probability (For example, the probability of changing the state anger to confusion, confusion to jealousy..etc.). In short our whole life is a matrix of these state transition probabilities.
If the state space is finite(number of years you live for), the transition probability distribution can be represented as a matrix, called the transition matrix, with the (i, j)'th element equal to Pij = P(Xn+1 =i | Xn =j)
In this formulation, element (i, j) is the probability of a transition from j to i. An equivalent formulation is sometimes given with element (i, j) equal to the probability of a transition from i to j. In that case the transition matrix is just the transpose of the one given here.
For a discrete state space, the integrations in the k-step transition probability are summations, and can be computed as the k'th power of the transition matrix. That is, if P is the one-step transition matrix, then Pk is the transition matrix for the k-step transition.
A Markov chain is characterized by the conditional distribution P(Xn+1 | Xn)
which is called the transition probability of the process. This is sometimes called the "one-step" transition probability. The probability of a transition in two, three, or more steps is derived from the one-step transition probability and the Markov property:
P(Xn+2 | Xn) = Integration{ P(Xn+2,Xn+1 | Xn) dXn+1
= Integration { P(Xn+2 | Xn+1) P(Xn+1 | Xn)}
Likewise,
P(Xn+3 | Xn) =
Integration{ P(Xn+3 | Xn+2) Integration { P(Xn+2 | Xn+1) P(Xn+1 | Xn)dXn+1}dXn+2}
These formulas generalize to arbitrary future times n + k by multiplying the transition probabilities and integrating k times.
So our change of mind state may be one step, two step or more…but the state transition probability for each of this transition can be calculated. We have only six states of mind.Other mind states are just combination of these six states.
The whole life is a matrix of these transition probabilities. Now this matrix is different for all human beings. Its very difficult to calculate these probabilities and that too on what basis?
If such could be accomplished, we can control every single state of our mind. Hindus achieve this control by YOGA with which you discipline your mind to do the things which you want. With the process called “Meditation” you control your mind hence the senses and remain in a state of “bliss” which is altogether a different state than the above six states. Normally for most of the people, their mind has the control over them because of which they can not control the state transition and they remain in state which “they don’t want.”
posted by FIVE ELEMENTS at
11/13/2005
4 Comments
