Chinna Kannan Azhaikkiraan

November 29, 2009 in Music | Tags: chinna kannan, Music, ragam, tamizh | Leave a comment

This is a beautiful song in Reethigowla Ragam.

(I do not know the proper translation of this song. If I do get to know, I might post it. I do not know anything about Ragams too. Please feel free to correct any such mistakes.)

Here is the Youtube link to the song.

Here is some beautiful instrumental music in the same ragam.

Longest Path: Method of Random Orientations

November 24, 2009 in Hey Math, Theoretical Computer Science | Tags: CS, maths, Theory | Leave a comment

In this post, we shall consider an NP-complete problem, namely that of determining whether a simple path of length k exists in a given graph, G = (V,E).

Formally,

LONGEST PATH PROBLEM

Input: undirected graph, G = (V,E), integer $k \geq 0$ .

Parameter: k

To find: Does G contain a simple path of length, k?

(Note: length refers to edge length here. In particular, a simple path of length k has k edges.)

The problem has a natural extension:-

EXTENDED LONGEST PATH PROBLEM

Input: undirected graph, G = (V,E), integer $k \geq 0$ .

Parameter: k

To find: All pairs of vertices $(i,j) \in V \times V$ , such that there exists a simple path of length k between i and j in G.

=======

This article is based on the seminal paper on Color-Coding by Noga Alon, Raphael Yuster, Uri Zwick [1995]. The method of random orientations is mentioned in the paper prior to a description of the color-coding approach.

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We concern ourselves with the Extended Longest Path problem.

Consider the adjacency matrix, A of input graph, G. (A is an $|V| \times |V|$ matrix, with 0 / 1 entries, which we interpret as integers.)

We have, $A[i][j] \neq 0$ iff there exists an edge ${i,j} \in E$ .

(Note: $A[i][j]$ represents the entry at the $i^{th}$ row and $j^th$ column of matrix A.)

Consider the matrix, $A^2 = A \times A$ .

$A^2[i][j] \neq 0$ iff there exists a path of length two between i and j in G. (Why? Verify for yourself.)

Generalizing, we can make the following statement for the matrix $A^k = A^{k-1} \times A$ .

$A^k[i][j] \neq 0$ iff there exists a path of length k between i and j in G. (Why? use induction to prove this.)

Question: Do all paths represented in the matrix entries correspond to simple paths of G?

In other words, is the following statement true:

$A^k[i][j] \neq 0$ iff there exists a simple path of length k between i and j in G.

–

By a little observation, it can be seen that for the matrix entry $A^k[i][j]$ to be non-zero, the path between vertices i and j need not necessarily be simple. In other words, the path may contain cycles.

Hence, we can not infer from the fact of having $A^k[i][j] \neq 0$ , the conclusion that there exists a simple path of length k between i and j in G.

—

How do we fix this problem?

Consider a graph, H that does not have any cycles (i.e. acyclic graph). Clearly, all paths in H are necessarily simple. (For a path to not be simple, the path needs to contain a cycle, which is precluded by the fact of H being acyclic.)

Let B denote the adjacency matrix of acyclic graph, H.

We can make the following statements:-

$B^k[i][j] \neq 0$ iff there exists a path of length k between i and j in H.

And since all paths of H are necessarily simple, the above statement is equivalent to:-

$B^k[i][j] \neq 0$ iff there exists a simple path of length k between i and j in H.

Therefore, if the input graph is acyclic, raising the adjacency matrix to the power k solves the Extended Longest Path Problem.

—-

Question: How do we obtain an acyclic graph, H from the given input graph, G?

Prior to answering this question, we shall digress briefly to the look at the notion of a Directed Acyclic Graph (abbreviated as DAG).

—

Consider an undirected graph, G = (V,E) on $n$ vertices. We shall construct a directed acyclic version of G.

Let $\pi$ be a permutation of the vertices i.e. $\pi : V -> \{1,...,|V|\}$ , ( $\pi$ is one-one and onto, i.e. bijective.)

Call the directed version of G as $G_{dir}$ . The vertex set of $G_{dir}$ is V (same as G). For every edge of G, we have a corresponding directed edge in $G_{dir}$ .

For each edge $\{i,j\} \in E$ of G, add edge $(i,j)$ to $G_{dir}$ iff $\pi (i) < \pi (j)$ .

(i.e. Orient every edge of G from the vertex having lower $\pi$ value to the vertex having greater $\pi$ value. )

Claim 1. $G_{dir}$ is acyclic.

Proof. Assume to the contrary that $G_{dir}$ has a cycle, $C = (v_1, v_2, ..., v_i, v_1)$ .

Hence, we have the following $i$ inequalities:-

$\pi (v_1) < \pi (v_2)$

$\pi (v_2) < \pi (v_3)$

…

$\pi (v_{i-1}) < \pi (v_i)$

$\pi (v_i) < \pi (v_1)$ .

From the first ${i - 1}$ inequalities, we obtain:-

$\pi (v_1) < \pi (v_i)$ , which is contrary to the $i^{th}$ inequality.

Hence, $G_{dir}$ is acyclic. QED.

Claim 2 (Converse of Claim 1.). Given a Directed Acyclic Graph, G = (V,E), we can obtain a bijection $\pi : V {->} \{1,..., |V|\}$ , such that for every edge $(i,j) \in E$ , the following condition holds: $\pi (i) < \pi (j)$ .

Proof-sketch.

Given any directed acyclic graph, G = (V,E), we have:-

$\exists v \in V$ such that $\forall i \in V, (i,v) \notin E$ .

(In other words, we can find a vertex in V, which has no incoming edges.)

Assign $\pi (v) = 1$ for one such vertex, v.

Remove $v$ from $G$ to get a new directed acyclic graph. Find a vertex, u that satisfies the above condition in this new graph, assign $\pi (u) = 2$ .

Proceed in this manner until all vertices are assigned a value under the function, $\pi$ .

End of proof-sketch.

===

We can now return to the question raised prior to the discussion on directed acyclic graphs.

To restate:

Question: How do we obtain an acyclic graph, H from the given input graph, G?

Solution: Take a random (What does “random” mean?) permutation $\pi : V {->} \{1, ..., |V| \}$ . Create an directed acyclic version of G as outlined in the preceding discussion. Call this graph, $G_{dir}$ .

(By “random”, we mean a permutation selected uniformly at random from the set of n! possible permutations of the vertex set, V.)

Denote the adjacency matrix of $G_{dir}$ by B.

As seen earlier, we have:-

$B^k [i][j] \neq 0$ iff there exists a simple path in between i and j in $latex G_{dir} $ of length k.

Since every simple path in $G_{dir}$ is also a simple path in G (Why is this true?), we have:-

If $B^k [i][j] \neq 0$ , then $\exists$ a simple path between i and j in G of length k.

Question: Is the converse of this above statement true?

In other words, is the following statement true:-

If there exists a simple path between i and j in G of length k, then $B^k[i][j] \neq 0$ .

Answer: No.

The above question can also be rephrased as:

Are all simple paths in G carried over into $G_{dir}$ ?

(Take a simple path, p in G, and figure out for yourself how the edges of p need to be oriented for path, p to exist in $G_{dir}$ . In particular, what does this imply about the $\pi$ values of the vertices along the path?)

Now, we can ask the question:

Question: What is the probability that a particular simple path, $p = (v_1, v_2, ..., v_k)$ of length k in G gets preserved in $G_{dir}$ given that we take a random permutation, $\pi : V {->} \{1, ..., |V| \}$ to obtain $G_{dir}$ from $G$ ?

Solution: There are only two ways in which path $p$ can get preserved in $G_{dir}$ -

either as the directed path, $p1 = (v_1, v_2, ..., v_k)$ ,

or as the directed path, $p2 = (v_1, v_2, ..., v_k)$ .

Path $p1$ exists only if $\pi (v_1) < \pi (v_2) <... < \pi (v_k)$ .

Path $p2$ exists only if $\pi (v_1) > \pi (v_2) > ... > \pi (v_k)$ .

Note that we are not concerned with the $\pi$ values of any of the other $n-k$ vertices of G.

Hence, we obtain the following:

Probability that a particular path, p in G, of length k, is preserved in $G_{dir}$ = 2 / (k+1)!.

(How do we get that?)

===

The above probability implies that to preserve any particular simple path of G (having length k), we need to take an expected number of (k+1)! / 2 random permutations.

===

Running time of the algorithm:

We can state the expected running time of the algorithm. We need to perform the following steps.

1. Given a particular random permutation, $\pi : V {->} \{1, ..., |V| \}$ .

Raise the adjacency matrix, B of $G_{dir}$ to the power k.

This can be done via $O(log$ $k)$ matrix multiplications, each of which takes $O(V^\omega)$ time. (Here $\omega$ is the exponent for matrix multiplication $(\omega < 2.376)$ . )

2. Repeating the same for an expected number of $O( (k+1)! )$ random permutations.

3. Keep track of of the $n \times (n-1) / 2$ pairs of vertices, for each of which we need to output a boolean Yes or No value (corresponding to whether or not a simple path of length k exists in G between that pair of vertices.) (Note: n = |V|).

Initialize all $n \times (n-1) / 2$ values of this global list to No at the beginning of the algorithm. For each permutation, if the matrix entry, $B^k [i][j] \neq 0$ and if the value corresponding to pair (i,j) is listed as No in the global list, change it to Yes.

Hence, the expected running time of the algorithm is $O( (k+1)!$ . $log$ $k.$ $V^\omega)$ .

(We have ignored certain polynomial (in the size of the graph) factors in the running time. That is justified owing to the “supremacy” of the (k+1)! term over other factors.)

Am I the dreamer or the dreamed?

November 16, 2009 in Ideas | Tags: poem | Leave a comment

I close my eyes and drift
into a dark abyss, into a dark chaos.
Sleep is familiar, so I am not afraid
to dissolve into the unknown wilderness,
the vast ocean of non-existence.

A while later, as if in a dream,
another being arises,
out of the ashes of oblivion,
assuming a new form, a new identity.

With the golden rays of dawn
There is a dissolution. It happens again
And again, and again – every single day!
Sleep is familiar, so I am not afraid.

But the question always remains-
Am I the dreamer or the dreamed?

[This beautiful poem was written by my sister. Many more such beautiful poems are at http://perpetuated.blogspot.com/]

Vertex Cover and Set Cover – 4

November 13, 2009 in Hey Math, Theoretical Computer Science | Tags: CS, graph, math, reduction, Set Cover, Theory, Vertex Cover | Leave a comment

Question: We are given an instance of the Vertex Cover problem. We are also given an algorithm for the Set Cover problem. Using this algorithm as a black box, solve the given instance of the Vertex Cover problem.

Solution:

Given instance of Vertex Cover problem: undirected graph, G = (V, E); positive integer k.
Question: Does G have a vertex cover of size at most k?

===

[To recapitulate, this is what an instance of the Set Cover problem looks like:

Given: Set S = { $a_1, a_2, ..., a_p$ }; subsets of S: $B_1, B_2, ..., B_q$ ; positive integer k.
Question: Does S have a Set Cover of size at most k? ]

===

We have the following Vertex Cover instance specified to us in the question:

E = { $e_1, e_2, ...., e_m$ }.

V = { $v_1, v_2, ..., v_n$ }.

We will convert this into an instance of the Set Cover problem, and apply the algorithm for the Set Cover problem to solve it.

Idea:

1. In the Vertex Cover problem, we need to cover edges of the graph. In the Set Cover problem we need to cover elements of a set, S. So, we will convert each edge into an element of a set, S, and try to cover that set.

2. In the Vertex Cover problem, we need to cover the edges using limited number of vertices. In the Set Cover problem, we need to cover elements of a set using limited number of subsets. So this gives us the idea of mapping a vertex of the Vertex Cover problem instance to a subset of the Set Cover problem instance.

Now, what all elements does a subset $B_i$ cover? It covers all the elements contained in $B_i$ .

Now again, what all edges does a vertex, $v_i$ cover? It covers all edges that are incident upon it.

So, now the conversion of the Vertex Cover instance into a Set Cover instance is much clearer.

1. Corresponding to each edge, $e_i$ , introduce an element $a_i$ . (Call this set of m elements, corresponding to the m edges, as S.)

2. Corresponding to each vertex, $v_i$ , introduce a subset of S, called $B_i$ .

The set $B_i$ contains all elements $a_j$ for which the corresponding edge, $e_j$ is incident upon vertex, $v_i$ .

(For example, if edges $e_3, e_5, e_7$ are incident upon vertex, $v_2$ , then set, $B_2 =$ { $a_3, a_5, a_7$ }. )

We were asked to find whether a Vertex Cover of size at most k exists. In the Set Cover instance that we have produced, this gets converted into the question: Does there exist a Set Cover of size at most k?

We have thus completely specified an instance of the Set Cover problem, derived from the original Vertex Cover problem that we were presented with.

Now, we can apply the algorithm to the Set Cover problem to solve this new instance. (The instance of the Set Cover problem that we derive from the Vertex Cover instance, is known as a reduced instance. i.e. The Vertex Cover problem was reduced to the Set Cover problem.)

Question: Does this reduced instance of the Set Cover problem have a set cover of size at most k?

If the answer is “yes”: This implies that there exists a collection of at most k subsets $B_i$ through which we covered all elements, $a_j$ . If we go back to the original Vertex Cover instance, this implies that there exists a subset of at most k vertices $v_i$ which covers all edges, $e_i$ of the graph. Hence, the answer to the Vertex Cover instance is also “yes”.

In other words: If the answer to the reduced Set Cover instance is “yes”, then the answer to the original Vertex Cover instance is “yes”.

If the answer of the reduced Set Cover instance is “no”: This implies that we cannot cover all elements of S using any collection of at most k subsets.

This implies that we cannot cover all edges of the graph, G using any set of at most k vertices. (We can prove this by contradiction: If suppose, we are able to cover all edges using a set of at most k vertices, then by using the corresponding collection of at most k subsets, we can cover all elements of S. i.e. We arrive at a contradiction, and hence, we cannot cover all edges of the graph G using any set of at most k vertices.) This means that the answer to the Vertex Cover instance is “no”.

In other words: If the answer to the reduced Set Cover instance is “no”, then the answer to the original Vertex Cover instance is “no”.

====

Thus, in order to solve the original Vertex Cover instance:

1. We reduced it to an instance of the Set Cover problem.

2. We solved that instance using an algorithm for the Set Cover problem.

3. If the answer to the Set Cover instance comes out to be “yes”, it implies that answer to original Vertex Cover instance is “yes”.

4. Else (if the answer to the Set Cover instance is “no”), the answer to the orginal Vertex Cover instance is “no”.

====

Vertex Cover and Set Cover – 3

November 13, 2009 in Hey Math, Theoretical Computer Science | Tags: CS, graph, math, Set Cover, Theory, Vertex Cover | Leave a comment

Consider the Vertex Cover problem.

To recapitulate:
Given: Undirected graph, G = (V, E), positive integer, k.
Question: Does G have a Vertex Cover of size at most k?

Now, we shall look at a problem related to the above question.

How do we verify the validity of a answer to the Vertex Cover problem?

Consider the following example graph, G = (V, E):

Consider the following conversation between a teacher and a student.

Teacher: Does the above graph have a Vertex Cover of size $\leq 5$ ?
Student: Yes
Teacher: Give me some proof of your answer that I can check quickly.
Student: Consider the set of vertices: X= {v3, v5, v7}.This set is a Vertex Cover of G of size $\leq 5$ .

The teacher needs to check 2 things now:
(1) Is the size of set X $\leq 5$ ?
(2) Is set X a Vertex Cover of the graph?
If the answer to both of the above questions is “yes”, then the student’s answer has been validated.

Both these questions about set, X can be answered quickly.

That is obvious for the first question. You need to find out the size of the set, and compare that with 5.

For the second question: We will check for each edge whether that edge is covered by X i.e. whether at least one of its end points is in X. This can also be done quickly. [Checking for a particular edge requires time proportional to the size of X. We need to check this for all edges of G. Hence, this can be done in time O(|E|.|X|).]

What we observed here is a very important concept related to complexity theory.

We are given a decision problem (i.e. a problem whose answer is “yes” or “no”). If we are able to provide a “short and efficiently-verifiable proof” of the answer, when the answer is “Yes”, then the problem is said to belong to a class of problems called as NP.

Notes:

1. What is meant by “short proof”?
“Proof” is also termed as “Certificate”. A “short” certificate means that the size of the certificate is bounded by a polynomial in the input size. For the Vertex Cover problem, the input is the graph G = (V, E) and the positive integer, k. So, a certificate whose size is bounded from above by a polynomial in |V|, |E|, and k, is said to be a “short” certificate.

2. What is meant by “efficiently-verifiable proof/certificate”?
Using the certificate, we should be able to prove or disprove the answer to the decision problem in a time that is polynomially bounded in the input size.When the answer to the Vertex Cover problem is “Yes”, a short and efficiently-verifiable certificate is a set of vertices of cardinality $\leq k$ that forms a vertex cover of the input graph.

3. Problem vs. Instance of a problem: The Vertex Cover problem and the Set Cover problem are examples of problems. An instance of a problem is different. For the Vertex Cover problem, an instance of the problem is a particular graph G = (V, E) and a positive integer, k. For example, the graph drawn above and question asked by the teacher setting k=5, formed one particular instance of the Vertex Cover problem.

“Yes” instance: If the answer to a particular instance of a decision problem is “Yes”, then it is called a “yes”-instance of the problem.

“No” instance: If the answer to a particular instance is “No”, then that instance is termed as a “no”-instance of the problem.

4. NP stands for Non-deterministic Polynomial time. This means that the answer to a “yes”-instance of a decision problem in NP can be verified in polynomial time. (In other words, there exists a short and efficiently-verifiable certificate for every “yes”-instance of a problem in NP.)

—–

Let us continue the teacher-student conversation from above.

Teacher: Does the given graph have a Vertex Cover of size $\leq 2$ ?
Student: No.
Teacher: Give me a short and efficiently-verifiable certificate for your answer.

A possible certificate for this would be to enumerate all possible sets of vertices of size $\leq 2$ .

There are n(n-1)/2 + n such sets. (Here, n = |E|.)

The general Vertex Cover problem instance has input parameters as |V|, |E| and k. If the instance turns out to be a “no”-instance, a certificate on the lines of the one given above would include all sets of vertices of size $\leq k$ . (We can also use sets of vertices of size exactly k as certificate. The cases for sets of smaller size get covered by sets of size exactly k.) Number of such sets (of size exactly k) is (n choose k) which is NOT polynomially bounded in n and k. Hence, this is not a short certificate.

In order to verify the validity of the answer (which was “no”) using the abover certificate we will have to consider all suts of size k, and check whether any of those is a Vertex Cover. Checking for a particular set takes polynomial time. But since we need to check for all sets to validate the answer, verifying this certificate takes time that is not polynomially bounded in the input size. Hence, this is not an efficiently-verifiable certificate.

Notes:

5. We observe a dichotomy between “yes”-instances and “no”-instances of the Vertex Cover problem. We can efficiently verify the answer to a “yes”-instance of the Vertex Cover problem. But, doing the same for a “no”-instance seems to be difficult. Note that we are not saying that it is impossible. Simply, that efficient answer verification for a “no”-instance of the Vertex Cover problem is not known as yet. It is an open problem. Solving this would solve a celebrated open question in complexity theory: Is NP = co-NP? [co-NP is the class of problems for which the "no"-instance can be verified efficiently.]

Points to ponder:

1. Prove that the Set Cover problem belongs to NP.

Vertex Cover and Set Cover – 2

November 13, 2009 in Hey Math, Theoretical Computer Science | Tags: CS, graph theory, math, Set Cover, Theory, Vertex Cover | Leave a comment

Having looked briefly at the Vertex Cover problem, here we shall define the Set Cover problem.

As the name suggests, we have a set, and we need to “cover” something.

Consider the following example:

We have a set of cities, S = {Madras, Delhi, Pilani, Los Angeles, London, Paris}.

We are also given the following subsets of S:
$B_1$ = {Madras, Delhi, Pilani}.
$B_2$ = {Pilani, London, Paris}.
$B_3$ = {Delhi, Los Angeles}.
$B_4$ = {Madras, Paris}.

If we consider the sets $B_1, B_2, B_3$ , then we cover all the cities of S. Similarly, if we select $B_2, B_3, B_4$ , we again cover all cities of S. (A city is “covered” if it is part of any of the subsets that we select.)

We can now state the Set Cover Problem more formally.

We are given a set, S = { $a_1, a_2, ..., a_n$ } of $n$ elements.

We are also given certain subsets of the set S: $B_1, B_2, ..., B_m$ .

We wish to find a collection of these subsets so as to cover the set S. We wish to find a collection of minimum number of subsets that covers the set S. (The number of subsets in the chosen collection is called the size of the Set Cover.)

The Set Cover Problem is defined as a vatriant of the above problem. Instead of finding a minimum-sized collection of subsets, we are given a positive integer, k, and are asked the following question: “Does there exist a Set Cover of size less than or equal to k?”.

(Note the similarity with the definition of the Vertex Cover problem.)

Vertex Cover and Set Cover – 1

November 13, 2009 in Hey Math, Theoretical Computer Science | Tags: complexity, CS, graph theory, math, NP, Set Cover, Theory, Vertex Cover | Leave a comment

Here we will look at two very interesting problems. One is known as the Vertex Cover Problem, and the other as the Set Cover Problem. Both are quite simple to define, and visualize (and equally difficult to solve efficiently ).

Let us consider the Vertex Cover Problem first. As the name suggests, we have to “cover” something. We are given an undirected graph, G = (V, E). We need to select a set of vertices from V, so that all edges are “covered” by this set of vertices.

What exactly do we mean by covering? A vertex “covers” all edges that are incident upon it. This does seem to be quite a natural definition.

Example:

In the above graph, the vertex, v2 covers edges {v2,v1}, {v2,v3}, {v2,v4}. Analogously, edge {v2,v4} is covered by vertices, v2 and v4. (It is clear that every edge can be covered by at most two vertices. No vertex other than its end points can cover an edge.)

A set of vertices, S, covers all edges that are incident upon any vertex of S.

For example, in the above graph, the vertex set {v3, v4, v5} covers edges {v3,v2}, {v4,v2} and {v4,v5}.

Now that we know what it means to cover an edge, we repeat what we stated earlier the question: What is a Vertex Cover? A Vertex Cover is simply a set of vertices which covers all edges of the graph.

For instance, in the above graph, the set {v1, v3, v4} is a vertex cover. (Note that the set, V is trivially a vertex cover for the graph, G = (V, E). )

From the above, it might seem that finding a vertex cover seems to be a simple task, and as such does not merit special mention. Indeed that is true.

But what is not so easy is finding a Vertex Cover of minimum possible cardinality, i.e. we need to cover all edges of the graph using as few vertices as possible.

Specifically, we are given an undirected graph G = (V, E) and a positive integer, k, and are asked to find out whether there exists a Vertex Cover of size (i.e. cardinality) less than or equal to k. This now, is the definition for our Vertex Cover Problem (and as stated at the very beginning, this is not the easiest problem to solve ).

Let us go back to the graph drawn above, and ask the following questions:

(1) Does there exist a Vertex Cover of size $\leq 3$ ?
The answer is an emphatic, “Yes”. (The set {v1, v3, v4} is a proof that our answer is correct.)

(2) Does there exist a Vertex Cover of size $\leq 2$ ?
Again, the answer is “yes”. (The set, {v2, v4} is a proof of the correctness of the answer.)

(3) Does there exist a Vertex Cover of size $\leq 1$ ?
Here, the answer is “No”. And how do we verify this answer? One way is the obvious brute force method. Enumerate all sets of vertices of size $\leq 1$ , and check whether any of them is a vertex cover. If none of them is, then the answer is correct.

(Note: It is highly possible that there would be errors in this series of posts. I am sorry for that. It would be great if you could point them out.)

Hindu Rashtra and co-existence of religions

November 10, 2009 in Books, Dharma, Ideas | Tags: Bharat, bunch of thoughts, Dharma, hinduism, religion | Leave a comment

(This passage is from Sri M.S. Golwalkar’s book, Bunch of Thoughts. In this excellent passage, he describes the salient features of Hindu thought vis-a-vis the parallel development of other religious faiths. Through historical and modern examples, he brings forth the idea of a society where harmonious co-existence of different religions is possible. The phrase “religious tolerance” is a modern and diluted version of one of the key aspects of Hinduism. “Tolerance” has a negative connotation implying a not overly positive attitude of condescension to “allow” or “permit” the co-existence of other religions. Hinduism transcended the level of mere “tolerance” to a stage where people professing other religions were actively considered an integral part of the universal brotherhood, thus implying as a natural consequence, harmonious and symbiotically-beneficial co-existence, obviating and transcending the idea of a “superior” entity “tolerating” the existence of an “inferior” one. Do read the following with an open mind.)

HINDU RASHTRA AND “MINORITIES”

The answer to the so-called problem of ‘religious minorities’ can be found only in the historically correct, rational and positive approach of Hindu Rashtra. Otherwise, the so-called minorities are bound to become more and more hardened in their separate shells of religion and turn into a dreadful source of disruption of our body-politic.

So, all that is expected of our Muslim and Christan co-citizens is the shedding of the notions of their being ‘religious minorities’ as also their foreign mental complexion and merging themselves in the common national stream of this soil. As far as the national tradition of this land is concerned, it never considers that with a change in the method of worship, an individual creases to be the son of the soil and should be treated as an alien. Here, in this land, there can be no objection to God being called by any name whatever. Ingrained in this soil is love and respect for all faiths and religious beliefs. He cannot be a son of this soil at all who is intolerant of other faiths.

A Lesson From Neighbours

In this connection, it would be beneficial for our Muslim friends here to take a lesson from their co-religionists in Iran, Turkey and Indonesia. Though Persia became Islamic, Persians did not change their script and take to the Arabic script. They did not take to the Arabic way of life; they stuck to their own. They have been sticking to the memory of their great forefathers. Even now a Persian will remember his forefathers, will speak of Rustom with great respect and honour. Rustom was not a Muslim. Kamal Pasha ‘the Maker of Modern Turkey’ restored the age-old national pattern of life and limited the role of Islam to personal worship of God.

The example of Indonesia is extremely revealing. Majority of the Indonesians profess Islam. However, Saraswati and Ganesh are the presiding deities of their learning and knowledge. Children start their ABC in education with pictorial Ramayana. One of our countrymen was amazed to see this when he had gone there. He asked a leading Indonesian, “How is it, though you are Muslims, you teach Ramayana to your Children?” The Indonesian replied with pride, “Because. Sri Ramachandra is our national hero par excellence. We very much desire that our children should emulate his lofty ideal. No doubt we belong to the Islamic faith. But that does not mean that we should give up our precious national heritage and values of life.” What an excellent lesson for our Muslim friends here! There the names too are hundred per cent Hindu. Their previous President was Sukarna. His son, Kartikeya. The present President is Suhrida (distorted as Suharto in English) meaning ‘a true friend’. Women too bear the proud names of Sita, Savitri, Damayanti etc. Garuda, the mount of Vishnu, adorns the name of their airways. Their constitution begins with the declaration “Dharmo Rakshati Rakshitah.”

This is the real and abiding cornerstone of national harmony and integration, subscribing to common national ideals irrespective of personal religious creeds. And it is this concept as applied to our country, that we call Hindu Rashtra, the only rational, practical and right concept.

Hindu Rashtra in Living Practice

To disabuse the minds of genuinely doubtful souls we may recapture here the historical tradition of Hindu Rashtra vis-à-vis the foreign religious groups. The glaring fact inscribed on every page of our history and testified by even foreign historians and travellers, is that we never discriminated against any one on the score of religion in any sphere of our national life.

The Muslims enjoyed perfect freedom and equality in the powerful Hindu empire under the Vijaynagar Kings or in the Punjab under Sikh heroes. The latest Hindu Power, which rose under the great Shivaji, too, did not discriminate against Muslims on the score of religion.

To cite a few instances, the naval chief of Charapati Shivaji, Darya Sarang, was a Muslim, and two of his main lieutenants were Ibrahim Khan and Daulat Khan. At the time of the grim encounter with Afzal Khan, out of the ten trusted bodyguards who accompanied Shivaji, three were Muslims. Again, the 18-year old lad who accompanies Shivaji to Agra and who played a key role in the thrilling escape of Shivaji from the grip of Aurangzeb was Madari Mehtar, a Muslim. Countless instances are there of Shivaji gifting land and annual grant to masjids and dargas. He even made arrangements for the offering of worship according to Islam to the tomb of Afzal Khan on Pratapgad. Even the most fanatic Muslim chroniclers of those times have noted with admiration that Shivaji treated with utmost respect their Koran, masjids and dargas, their holy men and their womenfolk. And all this, when exactly the opposite was being perpetrated by the Muslim on Hindus all round.

Even later on, on the battlefield of Panipat in 1761, in the crucial struggle for the survival of Swaraj, the key position of the Artillery Chief on the side of the Hindus was held by Ibrahim Gardi, who ultimately fell fighting on the battleground.

Hindusthan lived a life of unchallenged glory and power for thousands of years and spread its spiritual and cultural effulgence over vast areas of the globe-right from Mexico to Japan. Never has its flag waded towards military victory through the blood and tears of those races. Its victory had always been moral and cultural. It was a victory joyously welcomed by the local populace, a victory of selflessness, character and catholicity of spirit which, evoked gratitude instead of revolt from them. Passage of centuries has not dimmed their feelings towards this land. Even to this day the inmost wish of many a devout soul of those lands is to come to the ‘holy land’ of Hindusthan and take a dip in the Ganga. For them, it is never a simple ‘visit’ to this country, it is always a ‘pilgrimage’. From all this, one can easily visualize the unique and matchless life-values that formed the very core of this nation.

Call to Motherhood

November 7, 2009 in Books, Dharma, Ideas, Inspiration | Tags: bunch of thoughts, Dharma, duty, India, society | Leave a comment

(This is from Sri M. S. Golwalkar’s book, Bunch of Thoughts. Here he talks about the manner in which the womenfolk in our society can elevate the collective social consciousness, and work for the general uplift of the society.)

Epics in Heroic Motherhood

As we are well aware, our nation is beset with ever so many perils. Attempts to undermine the integrity of our motherland and our society are on. Challenges to the time-honoured values of our spiritual heritage are mounting. Conflicts and confrontations are thick in the air. Under such conditions, what is the type of training that we have to impart to our children? Shall we teach them to seek safety in their homes and not to stir out? Should we harp upon things pertaining to their own happiness and future and ask them out not to “dabble in other things”? What shall we teach?

There is a beautiful anecdote narrated in Mahabharata. There was a queen by name Vidula. She sent her son Sanjay to the war-field but the fellow became nervous and terror-stricken. He turned his back to the enemies and galloped to his capital. When Vidula saw her son in that crestfallen state she closed the entrance to the fort and severely chastised him. That conversation between the mother and the son has become famous as Vidula-Sanjay-Samvad, wherein Vidula instructs her son as to how a brave warrior should conduct himself on the battlefield. She then orders him to go back to war and return as a victorious hero. As the story goes, Sanjay sallied forth into the battlefield, displayed exemplary valour and came back to be received by his mother with honour.

The words of Kunti when the five Pandavas came to seek her blessing before proceeding to give battle are remarkable for their heroic tone. She says:
यदर्थं क्षत्रिया सूते तस्य कालोयमागतः ।
न हि वैरं समासाद्य सींदति पुरुषर्षर्भाः ।।

(The moment has arrived for which Kshatriya mothers give birth to sons. Lion-hearted men are not cowed down in the face of enemies.)

There is one more couplet in Mahabharata which says: may no woman give birth to one who would mutely suffer insults, who is devoid of vigour and manly prowess and one who would bring joy to the enemies.

Duty Towards Neighourhood

There is a special burden upon our mothers of serving our needy sisters in society. True, a majority of our mothers will not be in a position to go to far-off places to carry on social work among the distressed and the destitute. However, this does not mean that they should sit back in their homes all the while. They could establish useful contacts among the womenfolk in their own neighbourhood and carry out programmes, which would inculcate our cherished ideas among them and their children. The spirit of mutual help and service would also have to be made popular through our day-to-day social intercourse. Our womenfolk should not be allowed to develop inferiority complex or a feeling of helplessness. They should be taught that they are the living emblems of parashakti.

There are quite a few of our educated mothers who have spare time and energy, which is often wasted in gossip of fashionable clubs. Here is one useful hint for them. There will be many small boys and girls in their neighbourhood who do not go to schools. They can make such children gather either in their own house or in some other convenient place and engage them in games, stories, songs, etc.

Arousing the warrior spirit

November 6, 2009 in Books, Dharma, Ideas, Inspiration | Tags: Bharat, Dharma, duty, Ideas, India, Inspiration | Leave a comment

(This is from Sri M. S. Golwalkar’s book, Bunch of Thoughts. Here he talks about arousing our dormant warrior spirit for the protection of the sanctity of our motherland.)

Steel People’s Will

The first requisite is to steel our will for a nation-wide, determined and organised effort. The struggle is likely to be long and bitter. All of us will be called upon to undergo suffering and sacrifices. Let all of us face these difficulties steadfastly and with good cheer. There is no doubt that the adoration for our motherland which had been lying dormant in our hearts so long will now bring forth and dispel all dark shadows of selfishness and mutual jealousies. It is indeed encouraging to see so many people coming forward to contribute to the National Defence Fund. I hope more and more of them will give still more. Let all persons physically fit be ready for military service. And let their mothers bless and send forth their sons at this hour of trial. When the five Pandavas went to seek the blessings of their mother Kunti before the commencement of the Mahabharata war, she blessed them saying, “Go ye all to the battle. This is the occasion for which Kshatriya women give birth to sons. Go and give your best in this dharmayuddha.” Let every mother speak in the same heroic strain to her sons even now.

Modern wars, be it remembered, are total wars. They are not merely pitched battles between armies. Every one, right from the scientist and industrialist to the labourer and farmer, will have to work harder and longer in a spirit of national dedications, shelving aside all other considerations of personal and group interests, disputes and claims for the time being.

The Living Ideal

It is a matter of common experience that character and morality are wanting even in the very high strata of our national life. Those in the higher strata of life are intelligent and educated. They know what is morality and what is immorality. They can even deliver excellent sermons on the subject. Then, what are we going to achieve merely by advising such persons?

In fact, there is only one way by which selfishness can be restrained. Give the man an ideal to work for, to live for and die for. Then that person, in his devotion to that ideal, will be able to control the pulls of his self-interest and build up a better character. There is no other way. Give the people an ideal, high and holy, an ideal, which naturally resonates in their hearts, throbs in their blood and which has been with them for generations. Then even the ordinary man in the street will be able to feel the rise of devotion and character in him. Such an inspiring ideal is the realisation of the glory and greatness of our scared Hindu Rashtra.

“I am a child of this great Hindu nation. For generations, my great forefathers have striven to make this the greatest and noblest nation – an ideal nation of ideal men – on the face of the earth. I, too, will live and strive for the same goal.” – This is the natural impulse that we have inherited. We feel it in our blood. If this natural sublime urge is roused then our people will be able to rise above their selfish pulls and manifest chaste national character in their day-to-day life.

The Vision that Inspires

Even in the present times of national crisis we cannot afford to ignore this content of idealism. Let us not forgot that it was on the battlefield of Kurukshetra, when war-drums were beating, trumpets were blowing and Arjuna was standing in the centre of the two armies, that Sri Krishna taught him the eternal and inspiring message of selfless action in the cause of dharma and spurred him to matchless valour and victory. It is only when a hero is inspired with the vision of an ideal that he will be able to put forth the best in him. He should be clear in his mind about the life values for which he is to fight and die, if need be. Talk of economic plans and industrial glory cannot stir the people to suffer and sacrifice. Dry and disparaging descriptions of our motherland as ’snow-bound’, ‘unfit for human habitation’, ‘not a blade of grass growing there’, etc., will only kill the spirit of the people who will then see no difference even if such a piece of land is occupied by the enemy. So it is absolutely essential that the eternal and inspiring call of devotion to our holy motherland and our national ideals is engraved in the heart of every son of this soil.

All our valiant freedom fighters in the past and in modern times were inspired with the living vision of Hindu Rashtra. That was the only effective rallying cry to rouse our masses to action from one corner of the country to the other. And whenever that vision was blurred or lost sight of, the people too relapsed into inactivity and servility.

It is only when the people are inspired with this age-old national vision that it is possible to make them rise to heights of selflessness, sacrifice and heroism and to forge them into a single living national entity from one end of the land to the other and build up an unassailable national strength.

Purpose in life – 2

November 3, 2009 in Dharma, Ideas, Inspiration | Tags: Dharma, duty, knowledge, purpose | 1 comment

[Here is the first post in the topic.]

Lead a life which is of service to others. Living only for the sake of one’s own self is extreme selfishness.

There are many in need of help, encouragement, protection, comforting words. Be a beacon of light in the lives of those looking for such inspiration.

A drowning man cannot save a friend from drowning. So, elevate yourself through sacrifice and practice to a position from where you can be of better service to others.

Acquire knowledge which elevates. Through continuous acquisition of proper knowledge one can soon reach a stage from where one’s presence itself is a benediction to others. Knowledge that enables us to elevate our lives is proper knowledge.

(It is mentioned in Srimad Bhagavatam: A saintly sage is happy and pleasing in his external behavior, whereas internally he is most grave and thoughtful. Because his knowledge is immeasurable and unlimited he is never disturbed, and thus in all respects he is like the tranquil waters of the unfathomable and unsurpassable ocean.)

So, acquire knowledge. The urgency and the importance of acquisition of proper knowledge cannot be overstated.

Strive to acquire the qualities of saintly persons as mentioned in the scriptures. Acquire knowledge of the Self and God.

Utilize opportunities where you can uplift the lives of others. Your life will be blessed.

Qualities of saintly persons – 8

November 3, 2009 in Books, Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, qualities, saintly, Sanskrit, Srimad Bhagavad Gita | Leave a comment

om sri gurave namah

Arjuna asks Lord Krishna to explain to him the characteristics of one who is situated in transcendental consciousness. In response, Krishna mentions different such characteristics.

[These verses are in Chapter 2 of Srimad Bhagavad Gita.]

[54] Arjuna said: O Krishna, what are the signs of one absorbed in transcendental consciousness? How does one steadfast in spiritual consciousness talk? How does he sit? And how does he walk?

[55] Lord Krishna said: O Arjuna, when one gives up all varieties of desire for sense gratification, which arise from mental concoction, and when one’s mind, thus purified, finds satisfaction in the self alone, such a person is said to be in pure transcendental consciousness.

[56] One who remains undisturbed in distress, is unattached/passive when joyous events occurs, is free from attachment, fear and anger, is said to be a sage of steady mind.

[57] One who is without any attachment, and neither rejoices or curses on obtaining good or evil, is said to be firmly situated in perfect knowledge.

[58] One who completely withdraws his senses from the sense objects, just like a tortoise withdraws its limbs into its shell, is said to be in perfect knowledge.

Here are the verses in Samskritam:

Here is the transliteration:

[54]arjuna uvāca
sthita-prajñasya kā bhāshā
samādhi-sthasya keśava
sthita-dhīh kiḿ prabhāsheta
kim āsīta vrajeta kim

[55]śrī-bhagavān uvāca
prajahāti yadā kāmān
sarvān pārtha mano-gatān
ātmany evātmanā tushtah
sthita-prajñas tadocyate

[56]duhkheshv anudvigna-manāh
sukheshu vigata-sprhah
vīta-rāga-bhaya-krodhah
sthita-dhīr munir ucyate

[57]yah sarvatrānabhisnehas
tat tat prāpya śubhāśubham
nābhinandati na dveshti
tasya prajñā pratishthitā

[58]yadā saḿharate cāyaḿ
kūrmo ‘ńgānīva sarvaśah
indriyānīndriyārthebhyas
tasya prajñā pratishthitā

[I took material for the above from here, here, and elsewhere on the Internet.]

Qualities of saintly persons – 7

November 2, 2009 in Books, Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Books, Dharma, Krsna, qualities, saintly, Sanskrit, Srimad Bhagavad Gita | Leave a comment

Here are six more of the 26 qualities of the divine nature that Lord Krishna mentions to Arjuna in Srimad Bhagavad Gita.

[These 26 qualities are mentioned in the first 3 verses of Chapter 16.]

21. Radiance/lustre (this is an illustrious proof of the efficacy of spiritual practice); Vigor/strength to aid those in need to protection and help.

22. Forgiveness (Do not harbor feelings of vengeance against those by whom you are wronged. Do not get angry at those who offend you.)

23. Fortitude (Defending/upholding righteousness and steadying the mind, even when you are under great duress.)

24. Cleanliness/Purity (Both internal and external cleanliness to be spiritually worthy. Purity not only in the mind and body, but also in one’s dealings.)

25. Absence of envy (Become free from all feelings of envy towards others.)

26. Lack of desire for honor or prestige/ Absence of false ego.

These are the 26 divine qualities that Lord Krishna mentions. Let us strive to inculcate these in our lives.

Here are the 3 verses in Samskritam [Chapter 16, verses 1,2,3]:

Here is the transliteration:

śrī-bhagavān uvāca
abhayaḿ sattva-saḿśuddhir
jñāna-yoga-vyavasthitih
dānaḿ damaś ca yajñaś ca
svādhyāyas tapa ārjavam
ahiḿsā satyam akrodhas
tyāgah śāntir apaiśunam
dayā bhūteshv aloluptvaḿ
mārdavaḿ hrīr acāpalam
tejah kshamā dhrtih śaucam
adroho nāti-mānitā
bhavanti sampadaḿ daivīm
abhijātasya bhārata

[This was taken from here, and other sites.]

Qualities of saintly persons – 6

November 1, 2009 in Books, Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, qualities, saintly, Srimad Bhagavad Gita | Leave a comment

om sri gurave namah

Here are five more divine qualities that Lord Krishna mentions to Arjuna in Srimad Bhagavad Gita. Let us strive to inculcate these qualities in our lives.

[The Supreme Person, Krishna mentions 26 qualities in all in the first 3 verses of Chapter 16.]

16. Mercy/Compassion towards all living entities: (We should feel compassion towards all beings, especially if they are in distress. Strive to alleviate their misery.)

17. Absence of greed/ Non-covetousness: Do not have greed for sense gratification; be satisfied with what is allotted to you in life.

18. Gentleness/Humility: Such behavior is appropriate for saintly association. Strive to be free from cruelty and harshness.

19. Modesty: Shyness in decorum, and hesitancy even in the thought of wrong-doing.

20. Determination/ Absence of fickleness: This is needed to keep trying even in the face of perceived failure; Determination to remain firm against temptations presented to one; Avoidance of frivolous activities.

Here is the verse from Srimad Bhagavad Gita [Chapter 16, verse 2].

Here is the transliteration:

ahiḿsā satyam akrodhas
tyāgah śāntir apaiśunam
dayā bhūteshv aloluptvaḿ
mārdavaḿ hrīr acāpalam

[Material for the above was taken from here, and other sites. All mistakes in the above presentation are mine.]

Qualities of saintly persons – 5

October 31, 2009 in Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, qualities, saintly, Srimad Bhagavad Gita | Leave a comment

Five more of the 26 qualities that Lord Krishna tells Arjuna about saintly persons in Srimad Bhagavad Gita [Chap 16, verses 1-3]

11. Truthfulness

12. Freedom from anger

13. Renunciation (renounce anything that is opposed to realization of the self)

14. Peacefulness/Calmness (do not let the mind get agitated).

15. Aversion to fault-finding (fault-finding in others is a quality that many of us are afflicted with)

Here is the corresponding verse in Samskritam [Chapter 16, verse 2].

Transliteration

ahiḿsā satyam akrodhas
tyāgah śāntir apaiśunam
dayā bhūteshv aloluptvaḿ
mārdavaḿ hrīr acāpalam

[The material for the above was taken from here, and other sites.]

Qualities of saintly persons – 4

October 31, 2009 in Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, qualities, Srimad Bhagavad Gita | Leave a comment

Here are five more saintly qualities mentioned by Lord Krishna to Arjuna in Srimad Bhagavad Gita.

(Twenty six such qualities are mentioned in the first 3 verses of Chapter 16.)

6. Performance of sacrifice

7. Study of Vedic scriptures

8. Austerity

9. Simplicity

10. Non violence

Here are the first two verses in Samskritam:

Transliteration:

(The above was taken from sites on the Internet.)

Qualities of saintly persons – 3

October 30, 2009 in Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, qualities, spirituality, Srimad Bhagavad Gita | Leave a comment

om ajnAna-timirAndhasya
jnAnAnjana-shalAkaya
cakshur unmIlitam yena
tasmai srI-gurave namah

“I was born in the darkest ignorance, and my guru, my spiritual master, opened my eyes with the torch of knowledge. I offer my respectful obeisances unto him.”

Lord Krishna mentions to Arjuna, twenty six qualities, which we should aspire to inculcate in our nature. (The earlier two posts on the same topic, dealt with verses from Srimad Bhagavatam, while this is from Srimad Bhagavad Gita.)

These are mentioned in the first three verses of Chapter 16 of Srimad Bhagavad Gita.

Here are the first five of these qualities:

1. Fearlessness - The first quality mentioned is fearlessness (abhayam).

2. Pure-heartedness or purification of one’s existence.

3. Cultivation of spiritual knowledge

4. Charity (given to worthy recipients from what one legitimately owns)

5. Self-restraint (controlling the mind from being influenced by sense objects)

Here is the first verse in Samsritam:

Transliteration:

śrī-bhagavān uvāca
abhayaḿ sattva-saḿśuddhir
jñāna-yoga-vyavasthitih
dānaḿ damaś ca yajñaś ca
svādhyāyas tapa ārjavam

(The above material was collected from sites on the Internet.)

How to perform actions

October 29, 2009 in Dharma, Ideas, Sanskrit | Tags: action, Arjuna, Dharma, Karma Yoga, Krsna, Srimad Bhagavad Gita | Leave a comment

Lord Krishna explains to His friend and devotee, Arjuna the way to perform action so as to not be entangled by the results.

Here are five verses from Chapter 5 of Srimad Bhagavad Gita.

(This is from Srila Prabhupada’s writings, available here.)

[3] One who neither hates nor desires the fruits of his activities is known to be always renounced. Such a person, free from all dualities, easily overcomes material bondage and is completely liberated, O mighty-armed Arjuna.

[7] One who works in devotion, who is a pure soul, and who controls his mind and senses is dear to everyone, and everyone is dear to him. Though always working, such a man is never entangled.

[8-9] A person in the divine consciousness, although engaged in seeing, hearing, touching, smelling, eating, moving about, sleeping and breathing, always knows within himself that he actually does nothing at all. Because while speaking, evacuating, receiving, or opening or closing his eyes, he always knows that only the material senses are engaged with their objects and that he is aloof from them.

[10] One who performs his duty without attachment, surrendering the results unto the Supreme Lord, is unaffected by sinful action, as the lotus leaf is untouched by water.

Samskritam

Sanskrit

[3] jñeyah sa nitya-sannyāsī
yo na dveshti na kāńkshati
nirdvandvo hi mahā-bāho
sukhaḿ bandhāt pramucyate

[7] yoga-yukto viśuddhātmā
vijitātmā jitendriyah
sarva-bhūtātma-bhūtātmā
kurvann api na lipyate

[8-9] naiva kiñcit karomīti
yukto manyeta tattva-vit
paśyañ śṛṇvan spṛśañ jighrann
aśnan gacchan svapan śvasan
pralapan visṛjan gṛhṇann
unmiṣan nimiṣann api
indriyāṇīndriyārtheṣu
vartanta iti dhārayan

[10] brahmany ādhāya karmāni
sańgaḿ tyaktvā karoti yah
lipyate na sa pāpena
padma-patram ivāmbhasā

Krishna’s Mystic Opulence – 2

October 29, 2009 in Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, mystic opulence, Srimad Bhagavad Gita | 2 comments

Lord Krishna tells Arjuna about His mystic opulence in the soul-stirring discourse contained in Srimad Bhagavad Gita.

(This is from Srila Prabhupada’s writings, which is available here.) [These 3 verses are from Chapter 9.]

[17] I am the father of this universe, the mother, the support and the grandsire. I am the object of knowledge, the purifier and the syllable oḿ. I am also the Ṛg, the Sāma and the Yajur Vedas.

[18] I am the goal, the sustainer, the master, the witness, the abode, the refuge, and the most dear friend. I am the creation and the annihilation, the basis of everything, the resting place and the eternal seed.

[19] O Arjuna, I give heat, and I withhold and send forth the rain. I am immortality, and I am also death personified. Both spirit and matter are in Me.

Samskritam

Sanskrit

[17]pitāham asya jagato
mātā dhātā pitāmahah
vedyaḿ pavitram oḿkāra
rk sāma yajur eva ca

[18]gatir bhartā prabhuh sākshī
nivāsah śaranaḿ suhrt
prabhavah pralayah sthānaḿ
nidhānaḿ bījam avyayam

[19]tapāmy aham ahaḿ varshaḿ
nigrhnāmy utsrjāmi ca
amrtaḿ caiva mrtyuś ca
sad asac cāham arjuna

Krishna’s Mystic Opulence

October 29, 2009 in Dharma, Ideas, Inspiration, Sanskrit | Tags: Arjuna, Dharma, Krsna, mystic opulence, Srimad Bhagavad Gita | Leave a comment

Lord Krishna in His immortal discourse to Arjuna describes His mystic opulence.

These five verses are from Chapter 9 of Srimad Bhagavad Gita.

(This is taken from Srila Prabhupada’s writings, available here.)

[6] Understand that as the mighty wind, blowing everywhere, rests always in the sky, all created beings rest in Me.

[7] O son of Kuntī, at the end of the millennium all material manifestations enter into My nature, and at the beginning of another millennium, by My potency, I create them again.

[8] The whole cosmic order is under Me. Under My will it is automatically manifested again and again, and under My will it is annihilated at the end.

[9] O Dhanañjaya, all this work cannot bind Me. I am ever detached from all these material activities, seated as though neutral.

[10] This material nature, which is one of My energies, is working under My direction, O son of Kuntī, producing all moving and nonmoving beings. Under its rule this manifestation is created and annihilated again and again.

Samskritam:-

Sanskrit:

[6] yathākāśa-sthito nityaḿ
vāyuh sarvatra-go mahān
tathā sarvāni bhūtāni
mat-sthānīty upadhāraya

[7] sarva-bhūtāni kaunteya
prakrtiḿ yānti māmikām
kalpa-ksaye punas tāni
kalpādau visrjāmy aham

[8]prakrtiḿ svām avastabhya
visrjāmi punah punah
bhūta-grāmam imaḿ krtsnam
avaśaḿ prakrter vaśāt

[9]na ca māḿ tāni karmāni
nibadhnanti dhanañjaya
udāsīna-vad āsīnam
asaktaḿ tesu karmasu

[10]mayādhyaksena prakrtih
sūyate sa-carācaram
hetunānena kaunteya
jagad viparivartate

Duty towards Bharat – 2

October 29, 2009 in Dharma, Ideas | Tags: Bharat, Dharma, duty, India | Leave a comment

Assimilate the Good

It is said that our people who go abroad are carried away by the superficial attractions there and do not try to go deeper to find out the really good points in the life of those people. No people on the face of this earth are entirely without some abiding virtues, nor will they be endowed with all the necessary noble qualities. We should be able to discriminate and make a dispassionate assessment of their virtues and vices, and so also, of our own strong points and weak points. We shall then be able to achieve a harmonious blend of the elements of excellence in both the systems. Our intelligent young men who are staying abroad should take up such a comparative study and enlighten our other brethren there with the results of their findings.

There are indeed very pious people worthy of emulation in all countries. We should do well to emulate their examples. There is the recent example of a great and saintly American, who was so full of piety and love for all living creatures that when he would sit with his hands immersed in a tank, fish would swarm and play around without the least fear or hesitation. Such was his spirit of identity with the entire living creation.

Pick Up Such Gems

There are so many inspiring items of their literature which we could pick and make them our own. Many of our sublime thoughts are echoed in their poetry and philosophical works. I remember a most touching poem “Abou Ben Adhem” by Leigh Hunt.

ABOU BEN ADHEM (may his tribe increase!)

Awoke one night from a deep dream of peace,
And saw, within the moonlight in his room,
Making it rich, and like a lily in bloom,
An angel writing in a book of gold.
Exceeding peace had made Ben Adhem bold,
And to the presence in the room he said,
“What writest thou?” The vision raised its head,
And with a look made of all sweet accord,
Answer’d , “the names of those who love the lord.”
“And is mine one?” said Abou. “Nay, not so,”
Replied the Angel. Abou spoke more – low,
But cheerly still, and said, “I pray thee, then,
Write me as one that loves his fellowmen.”
The angel wrote, and vanished. The next night,
It came again with a great wakening light,
And showed the names whom love of God had blest,
And lo! Ben Abhem’s name led all the rest.

Respond to Local Aspirations

Then there is the important aspect of cultivating the right attitude and pattern of behaviour towards the local population.

The first thing that our brothers abroad have to bear in mind is, that while carrying on a profession or an employment there, earning and amassing money should bot be sole aim. They should understand and appreciate the problems of the local people and sympathise with their aspirations. Some portion of their earnings should be kept apart for promoting their welfare and enlightening them on the great principles and values of Hinduism. At the same time, they should, by their personal example and living, demonstrate that they are coming from the land of a great and hoary culture and thus set a personal example to others.

Be world Missionaries

In a nutshell, our brethren abroad will have to bring about a total transformation in their thoughts and life-styles if they have to lead a happier, richer and more honoured life abroad and also make the image of Bharat shine brighter in those countries. And in order to do this the one supreme conviction that we are a great people charged with a World Mission, should ever be vibrant in our breasts; that a sacred duty and trust is cast upon us of bringing home to the entire humanity the sublime truths embedded in our Dharma and that the various ills and challenges being faced by it could be met successfully on the basis of the all-comprehensive, scientific yet spiritual outlook of Hinduism. If this ultimate vision is kept constantly is view then everything else will become clear as crystal.

(This is from Sri Golwalkar’s Bunch of Thoughts.)

Duty towards Bharat – 1

October 29, 2009 in Dharma, Ideas | Tags: Bharat, Dharma, duty, India | Leave a comment

The first point to be borne in mind by our brothers and sisters living abroad is to keep alive their day-to-day behaviour a spirit of intense national self-respect. And for this, a keen awareness of the glorious heritage that our forbears have left for us should ever be present in our minds.

There is even now living evidence of the glory that Bharat was in ancient times.

What the World Expects

Right from Mexico in South America to the tiny islands in the Far Eastern Pacific, our Hindu missionaries had traveled far and wide and carried with them the fragrance of our ancient wisdom. Everywhere, they made a gift of the fruits of their achievements in medicine, mathematics, science, arts and culture. But more than anything else, it was the abiding spiritual values which they preached and practised that has left the deepest impression on the human mind all over.

When Siam became independent and their parliament was to meet in the hall, they all unanimously decided to place the statue of Manu as the presiding deity. The inscription in Siamese reads: “Bhagwan Manu, the first and the greatest lawgiver of mankind.” Indonesia is another country where the local Muslims are infused with the Hindu traditions. Their names, their songs, their drama, their national symbols – all carry the imprint of our epics like Ramayana.

True Ambassadors

It should be kept in mind that whenever a person goes out, he will go out as a representative of the country, the national culture and values of life – which have given birth to him. The world assesses the values and greatness of that country and its people on the touchstone of HIS behaviour. This is all the more true in the case of a great and ancient nation such as ours. If our conduct is not in keeping with the high cultural standards and becomes but a pale reflection of those lands themselves, the image of our country too will go down in their eyes. The respect and esteem that our country suffers will do incalculable harm both to our countrymen residing there and also to our country. It is only when their conduct is imbued with the right spirit of our dharma and samskriti that they can stand up as ideal Hindus and would be able to present an inspiring image of our nation and also receive a similar response from those people.

To Impart Samskars

It is necessary, therefore, that our Hindu brethren there, who have imbibed the right samskars here, should meet regularly with a view to rekindling among all our people there the spirit of national pride, the awareness of our all-round achievements in the past and our mission while abroad.

The children should be taught to recite the same with due devotion and earnestness. And wherever there are our temples the Hindus should cultivate the habit of congregating on certain holy occasions and conduct programmes like satsangs and havans.

Keeping close contact with the learned men and spiritual teachers who visit those countries from time to time and arranging suitable programmes would be of great help in furthering the above-mentioned objective.

(This is taken from Sri M.S. Golwalkar’s book, Bunch of Thoughts (here). )

Immortal verses from Srimad Bhagavad Gita – 2

October 28, 2009 in Dharma, Ideas, Sanskrit | Tags: Arjuna, Dharma, Krsna, Srimad Bhagavad Gita | Leave a comment

Lord Krishna imparts transcendental knowledge to His devotee Arjuna in Srimad Bhagavad Gita. Here are three verses from Chapter 4.

(This is taken from Srila Prabhupada’s writings, available here.)

Translation in English:-

[9] One who knows the transcendental nature of My appearance and activities does not, upon leaving the body, take his birth again in this material world, but attains My eternal abode, O Arjuna.

[10] Being freed from attachment, fear and anger, being fully absorbed in Me and taking refuge in Me, many, many persons in the past became purified by knowledge of Me — and thus they all attained transcendental love for Me.

[11] As all surrender unto Me, I reward them accordingly. Everyone follows My path in all respects, O son of Prithā.

Sanskrit

[9] janma karma ca me divyam
evaḿ yo vetti tattvatah
tyaktvā dehaḿ punar janma
naiti mām eti so ‘rjuna

[10] vīta-rāga-bhaya-krodhā
man-mayā mām upāśritāh
bahavo jñāna-tapasā
pūtā mad-bhāvam āgatāh

[11] ye yathā māḿ prapadyante
tāḿs tathaiva bhajāmy aham
mama vartmānuvartante
manushyāh pārtha sarvaśah

Samskritam

Immortal verses from Srimad Bhagavad Gita – 1

October 28, 2009 in Dharma, Ideas, Sanskrit | Tags: Arjuna, Dharma, Krsna, Srimad Bhagavad Gita | Leave a comment

In Srimad Bhagavad Gita, Lord Krishna imparts transcendental knowledge to Arjuna. Here are four such immortal verses taken from Chapter 4.

(These are from Srila Prabhupada’s writings, taken from here.)

Here is a pdf file of Srimad Bhagavad Gita in Devanagari script.

Translation in English:-

[5] The Personality of Godhead said: Many, many births both you and I have passed. I can remember all of them, but you cannot, O subduer of the enemy!

[6] Although I am unborn and My transcendental body never deteriorates, and although I am the Lord of all living entities, I still appear in every millennium in My original transcendental form.

[7] Whenever and wherever there is a decline in religious practice, O descendant of Bharata, and a predominant rise of irreligion — at that time I descend Myself.

[8] To deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I Myself appear, millennium after millennium.

Sanskrit:

[5] śrī-bhagavān uvāca
bahūni me vyatītāni
janmāni tava cārjuna
tāny ahaḿ veda sarvāni
na tvaḿ vettha parantapa

[6] ajo ‘pi sann avyayātmā
bhūtānām īśvaro ‘pi san
praktiḿ svām adhihāya
sambhavāmy ātma-māyayā

[7] yadā yadā hi dharmasya
glānir bhavati bhārata
abhyutthānam adharmasya
tadātmānaḿ sjāmyaham

[8] paritrānāya sādhūnāḿ
vināśāya ca dushkrtām
dharma-saḿsthāpanārthāya
sambhavāmi yuge yuge

Samskritam

BGch4

Qualities of a saintly person – 2

October 28, 2009 in Dharma, Ideas, Inspiration | Tags: Dharma, saint, Srimad Bhagavatam | Leave a comment

In Srimad Bhagavatam, Lord Krishna relates to His cousin Uddhava, a conversation between King Yadu and a brahmana avadhuta (one who is liberated). Here the brahmana explains to Maharaja Yadu what all he learnt from his 24 gurus.

(Please see this earlier post on the same conversation.) This is taken from here, here, and here.

The various phases of one’s material life, beginning with birth and culminating in death, are all properties of the body and do not affect the soul, just as the apparent waxing and waning of the moon does not affect the moon itself. Such changes are enforced by the imperceptible movements of time.

The flames of a fire appear and disappear at every moment, and yet this creation and destruction is not noticed by the ordinary observer. Similarly, the mighty waves of time flow constantly, like the powerful currents of a river, and imperceptibly cause the birth, growth and death of innumerable material bodies. And yet the soul, who is thus constantly forced to change his position, cannot perceive the actions of time.

Just as the sun evaporates large quantities of water by its potent rays and later returns the water to the earth in the form of rain, similarly, a saintly person accepts all types of material objects with his material senses, and at the appropriate time, when the proper person has approached him to request them, he returns such material objects. Thus, both in accepting and giving up the objects of the senses, he is not entangled.

A saintly sage is happy and pleasing in his external behavior, whereas internally he is most grave and thoughtful. Because his knowledge is immeasurable and unlimited he is never disturbed, and thus in all respects he is like the tranquil waters of the unfathomable and unsurpassable ocean.

During the rainy season the swollen rivers rush into the ocean, and during the dry summer the rivers, now shallow, severely reduce their supply of water; yet the ocean does not swell up during the rainy season, nor does it dry up in the hot summer. In the same way, a saintly devotee who has accepted the Supreme Personality of Godhead as the goal of his life sometimes will receive by providence great material opulence, and sometimes he will find himself materially destitute. However, such a devotee of the Lord does not rejoice in a flourishing condition, nor is he morose when poverty-stricken.

After many, many births and deaths one achieves the rare human form of life, which, although temporary, affords one the opportunity to attain the highest perfection. Thus a sober human being should quickly endeavor for the ultimate perfection of life as long as his body, which is always subject to death, has not fallen down and died. After all, sense gratification is available even in the most abominable species of life, whereas Krsna consciousness is possible only for a human being.

Nama Ramayana

October 28, 2009 in Dharma, Sanskrit | Tags: Dharma, Nama Ramayana, ramayana | Leave a comment

Nama Ramayana is one of the most beautiful songs describing the life of Lord Rama. Listening to this would bring a sense of devotion to one’s heart.

Here, Rama is described by many names, and by the sequence of these names, the whole epic, Ramayana is summarized.

Here is a beautiful rendition of this song in M.S. Subbulakshmi’s heavenly voice (in 2 parts).

Here is a (partial) translation in English:-

bAla kAnda

My Rama, Essence of all that is Godly, My Rama
My Rama, Essence of the destroyer, My Rama
My Rama, Who sleeps on the snake Sesha, My Rama
My Rama, Who was saluted by Brahma and all Devas, My Rama
My Rama, Who was born in Sun’s dynasty, My Rama
My Rama, Who was a source of joy to Dasaratha, My Rama
My Rama, Who made Kausalya’s life very happy, My Rama
My Rama, Who was most dear to Viswamitra, My Rama
My Rama, Who killed the ogress Thadaka in the deep forest, My Rama
My Rama, Who drove away Maricha, My Rama
My Rama, Who saved the prestige of Koushika, My Rama
My Rama, Who helped Ahalya to regain form, My Rama
My Rama, Who was worshipped by Goutama the sage, My Rama
My Rama, Who was given boons by Gods and Sages, My Rama
My Rama, Who was the darling of people of Mithila, My Rama
My Rama, Who broke the bow of Trayambaka, My Rama
My Rama, Who was garlanded by Princess Sita, My Rama
My Rama, Who became happy marrying Sita, My Rama
My Rama, Who destroyed the ego of ParasuRama, My Rama
My Rama, Who looked after the people of Ayodhya, My Rama

ayodhyA kAnda

My Rama, Who is personification of all good, My Rama
My Rama, Who was the darling of all citizens, My Rama
My Rama, Who was like the full moon in a cloudless sky, My Rama
My Rama, Who obeyed the words of His father, My Rama
My Rama, Who was worshipped by His friend Guha, My Rama
My Rama, Who was taken care of by Guha, My Rama
My Rama, Who was worshipped by Sage Bharadwaja, My Rama
My Rama, Who lived in Chitra Koota Mountains, My Rama
My Rama, Who became sad by the death of Dasaratha, My Rama
My Rama, Who was requested to return by Bharata, My Rama
My Rama, Who did the obsequies for His father, My Rama
My Rama, Who gave His shoes to Bharata, My Rama
My Rama, Who went to Dhandaka Forests, My Rama

aranya kAnda

My Rama, Who killed the Bad Virata, My Rama
My Rama, Who was worshipped by Sage Sarabhanga, My Rama
My Rama, Who was blessed by Sage Agastya, My Rama
My Rama, Who was honoured by the King of Eagles, My Rama
My Rama, Who lived near five banyans, My Rama?
My Rama, Who insulted the voracious Surpanaka, My Rama
My Rama, Who killed Khara and Dhushana, My Rama
My Rama, Who chased the deer wanted by Sita, My Rama
My Rama, Who killed Mareecha in deer’s form, My Rama
My Rama, Who started searching for the lost Sita, My Rama
My Rama, Who Sent the King of Eagles to Heaven, My Rama
My Rama, Who ate the fruits given by Sabari, My Rama
My Rama, Who cut the hands of Kabanda, My Rama

kishkindA kAnda

My Rama, Who was served by Hanuman, My Rama
My Rama, Who promised to help Sugreeva, My Rama
My Rama, Who killed the proud Bali, My Rama
My Rama, Who sent monkeys all over the world, My Rama
My Rama, Who was consoled by Lakshmana, My Rama

sundara kAnda

My Rama, Who was worshipped by the Great Monkeys, My Rama
My Rama, Who removed all obstacles from their path, My Rama
My Rama, Who is the support of Sita’s life, My Rama
My Rama, Who was abused by the bad Ravana, My Rama
My Rama, Who was praised by the great Hanuman, My Rama
My Rama, Who became upset because Sita cried, My Rama
My Rama, Who saw the Chudamani of Sita, My Rama
My Rama, Who was consoled by the great monkey, My Rama

yuddha kAnda

My Rama, Who marched towards Ravana’s place, My Rama
My Rama, Who was accompanied by the army of monkeys, My Rama
My Rama, Who gave protection to Vibhishana, My Rama
My Rama, Who built the bridge across the sea, My Rama
My Rama, Who killed Kumbhakarna, My Rama
My Rama, Who defeated the army of Asuras, My Rama
My Rama, Who made Ravana helpless, My Rama
My Rama, Who slew Ravana in battle, My Rama
My Rama, Who destroyed the bad asuras, My Rama
My Rama, Who saw Dasaratha from the heavens, My Rama
My Rama, Who became Happy on seeing Sita, My Rama
My Rama, Who made Vibhishana the king of Lanka, My Rama
My Rama, Who traveled back in Pushpaka plane, My Rama
My Rama, Who was honoured by Sage Bharadwaja, My Rama
My Rama, Who saved the life of Bharatha, My Rama
My Rama, Who was an ornament to the city of Ayodhya, My Rama
My Rama, Who made everybody happy, My Rama
My Rama, Who sat on the throne of gems, My Rama
My Rama, Who was the greatest of Sun dynasty, My Rama
My Rama, Who got respect from Vibhishana, My Rama
My Rama, Who was honoured by the dynasty of monkey kings, My Rama
My Rama, Who ruled over the entire world, My Rama
My Rama, Who granted all boons to His devotees, My Rama
Rama, Rama, Victory to you Rama, Rama, Rama
Rama, Rama, Victory to you, Sita Rama

Sanskrit:

NR9

NR3

Samskritam:-

NRS9

NRS10

NRS11

(Note: The Sanskrit text for the above (Roman script as well as Devanagari script) was taken from here. The English translation was taken from here. The mp3 version of Nama Ramayana sung by M.S. Subbulakshmi can be downloaded from here. I’m sorry for any mistakes in the post. It would be great if you point them out.)

(In the English transliteration of the song, the heading:”Yuddha Kanda” appears twice. The second occurrence should be replaced by “Uttara Kanda”.)

Qualities of a saintly person

October 27, 2009 in Dharma, Ideas, Inspiration | Tags: Dharma, qualities, Srimad Bhagavatam | 1 comment

In Srimad Bhagavatam, there is a very interesting conversation between a brahmana avadhuta and King Yadu. The avadhuta (one who is liberated) explains to Maharaja Yadu what he learnt from his 24 gurus, which include the earth, wind, sky, water, and fire, among others.

This has been taken from here.

Maharaja Yadu once observed a certain brahmana avadhuta, who appeared to be quite young and learned, wandering about fearlessly. Being himself most learned in spiritual science, the King took the opportunity and inquired from him as follows. Sri Yadu said: O brahmana, I see that you are not engaged in any practical religious activity, and yet you have acquired a most expert understanding of all things and all people within this world. Kindly tell me, sir, how did you acquire this extraordinary intelligence, and why are you traveling freely throughout the world behaving as if you were a child?

Generally human beings work hard to cultivate religiosity, economic development, sense gratification and also knowledge of the soul, and their usual motive is to increase the duration of their lives, acquire fame and enjoy material opulence. You, however, although capable, learned, expert, handsome and most eloquent, are not engaged in doing anything, nor do you desire anything; rather, you appear stupefied and maddened as if you were a ghostly creature.

O brahmana, we see that you are devoid of any contact with material enjoyment and that you are traveling alone, without any companions or family members. Therefore, because we are sincerely inquiring from you, please tell us the cause of the great ecstasy that you are feeling within yourself.

The brahmana said: My dear King, with my intelligence I have taken shelter of many spiritual masters. Having gained transcendental understanding from them, I now wander about the earth in a liberated condition. Please listen as I describe them to you.

(The brahmana then lists the 24 gurus from whom he has learned, and then proceeds to describe what he learnt from each of them. Some of them are given below.)

A sober person, even when harassed by other living beings, should understand that his aggressors are acting helplessly under the control of God, and thus he should never be distracted from progress on his own path. This rule I have learned from the earth.

A saintly person should learn from the mountain to devote all his efforts to the service of others and to make the welfare of others the sole reason for his existence. Similarly, as the disciple of the tree, he should learn to dedicate himself to others.

Even a transcendentalist is surrounded by innumerable material objects, which possess good and bad qualities. However, one who has transcended material good and evil should not become entangled even when in contact with the material objects; rather, he should act like the wind.

Although a self-realized soul may live in various material bodies while in this world, experiencing their various qualities and functions, he is never entangled, just as the wind which carries various aromas does not actually mix with them.

Saintly persons become powerful by execution of austerities. Their consciousness is unshakable because they do not try to enjoy anything within the material world. Such naturally liberated sages accept foodstuffs that are offered to them by destiny, and if by chance they happen to eat contaminated food, they are not affected, just like fire, which burns up contaminated substances that are offered to it.

A saintly person, just like fire, sometimes appears in a concealed form and at other times reveals himself. For the welfare of the conditioned souls who desire real happiness, a saintly person may accept the worshipable position of spiritual master, and thus like fire he burns to ashes all the past and future sinful reactions of his worshipers by mercifully accepting their offerings.

O King, a saintly person is just like water because he is free from all contamination, gentle by nature, and by speaking creates a beautiful vibration like that of flowing water. Just by seeing, touching or hearing such a saintly person, the living entity is purified, just as one is cleansed by contact with pure water. Thus a saintly person, just like a holy place, purifies all those who contact him because he always chants the glories of the Lord.

Verses from Srimad Bhagavad Gita – 3

October 27, 2009 in Dharma, Ideas, Sanskrit | Tags: Dharma, Sanskrit, Srimad Bhagavad Gita | 2 comments

Here are 3 verses from Chap. 2 of Srimad Bhagavad Gita. The translation is by Srila Prabhupada, and is available here.

Note: Verses [22, 23, 24] are below. Verses [14, 15, 16, 17, 18] are here; and verses [19, 20, 21] are here.

[22] As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones.

[23]The soul can never be cut to pieces by any weapon, nor burned by fire, nor moistened by water, nor withered by the wind.

[24] This individual soul is unbreakable and insoluble, and can be neither burned nor dried. He is everlasting, present everywhere, unchangeable, immovable and eternally the same.

Sanskrit:

[22] vasamsi jirnani yatha vihaya
navani grhnati naro ‘parani
tatha sarirani vihaya jirnany
anyani samyati navani dehi

[23] nainam chindanti sastrani
nainam dahati pavakah
na cainam kledayanty apo
na sosayati marutah

[24] acchedyo ‘yam adahyo ‘yam
akledyo ’sosya eva ca
nityah sarva-gatah sthanur
acalo ‘yam sanatanah

Samskritam:-

(22)

BG2221

BG2222

(23)

BG223

(24)

BG224

Verses from Srimad Bhagavad Gita – 2

October 27, 2009 in Dharma, Ideas, Sanskrit | Tags: Dharma, Sanskrit, Srimad Bhagavad Gita | 4 comments

Here are three verses from Chapter 2 of Srimad Bhagavad Gita. This is taken from Srila Prabhupada’s writings which is available here.

Note: Verses [19, 20, 21] are below. Verses [14, 15, 16, 17, 18] are here ; and verses [22, 23, 24] are here.

Translation:

[19] Neither he who thinks the living entity the slayer nor he who thinks it slain is in knowledge, for the self slays not nor is slain.

[20] For the soul there is neither birth nor death at any time. He has not come into being, does not come into being, and will not come into being. He is unborn, eternal, ever-existing and primeval. He is not slain when the body is slain.

[21] O Pārtha, how can a person who knows that the soul is indestructible, eternal, unborn and immutable kill anyone or cause anyone to kill?

Sanskrit:

[19] ya enam vetti hantaram
yas cainam manyate hatam
ubhau tau na vijanito
nayam hanti na hanyate

[20] na jayate mriyate va kadacin
nayam bhutva bhavita va na bhuyah
ajo nityah sasvato ‘yam purano
na hanyate hanyamane sarire

[21] vedavinasinam nityam
ya enam ajam avyayam
katham sa purusah partha
kam ghatayati hanti kam

Samskritam:

(19)

(20)

(21)

(The Sanskrit texts have been taken from the Internet. Thanks to Sharadh for asking for these verses to be included.)

Verses from Srimad Bhagavad Gita

October 26, 2009 in Dharma, Ideas, Sanskrit | Tags: Atman, Hindu, spirituality, Srimad Bhagavad Gita | 5 comments

om ajnana-timirandhasya
jnananjana-salakaya
caksur unmilitam yena
tasmai sri-gurave namah

“I was born in the darkest ignorance, and my spiritual master opened my eyes with the torch of knowledge. I offer my respectful obeisances unto him.“

Lord Krishna instructs Arjuna on the battlefield of Kurukshetra, on spiritual knowledge. Arjuna, the great warrior, on seeing his relatives, gurus, and respected elders arrayed in the opposing army, feels mentally incapable of fighting against them; and decides it is better to die unarmed rather than fighting such persons. At this juncture, Krishna imparts the divine spiritual knowledge to the distraught Arjuna.

Here are verses from Chapter 2 of Bhagavad Gita, addressed by Krishna to Arjuna. These are from Srila Praphupada’s writings. The verses of the Bhagavad Gita are available here.

Note: Verses [14, 15, 16, 17, 18] are below. Verses [19, 20, 21] are here, and [22, 23, 24] are here.

[14] O son of Kunti, the nonpermanent appearance of happiness and distress, and their disappearance in due course, are like the appearance and disappearance of winter and summer seasons. They arise from sense perception, O scion of Bharata, and one must learn to tolerate them without being disturbed.

[15] O best among men [Arjuna], the person who is not disturbed by happiness and distress and is steady in both is certainly eligible for liberation.

[16] Those who are seers of the truth have concluded that of the nonexistent there is no endurance, and of the existent there is no cessation. This, the seers have concluded by studying the nature of both.

[17] Know that which pervades the entire body is indestructible. No one is able to destroy the imperishable soul.

[18] Only the material body of the indestructible, immeasurable and eternal living entity is subject to destruction; therefore, fight, O descendant of Bharata (i.e. Arjuna).

Here are the Sanskrit verses.

[14] matra-sparsas tu kaunteya
sitosna-sukha-duhkha-dah
agamapayino ‘nityas
tams titiksasva bharata

[15] yam hi na vyathayanty ete
purusam purusarsabha
sama-duhkha-sukham dhiram
so ‘mrtatvaya kalpate

[16] nasato vidyate bhavo
nabhavo vidyate satah
ubhayor api drsto ‘ntas
tv anayos tattva-darsibhih

[17] avinasi tu tad viddhi
yena sarvam idam tatam
vinasam avyayasyasya
na kascit kartum arhati

[18] antavanta ime deha
nityasyoktah saririnah
anasino ‘prameyasya
tasmad yudhyasva bharata

Samskritam:-

(14)

BG214

(15)

BG215

(16)

BG216

(17)

BG217

(18)

BG218

Bhaja Govindam (Worship Govinda, O fool!)

October 25, 2009 in Dharma, Sanskrit | Tags: Bhaja Govindam, Sankara, Sanskrit | Leave a comment

Bhaja Govindam was composed by Sri Adi Shankara. Shankara (788 – 820 CE) is one of the greatest philosopher-saints ever. Here is an article on Shankara.

Here are ten verses from Bhaja Govindam divinely sung by M.S. Subbulakshmi.

Translation in English (of the ten verses sung above.)

1. Adore the Lord, adore the Lord, adore the Lord, O fool! when the appointed time (for departure) comes, the repetition of grammatical rules will not, indeed, save you.

2. O fool! leave the desire for accumulation of wealth; create in the mind, thoughts about Reality, devoid of passion. What you get – i.e. what you have achieved through your past deeds – with that, satisfy your mind.

3. As long as you have the ability to earn money, so long will your dependents be attached to you. After that, when you live with an infirm body no one would even speak a word to you.

4. Do not be proud of wealth, kindred, and youth; Time takes away all these in a moment. Leaving aside this entire (world) which is of the nature of an illusion, and knowing the state of Brahman, enter into it.

5. Living in temples or at the foot of trees, sleeping on the ground, wearing deer-skin, renouncing all possessions and their enjoyment – to whom will not dispassion bring happiness?

6. For him, who has studied the Bhagavadgitá even a little, who has drunk a drop of the Gañgá-water, and who has performed the worship of the Destroyer of the demon Mura (i.e. Krishna) at least once, there is no tiff with Yama (the lord of death).

7. Repeated birth, repeated death, and repeated lying in mother’s womb – this transmigratory process is extensive and difficult to cross; save me, O Destroyer of Mura (O Krishna), through Your grace!

8. The Bhagavadgitá and the Sahasranáma should be sung; the form of the Lord of Lakshmi (Vishnu) should always be meditated on; the mind should be led to the company of the good; and wealth should be distributed among the indigent.

9. `Wealth is no good’; thus reflect always; there is not the least happiness therefrom; this is the truth. For the wealthy, there is fear even from a son; everywhere this is the regular mode.

10. Being devoted completely to the lotus-feet of the Master, become released soon from the transmigratory process. Thus, through the discipline of sense and mind-control, you will behold the Deity that resides in your heart.

Sanskrit:

bhajagovindam bhajagovindam
govindam bhajamuudhamate
sampraapte sannihite kaale
nahi nahi rakshati dukrijnkarane

mudha jahiihi dhanaagamatrishhnaam
kuru sadbuddhim manasi vitrishhnaam
yallabhase nijakarmopaattam
vittam tena vinodaya chittam

yaavadvittopaarjana saktah
staavannija parivaaro raktah
pashchaajjiivati jarjara dehe
vaartaam koapi na prichchhati gehe

maa kuru dhana jana yauvana garvam
harati nimeshhaatkaalah sarvam
maayaamayamidamakhilaM hitvaa
brahmapadaM tvaM pravisha viditvaa

sura mandira taru muula nivaasah
shayyaa bhuutala majinam vaasah
sarva parigraha bhoga tyaagah
kasya sukham na karoti viraagah

bhagavad giitaa kijnchidadhiitaa
gangaa jalalava kanikaapiitaa
sakridapi yena muraari samarchaa
kriyate tasya yamena na charchaa

punarapi jananam punarapi maranam
punarapi jananii jathare shayanam
iha samsaare bahudustaare
kripayaa apaare paahi muraare

geyam giitaa naama sahasram
dhyeyam shriipati ruupamajasram
neyam sajjana sange chittam
deyam diinajanaaya cha vittam

arthamanartham bhaavaya nityam
naastitatah sukhaleshah satyam
putraadapi dhana bhaajaam bhiitih
sarvatraishhaa vihiaa riitih

10.

gurucharanaambuja nirbhara bhakatah
samsaaraadachiraadbhava muktah
sendriyamaanasa niyamaadevam
drakshyasi nija hridayastham devam

Samskritam:

भज गोविन्दं

भजगोविन्दं भजगोविन्दं
गोविन्दं भजमूढमते
संप्राप्ते सन्निहिते काले
नहि नहि रक्षति डुकृञ्करणे (1)

मूढ जहीहि धनागमतृष्णां
कुरु सद्बुद्धिं मनसि वितृष्णाम् .
यल्लभसे निजकर्मोपात्तं
वित्तं तेन विनोदय चित्तम् (2)

यावद्वित्तोपार्जन सक्तः
स्तावन्निज परिवारो रक्तः .
पश्चाज्जीवति जर्जर देहे
वार्तां कोऽपि न पृच्छति गेहे (3)

मा कुरु धन जन यौवन गर्वं
हरति निमेषात्कालः सर्वम् .
मायामयमिदमखिलं हित्वा
ब्रह्मपदं त्वं प्रविश विदित्वा (4)

सुर मंदिर तरु मूल निवासः
शय्या भूतल मजिनं वासः .
सर्व परिग्रह भोग त्यागः
कस्य सुखं न करोति विरागः(5)

भगवद् गीता किञ्चिदधीता
गङ्गा जललव कणिकापीता.
सकृदपि येन मुरारि समर्चा
क्रियते तस्य यमेन न चर्चा (6)

पुनरपि जननं पुनरपि मरणं
पुनरपि जननी जठरे शयनम् .
इह संसारे बहुदुस्तारे
कृपयाऽपारे पाहि मुरारे (7)

गेयं गीता नाम सहस्रं
ध्येयं श्रीपति रूपमजस्रम् .
नेयं सज्जन सङ्गे चित्तं
देयं दीनजनाय च वित्तम् (8)

अर्थमनर्थं भावय नित्यं
नास्तिततः सुखलेशः सत्यम् .
पुत्रादपि धन भाजां भीतिः
सर्वत्रैषा विहिआ रीतिः (9)

गुरुचरणाम्बुज निर्भर भकतः
संसारादचिराद्भव मुक्तः .
सेन्द्रियमानस नियमादेवं
द्रक्ष्यसि निज हृदयस्थं देवम् (10)

(All of the above: translation, and the texts: have been taken from different sites on the Internet.)

The Wonder that is Sanskrit – 4

October 25, 2009 in Linguistics, Sanskrit | Tags: Linguistics, Poetry, Sanskrit | 4 comments

Here are two verses, each of which when reversed creates a new verse. This passage is from the amazing book, “The Wonder that is Sanskrit”. See also the previous three posts from the same book.

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The Wonder that is Sanskrit – 3

October 24, 2009 in Linguistics, Sanskrit | Tags: Linguistics, Poetry, Sanskrit | Leave a comment

Here are three amazing verses. The first is an astonishing verse using only one consonant and vowel, while the next two are palindromic verses. These, as well as this and this, are from the wonderful book, “The Wonder that is Sanskrit”.

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The Wonder that is Sanskrit – 2

October 24, 2009 in Linguistics, Sanskrit | Tags: Linguistics, Poetry, Sanskrit | 1 comment

Here are three amazing verses. The first two have written using only a single consonant, and the third is equally amazing! This passage, as well as this one, are excerpts from the wonderful book, “The Wonder that is Sanskrit”.

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The wonder that is Sanskrit – 1

October 24, 2009 in Linguistics, Sanskrit | Tags: Linguistics, Poetry, Sanskrit | 2 comments

This is a passage from the excellent book, “The Wonder that is Sanskrit”. There are some amazingly beautiful compositions in Sanskrit. Knowledge of the existence of such verses leaves one in awe of the genius minds that have mastered Sanskrit. The following anecdotes are from the time of Raja Bhoja, whose court was graced by the legendary Kalidasa.

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Atma Shatakam/Who am I

October 23, 2009 in Dharma, Ideas | Tags: atma shatakam, Dharma, nirvana shatakam | Leave a comment

Sri Adi Shankara (788 – 820 CE) was wandering in search of a Guru. At that time, he met Sri Govindapada, who asked him: “Who are you?”. In response, Shankara, who was eight years old at that time, spontaneously composed six verses in reply. This is known as Atma Shatakam or Nirvana Shatakam.

Here is a very beautiful rendering of the verses with music. Do listen to this.

Translation

1) I am not mind, nor intellect, nor ego
nor the reflections of inner self (chitta).
I am not the five senses.
I am beyond that.
I am not the ether, nor the earth,
nor the fire, nor the wind (the five elements).
I am indeed,
That eternal knowing and bliss, Shiva,
love and pure consciousness.

2) Neither can I be termed as energy (prana),
nor five types of breath (vayus),
nor the seven material essences,
nor the five coverings (pancha-kosha).
Neither am I the five instruments of elimination,
procreation, motion, grasping, or speaking.
I am indeed,
That eternal knowing and bliss, Shiva,
love and pure consciousness.

3) I have no hatred or dislike,
nor affiliation or liking,
nor greed,
nor delusion,
nor pride or haughtiness,
nor feelings of envy or jealousy.
I have no duty (dharma),
nor any money,
nor any desire (kama),
nor even liberation (moksha).
I am indeed,
That eternal knowing and bliss, Shiva,
love and pure consciousness.

4) I have neither merit (virtue),
nor demerit (vice).
I do not commit sins or good deeds,
nor have happiness or sorrow,
pain or pleasure.
I do not need mantras, holy places,
scriptures (Vedas), rituals or sacrifices (yagnas).
I am none of the triad of
the observer or one who experiences,
the process of observing or experiencing,
or any object being observed or experienced.
I am indeed,
That eternal knowing and bliss, Shiva,
love and pure consciousness.

5) I do not have fear of death,
as I do not have death.
I have no separation from my true self,
no doubt about my existence,
nor have I discrimination on the basis of birth.
I have no father or mother,
nor did I have a birth.
I am not the relative,
nor the friend,
nor the guru,
nor the disciple.
I am indeed,
That eternal knowing and bliss, Shiva,
love and pure consciousness.

6) I am all pervasive.
I am without any attributes,
and without any form.
I have neither attachment to the world,
nor to liberation (mukti).
I have no wishes for anything
because I am everything,
everywhere,
every time,
always in equilibrium.
I am indeed,
That eternal knowing and bliss, Shiva,
love and pure consciousness.

Samskritam:

nirvana_shatakam

Sanskrit:

1) Mano Buddhi Ahankara Chitta Ninaham
Nacha Shrotra Jihve Na Cha Ghrana Netre
Nacha Vyoma Bhoomir Na Tejo Na Vayu
Chidananda Rupa Shivoham Shivoham

2) Na Cha Prana Sangyo Na Vai Pancha Vayu
Na Vaa Sapta dhatur Na Vaa Pancha Koshah
Na Vak Pani Padam Na Chopastha Payu
Chidananda Rupa Shivoham Shivoham

3)Na Me Dvesha Ragau Na Me Lobha Mohau
Mado Naiva Me Naiva Maatsarya Bhavah
Na Dharmo Na Chartho Na Kamo Na Mokshah
Chidananda Rupa Shivoham Shivoham

4)Na Punyam Na Papam Na Saukhyam Na Dukham
Na Mantro Na Teertham Na Veda Na Yajnaha
Aham Bhojanam Naiva Bhojyam Na Bhokta
Chidananda Rupa Shivoham Shivoham

5) Na Mrityu Na Shanka Na Me Jati Bhedah
Pita Naiva Me Naiva Mata Na Janma
Na Bandhur Na Mitram Gurur Naiva Shishyah
Chidananda Rupa Shivoham Shivoham

6) Aham NirvikaLpo Nirakara Roopo
Vibhut Vaakhya Sarvatra Sarvendriyanam
Sada Me Samatvam Na Mukthir Na Bandhah
Chidananda Rupa Shivoham Shivoham

(The above texts and translation are taken from here, here, and one other site. I am very sorry for errors in the above.)

Happiness

October 22, 2009 in Ideas, Inspiration | Tags: happiness, life | Leave a comment

The happiness you obtain by seeing the happiness of others is truly liberating. When you see everyone in you, and yourself in everyone, you are on a plane of glorious happiness. Make every effort to strive for the happiness of others. Lend a comforting shoulder to those in need of one, lend an encouraging hand to others, motivate those in need of motivation, become a source of inspiration to others. When you identify yourself with the joys and sorrows of those around you, it is a great feeling. Enjoy this beautiful journey of life.

The Beautiful Life

October 21, 2009 in Fun Stuff | Tags: beautiful life, poem | 2 comments

(This is a poem I wrote in my first year at BITS. )

The Beautiful Life

Just like the stars twinkling in the sky
As the past and present go by
Can not this phase stay on
on for ever
to the harking call of dawn.

For every boy and every girl
goes the fearless carnival
On the path to eternity
As the world keeps spinning around
it goes on
on till it is found.

The world governs the man
Man makes the world
So life goes on
without being unfurled
the flag of life
Of beauty and change
from things sweet to the strange
for the present and antiquity
to the future of beauty.

Till the world keeps spinning around
As long as the mind stays sound
With nature by its side
Life will celebrate the arrival
of life and carnival
And the beautiful life will go on
to the harking call of dawn.

Construction of the Ranganatha temple

October 20, 2009 in Dharma | Tags: Dharma, Ranganatha temple | Leave a comment

THE GREAT DEVOTEE TIRUMANGAI

Of all the temples in India, that of Lord Ranganatha, situated on an island in the Kaveri River, is certainly the largest. The story of how this temple came to be built is very interesting.

About three hundred years before the birth of Ramanujacharya, which was in AD 1017, there lived in south India a devotee named Tirumangai. His heart was always filled with devotion for Lord Vishnu, and in this mood of pure love he would compose beautiful poetic prayers.

From the time of his youth he was in the habit of travelling throughout the country to visit the various holy places of pilgrimage. In the course of his travels four great mystics had become attracted by his exalted nature and had become his disciples. Each of these disciples had a particular ability that set him apart from ordinary men.

The first disciple was named Tola Vazhakkan, and he was famous for his ability to vanquish any opponent in a debate. The second disciple was named Taluduvan, and he had the ability to open any lock without the need of a key. The third and fourth disciples both possessed most unusual talents. The third, Nizhalai Mithippan, could force any man to remain still simply by stepping on his shadow, while the fourth, Nirmal Nadappan, had developed the laghima siddhi, which enabled him to walk on water.

TIRUMANGAI’S VISIT TO SRI RANGAM

After touring many holy places of pilgrimage, Tirumangai at last came to the temple of Lord Ranganatha. The Deity of Ranganatha had originally been installed by Vibhisana, the brother of Ravana, but at the time of Tirumangai the temple was completely dilapidated and filled with bats. Once a day a priest would come there to offer a few flowers and a little water to the Deity before hurrying away out of fear of the wild animals that dwelt in the surrounding forest.

When he saw this unhappy state of affairs, a strong desire arose in the mind of Tirumangai to build a beautiful, opulent temple for Lord Ranganatha. However, he did not have a penny to his name and no more did any of his disciples. After consulting together they decided to approach every rich man they could find and beg him to give money for the building of a temple. Unfortunately, the effects of Kali-yuga having set in, not one of these rich men would give even a small coin and they frequently blasphemed the devotees by calling them rogues or thieves.

ADOPTING THE WAYS OF ROBBERS

Being a humble devotee, Tirumangai was not disturbed by this treatment, but the thought of the Supreme Lord standing uncared for in a wild forest full of jackals and hyenas caused him great pain. At last he could tolerate the situation no longer and exclaimed in front of his four disciples, “We have wasted enough time trying to persuade these rascals to serve the Lord. They will always remain atheists and unbelievers. Which is better – to beg from these villains while Lord Ranganatha remains in this sorry condition, or to humble them by building a temple for the Lord so magnificent that it will force them to bow down at his feet?”

The disciples answered, “The service of the Lord is our duty, not acting as the servants of these rogues.”

“Then prepare yourselves,” continued Tirumangai, “for from this day we will see to it that the wealth of these greedy men is spent for building a temple. These wealthy landowners, who are cruel by nature, have passed their lives taking from the poor, hard-working people and leaving them without enough to eat. Now then, let us rob these rascals and use their money for building a temple and feeding the poor.”

The four disciples readily agreed to this proposal, and each of them spoke in turn. Tola Vazhakkan said, “No one can defeat me in argument. So, while I engage some rich man and his attendants in a debate, they will forget everything else and you will easily be able to carry off their wealth.”

Taludhuvan said, “I have the ability to open any lock without a key. Therefore, no treasury door will ever be closed to us.”

Nizhalai Mithippan said, “Anyone whose shadow is touched by my feet loses all power of movement. Therefore, it will be easy for us to stop rich travellers along the roads.”

Nirmal Nadappan said, “The big houses of rich landowners, which are surrounded by moats of water, are always open to me, for I can easily walk over water. Therefore from today, all the treasure of kings is yours”

CONSTRUCTION OF THE RANGANATHA TEMPLE

With the assistance of his four disciples, Tirumangai soon became the leader of a large gang of robbers. Together they accumulated a great hoard of riches that was kept concealed in a secret place on Lord Ranganatha’s island. Spending large sums of money, Tirumangai brought the best architects in the land to design a huge temple for the Lord and at an auspicious moment he laid the foundation stone.

The inner temple room, encircled by the first ring of walls and crowned with a high tower, was completed in two years. Thousands of builders were engaged to take part in the construction, but even so it took four years to complete the next ring of walls and apartments, six years for the second, eight years for the third, ten years for the fourth, twelve years for the fifth, and eighteen years for the sixth. In all it took sixty years to complete the construction of the temple, and by this time Tirumangai was over eighty years old.

After the construction of the inner temple, kings began to send money to Tirumangai of their own accord, convinced now that he was a genuine devotee. Moreover, he was now the leader of a gang of over one thousand robbers and other wealthy landowners gave money liberally to assist with the work, fearing that all of their property would otherwise be plundered. Despite all this, Tirumangai still lived the simple life of a devotee, eating only once a day prasadam cooked by his own hand and prepared from food he obtained by begging. He would also ensure that all the people in that area never suffered for want of food -only the rich lived in fear of the sage Tirumangai.

(This is taken from the book, The Life of Ramanujacarya, available online here.)

Multiway cut – 2

October 19, 2009 in Hey Math, Theoretical Computer Science | Tags: approximation algorithms, CS, graph theory, multiway cut, Theory | Leave a comment

In the previous post on this topic, we saw an algorithm with an approximation guarantee of 2 for the multiway cut problem. Some guidelines were also given on developing a factor (2-2/k) approximation algorithm based on the ideas of the original algorithm.

Let us briefly review that.

Problem: Given a set, S = ${s_1, s_2, ..., s_k}$ of k vertices, find a cut of minimum size (in terms of weights of edges) that separates each $s_i$ from all other vertices in S.

Algorithm:

1. Find an isolating cut for each $s_i$ . Call each such isolating cut $C_i$ .

2. Output the union of the k-1 lightest isolating cuts. (i.e. exclude the heaviest of the $C_i's$ and output the union of the rest.)

The above set of edges is a multiway cut.

We saw how the set of edges $C_1 \cup C_2 \cup ... \cup C_k$ formed a 2 – factor approximation to the optimal cut. Using this fact, convince yourself that the above algorithm outputs a (2-2/k) factor approximation of the optimum.

Another multiway cut algorithm:

We now present a mulitway cut algorithm that performs no worse than the above (2-2/k) factor algorithm, and indeed performs better than the above in examples which we will see.

The algorithm inherits the idea of finding an isolating cut for each vertex in the set, S. Then, it performs a greedy choice, and picks the isolating cut, $C_i$ having minimum size. It then removes the edges of cut, $C_i$ from the graph, G to get a new graph G’. The vertex $s_i$ is removed from the set, S. The same procedure is repeated on this new graph. (i.e. the isolating cuts are again computed for each of the k-1 vertices left in S, and the minimum cut is selected for removal from the graph.)

Once the above procedure is repeated k-1 times, we get the required multiway cut, which has an approximation guarantee of (2-2/k), and which additionally performs better than the above (2-2/k) factor algorithm in specific test cases.

The algorithm is repeated below step-wise.

1. Let $G_1 = G.$ and $S_1 = S.$

Initially, i = 1. The required multiway cut, C is initially the Null Set.

Repeat the following (Steps 2-7) k-1 times.

2. Compute isolating cuts (wrt vertices in $S_i$ ) – $C_i$ for each vertex in $S_i.$

3. Let $C_j$ be the minimum of the cuts computed in the previous step.

4. Remove the edges of $C_j$ from $G_i$ to get a new graph, $G_{i+1}$ .

5. Add the edges of $C_j$ to C. i.e. $C = C \cup C_j.$

6. Remove vertex, $s_j$ from $S_i$ to get a new set, $S_{i+1}.$

7. Increment i by one.

End of algorithm.

The set, C is the required multiway cut.

—–

Things to think about:

1. Convince yourself that k-1 iterations are sufficient to generate a multiway cut. (i.e. after k-1 iterations, each of the vertices in set, S is disconnected from all other vertices in S.)

2. Can you see why this algorithm will generate a cut that is no worse than the cut produced by the earlier (2-2/k) factor algorithm.

At each step , we remove a particular vertex from the set, S, and recompute the values of the isolating cuts for the remaining vertices, based on this new S. Can you see why this could lead to a better isolating cut for a particular vertex in S than was possible under the earlier algorithm.

Let us consider an example:

Example for multiway cut: the edge weights are indicated alongside the edges.

In the above example:

The minimum isolating cut for $s_3$ has value = 20. (One such candidate for $C_3$ is the set of edges { {s2,s3), {s3,C}}.
The minimum isolating cut for $s_1$ has value = 15. There can be more than one such cut with value = 15. Let the choose this one: {{A,B}, {A,C}}.
Similarly, value of minimum isolating cut for $s_2$ is 15; and one such cut is given by: {{s2,B}, {s2,s3}}.

Now, how would the first algorithm proceed?

The union of the 2 lightest isolating cuts is outputted. Hence, the multiway cut produced by the algorithm is: {{A,B}, {A,C}, {s2,B}, {s2,s3}}. The value of this cut is 30.

How does the 2nd algorithm perform in this example?

Take a minimum value cut from the set of isolating cuts and add it to C. We can add either $C_1$ or $C_2$ since both have equal minimum value. Suppose, we add $C_1$ to C. Now, C = {{A,B}, {A,C}}.
Remove edges of $C_1$ from G, and recompute minimum isolating cuts for $s_2$ and $s_3$ on the new set, S = {s2, s3}.
We get a minimum isolating cut of value = 10 for both $s_2$ and $s_3$ . This is given by the edge {s2,s3}.
Add this edge to C, and we are done.

Therefore, C = {{A,B}, {A,C}, {s2,s3}}.

Value of this multiway cut = 25.

Hence, we can see how the 2nd algorithm performs better than the first in this example.

On a separate note, convince yourself that the second algorithm will perform no worse than the first on any input graph.

———

Another example (here the second performs asymptotically twice as better as the first):

Example for multiway cut

Note: In the above diagram, the letter e has been used to denote $\epsilon > 0$ .

The set, S consists of k vertices, $s_1$ through $s_k$ as shown. (The diagram is for k=5)

Performance of first algorithm on above instance:
Value of $C_1 = 2 - 2 \epsilon$ .
For all other vertices in S, value of $C_i = 2 - \epsilon.$

Therefore, the value of cut produced by algorithm = $(k-2) \times (2-\epsilon) + (2 - 2 \epsilon).$

Performance of second algorithm on above instance:
Value of minimum $C_i$ is $2- 2 \epsilon$ given by $C_1$ . On removing $C_1$ from G and $s_1$ from S, we find that the values of all other isolating cuts become equal to one. (See the diagram.) We proceed through the algorithm as specified to get cut, C.

Value of cut, C thus produced = $(k-2) \times 1 + (2 - 2 \epsilon)$ .

Verify that for large values of k, as $\epsilon$ —> 0, the ratio of values of the two cuts approaches 2.

Hence, the second algorithm performs twice as better asymptotically in this case.

3. Consider this example:

A tight example for both algorithms.

(Note: The letter, e has been used in the diagram to represent, $\epsilon >0$ .

Verify for yourself the following:

1. The optimal multiway cut for the above instance is of value = k. (Consider removing all edges of the cycle.)

2. The first algorithm produces a cut of value = $(k-1) \times (2 - \epsilon)$ .

3. The second algorithm produces a cut of value = $(k-1) \times (2 - \epsilon).$

4. Asymptotically, both algorithms achieve an approximation factor of (2-2/k).

(I’m sorry for any errors in this post.)

Purpose in Life

October 19, 2009 in Ideas, Inspiration | Tags: Ideas, life, purpose | 2 comments

Every life has to have a purpose. One beautiful feature of leading a purposeful life is the sense of satisfaction and fulfillment that will fill your life. You will discover yourself to be stronger, more capable, and a much better person than you ever imagined yourself to be.

One simple method of obtaining happiness is to be actively involved in giving happiness to others. The more happiness you bring to others, the greater the sense of fulfillment you bring to your own life.

(Sri Ramanuja was given a sacred secret mantra by his Guru after a lot of effort on the part of Ramanuja. This mantra was the mantra that could lead a person to moksha or liberation. Ramanuja was told by his Guru not to disclose the mantra to anybody, and warned that any such action on his part would certainly land him in hell. Ramanuja immediately went to the temple top, and called out loud to all people that he had obtained a priceless jewel which he wanted to give to them. He then recited the mantra for all those assembled there. This action on Ramanuja’s part greatly enraged his Guru. On seeing his Guru’s outrage at his transgression despite the warning, Ramanuja calmly replied: “By knowing this mantra, so many people are now liberated. If an insignificant mortal such as myself has to go to hell in return for the liberation of so many people, then I am ready to joyfully accept that.” On hearing this, his Guru was filled with reverence for the infinite compassion that Ramanuja had for everyone, and understood that Ramanuja was a much greater person than himself.)

(Sri Ramanuja (1017 – 1137 A.D.) is the most important saint-philosopher in Sri Vaishnavism.)

Once you start solving problems for others, the seemingly difficult problems in your own life begin to seem trivial and inconsequential.

Always be willing to help one who is in need of help. You will never be without help when you need it.

Give selflessly, and with purity. Your heart will be purified through such actions. You will receive miraculous gifts when you least expect them.

There are many who can be benefitted by your help. The blessings that will accrue through such an action on your part will indeed prove to be a great antidote to all negativity, and will be a harbinger of peace. The persons who are today helped by you, would tomorrow become healers themselves and serve a great many people.

There are many qualities that will be gained through such endeavor: one is a sense of perspective (you will see your problems in perspective, and realize their insignificance), another is fearlessness (by helping others, you will overcome your own limiting fears.)

Fearlessness is a quality of prime importance. You are the Children of Immortal Bliss. Stand tall in the face of all fears, and they will disappear.

There is no problem that you face that does not have a solution. There has never been such a problem, and there never will be.

Wake up each day with a sense of bringing great happiness to the world. Act like the sunshine that brightens people’s faces and gladdens their hearts.

May the mercy of God act through these words to enable them to transform your lives.

Quotes on the Joys of Reading – 2

October 17, 2009 in Books, Ideas | Tags: Books, quotes, reading | Leave a comment

No matter how busy you may think you are, you must find time for reading, or surrender yourself to self-chosen ignorance. (Confucius)

A truly good book teaches me better than to read it. I must soon lay it down, and commence living on its hint. What I began by reading, I must finish by acting. (Henry David Thoreau)

A man only learns in two ways, one by reading, and the other by association with smarter people. (Will Rogers)

The reading of all good books is like a conversation with the finest minds of past centuries. (Descartes)

Don’t ask me who’s influenced me. A lion is made up of the lambs he’s digested, and I’ve been reading all my life. (Charles de Gaulle)

When I get a little money, I buy books; and if any is left, I buy food and clothes. (Erasmus)

I often feel sorry for people who don’t read good books; they are missing a chance to lead an extra life. (Scott Corbett)

Force yourself to reflect on what you read, paragraph by paragraph. (Samuel Taylor Coleridge)

The best effect of any book is that it excites the reader to self activity. (Thomas Carlyle)

It is well to read everything of something, and something of everything. (Lord Henry P. Brougham)

Books are not made for furniture, but there is nothing else that so beautifully furnishes a house. (Henry Ward Beecher)

He that loves a book will never want a faithful friend, a wholesome counselor, a cheerful companion, an effectual comforter. By study, by reading, by thinking, one may innocently divert and pleasantly entertain himself, as in all weathers, as in all fortunes. (Barrow)

Read not to contradict and confute; nor to believe and take for granted; nor to find talk and discourse; but to weigh and consider. Some books are to be tasted, others to be swallowed, and some few to be chewed and digested: that is, some books are to be read only in parts, others to be read, but not curiously, and some few to be read wholly, and with diligence and attention. (Francis Bacon)

I‘ve traveled the world twice over,
Met the famous; saints and sinners,
Poets and artists, kings and queens,
Old stars and hopeful beginners,
I’ve been where no-one’s been before,
Learned secrets from writers and cooks
All with one library ticket
To the wonderful world of books. (Anonymous)

Show me the books he loves and I shall know the man far better than through mortal friends. (Dawn Adams)

Quotes on the Joys of Reading – 1

October 17, 2009 in Books, Ideas | Tags: Books, quotes, reading | Leave a comment

A home without books is a body without soul. (Marcus Tullius Cicero)

Every man who knows how to read has it in his power to magnify himself, to multiply the ways in which he exists, to make his life full, significant and interesting. (Aldous Huxley)

What we become depends on what we read after all of the professors have finished with us. (Thomas Carlyle)

What you will be five years from now depends on two primary influences: the people you associate with, and the books you read. (Robin Sharma)

Reading is to the mind what exercise is to the body. (Joseph Addison)

If we encounter a man of rare intellect, we should ask him what books he reads. (Ralph Waldo Emerson)

There is more treasure in books than in all the pirate’s loot on Treasure Island. (Walt Disney)

Books are the quietest and most constant of friends; they are the most accessible and wisest of counselors, and the most patient of teachers. (Charles W. Eliot)

To sit alone in the lamplight with a book spread out before you, and hold intimate converse with men of unseen generations – such is a pleasure beyond compare. (Kenko Yoshida)

Medicine for the soul. ~Inscription over the door of the Library at Thebes

To read without reflecting is like eating without digesting. (Edmund Burke)

To acquire the habit of reading is to construct for yourself a refuge from almost all the miseries of life. (W. Somerset Maugham)

The man who does not read good books is no better than the man who can’t. (Mark Twain)

To read a book for the first time is to make an acquaintance with a new friend; to read it for a second time is to meet an old one. (Chinese saying)

The time to read is any time: no apparatus, no appointment of time and place, is necessary. It is the only art which can be practised at any hour of the day or night, whenever the time and inclination comes, that is your time for reading; in joy or sorrow, health or illness. (Holbrook Jackson)

How many a man has dated a new era in his life from the reading of a book. (Henry David Thoreau)

Multiway Cut

October 17, 2009 in Hey Math, Theoretical Computer Science | Tags: approximation algorithms, CS, graph theory, multiway cut | 1 comment

A cut, C in a graph, G= (V, E) is a set of edges, whose removal from G disconnects G. i.e. G’ = (V, E – C) is disconnected. (A graph is said to be connected if there exists a path between any two vertices in the graph. Hence, a graph is said to be disconnected if there exist two vertices in the graph, say u and v, such that there exists no path between u and v in the graph.)

An s-t cut, C is a set of edges whose removal from the graph, disconnects s and t.

(Note: Throughout this discussion, we shall talk only about undirected, edge-weighted, connected graphs. Also, all edge weights are integers.)

Size of a cut: This means the total weight of all edges forming the cut.

We want to disconnect the graph; but we want to do so by removing as few (in terms of weight) edges as possible. That, we wish to find a cut of minimum size. Such a cut is called a min – cut.

Example for min – cut:

Min Cut example: All edges in the graph have weight = 20, other than the 3 highlighted edges. Those 3 edges form the min cut.

An s-t min cut, as is clear from the name, is a cut of minimum size that separates vertex s from vertex t.

Example for s- t min cut:

Example for s-t min cut

(The highlighted edges form an s-t min cut of value = 40. Note that the min cut value for this graph is 5 (obtained by removing edge {a,b}.)

=========

A multiway cut is a generalization of an s-t cut.

Here, instead of two vertices, s and t, we have to separate a set of k vertices, ${s_1, s_2, ..., s_k}$ from each other.

In other words, find a set of edges, say C, such that on removing C from the graph, there exists no path between $s_i$ and $s_j$ for any $i, j \in {1,2, ..., k}$ .

Our task is to find a multiway cut of minimum size.

Example of multiway cut:

By removing all edges shown in the figure, we can separate vertices, s1, s2, .., sk, from one another. (Note that within each ellipse around each si, there may be a number of vertices and edges between those vertices. They have not been shown for sake of clarity.)

(The above example shows a multiway cut.)

========

Question: How do you find a multiway cut of minimum size?

It turns out that it is hard to find such a cut in polynomial time. But that’s not the end of the story. What we can do efficiently (in general, an algorithm is efficient if it runs in polynomial time) is to find a multiway cut that is within a factor of 2 from the optimal. In other words, if the value of the optimal multiway cut of a graph, G is $OPT (G)$ , our algorithm will produce a cut of value $\leq 2 \times OPT (G)$ for every graph, G.

(So, even though we don’t find an optimal cut, we find one that is guaranteed to be “close” to optimal.)

========

Even though, we do not know of any efficient algorithm, for solving a multiway cut problem exactly for arbitrary values of k, we do know how to solve it efficiently for k = 2. (Note that for k = 2, the multiway cut problem is just the s-t cut problem. An optimal s-t cut can be found efficiently. [It is actually quite simple to do it; but that is not our concern here.] )

We will use this efficient s-t min cut algorithm to find our approximate multiway cut.

————–

Let us review once again what we want. Let us denote by S the set of k vertices, ${s_1, s_2, ..., s_k}$ .

We want to remove a set of edges, such that on their removal:
- there exists no path from $s_1$ to $s_2$ , $s_1$ to $s_3$ , and so on till $s_1$ to $s_k$ .
- there exists no path from $s_2$ to $s_1$ , $s_2$ to $s_3$ , and so on till $s_2$ to $s_k$ .
- there exists no path from $s_3$ to any of the other vertices in S.
- and so on, for each vertex in the set, S.

The above explanation of the problem actually provides us with a straightforward algorithm for the same.

Take vertex, $s_1$ . Find a set of edges, removing which would disconnect $s_1$ from every other vertex in S.
Let $C_1$ be such a set of minimum size (i.e. minimum total weight).

How do we find C_1? Simple; we want a min cut that separates $s_1$ from all other vertices of S. What we’ll do is merge all these other vertices of S into one single vertex, call it t. Find an s-t min cut with $s_1$ as the vertex, s, and the merged vertex as t.

(Merging: When we merge any two or more vertices, the edges between these merged vertices disappear. The other edges that were incident upon these vertices, remain as such, and are now incident upon the new merged vertex.

Example for merging vertices:

The graph on the right is obtained by merging vertices, C, D, E and F into one "super-vertex" denoted by {C,D,E,F}. Note that there are multiple edges between the "super-vertex" and some other vertices of the graph.

(Each of the edges {F,G} and {E,G} translates into an edge between the super-vertex and G. Hence, there are 2 edges between {C,D,E,F} and G.)

Therefore, using the efficient algorithm for finding an s-t min cut, we can compute $C_1$ . On removing the edges of $C_1$ , vertex $s_1$ will be disconnected from all other vertices in S.

So, the first part of our job is done (disconnecting $s_1$ from all others in S.)

(Note: We call $C_1$ as an “isolating cut” for vertex, $s_1$ .)

Similarly, find isolating cut $C_2$ corresponding to vertex $s_2$ . On removing the edges of $C_2$ , $s_2$ is disconnected from every other vertex of S.

Therefore, by removing the union of $C_1$ and $C_2$ , we can disconnect $s_1$ and $s_2$ from every other vertex in S (and obviously, from each other also).

Now, you get an idea of how to proceed, right?

Find an isolating cut $C_i$ corresponding to each vertex, $s_i$ in the set, S.

The union of all these isolating cuts, i.e. $C_1 \cup C_2 \cup ... \cup C_k$ is a multiway cut separating $s_1, s_2, ..., s_k$ from one another.

=========

Question: We had claimed that the cut produced by the algorithm is always within a multiplicative factor of 2 within the optimal. How do we prove this?

Let us call the cut produced by the above algorithm as C. i.e. $C = C_1 \cup C_2 \cup ... \cup C_k$ .

Let us call the optimal cut as A.

Now, on removing the edges of A from G, we would get k (disjoint) connected components in the graph, one connected component for each vertex, $s_i$ .

Let $A_1$ be the subset of edges from A, that is incident upon the connected component of $s_1$ .

Graph showing A1. (A1 is the set of dashed edges.) (Note that within the connected components of vertices other than s1 have not been shown. Also, the edges between the various connected components other than the one containing s1 have not been shown, for sake of clarity.)

Graph showing A1. (A1 is the set of dashed edges.) (Note that vertices and edges within the connected components of vertices other than s1 have not been shown. Also, the edges between the various connected components other than the one containing s1 have not been shown, for sake of clarity.)

As is quite obvious, $A = A_1 \cup A_2 \cup ... \cup A_k$ .

It is also clear that each edge of A appears in exactly two $A_i 's$ . (If an edge of A is between the connected component of vertex $s_i$ and $s_j$ , then it appears in the sets $A_i$ and $A_j$ . )

From this, we have that:

$\sum_{i=1}^{k} w(A_i) = 2 \times w(A)$ . —————————Eqn. (1)

Here, w(X) denotes the total weight of edges in set, X.

Now, we know that $C_1$ is an isolating cut of minimum size for $s_1$ .

Therefore, $w(C_1) \leq w(A_1)$ .

Similarly, $w(C_i) \leq w(A_i)$ for all $i \in {1, 2, ..., k}$ .

Therefore, $\sum_{i=1}^{k} C_i \leq \sum_{i=1}^{k} A_i$ .

Combining the above equation with Eqn. (1), we get that:-

$\sum_{i=1}^{k} C_i \leq 2 \times w(A)$ .

i.e. the cut produced by our algorithm is always within a factor of 2 of the optimal multiway cut.

In other words, we are done.

Points to ponder:

1. Do we necessarily need to take the union of all k sets $C_1$ till $C_k$ to obtain a multiway cut? What if we take the union of only k-1 of these sets? Will that union be a valid multiway cut?

2. As an extension of the above point: which k-1 sets should we choose in order to minimize the size of the cut produced? (Hint: you can discard the heaviest among the $C_i 's$ and output the union of the rest.) We know that outputting the union of all k sets results in a factor-2 approximation algorithm. What is the approximation factor for this improved algorithm? (Hint: Prove that the approximation factor is (2 – 2/k). )

(The topic of multiway cut is dealt in Chap. 4 of “Approximation Algorithms” by Vijay Vazirani.)

Quotes on India – 2

October 14, 2009 in Inspiration | Tags: India, quotes | Leave a comment

Access to the Vedas is the greatest privilege this century may claim over all previous centuries. – J. Robert Oppenheimer

The Indian way of life provides the vision of the natural, real way of life. We veil ourselves with unnatural masks. On the face of India are the tender expressions which carry the mark of the Creators hand. – George Bernanrd Shaw

While Greece is the country of my birth, India is the country of my soul. – Queen Fredricka

For me the most important thing is to spread the Hindu knowledge about the soul. This is more important than any other knowledge and is my main priority. – Alfred Ford

The Hindu mind represents humanity’s oldest and most continuous stream of conscious intelligence on the planet. Hindu sages, seers, saints, yogis and jnanis have maintained an unbroken current of awareness linking humanity with the Divine since the dawn of history, and as carried over from earlier cycles of civilization in previous humanities unknown to our present spiritually limited culture. – David Frawley

After gradual research; I have come to the conclusion that long before all heavenly books, God had revealed to the Hindus, through the Rishis of yore, of whom Brahma was the Chief, His four books of knowledge, the Rig Veda, the Yajur Veda, the Sama Veda and the Atharva Veda.The Quran itself made veiled references to the Upanishads as the first heavenly book and the fountainhead of the ocean of monotheism. – Muhammad Dara Shikoh

India is the only country which has known God and if anyone wants to know God he must know India. – Vecente Avelino

In the morning I bathe my intellect in the stupendous and cosmogonal philosophy of the Bhagavad Gita in comparison with which our modern world and its literature seem puny and trivial. - Henry David Thoreau

In India I found a race of mortals living upon the Earth. but not adhering to it. Inhabiting cities, but not being fixed to them, possessing everything but possessed by nothing. – Apollonius Tyanaeus

The Indians possessed a knowledge of the true God, conceived and expressed in noble, clear and grand language…Even the loftiest philosophy of the Europeans, the idealization of reason, as set forth by the Greeks, appears in comparison with the abundant light and vigor of oriental idealism, like a feeble spark in the full flood of the noonday sun. – Frederich von Scheigel

There is no language in the world, even Greek, which has the clarity and the philosophical precision of Sanskrit. – Frederich von Scheigel

Among all the great religions of the world there is none more catholic, more assimilative, than the mass of beliefs which go to make up what is popularly known as Hinduism. – W. Crooke

Sanskrit literature is a great literature. We have the great songs of the Vedas, the splendor of the Upanishads, the glory of the Upanishads, the glory of the Bhagavad-Gita, the vastness (100,000 verses) of the Mahabharata, the tenderness and the heroism found in the Ramayana, the wisdom of the fables and stories of India, the scientific philosophy of Sankhya, the psychological philosophy of yoga, the poetical philosophy of Vedanta, the Laws of Manu, the grammar of Panini and other scientific writings, the lyrical poetry, and dramas of Kalidasa. Sanskrit literature, on the whole, is a romantic literature interwoven with idealism and practical wisdom, and with a passionate longing for spiritual vision. – Juan Mascaro

I can venture to affirm, without meaning to pluck a leaf from the never-fading laurels of our immortal Newton, that the whole of his theology, and part of his philosophy, may be found in the Vedas. – Sir William Jones

Their (Indian philosophers’) subtleties make most of the great European philosophers look like schoolboys. – T. S. Eliot

Quotes on India

October 14, 2009 in Inspiration | Tags: India, quotes | Leave a comment

Whenever I have read any part of the Vedas, I have felt that some unearthly and unknown light illuminated me. In the great teaching of the Vedas, there is no touch of sectarianism. It is of all ages, climbs, and nationalities and is the royal road for the attainment of the Great Knowledge. When I read it, I feel that I am under the spangled heavens of a summer night. – Henry David Thoreau

If I were asked under what sky the human mind has most fully developed some of its choicest gifts, has most deeply pondered on the greatest problems of life, and has found solutions, I should point to India. – Max Mueller

After the conversations about Indian philosophy, some of the ideas of Quantum Physics that had seemed so crazy suddenly made much more sense. – Werner Heisenberg

In the great books of India, an empire spoke to us, nothing small or unworthy, but large, serene, consistent, the voice of an old intelligence, which in another age and climate had pondered and thus disposed of the questions that exercise us. – Ralph Waldo Emerson

In religion, India is the only millionaire – the One land that all men desire to see, and having seen once, by even a glimpse, would not give that glimpse for all the shows of all the rest of the globe combined. – Mark Twain

India is, the cradle of the human race, the birthplace of human speech, the mother of history, the grandmother of legend, and the great grand mother of tradition. our most valuable and most instructive materials in the history of man are treasured up in India only. – Mark Twain

If there is one place on the face of earth where all the dreams of living men have found a home from the very earliest days when man began the dream of existence, it is India. – Romain Rolland

It is already becoming clear that a chapter which had a Western beginning will have to have an Indian ending if it is not to end in the self-destruction of the human race. At this supremely dangerous moment in history, the only way of salvation for mankind is the Indian Way. – Arnold Tonybee

The Sanskrit language, whatever be its antiquity is of wonderful structure, more perfect than the Greek, more copious than the Latin and more exquisitely refined than either. – Sir William Jones

It is true that even across the Himalayan barrier India has sent to us such questionable gifts as grammar and logic, philosophy and fables, hypnotism and chess, and above all our numerals and our decimal system. But these are not the essence of her spirit; they are trifles compared to what we may learn from her in the future. – Will Durant

It is India that gave us the ingenious method of expressing all numbers by ten symbols, each receiving a value of position as well as an absolute value, a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Appollonius, two of the greatest men produced by antiquity. – Laplace

The marvel of the Bhagavad-Gita is its truly beautiful revelation of life’s wisdom which enables philosophy to blossom into religion. – Herman Hesse

So far as I am able to judge, nothing has been left undone, either by man or nature, to make India the most extraordinary country that the sun visits on his rounds. Nothing seems to have been forgotten, nothing overlooked – Mark Twain

India was the mother of our race and Sanskrit the mother of Europe’s languages. She was the mother of our philosophy, mother through the Arabs, of much of our mathematics, mother through Buddha, of the ideals embodied in Christianity, mother through village communities of self-government and democracy. Mother India is in many ways the mother of us all. – Will Durant

I go into the Upanishads to ask questions. – Niels Bohr

Not until we see the richness of the Hindu mind and its essential spirituality can we understand India – Lyn Yutang

When I read the Bhagavad-Gita and reflect about how God created this universe everything else seems so superfluous. – Albert Einstein

India – The land of Vedas, the remarkable works contain not only religious ideas for a perfect life, but also facts which science has proved true. Electricity, radium, electronics, airship, all were known to the seers who founded the Vedas. – Wheeler Wilcox

From the Vedas we learn a practical art of surgery, medicine, music, house building under which mechanized art is included. They are encyclopedia of every aspect of life, culture, religion, science, ethics, law, cosmology and meteorology. – William James

There is no book in the world that is so thrilling, stirring and inspiring as the Upanishads. – Max Mueller

Vedas are the most rewarding and the most elevating book which can be possible in the world. – Schopenhauer

An examination of Indian Vedic doctrines shows that it is in tune with the most advanced scientific and philosophical thought of the West. – Sir John Woodroffe

Our present knowledge of the nervous system fits in so accurately with the internal description of the human body given in the Vedas (5000 years ago). Then the question arises whether the Vedas are really religious books or books on anatomy of the nervous system and medicine. – B.G. Rele

Vedanta teaches that consciousness is singular, all happenings are played out in one universal consciousness and there is no multiplicity of selves. – Erwin Schrodinger

The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. – Erwin Schrodinger

The Hindu religion is the only one of the world’s great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond, to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang. And there are much longer time scales still. – Carl Segan

Sri Yamunacharya’s debate

October 14, 2009 in Dharma, Ideas | Tags: Dharma, knowledge, Yamunacarya | Leave a comment

In the south of India many great devotees have appeared to spread the glories of the Lord. Of all these devotees, perhaps the most famous is Sri Ramanujacarya. However, just before Ramanuja there lived another great Vaisnava whose life and teachings had a tremendous influence on Ramanuja. This was Sri Yamunacarya, also known as Alabandara – “The Conqueror.”

Yamunacarya was born around AD 918 in the city of Madurai in south India, which was then the capital of the mighty Pandya kings. After the untimely death of his father, Yamunacarya was left to be brought up by his mother and aged grandmother, living a life of great poverty.

THE CHALLENGE

When he was five years old, Yamunacarya went to study at the school of Bhasyacarya and quickly won his teacher’s affection, both for his sweet nature and his ability to learn quickly. He studied hard, and by the time he was twelve years old he was Bhasyacarya’s best student.

In those days in India, great scholars used to challenge one another to see who was the more learned in Vedic scriptures and more skilled in the science of logic. While Yamunacarya was studying at the school of Bhasyacarya, there was a great scholar who lived at the court of the Pandya king. His name was Kolahala, and he was a great favorite of the king because he could defeat any other scholar in a debate. In fact, the king had passed a law decreeing that every scholar who had been defeated by Kolahala must pay a tax to him every year – if anyone refused he would be put to death.

Now Yamunacarya’s teacher, Bhasyacarya, had also been defeated by Kolahala, and so he too was obliged to pay this tax. However, because he was a very poor man, he had not been able to pay for the past two years. One day, when Bhasyacarya was away on business and all the other students had gone home, Yamunacarya was left alone in the school. At that time one of Kolahala’s disciples came there to collect the overdue tax from Bhasyacarya.

“Where is your teacher?” he demanded in imperious tones when he saw that Yamunacarya was alone in the school.

“Might I know, sir, who has sent you here?” replied Yamunacarya in a very gentle voice, anxious not to give any offense.

“What!” exclaimed the disciple, “do you not know that I am a disciple of the greatest and most erudite scholar in all of India? Kolahala is the terror of all other scholars, and even the great Pandya king is his obedient servant. All those scholars defeated by the great Kolahala must pay a yearly tax or else forfeit their lives. Has your teacher become insane that he dares to withhold payment for two years? Or is it that he intends to challenge my master again, just as a moth rushes into a blazing fire.”

Yamunacarya was by nature very kindhearted, and he hardly ever quarreled with his fellow students. However, he also had great love and respect for his teacher. Therefore, when he heard Bhasyacarya being spoken of in that contemptuous manner, he felt such pain at heart that he could not restrain himself and replied very strongly to Kolahala’s messenger. “How foolish you are and how foolish your teacher is as well, for who but the greatest fool would train his disciple to possess such monumental pride, instead of removing such qualities from his heart. Why should my noble teacher waste his time debating with such a man? Go and tell your master that the lowest disciple of the great Bhasyacarya challenges him to a debate. If he dares to face me, let him send his reply at once.”

PREPARATIONS FOR THE DEBATE

Kolahala’s disciple was so astonished and indignant that he could not think of anything to say, but left in a furious rage to inform his teacher of this insult. When Kolahala heard what had happened, he could not help but laugh on hearing the age of his rival. The Pandya king decided to send another messenger to the boy to see whether he was insane, and, if he was serious about the debate, to bring him immediately. When the royal messenger came and told Yamunacarya of the king’s command, the boy replied, “I will certainly obey the command of his majesty the king; but if I am to be accepted as a proper opponent of the great Kolahala, then surely a conveyance should be sent to bring me to the palace”

After discussing Yamunacarya’s reply, the king and his courtiers agreed that the boy’s statement was fitting and sent a costly palanquin and one-hundred soldiers to conduct him to the palace. In the meantime news of these events had spread all over the city of Madurai, and Bhasyacarya heard the whole story as he was returning home. He was very unhappy to learn of the danger his favorite student was facing, for though the king was generous by nature, it was well known that he dealt very severely with anyone who insulted the court pandita.

Yamunacarya, however, was not in the least concerned. “There is no reason, revered sir, for you to be alarmed,” he consoled his teacher when he returned to the school, “for you can be certain that, by your grace, I will smash the pride of Kolahala.”

While they were thus talking, the king’s men arrived at the school with the palanquin. Yamunacarya worshipped the feet of his guru and calmly climbed into the palanquin, preparing himself for the great debate that was about to take place. A large crowd of people had gathered along the way, for it was unheard of that a twelve-year-old boy should challenge the court pandita and everyone wanted to catch a glimpse of the wonderful child. The brahmanas, many of whom had already been defeated by Kolahala, offered him blessings, saying, “May you defeat this insolent pandita, just as Visnu in the form of a dwarf brahmana displaced Bali Maharaja, the king of the asuras.”

Meanwhile, in the royal court a difference of opinion arose between the king and queen about Yamunacarya. The king said, “Just as a cat plays with a mouse, so will Kolahala defeat and destroy the boy”. But the queen was more thoughtful, realizing that Yamunacarya was no ordinary child. “Just as a small spark,” she said, “can turn a mountain of cloth to ashes, so will this boy destroy the mountain-like pride of Kolahala.”

“How can you really believe that this is possible?” exclaimed the king in amazement. “If you truly have faith in the child, then you must make a wager to back your words”. “Very well,” replied the queen, “I will make a wager. If the boy does not defeat and humble the proud Kolahala, I will become the servant of your maidservant.”

“This is certainly a mighty wager,” said the king, “but I will match it. If the boy defeats Kolahala, as you say, then I will give him half of my kingdom.” While the king and queen were thus exchanging wagers, the palanquin arrived and Yamunacarya entered the palace. When Kolahala saw him, he looked at the queen and smiled sarcastically. “Ala-bandara,” he said, meaning, “Is this the boy who will conquer me?”

“Yes,” replied the queen quietly, “Ala-bandara. This is he who has come to conquer you.”

THE CONTEST

When the contestants were seated, Kolahala began the debate by putting simple questions on Sanskrit grammar to Yamunacarya. When, however, he found the boy could answer them with ease, he began to pose really difficult grammatical problems; but still, Yamunacarya replied to them all without difficulty.

He then spoke to the great pandita with a playful smile on his lips. “Because I am just a boy, you are insulting me by asking these simple questions. Remember that Astavakra was no older than myself when he defeated Bandi at the court of King Janaka. If you judge a person’s learning by his size, then surely it follows that the water buffalo will be a greater scholar than yourself.”

Although Kolahala winced at these words, he controlled his anger and replied smilingly, “Well answered. Now it is your turn to put questions to me”.

“Very well,” Yamunacarya responded, “I will put three propositions before you, and, if you can refute them, I shall accept defeat.” Kolahala agreed and prepared to refute Yamunacarya’s statements. “My first proposition is this,” Yamunacarya spoke out clearly and boldly, “that your mother is not a barren woman. Refute this if you can.”

Hearing this, Kolahala remained silent. “Had my mother been barren, my birth would not have been possible,” he thought. “How can I refute his statement” Seeing Kolahala as silent as a dumb man, all the courtiers were astonished. Although the great pandita tried to conceal his anxiety, he could not prevent a flush from crossing his cheeks.

Yamunacarya spoke again, “Sir, if in spite of your all-conquering intelligence you are unable to refute my first proposition, then please hear my second. It is this, that the Pandya king is supremely righteous. Refute this if you can.” On hearing this Kolahala, was deeply disturbed, sensing his imminent defeat. With the king seated there in front of him, how could he deny the boy’s statement? Again he remained silent, the color draining from his face as he was scarcely able to control his anger.

Yamunacarya spoke again, “Here is my third proposition-that the queen of the Pandya king is as chaste and faithful to her husband as was Savitri. Refute this if you can.”

Seeing how he had once again been trapped by the intelligent boy, Kolahala could no longer restrain his anger. “You rascal,” he screamed, “how can any loyal subject say that his king is unrighteous or his queen unfaithful to her husband? It is true I have not replied to your statements, but that does not mean I am defeated. First you must refute your own propositions, and, if you cannot, you should be put to death, for the implications of your words are treason against your king and queen.”

When Kolahala shouted out these words, all his disciples and supporters cheered; but all those who favored Yamunacarya cried, “No, Kolahala is defeated. He is simply letting forth his anger, because he could not refute the statements of Yamunacarya as he promised to do.”

Thus an argument broke out in the palace, but in the midst of the contention Yamunacarya quieted them all by saying, “Please stop this argument, for it is unnecessary. I shall refute all my propositions one by one. Please hear me” At this everyone fell silent and turned their attention to Yamunacarya, wondering how he could possibly do this and yet not offend the king and queen.

“My first statement,” he continued, “was that our great pandita’s mother was not a barren woman. However, it is stated in the Manusamhita that a woman who has only one child is to be considered barren. As your mother gave birth to only one son, even though he is a man of such merit as yourself, according to the sastra, she must be considered barren. Secondly, I stated that the king of the Pandyas is a most righteous man. However, the Manu’ samhita states that a king enjoys the benefit of one sixth of the religious acts of his subjects, but also has to bear the burden of one sixth of their sinful deeds. Because in the present age of Kali men are more prone toward sinfulness than piety, it must follow that our king, although flawless in his own character, is bearing a heavy burden of unrighteousness. And now to my third proposition, which stated that our queen is as chaste and faithful as was Savitri. But again, if we consult the laws of Manu, it is said that the king is the representative of Agni, Vayu, Surya, Candra, Yama, Kuvera, Varuna, and Indra. Therefore, the queen is married not just to one man, but to these eight demigods as well. So how can it be said that she is chaste?”

On hearing these wonderful answers, all the people were filled with amazement and the queen joyfully cried out, “Alabandara! Alabandara!- He has conquered! He has conquered!”

The king immediately came forward and embraced Yamunacarya. “Just as on the rising of the sun,” he said, “all the insignificant stars fade away, so you, 0 learned Alabandara, have conquered the proud Kolahala by your learning and skill. This fellow just a short while ago was demanding your death, now you may deal with him as you see fit. I have also promised to give you half my kingdom as a prize for this victory, and that promise I will certainly fulfill.”

Of course, Yamunacarya forgave Kolahala, and, although he was but a boy of twelve years, he began at once to rule the kingdom he had won. Thus his days of poverty were over.

(This has been taken from the excellent book titled, The Life of Ramanujacarya, by Sri Naimisaranya das. This book is available online here.)

Yudhisthira’s answers to the Yaksha

October 13, 2009 in Dharma, Ideas | Tags: answers, Dharma, questions, yaksha, yudishtira | 2 comments

In the great epic Mahabharata, Maharaja Yudhisthira, the son of Dharmaraja is the embodiment of all good qualities. For this reason, he is often referred to as Ajatasatru, one who has no enemies. In many conversations Yudhisthira reveals his deep understanding of the Vedic scriptures and their practical applications. One day while living in exile in the forest, Yudhisthira finds that while attempting to drink water from a lake, all his brothers have been killed by a mysterious Yaksha (a celestial entity). When Yudhisthira arrives, the Yaksha challenges him to answer all his questions or else face the same consequences as his brothers. These questions-answers are like Vedic sutras, short, pithy and practical, and deal with piety and religiosity.

Yaksha:: Who is really a helpful companion?

Yudhisthira: Steady intelligence is a very good friend, and can save one from all dangers.

Yaksha: How can one acquire something very great?

Yudhisthira: Everything desirable can be attained by the performance of austerity.

Yaksha: What is amrita (nectar)?

Yudhisthira: Milk is just like nectar.

Yaksha: What is the friend bestowed upon man by the demigods?

Yudhisthira: Wife is such a friend.

Yaksha: What is the best of happiness?

Yudhisthira: True happiness comes as a result of contentment.

Yaksha: Why does one give in charity to brahmanas, artists, servants and kings?

Yudhisthira: For religious merit, prestige, maintenance and protection, respectively.

Yaksha: Why does one forsake friends?

Yudhisthira: Lust and greed drives one to forsake friends.

Yaksha: What is the only food?

Yudhisthira: The cow is the only food, for the milk that she produces is used to make ghee (clarified butter), which is used to perform sacrifices, pleased by which the demigods give rain, which causes the grains to grow. Therefore it should be understood that the cow is the root cause of all kinds of food.

Yaksha: What is the king of knowledge?

Yudhisthira: Knowledge pertaining to the Supreme Personality of Godhead is the king of all kinds of knowledge.

Yaksha: What is ignorance?

Yudhisthira: Not knowing one’s constitutional duty.

Yaksha: What is the best bath?

Yudhisthira: That which cleanses the mind of all impurities.

Yaksha: What is real charity?

Yudhisthira: Real charity is protecting one from the onslaughts of material nature.

Yaksha: Since dharma (virtue), artha (profit) and kama (desire) are opposed to each other, how can they co-exist harmoniously?

Yudhisthira: These three become congenial to one another when one has a virtuous wife.

Yaksha: Who is condemned to everlasting hell?

Yudhisthira: When one promises a brahmana charity, but upon his arrival refuses to give him charity.

Yaksha: What make one a brahmana, birth, learning or behavior?

Yudhisthira: It is behavior alone that make a person a brahmana. Even one who is expert in the four Vedas, born of brahmana parents, but whose behavior is not proper, should be considered a sudra.

Yaksha: Who is pleasing?

Yudhisthira: A person who speaks in a pleasing manner.

Finally the Yaksha asked Yudhisthira four questions of great significance:

Yaksha: Who is truly happy?

Yudhisthira: One who cooks his own food (is not dependant on anyone), is not a debtor (does not spend more than he can afford), does not have to leave home to make in order to earn his livelihood (does not over endeavor for material things) is truly happy.

Yaksha:What is the most wonderful thing?

Yudhisthira: The most amazing thing is that even though every day one sees countless living entities dying, he still acts and thinks as if he will live forever.

Yaksha: What is the real path to follow in this life?

Yudhisthira: The best path is to follow in the footsteps of the pure devotees, for they are the actual Mahajanas whose hearts are the sitting places of the real truths regarding religion.

Yaksha: What is news? (that is What is real situation in the material world?)

Yudhisthira: The material world is like a frying pan. The Sun is the fire, the day and nights are the fuel. The passing seasons are the stirring ladle, and time is the cook. All living entities are being thus fried in this pan. This is the real news of what is happening in the material world, which is a miserable place full of ignorance.

These questions and answers cover a wide gamut of instructions from being successful to pious to religious. Pleased by the answers of Yudhisthira, the Yaksha who was none other than Dharmaraja (the father of Yudhisthira and the embodiment of religiosity) revives all the brothers of Yudhisthira and offers him many benedictions.

(This is from here.)

Science quotes

October 13, 2009 in Fun Stuff | Tags: math, quotes, science | Leave a comment

If anybody says he can think about quantum physics without getting giddy, that only shows he has not understood the first thing about them. – Niels Bohr

Prediction is very difficult, especially if it’s about the future. – Niels Bohr

There are things that are so serious that you can only joke about them. – Werner Heisenberg

Before I came here I was confused about this subject. Having listened to your lecture I am still confused. But on a higher level. – Enrico Fermi

If I could remember the names of all these particles, I’d be a botanist. – Enrico Fermi

This isn’t right. This isn’t even wrong. – Wolfgang Pauli

There is in my opinion a great similarity between the problems provided by the mysterious behavior of the atom and those provided by the present economic paradoxes confronting the world. – Paul Dirac

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite. – Paul Dirac

Access to the Vedas is the greatest privilege this century may claim over all previous centuries.- J. Robert Oppenheimer

No man should escape our universities without knowing how little he knows. – J. Robert Oppenheimer

The optimist thinks this is the best of all possible worlds. The pessimist fears it is true. – J. Robert Oppenheimer

God may not play dice with the universe, but something strange is going on with the prime numbers. – Paul Erdos

In the old days when people invented a new function they had something useful in mind. – Henri Poincare

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven? – David Hilbert

For a virile national life

October 12, 2009 in Dharma, Ideas, Inspiration | Tags: bunch of thoughts, Dharma, strength | Leave a comment

Strength is Virtue, Weakness is Sin

Whatever the external conditions, it is the weak who suffer. No amount of external adjustment or juxtapositions will be able to save a nation if it is inherently weak. To remain weak is the most heinous sin in this world, as that would destroy oneself and also incite feelings of violence in others. Our forefathers have said that physical survival is part of the highest religion and for physical survival strength is the only basis. It is said of Vishwamitra that once during an acute famine he did not get any food for days together. One day he saw the rotting leg of a dead dog lying in a Chandala’s house. Vishwamitra snatched it and got ready to eat it by first making an offering to God. The Chandala exclaimed, “Oh, sage, how is it you are eating a dog’s leg?” Vishwamitra replied, “Yes I must first live and be strong enough in order to do penance and good deeds in the world.”

But the thinking in our country during the last few decades has been one of looking down upon strength as something sinful and reprehensible. A wrong interpretation of ‘non-violence’ has deprived the national mind of the power of discrimination. We have begun to look upon strength as ‘violence’ and to glorify our weakness.

Once a Sadhu said, ” A person sufficiently strong to do himsa, but not doing so out of restraint, discretion and compassion can alone be said to be practising ahimsa. Suppose a strong man is going in a road and somebody knocks against him. If the strong man says with compassion, “All right, my dear fellow, I excuse you for the wrong you have done me”, then we say that the strong man has practised non-violence. For, though he is capable of giving him a blow and smashing his skull, he has restrained himself. Suppose, a thin, lean man – just a mosquito! – is going and somebody pulls his ears and the ‘mosquito’ trembling form head to foot says, “Sir, I excuse you”, who will believe him? Who will say that he is practising non-violence? He is like a man who, unable to check the dacoits plundering his house, loudly proclaims vasudhaiva kutumbakam (the entire world is my home)! People will only say that he is a coward and hypocrite, that he dare not to do anything and is only hiding his cowardice behind big platitudes. The atmosphere of our country today is charged with such misconceptions and platitudes of self-deception. A dense cloud of dust is raised in the form of high-sounding words like ‘peace’ and ‘non-violence’ with an assumed air of moral authority only to cover up our imbecility.

Non-Violence of the Imbecile

It is because of such perverse notions that we have been losing all-round. We find our frontiers shrinking. No one is in a mood to protect the integrity and honour of the motherland. Every national insult is covered up under the mast of ‘peace’. All these we gulp down saying that we are devotees of ‘peace’! It is said in the Mahabharata that a person who goes on swallowing insults is neither a male nor a female.

एतावानेव पुरुषो यदमर्षी यदक्षमी ।
क्षमावान् निरमर्षश्च नैव स्त्री न पुनः पुमान् ।।

(He alone is a man who does not brook or forgive insults. One who remains cold and tolerant in the face of insults is neither a male not a female.)

The Great Examples

Our philosophy tells us that man should be humble only when he is capable of humbling others. When can one be forgiving? Only when one becomes powerful enough to strike down those who insult him. When should one serve others? Only when he becomes worthy of commanding the willing service of the entire world.

We see this ideal in Sri Krishna who preached ahimsa in Gita, after annihilating the many evil demons one after another right form his childhood. It was he who slew Kamsa, reinstated Ugarasena on the throne but himself remained as the sentinel at the court entrance, welcoming the royal guests. It was again he who took upon himself the menial service of removing the leaves after meals in the great Rajasuya Yaga of Yudhishthira, where he was the person honoured with Agrapooja! Such is the message of our philosophy.

And again in the Mahabharata Sri Krishna, on the battle-field of Kurukshetra, invoked manliness in Arjuna with the call:

क्लैब्यं मा स्म गमः पार्थ ।

(Yield not to imbecility, O Partha!)

Not only the message of the Gita, but the context in which it was delivered, the preceptor who gave it out, and the pupil, are all cast in a heroic setting. Sri Krishna, the preceptor, was accepted on all hands as the supreme hero of that Yuga. Arjuna, the pupil, too was a warrior par excellence, only next to Sri Krishna. And Bhagvad – Gita, the greatest treasure-house of spiritual knowledge, is the dialogue on the battlefield between these two great heroes of those times.

This only highlights the fact of human life that the establishment of righteousness and virtues in this world of conflicts is not possible without the quality of fearlessness and heroism. Of course, Arjuna was not a coward. But having seen his own elders and preceptors ranged against him, he was riddled with doubts about the rectitude of his course of action. He did not want to run away from the battlefield. On the contrary, keeping aside his arms, he wanted to die at hands of his adversaries, in a spirit of resignation.

यदि मामप्रतीकारमशस्त्रं शस्त्रपाणयः ।
धार्तराष्ट्रा रणे हन्युस्तन्मे क्षेमतरं भवेत् ।।

(Far better would it be for me if sons of Dhritarashtra, weapons in hand, should slay me in the battle, while I remain in non-retaliating and unarmed.)

The same confusion appears to have gripped the hearts of our leaders today. Words like ‘non-retaliation’, ‘peace’ etc., are being shouted form housetops. Of course, there is a vast difference between the mental conditions of the two. Arjuna was a hero to the very core; while the protestations of high-flown words like ‘non-retaliation’ etc., that we hear today are put up as a smoke-screen to cover up our imbecility.

The Right Philosophy

Of course, we should not indulge in unprovoked violence. At the same time, we should also not allow others to do violence to us. Allowing violence to be done to oneself is also violence and therefore adharma. Once a great Jain Sadhu explaining the significance of ahimsa said, “If you are faced with a brute force bent upon destroying you and you do nothing to protect yourself in the name of ahimsa, then you will have only encouraged the evil power to indulge in violence. You thus become an abettor in the crime and an abettor is as much guilty of the crime as the actual perpetrator.” He added, “Intention, and not the physical act, is the only criterion to decide whether the act is in the nature of himsa or ahimsa.”

The teaching of the really great ones have always guided us correctly in all such matters. Even a most compassionate saint like Tukaram defined compassion as:

दया तिचे नांव भूतांचें पालन आणिक निर्दलन कंटकांचें ।

(Compassion is protection of all living beings and destruction of the wicked elements).

There is an instance in the life of Buddha, significant in this connection. The commander-in chief of a particular kingdom came to him to receive deeksha and become his disciple. Buddha asked him as to what had prompted him to become a bhiksu. To that, the commander replied, “Enemies have invaded our territory. I am now required to lead our forces against them. But that will lead to violence and bloodshed on both sides. I felt that it would be sinful act. I therefore decided to relinquish the military responsibility and have come over here to follow your path of peace and non-violence.” Buddha counseled him: “Merely because you have come away, the enemies are not going to give up their aggression. They are bound to indulge in killing and ravaging. If you forsake your duty of protecting the innocents under your charge, the sin of all that violence will visit upon your head. Protection of the good and righteous is verily a duty enjoined by Dharma. No sin will attach to you while doing this duty. So, go back and carry our your assignment.” That was how Buddha interpreted the true meaning of ahimsa.

Sri Krishna has unequivocally and for all time to come declared that establishment of dharma implies the destruction of the evil-doers:

विनाशाय च दुष्कृताम् ।

Sri Krishna himself was the very embodiment of that principle. No doubt he exerted himself to the utmost to avoid war and bring about peace. But he clearly foresaw that the ultimate sanction lay in his own supreme strength. When he was about to go to Duryodhana for bringing about a compromise Dharmaraja (Yudhishtira) became anxious about his safety fearing that the evil-natured Duryodhana might harm Sri Krishna. Sri Krishna assured him that in that event Dharmaraja would get the kingdom without a war as he himself would destroy Duryodhana and his host of associates. That is the only right view regarding the role of strength while facing adversaries. To speak and act always in terms of applying force when it is not needed and when a just and honourable compromise is possible is inhuman and brutal. But to talk always of compromise and not to use force even when there is no other way out to undo injustice and insults is sheer cowardice and imbecility.

We, therefore, have to properly understand the true message of those great lives as lived by them in this world of hard realities. And the hard reality is that the world, as it is constituted today, understands but one language – the language of strength. It is on the unshakable foundation of immense strength alone that the nation rises and maintains itself in a glorious condition.

(The above is from Sri Golwalkar’s Bunch of Thoughts.)

Wondrous Assortment

HINDU RASHTRA AND “MINORITIES”

A Lesson From Neighbours

Hindu Rashtra in Living Practice

Epics in Heroic Motherhood

Duty Towards Neighourhood

Steel People’s Will

The Living Ideal

The Vision that Inspires

Assimilate the Good

Pick Up Such Gems

Respond to Local Aspirations

Be world Missionaries

What the World Expects

True Ambassadors

To Impart Samskars

Translation in English:-

Sanskrit

Samskritam

Sanskrit:

Samskritam:-

THE GREAT DEVOTEE TIRUMANGAI

TIRUMANGAI’S VISIT TO SRI RANGAM

ADOPTING THE WAYS OF ROBBERS

CONSTRUCTION OF THE RANGANATHA TEMPLE

THE CHALLENGE

PREPARATIONS FOR THE DEBATE

THE CONTEST

Strength is Virtue, Weakness is Sin

Non-Violence of the Imbecile

The Right Philosophy

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