### December 2008

Monthly Archive

December 28, 2008

In about 1902 a person named Sri Sivaprakasam Pillai met Sri Ramana Maharshi at the Virupaksha cave in Thiruvannamalai and posed his doubts on self realisation. His questions and Ramana Maharshi’s answers (about 28 in number) have been published as the book ‘Who Am I ‘ . These questions and their answers can be read here. I would like to highlight below one question which explains how to practice self inquiry. It may be used as a method to channelize ones thoughts. Here is a photo of Ramana in his young age.

**Qn: What is the means for constantly holding on to the thought Who am I ?**

**Ans: When other thoughts arise, one should not pursue them, but should inquire: ‘To whom do they arise?’ It does not matter how many thoughts arise. As each thought arises, one should inquire with diligence, “To whom has this thought arisen?”. The answer that would emerge would be “To me”. Thereupon if one inquires “Who am I?”, the mind will go back to its source; and the thought that arose will become quiescent. With repeated practice in this manner, the mind will develop the skill to stay in its source. When the mind that is subtle goes out through the brain and the sense-organs, the gross names and forms appear; when it stays in the heart, the names and forms disappear. Not letting the mind go out, but retaining it in the Heart is what is called “inwardness” (antar-mukha). Letting the mind go out of the Heart is known as “externalisation” (bahir-mukha). Thus, when the mind stays in the Heart, the ‘I’ which is the source of all thoughts will go, and the Self which ever exists will shine. Whatever one does, one should do without the egoity “I”. If one acts in that way, all will appear as of the nature of Siva (God).**

December 17, 2008

Posted by asymptotics under

Game Theory | Tags:

Game Theory |

[2] Comments
Let us consider the following problem which is a popular example in game theory.

A mother wants to divide a cake between her two children. To make both of them happy she has to ensure that each one gets an equal share. That is she has to cut the cake into two equal halves. But the problems is that the cake does not have a regular shape. Hence what is equal to her eyes may not be equal to the eyes of her children. The consequences of an unequal division are imaginable. So how can she make both her kids happy?

The solution is to ask one of the kids to cut the cake into two and the other to choose the piece. It can be verified that this solves the problem. The interesting thing about the solution is that the mother was able to satisfy both the kids even without knowing what will make them happy.

Now if the mother has N kids what will she do?

What will happen if some kids form a collusion and try to get a bigger share for them ?

December 11, 2008

Mathematicians often turn into poets. The joy induced by a mathematical argument often makes a mathematician go beyond theorems and proofs to praise it. I really liked this quote on reductio ad absurdum (proof by contradiction) which I found on Terence Tao’s blog . The existence of infinitely many primes has been proved by Euclid using this technique.

**“Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game ”.**

(G.H. Hardy, 1877-1947)