Friday, February 26, 2010

Open Day at IISc.

Its been a long time since I actually attended an Open day.In school it would happen a week after the exams and this would be the opportune for the teachers to update my parents with all the nonsense that I was upto(with books and without them!!!).
Any ways,today was a open day at IISc and contrary to my expectations it was of a different kind.For one,with me in my twenties the teachers have no reason to call my parents unless I have done something terribly wrong(which is pretty subjective too).
The open day at IISc is a time when students from neighboring schools colleges and institutes come to have a peep at what we are up to.It is a time when students visit other departments(sometimes for the first time).My department i.e Mathematics had two talks as part of the curriculum for the day.One was named 'The word problem' and the other 'Games people play'.
The former,even though it sounds pretty innocuous is a pretty deep problem in pure mathematics,however I would like to tell you about the latter.The title of the talk itself can have so many connotations,and it did have.It was about Game Theory,an area in Mathematics that intersects every practical aspect of life these days.
The talk was given by Prof. M.K Ghosh,the chairman of our department.He was in his element then,with his signature style of supplying a lot of golden rules for mathematics in particular and life in general.
To say the least,it was an elementary talk,with emphasis on motivation.We were introduced to the formal definition of a Game( Mathematicians are lost until a definition is made!!!),and from then on he gave us many examples.He defined what are called as 'Zero sum' games-Basically games in which one of the opponents gain is a loss for the other.Then spoke about mixed strategies and finally to make the talk mathematical(as many mathematicians believe,that a mathematics talk is not complete until a theorem is proved!!!)-stated a theorem,which got John Nash the Nobel prize in economics.
A lot of examples were discussed like The battle of Bismark,The prisoners Dilemma problem,The chicken problem,the battle of the sexes,....Among them I particularly liked the Chicken problem,it has nothing to do with the chicken we eat,its the usual term 'chicken' used in American slang.This problem has two players,to give a real life setup,two motorists entering a narrow road from opposite directions,the obvious thing that has to be done to ensure safety of both( and hence have victory) is that each one gives way to the other,however giving way would mean that he is a 'chicken'.So to protect ones ego both have to move in and hence collide and die.A solution to the problem involves getting the players from a lose-lose situation to a win-win one.Apparently it is still an open problem.
This problem has a bit of history and was in a way related to the Cold war,when the US and the USSR had a stand off in Cuba.

The prisoners dilemma is very interesting too,it is about two prisoners caught in crime together.They are kept in two different rooms.The deal is that both need to be questioned.If both of them conceal,then they are set free,if both reveal then both are imprisoned,and if one reveals and the other conceals then the concealer gets double the jail term.Now as you can clearly see that the best strategy is that bot of them conceal,however given the fact that they don't trust each other,both will find it beneficial to reveal,and hence be convicted.
A real life situation is attributed to the Nuclear arms programme between India and Pakistan,where lack of trust has led both nations to spend billions of rupees on acquiring nuclear weapons.

In all it was a great talk,interspersed with some general gyan like 'Sometimes in life you will play the right moves and still lose' and when this happens 'do not worry,just spend time to figure out why things happened the way they did' usually 'its due to reasons beyond you,factors which actually enhance the opponents game'
Another interesting comment was that 'when faced with an intelligent opponent,who knows every possible move that you can make,the way to hide your moves from him is to hide them from yourself!!!interesting right,and this is achieved in Probability by a process called 'Randomization'.'

Given my general dislike for probability,this talk was a welcome change.I have come to realize that every thing is related,and research is just one way to find these relations,sometimes you hit something big sometimes not ,but still I am sure whatever one finds will definitely make a difference!!!