It is been a long time since Blogspot has seen life in me. I was busy pandering to academic pressures and as a result lost track of my new found hobby. All said and done, the good news is that Bond is back, so you got to be happy. The past few months have be pretty eventful. I have been travelling all across the south. Was in Kerala in June, in Goa in July, in Bangalore in August in Hyderabad in August, back to Bangalore and now I am here in Chennai.
That covers all the four southern states and Goa as complementary. It has been fun all through.
This is the first time I am visiting Chennai and the Tamilians did not spare the opportunity to make it as eventful as possible as soon as I reached. Besides a few stray incidents it was a pretty smooth entry into the state. A friend had told me to be careful about the autowala's, about how they can fleece your dearness. Nonetheless I thought I could still give it a try, I asked one of them the cost of travelling to CMI, the dude gives me a blank look as though CMI does not exists in Chennai. Luckily the 'C' stands for 'Chennai'. Having no idea of where CMI is located, he decides to think for sometime and then after some deliberation blurts out "450 lagega!!!"- like if you dont know where to go just charge the maximum. Luckily I had just 200 in my wallet so I told him that it was too much and scurried away to the nearest bus-stop. The bus fares in Chennai are exorbitantly low... you could travel from one end to the other with just 10 ruppees. The crazy thing was that I boarded the right bus twice and was told that it is the wrong one, it was frustrating with all the luggage. I finally manged to reach CMI after about three hours of travelling. It took me five hours to reach Chennai and 3 hours to find CMI in Chennai, tragedy of sorts.
As of now I am kinda having fun. The food is pretty tasty. I finally managed to meet old friends after a long time. I haven't got the opportunity to travel around yet. Hope to go to Loyola College tomorrow, so will write more later. Bye for now and have fun!!!
Saturday, November 27, 2010
Saturday, May 22, 2010
A presentation and some introduction.....
Yesterday we had our MS project presentations, thats the last requirement for one to officially be a 'Master of something ' at IISc, I am still trying to find that out! Thought I would write about something that I said...
I studied some algebraic number theory as part of my Masters project, and proved a series of exercises that lead to the proof of what is know as the 'Kronecker-Weber theorem'.
It was a wonderful morning, in fact, it hardly dawned on me that it was morning when I went to sleep!!! So I got myself ready, and cycled to the department. It was 6:45 am, this was the first time that I reached the department so early (I have gone back to my room at this time from the department many a times though :P).
And then did the last minute preparations- check my slides, read my notes and blah blah blah.
My talk was scheduled at 10:10 am. The department had played it safe to ensure that there was a sizable audience, in that it had promised a delicious lunch to all those who attended the talks.
I made my last minute calls back home(with the number of exams that I have to answer reducing drastically, I do not miss an opportunity to let folks at home wish me 'best of luck').
So finally the moment arrived. I motioned to the screen, and began the jargon...
I mentioned before, I spoke on algebraic number theory. Here is some part of the my introduction -
The subject developed due to a rather silly comment of mathematician Pierre Fermat in the margin of Arithmetica by Diophantus as follows -I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it.
Fermat claimed that he had an elegant proof to prove the above fact. Unfortunately he was dead before one could publish books with fatter margins!!! The search for this coveted proof has lasted lifetimes of some of the best mathematicians in the past. This was notoriously labeled as the 'Fermats last theorem'(FLT). It was proved in 1994 by Prof Andrew Wiles at Princeton university. The proof is hardly elementary, it is about 290 pages long and uses some of the most sophisticated modern algebraic number theory. It definitely needs a lot more than a margin of a book.
However the alarming simplicity of the statement generated the most number of 'wrong proofs' for this problem in the history of mathematics( my attempt included-my undergraduate professor almost fainted when I told him that I was trying to prove the 'Fermats last theorem'!!!). In fact it was this theorem that in a way got me exited about mathematics. Very often it is difficult to prove some of the most simple questions in our lives. By simple I mean, ones with really simple statements, so simple that even a five year kid could understand them. Mathematics is flooded with such questions, and the FLT is a prime example.
The basic reason why many of the earlier proofs collapsed for due to the assumption of unique factorization in certain domains. Mathematics in general, and number theory in particular has a predominant inductive reasoning, in that I mean that, one proves something for something small and finite, and then extrapolates it to something much larger. A similar reasoning was applied to the set of integers. Integers have this marvelous property called the 'Fundamental theorem of arithmetic', which asserts that every integer can be written as a unique product of prime powers. One should note that this theorem(like many other useful theorems) has a dual nature, that is it not only talks about an existence of factorization but also guarantees its uniqueness. Uniqueness is a very important property, if something can be done uniquely, it means that it is independent of who does it. It also helps one to come up with important formulas(by computing something in two different ways and then equating them). This general principle was assumed for domains containing the integers, and this assumption was wrong. The moral of the story is that whilst proving something, check that the assumptions are proved to be correct-otherwise you might end up with absolute non-sense.
Algebraic number theory was developed to answer questions which generalize properties of integers to bigger and general domains... from here on the talk becomes a little technical and hence cannot write it up here...
I have still got to write out the report though, so will pushoff for now, till then all the best...may be you could start writing out conjectures in your textbooks, who know we might soon have a 'last theorem' after your name!!!
I studied some algebraic number theory as part of my Masters project, and proved a series of exercises that lead to the proof of what is know as the 'Kronecker-Weber theorem'.
It was a wonderful morning, in fact, it hardly dawned on me that it was morning when I went to sleep!!! So I got myself ready, and cycled to the department. It was 6:45 am, this was the first time that I reached the department so early (I have gone back to my room at this time from the department many a times though :P).
And then did the last minute preparations- check my slides, read my notes and blah blah blah.
My talk was scheduled at 10:10 am. The department had played it safe to ensure that there was a sizable audience, in that it had promised a delicious lunch to all those who attended the talks.
I made my last minute calls back home(with the number of exams that I have to answer reducing drastically, I do not miss an opportunity to let folks at home wish me 'best of luck').
So finally the moment arrived. I motioned to the screen, and began the jargon...
I mentioned before, I spoke on algebraic number theory. Here is some part of the my introduction -
The subject developed due to a rather silly comment of mathematician Pierre Fermat in the margin of Arithmetica by Diophantus as follows -I have discovered a truly marvelous proof that it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. This margin is too narrow to contain it.
Fermat claimed that he had an elegant proof to prove the above fact. Unfortunately he was dead before one could publish books with fatter margins!!! The search for this coveted proof has lasted lifetimes of some of the best mathematicians in the past. This was notoriously labeled as the 'Fermats last theorem'(FLT). It was proved in 1994 by Prof Andrew Wiles at Princeton university. The proof is hardly elementary, it is about 290 pages long and uses some of the most sophisticated modern algebraic number theory. It definitely needs a lot more than a margin of a book.
However the alarming simplicity of the statement generated the most number of 'wrong proofs' for this problem in the history of mathematics( my attempt included-my undergraduate professor almost fainted when I told him that I was trying to prove the 'Fermats last theorem'!!!). In fact it was this theorem that in a way got me exited about mathematics. Very often it is difficult to prove some of the most simple questions in our lives. By simple I mean, ones with really simple statements, so simple that even a five year kid could understand them. Mathematics is flooded with such questions, and the FLT is a prime example.
The basic reason why many of the earlier proofs collapsed for due to the assumption of unique factorization in certain domains. Mathematics in general, and number theory in particular has a predominant inductive reasoning, in that I mean that, one proves something for something small and finite, and then extrapolates it to something much larger. A similar reasoning was applied to the set of integers. Integers have this marvelous property called the 'Fundamental theorem of arithmetic', which asserts that every integer can be written as a unique product of prime powers. One should note that this theorem(like many other useful theorems) has a dual nature, that is it not only talks about an existence of factorization but also guarantees its uniqueness. Uniqueness is a very important property, if something can be done uniquely, it means that it is independent of who does it. It also helps one to come up with important formulas(by computing something in two different ways and then equating them). This general principle was assumed for domains containing the integers, and this assumption was wrong. The moral of the story is that whilst proving something, check that the assumptions are proved to be correct-otherwise you might end up with absolute non-sense.
Algebraic number theory was developed to answer questions which generalize properties of integers to bigger and general domains... from here on the talk becomes a little technical and hence cannot write it up here...
I have still got to write out the report though, so will pushoff for now, till then all the best...may be you could start writing out conjectures in your textbooks, who know we might soon have a 'last theorem' after your name!!!
Monday, May 10, 2010
The God particle...and blah blah blah...
Couple of days back I attended a talk by Prof B V Sreekantan on 'The LHC and the God Particle'. For those who do not know- LHC stands for 'Large Hadron Collider', the biggest particle accelerator ever built. A logical question to ask is 'Why the hell does one need a particle accelerator? leave alone the biggest. I hope to share my understanding of the subject through this post.
The basic question that every human being wants an answer for is sometimes as follows: Why am I here?
just four words long yet this questions has made the scientific community slog for centuries. It has made theists out of atheists and vice versa. It has had profound implications on philosophy, the way we think. In fact it has made us question the very reason of our existence.
The biological front has thrown light onto this through the theory of evolution perceived by Charles Darwin, which besides being a theory does have a lot of physical evidence.
The physical front however just has a theory, and the onus is on the LHC to provide the necessary evidence!!!
Getting to business, let me clarify that I am not an expert in this field( not that I am an expert in anything else!), so do not rely solely on what I say. If I have aroused enough interest do find time to enlighten yourself better.
The LHC is a technological marvel. The International space station is the only other experiment that matches the magnitude of this project. Its cost so far is about $5 billion(US), and still growing, there are about 10 thousand scientist all over the world working in coherence at any given time. In terms of physical dimensions, it is 27km long, uses 1232 dipole magnets, 1600 superconducting magnets and 27 tonnes of liquid helium, and is about 175 meters beneath the surface of the earth. It generates terabytes of data in seconds, leading to the development of the high speed network called The Grid. The enormity of the entire project transcends all human imagination.
Whats the deal, why do we even need it? A fundamental question in modern physics has been to find the most basic particles in the universe, basic means- smallest and indivisible. It so happens that the universe is not only about particles but also forces, and hence the real search is to find the most basic 'particles and forces', from these everything else evolves, and hence they are called fundamental particles.
Physicists have come with 'The standard model' for the universe and according to this model there are about a dozen fundamental particles(electrons, quarks, leptons,...) and four fundamental forces (strong nuclear, electromagnetic, weak nuclear and gravitational). The fermions are supposed to be the ultimate constituents of matter. This theory is pretty solid, and answers most of the questions, however the problem with this theory is that it does not answer why some particles are heavy while others have no mass at all(you see we need a theory that answers all the questions). The answer may be the so-called Higgs mechanism. According to the theory of the Higgs mechanism, the whole of space is filled with a ‘Higgs field’, and by interacting with this field particles acquire their masses. Particles that interact intensely with the Higgs field are heavy, while those that have feeble interactions are light. The Higgs field has at least one new particle associated with it, the Higgs boson(this was infamously called the 'God particle' by Prof Leon Lederman, director at Fermi labs, Illinois, one should read his book 'The God Particle' ). If such a particle exists, experiments at the LHC will be able to detect it. The existence of such a particle will answer questions related to the Big bang theory and the creation of the universe.
It is believed that the universe has a dual nature. For example corresponding to something hot there exists something cold, if there is light there exists darkness, then newtons third law says that every action has an equal and opposite reaction and so on. One could then ask, since there exists matter, does there exists something called anti-matter? The answer is believed to be in the affirmative, and again we rely on the LHC to get some answers.
However there are doubts whether the experiment will be a success. Many physicists feel that creating conditions similar to that at the time of Big bang is virtually impossible. Presently the accelerator is running at low energies, at higher energies, they claim that the accelerator will give rise to mini black holes(objects with extremely high densities) which would cause the earth to collapse onto itself, hence bring an end to this planet and in fact the entire solar system. The desire to know how it all began might just lead to a premature end!!!
Towards the end of the talk, we were told that what we see is just 3.5% of what is there, about 70% is what is called the Dark energy and another 25% of Dark matter( seems like we are almost totally in the dark!!!). The physics that we develop here, is subject to only 3.5% of the universe, most of which is beyond experimental reach(since what we see is light years away), and most of the theories, including the 'Standard model and insanely extrapolated to all of it.
The problem lands into philosophical and theological realms and deeply entwines with the question of the existence of God. Are we trying to grab more than what our hands can hold? It would be in Gods best interest that we know the universe that He has created. 'Ask and you shall be given, knock and the door shall be opened, search and you will find'-yes we shall search with faith that we will find the answers someday. Till then carry on with research...
The basic question that every human being wants an answer for is sometimes as follows: Why am I here?
just four words long yet this questions has made the scientific community slog for centuries. It has made theists out of atheists and vice versa. It has had profound implications on philosophy, the way we think. In fact it has made us question the very reason of our existence.The biological front has thrown light onto this through the theory of evolution perceived by Charles Darwin, which besides being a theory does have a lot of physical evidence.
The physical front however just has a theory, and the onus is on the LHC to provide the necessary evidence!!!
Getting to business, let me clarify that I am not an expert in this field( not that I am an expert in anything else!), so do not rely solely on what I say. If I have aroused enough interest do find time to enlighten yourself better.
The LHC is a technological marvel. The International space station is the only other experiment that matches the magnitude of this project. Its cost so far is about $5 billion(US), and still growing, there are about 10 thousand scientist all over the world working in coherence at any given time. In terms of physical dimensions, it is 27km long, uses 1232 dipole magnets, 1600 superconducting magnets and 27 tonnes of liquid helium, and is about 175 meters beneath the surface of the earth. It generates terabytes of data in seconds, leading to the development of the high speed network called The Grid. The enormity of the entire project transcends all human imagination.
Whats the deal, why do we even need it? A fundamental question in modern physics has been to find the most basic particles in the universe, basic means- smallest and indivisible. It so happens that the universe is not only about particles but also forces, and hence the real search is to find the most basic 'particles and forces', from these everything else evolves, and hence they are called fundamental particles.
Physicists have come with 'The standard model' for the universe and according to this model there are about a dozen fundamental particles(electrons, quarks, leptons,...) and four fundamental forces (strong nuclear, electromagnetic, weak nuclear and gravitational). The fermions are supposed to be the ultimate constituents of matter. This theory is pretty solid, and answers most of the questions, however the problem with this theory is that it does not answer why some particles are heavy while others have no mass at all(you see we need a theory that answers all the questions). The answer may be the so-called Higgs mechanism. According to the theory of the Higgs mechanism, the whole of space is filled with a ‘Higgs field’, and by interacting with this field particles acquire their masses. Particles that interact intensely with the Higgs field are heavy, while those that have feeble interactions are light. The Higgs field has at least one new particle associated with it, the Higgs boson(this was infamously called the 'God particle' by Prof Leon Lederman, director at Fermi labs, Illinois, one should read his book 'The God Particle' ). If such a particle exists, experiments at the LHC will be able to detect it. The existence of such a particle will answer questions related to the Big bang theory and the creation of the universe.It is believed that the universe has a dual nature. For example corresponding to something hot there exists something cold, if there is light there exists darkness, then newtons third law says that every action has an equal and opposite reaction and so on. One could then ask, since there exists matter, does there exists something called anti-matter? The answer is believed to be in the affirmative, and again we rely on the LHC to get some answers.
However there are doubts whether the experiment will be a success. Many physicists feel that creating conditions similar to that at the time of Big bang is virtually impossible. Presently the accelerator is running at low energies, at higher energies, they claim that the accelerator will give rise to mini black holes(objects with extremely high densities) which would cause the earth to collapse onto itself, hence bring an end to this planet and in fact the entire solar system. The desire to know how it all began might just lead to a premature end!!!
Towards the end of the talk, we were told that what we see is just 3.5% of what is there, about 70% is what is called the Dark energy and another 25% of Dark matter( seems like we are almost totally in the dark!!!). The physics that we develop here, is subject to only 3.5% of the universe, most of which is beyond experimental reach(since what we see is light years away), and most of the theories, including the 'Standard model and insanely extrapolated to all of it.
The problem lands into philosophical and theological realms and deeply entwines with the question of the existence of God. Are we trying to grab more than what our hands can hold? It would be in Gods best interest that we know the universe that He has created. 'Ask and you shall be given, knock and the door shall be opened, search and you will find'-yes we shall search with faith that we will find the answers someday. Till then carry on with research...
Saturday, May 1, 2010
Run maadi run.......Science and technology go for a run!!!
Hi, its been a long time, I am sure you guys missed me :P, anyways had a lot of activity happening. I was sick for sometime and then we had our end-semester exams, which went on for almost a fortnight(more about it sometime later :) ).
On the 10th of May we had the 'Science and technology run'. This is a time when the outside world tests how fit people in IISc are, they are surprised not only by our fitness but also the enthusiasm that some guys show!!!
It also surprised me, in fact there was a substantial crowd from the math dept, which defied the opinion about math researchers that many have.
The run started at 7:50 on a beautiful Sunday morning, before that, one had to register and then collect the t-shirt(a complementary gift which nobody wants to forsake). The marathon is open to the local community around IISc and also to the corporates(most of whom had dressed well with 'just do it' from head to toe-just made one feel that life will be rosy once we leave IISc, soon). This time the organizers had done a marvelous job, in that they had put up the route on display a week before the run, the publicity done well and they had live music playing.
The main marathon was for 10km, in fact they managed to keep the path within campus. In the process I got to explore some untrodden roads in IISc. It was fun, I managed to complete the run, that was a pretty consolation :), in fact was devoid of most of the post workout blues. My logic in running was the fact that I run about 3km regularly, which I insanely extrapolated to 10, it worked though.
There was an event for everyone. Besides the 10K marathon, there was a 5K half marathon, a 5K relay, a run for the children and for the old...truly, it was a celebration of running. It is essential that we spend time exercising regularly. We often resort to bikes and cars even to travel very short distances, and to do simple errands.
People of all ages participated. There was a prof. who completed it on a wheel chair, really inspiring. The skinny, the obese, the athletic and the not so athletic, the young and the old, all had a moment of fun and gaiety...they went back with tired legs but a unfatigued mindset...so lets run!!!
(All the photos are taken from http://gallery.iisc.ernet.in/main.php/v/anaska/SnTrun2010/)
On the 10th of May we had the 'Science and technology run'. This is a time when the outside world tests how fit people in IISc are, they are surprised not only by our fitness but also the enthusiasm that some guys show!!!
It also surprised me, in fact there was a substantial crowd from the math dept, which defied the opinion about math researchers that many have.The run started at 7:50 on a beautiful Sunday morning, before that, one had to register and then collect the t-shirt(a complementary gift which nobody wants to forsake). The marathon is open to the local community around IISc and also to the corporates(most of whom had dressed well with 'just do it' from head to toe-just made one feel that life will be rosy once we leave IISc, soon). This time the organizers had done a marvelous job, in that they had put up the route on display a week before the run, the publicity done well and they had live music playing.
The main marathon was for 10km, in fact they managed to keep the path within campus. In the process I got to explore some untrodden roads in IISc. It was fun, I managed to complete the run, that was a pretty consolation :), in fact was devoid of most of the post workout blues. My logic in running was the fact that I run about 3km regularly, which I insanely extrapolated to 10, it worked though.There was an event for everyone. Besides the 10K marathon, there was a 5K half marathon, a 5K relay, a run for the children and for the old...truly, it was a celebration of running. It is essential that we spend time exercising regularly. We often resort to bikes and cars even to travel very short distances, and to do simple errands.
People of all ages participated. There was a prof. who completed it on a wheel chair, really inspiring. The skinny, the obese, the athletic and the not so athletic, the young and the old, all had a moment of fun and gaiety...they went back with tired legs but a unfatigued mindset...so lets run!!!(All the photos are taken from http://gallery.iisc.ernet.in/main.php/v/anaska/SnTrun2010/)
Sunday, March 21, 2010
A morning with Cricket...surprisingly entertaining!!!
Well I am back, pretty soon this time. Sometimes incredible things happen in stuff that you absolutely deteste...well this would be too strong a statement to what I mean to refer to, however let me say what I am talking about...it's the game of Cricket.
As all of IISc was sleeping, a group of math students awoke to life and freedom, A moment comes, which comes but rarely in history, when we step out from the old to the new, when an age ends and when the soul of a Department, long suppressed, finds utterance...well this is what Pandit Jawaharlal Nehru would have said, had he seen our team play, today.
This posts will involve a lot of names, if you do not know them, don't worry, just build an analogy to your favorite team. To say the least, I reached the venue late, as usual. I had a valid reason this time. Yesterday, I fell off my bicycle under mysterious circumstances...if I try to recall properly I think I was day- dreaming whilst riding. In the course of the accident, I hit my head hard onto the road. Ever since I am trying to recall what I could have forgotten!!! Regarding the same, I had an appointment with the doctor today morning, and hence the delay justified!!!.
I reached exactly half way into the match. That's when we started batting. The opposite team had put up a monstrous score of 110 in 15 overs, so the "Math Geeks( or rather Gundas) " had to get to work as soon as possible. Our first wicket was the pair, Dheeraj and Ramiz, two very adept batsmen. They held fort for almost nine over, scoring 66 runs in partnership, Dheeraj seemed to have the extra lucky spark today, because, he had two consecutive drop catches, with the same guy...this fellow had a very big hand in our victory.
After Dheeraj was out(was caught right on the boundary), the game still seemed close at hand, in fact people in the audience had now developed this easy feeling 'we are winning'...especially when Tapan hit a six for the first ball he faced. It did not remain rosy for long, as in the same over Tapan was bowled out, then Sachin made his entry . Now things started getting a little messy, Ramiz was soon out and with him, all the experienced batsmen were on the bench. Now was the moment of truth, the onus was on the middle order, and this is why Sachin exists...not Tendulkar, but Sharma.
The scenario is as follows, we need 36 runs from 24 balls, we have about four wickets left...but not many balls. At this stage we should make mention of one of the stars in the team- Ravi Prakash, unfortunately he had a bad day. Due to some miscommunication between Sachin and him, he got himself run out. He left the field crying tantrums at Sachin. Now Sachin had a two fold responsibility in winning the game for us. One that he could then stay clear of Ravi's wrath, and secondly he was the last batsman known for batting!!!.
He did live up to the expectations. After Ravi, we had Prahllad on the field, but not for long. And then Arpan, who is primarily known for his deadly bowling.
One of Sachin's shot was stopped right at the boundary, there was some dispute with the decision...Well our very own self appointed 'Fourth umpire' i.e Avijit ran straight to the field and started clarifying to the fielder on how he was wrong and that we deserved a boundary, another instance of craziness!!!
Then it was Kaka's(lovingly called Santanu sometimes!!!) time to enter the bout. The game now was at 12 runs from 8 balls. And lo Sachin hits a six and a four out of the last two deliveries of the second last over. So we are down to 2 runs from 6 balls., and now Santanu(with love) is on strike. Well, this is one instance when things can get really crazy in cricket...you could either expect a six out of the last ball...or no runs of the entire last over!!!
The bowler bowls the first ball of the last over, and Santanu makes an attempt to hit a big one...no luck. Then the second ball, this time he tries to place the ball, but again in vain... the the third ball...and still the man can't make contact with the ball. Now the audience is getting jittery and superstitious, Samya gets a cigarette, and claims that this is the good luck charm...the women are busy praying...Rahul is thinking of a mathematical proof as to how we can not lose, Shubhamay was counting how much he would have to spend on the 'Juice treat' if we win, Suparna was busy in getting the audience in order, Shibu was busy in adjusting Diganto's balding, so that it could reflect light onto the bowler,and hence blind him, Ravi went off for a leak, ...and all hell broke loose. Everybody had Santanu's name on their lips (and I swear this name would have been a curse, if not for the positive outcome of the match), and then the fourth ball,and yo he manages to make contact with the ball, Sachin runs from the other end, Santanu runs, the fielder misses the wicket and they run for the winning run...and the crowd runs to them...Truly was a moment of ecstasy.
We won...we defeated a tough opponent...We are champions in our group!!!
We are just two games away from being champions...I have my fingers crossed...But deep within I know these guys have what it takes to attain the title...
Cheers to the Math Cricket Team!!!!
P.S- Thanks to the cheer-leading squad under the leadership of the Cheerful Suparna. In fact as the players were running between the wicket, Suparna was running between the score keeper and the audience..and hence was the score updating link!!!
As all of IISc was sleeping, a group of math students awoke to life and freedom, A moment comes, which comes but rarely in history, when we step out from the old to the new, when an age ends and when the soul of a Department, long suppressed, finds utterance...well this is what Pandit Jawaharlal Nehru would have said, had he seen our team play, today.
This posts will involve a lot of names, if you do not know them, don't worry, just build an analogy to your favorite team. To say the least, I reached the venue late, as usual. I had a valid reason this time. Yesterday, I fell off my bicycle under mysterious circumstances...if I try to recall properly I think I was day- dreaming whilst riding. In the course of the accident, I hit my head hard onto the road. Ever since I am trying to recall what I could have forgotten!!! Regarding the same, I had an appointment with the doctor today morning, and hence the delay justified!!!.
I reached exactly half way into the match. That's when we started batting. The opposite team had put up a monstrous score of 110 in 15 overs, so the "Math Geeks( or rather Gundas) " had to get to work as soon as possible. Our first wicket was the pair, Dheeraj and Ramiz, two very adept batsmen. They held fort for almost nine over, scoring 66 runs in partnership, Dheeraj seemed to have the extra lucky spark today, because, he had two consecutive drop catches, with the same guy...this fellow had a very big hand in our victory.
After Dheeraj was out(was caught right on the boundary), the game still seemed close at hand, in fact people in the audience had now developed this easy feeling 'we are winning'...especially when Tapan hit a six for the first ball he faced. It did not remain rosy for long, as in the same over Tapan was bowled out, then Sachin made his entry . Now things started getting a little messy, Ramiz was soon out and with him, all the experienced batsmen were on the bench. Now was the moment of truth, the onus was on the middle order, and this is why Sachin exists...not Tendulkar, but Sharma.
The scenario is as follows, we need 36 runs from 24 balls, we have about four wickets left...but not many balls. At this stage we should make mention of one of the stars in the team- Ravi Prakash, unfortunately he had a bad day. Due to some miscommunication between Sachin and him, he got himself run out. He left the field crying tantrums at Sachin. Now Sachin had a two fold responsibility in winning the game for us. One that he could then stay clear of Ravi's wrath, and secondly he was the last batsman known for batting!!!.
He did live up to the expectations. After Ravi, we had Prahllad on the field, but not for long. And then Arpan, who is primarily known for his deadly bowling.
One of Sachin's shot was stopped right at the boundary, there was some dispute with the decision...Well our very own self appointed 'Fourth umpire' i.e Avijit ran straight to the field and started clarifying to the fielder on how he was wrong and that we deserved a boundary, another instance of craziness!!!
Then it was Kaka's(lovingly called Santanu sometimes!!!) time to enter the bout. The game now was at 12 runs from 8 balls. And lo Sachin hits a six and a four out of the last two deliveries of the second last over. So we are down to 2 runs from 6 balls., and now Santanu(with love) is on strike. Well, this is one instance when things can get really crazy in cricket...you could either expect a six out of the last ball...or no runs of the entire last over!!!
The bowler bowls the first ball of the last over, and Santanu makes an attempt to hit a big one...no luck. Then the second ball, this time he tries to place the ball, but again in vain... the the third ball...and still the man can't make contact with the ball. Now the audience is getting jittery and superstitious, Samya gets a cigarette, and claims that this is the good luck charm...the women are busy praying...Rahul is thinking of a mathematical proof as to how we can not lose, Shubhamay was counting how much he would have to spend on the 'Juice treat' if we win, Suparna was busy in getting the audience in order, Shibu was busy in adjusting Diganto's balding, so that it could reflect light onto the bowler,and hence blind him, Ravi went off for a leak, ...and all hell broke loose. Everybody had Santanu's name on their lips (and I swear this name would have been a curse, if not for the positive outcome of the match), and then the fourth ball,and yo he manages to make contact with the ball, Sachin runs from the other end, Santanu runs, the fielder misses the wicket and they run for the winning run...and the crowd runs to them...Truly was a moment of ecstasy.
We won...we defeated a tough opponent...We are champions in our group!!!
We are just two games away from being champions...I have my fingers crossed...But deep within I know these guys have what it takes to attain the title...
Cheers to the Math Cricket Team!!!!
P.S- Thanks to the cheer-leading squad under the leadership of the Cheerful Suparna. In fact as the players were running between the wicket, Suparna was running between the score keeper and the audience..and hence was the score updating link!!!
Tuesday, March 16, 2010
A lecture, a conjecture and a problem...
Here I am, back after a not so hectic,but a busy week. Well good news first, my guides back from Canada, so that means a bonus to my reading.
Yesterday I attended a lecture on a the 'Fuglede's conjecture'. The statement of the conjecture by itself is pretty messy, but the underlying idea is beautiful.Actually I reached late,and missing the first few minutes was too dear for me. The reason was simple, every mathematical talk will begin with a definition, and if you have skipped that, you could as well skip the entire lecture. The speaker was Prof. Shobha Madan from IIT Kanpur.
Before saying anything more about the lecture let me mention something about the speaker. For one, she's a woman, and women in mathematics are very few- in fact those that exist are super-smart, talking from my experience. There was a rumour floating around that Shoba Madan had withdrawn her membership from the American Mathematical Society, because America attacked Iraq, in a lopsided battle. It is no longer a rumour though, as I found her letter to AMS regarding her resignation on the net,you can find it here- http://www.thehindu.com/fline/fl2009/stories/20030509006913000.htm
It is not that I support such boycott, yet her move is exemplary.
Getting to the lecture, my unpunctuality got me just a peripheral understanding of the topic. A lot of it was mathematical jargon, hower some ideas were good. There was mix of different branches of mathematics in her proofs, especially Functional Analysis, Algebra and good amount of Combinatorics.
Let me tell you the problem. You are given a bounded region D, and a certain shape T.You have to tell me if it is possible to tile (in the usual sense of tiling the floor or the roof) D using tiles of shape T.
Sounds pretty banal right. But thats not the case. I will not elaborate on this problem anymore however will give instances where one can apply these ideas. The Fuglede's Conjecture asserts that such a tiling always exists when the domain D is nice(in a certain mathematical sense- which you need not bother).
For example imagine a hexagonal room,can one tile this room with triangles? well seems obvious right. Cutting the floor along the diameter of the hexagon you see that just six equi-triangular tiles are sufficient. Note that here we made a choice in the type of triangle, so in a sense we have not answered the question in full generality. The heart of the problem is to check for the possibility of a tiling starting with an arbitrary triangle, which again is not true(relying on intuition). Then we need to classify all the possible triangles that fit the bill, and this step will put the problem to rest.
This problem has been the impetus for many masons of the past,,and a matter of secrecy, about their successful tiling assignments. With ever changing designs it is imperative that one answers a question of this type, as it will go a long way in efficient resource management.
In mathematics such problems are also called 'Packing problems' , and solutions to these are of utmost importance, in theory and and practice.
Let me get a little rigorous, one can easily picture that it is not possible to tile a region using circles, because there will always exist a non-trivial gap between the tiles. Extending this idea, one can ask ' what kind of regular polygons will result in possible tiling' It seems intuitive(but need not necessarily be true) that there should be a bound on the number of sides of the polygon-this is because as the number of sides increases the boundary of the polygon attains the shape of a circle(convince yourself,its easy!), and we know that a circle cannot tile ( this idea is due to Sandeep Bhupati ,my senior at IISc), its cool right. One often uses such methods to prove stuff in mathematics.
As the talk progressed I grappled with the proofs, finally decided to lay back and relax. It is not worth breaking ones head on technical jargon.
The talk was nice, actually I liked the speaker, she had this healthy confidence and composure throughout. I like to attend talks by experts, their understanding of the subject galvanizes me with a positive attitude to research in particular and life in general!!!
Here is a small problem if you would like to work out-
You are given a 8x8 chess board with two diagonally opposite corners deleted(note that we now have only 62 squares). The question is that if you have dominoes which cover exactly two squares of the chess board at a time,then is it possible to cover the 62 squares using exactly 31 pieces of dominoes?Whatever the answer, you got to tell me why!!!
Yesterday I attended a lecture on a the 'Fuglede's conjecture'. The statement of the conjecture by itself is pretty messy, but the underlying idea is beautiful.Actually I reached late,and missing the first few minutes was too dear for me. The reason was simple, every mathematical talk will begin with a definition, and if you have skipped that, you could as well skip the entire lecture. The speaker was Prof. Shobha Madan from IIT Kanpur.
Before saying anything more about the lecture let me mention something about the speaker. For one, she's a woman, and women in mathematics are very few- in fact those that exist are super-smart, talking from my experience. There was a rumour floating around that Shoba Madan had withdrawn her membership from the American Mathematical Society, because America attacked Iraq, in a lopsided battle. It is no longer a rumour though, as I found her letter to AMS regarding her resignation on the net,you can find it here- http://www.thehindu.com/fline/fl2009/stories/20030509006913000.htm
It is not that I support such boycott, yet her move is exemplary.
Getting to the lecture, my unpunctuality got me just a peripheral understanding of the topic. A lot of it was mathematical jargon, hower some ideas were good. There was mix of different branches of mathematics in her proofs, especially Functional Analysis, Algebra and good amount of Combinatorics.
Let me tell you the problem. You are given a bounded region D, and a certain shape T.You have to tell me if it is possible to tile (in the usual sense of tiling the floor or the roof) D using tiles of shape T.
Sounds pretty banal right. But thats not the case. I will not elaborate on this problem anymore however will give instances where one can apply these ideas. The Fuglede's Conjecture asserts that such a tiling always exists when the domain D is nice(in a certain mathematical sense- which you need not bother).
For example imagine a hexagonal room,can one tile this room with triangles? well seems obvious right. Cutting the floor along the diameter of the hexagon you see that just six equi-triangular tiles are sufficient. Note that here we made a choice in the type of triangle, so in a sense we have not answered the question in full generality. The heart of the problem is to check for the possibility of a tiling starting with an arbitrary triangle, which again is not true(relying on intuition). Then we need to classify all the possible triangles that fit the bill, and this step will put the problem to rest.
This problem has been the impetus for many masons of the past,,and a matter of secrecy, about their successful tiling assignments. With ever changing designs it is imperative that one answers a question of this type, as it will go a long way in efficient resource management.
In mathematics such problems are also called 'Packing problems' , and solutions to these are of utmost importance, in theory and and practice.
Let me get a little rigorous, one can easily picture that it is not possible to tile a region using circles, because there will always exist a non-trivial gap between the tiles. Extending this idea, one can ask ' what kind of regular polygons will result in possible tiling' It seems intuitive(but need not necessarily be true) that there should be a bound on the number of sides of the polygon-this is because as the number of sides increases the boundary of the polygon attains the shape of a circle(convince yourself,its easy!), and we know that a circle cannot tile ( this idea is due to Sandeep Bhupati ,my senior at IISc), its cool right. One often uses such methods to prove stuff in mathematics.
As the talk progressed I grappled with the proofs, finally decided to lay back and relax. It is not worth breaking ones head on technical jargon.
The talk was nice, actually I liked the speaker, she had this healthy confidence and composure throughout. I like to attend talks by experts, their understanding of the subject galvanizes me with a positive attitude to research in particular and life in general!!!
Here is a small problem if you would like to work out-
You are given a 8x8 chess board with two diagonally opposite corners deleted(note that we now have only 62 squares). The question is that if you have dominoes which cover exactly two squares of the chess board at a time,then is it possible to cover the 62 squares using exactly 31 pieces of dominoes?Whatever the answer, you got to tell me why!!!
Monday, March 8, 2010
The ten comandments of modern research....
Well the title seems to put light to my blowhard attitude,you could justifiably ask 'who are you to role out commandments'...well,the last time such an act took place,was,on Mount Sinai,where God gave the ten commandments to Moses,so that he could tell them to the Israelite s,Moses told the commandments,but he wasn't God.. So let me reiterate that my role in this act is only of a scribe...these are God given commandments,you should convince yourself about this fact before reading anything further.
Now the next logical question is when and how did God tell me these commandments?This is a logical question,but useless at this point.Just to tell you that I am in the company of Gods,one of them is 'The God of Complex manifolds'-now do you know what that means?If 'no',then don't bother...I guess the title God should be just good enough.
Getting to the heart of the matter,Here they go...
1)Believe and convince yourself that Research is what you are meant to do,otherwise you are wasting your time and somebody else's money-both are assets which could well have less asinine applications.
2)Learn the key words in your field.It helps in ways more than one.
For example,you can use Google more effectively(unless you think you are the only moron working on your problem!!!).It also helps to switch mathematical conversations into ordinary ones ,for example imagine a group of people discussing 'The invertiblity of the Fourier transform on Hilbert spaces over the field of Complex numbers' and you happen to barge in.Instead of having any knowledge of the Theorem as whole,its just enough to know about the key words in this statement,like,who cares what the Fourier transform is,I know who Fourier is(He is a great mathematician for one)!!!and if you are eloquent enough,you could even shift the focus from the 'Fourier transform ' to 'Fourier 'himself!
3)Remember 'Confusion' rules the world.If you cannot convince,try to confuse.It improves the perplexity of your statements.
By the way,in the past, Mathematics that was conceivable by the common man was considered to be an object of triviality.
4)Learn your topic in such a way that you can enlighten the common man and befuddle the expert.
5)Just because you have the 'researcher' tag...do not assume that people who don't have it are fools.They do research in topics which do not need a tag.Basically be humble and kind to people who do not know how to differentiate and integrate!!!
6)Besides doing purely abstract research,spend time in doing something that might have a more immediate application.It feels good sometimes to know that people actually use what you have found!!!
7)Treat your theorems like 'Chicken Jokes'.You see someone asked 'why did the chicken cross the road?' and lo- behold there was this revolution of jokes!!!Anyways wat I mean to say is that,most of the theorems came into being because of similar questions,in fact even sillier ones like'In how many ways can the chicken cross the road' or rather 'If the chicken takes too long to cross,then, will it still remain a chicken'...and so on.
8)Do not hesitate to ask trivial questions.
If you analyze,you will realize that most of the theorems are built using simple blocks.Newton says that he could do so much because the sat on the shoulders of giants.In fact as Hardy says in his book 'A mathematicians apology' that the most exemplary proof is the simple proof of the infinitude of primes.
9)Learn to work hard smartly.
10)Remember that the most valuable resource that you have is your time,use it wisely.
So do not waste too much time now,if you haven't already wasted the last 15 minutes...and get back to something more constructive...
Now the next logical question is when and how did God tell me these commandments?This is a logical question,but useless at this point.Just to tell you that I am in the company of Gods,one of them is 'The God of Complex manifolds'-now do you know what that means?If 'no',then don't bother...I guess the title God should be just good enough.
Getting to the heart of the matter,Here they go...
1)Believe and convince yourself that Research is what you are meant to do,otherwise you are wasting your time and somebody else's money-both are assets which could well have less asinine applications.
2)Learn the key words in your field.It helps in ways more than one.
For example,you can use Google more effectively(unless you think you are the only moron working on your problem!!!).It also helps to switch mathematical conversations into ordinary ones ,for example imagine a group of people discussing 'The invertiblity of the Fourier transform on Hilbert spaces over the field of Complex numbers' and you happen to barge in.Instead of having any knowledge of the Theorem as whole,its just enough to know about the key words in this statement,like,who cares what the Fourier transform is,I know who Fourier is(He is a great mathematician for one)!!!and if you are eloquent enough,you could even shift the focus from the 'Fourier transform ' to 'Fourier 'himself!
3)Remember 'Confusion' rules the world.If you cannot convince,try to confuse.It improves the perplexity of your statements.
By the way,in the past, Mathematics that was conceivable by the common man was considered to be an object of triviality.
4)Learn your topic in such a way that you can enlighten the common man and befuddle the expert.
5)Just because you have the 'researcher' tag...do not assume that people who don't have it are fools.They do research in topics which do not need a tag.Basically be humble and kind to people who do not know how to differentiate and integrate!!!
6)Besides doing purely abstract research,spend time in doing something that might have a more immediate application.It feels good sometimes to know that people actually use what you have found!!! 7)Treat your theorems like 'Chicken Jokes'.You see someone asked 'why did the chicken cross the road?' and lo- behold there was this revolution of jokes!!!Anyways wat I mean to say is that,most of the theorems came into being because of similar questions,in fact even sillier ones like'In how many ways can the chicken cross the road' or rather 'If the chicken takes too long to cross,then, will it still remain a chicken'...and so on.
8)Do not hesitate to ask trivial questions.
If you analyze,you will realize that most of the theorems are built using simple blocks.Newton says that he could do so much because the sat on the shoulders of giants.In fact as Hardy says in his book 'A mathematicians apology' that the most exemplary proof is the simple proof of the infinitude of primes.
9)Learn to work hard smartly.
10)Remember that the most valuable resource that you have is your time,use it wisely.
So do not waste too much time now,if you haven't already wasted the last 15 minutes...and get back to something more constructive...
Wednesday, March 3, 2010
Rangoli Holi et al...
Well on 1st March we celebrated Holi,was a different experience I should say.When in Goa we only celebrate the traditional Carnival,with pomp and gaiety(thats how the slogan goes)...if you have been to Goa you would know what I mean.The Carnival is a pagan celebration,which gets along with it a lot of vices,which if one avoids,its a pleasant experience.
Just a little digression,the previous day,the Hindi Samiti at IISc organized 'Rangoli competition'.I always thought it was a simple task to put powder on the floor in such a way that it represents some familiar design,wasn't the case.However our motives for participating were not so noble towards creativity ...the truth was that a friend of my friend told my friend that there was just one participant enrolled,and hence if we reached the venue on time at least, the 2nd prize was assured.So we decided to team up,and rush to the venue,on the way we happily discussed the posibility of winning the first prize(since the 2nd was already in our kitty!!!).The scene was different at the venue,this guy had told so many people about the scarcity in participants that,everybody rushed to compete for the 2nd prize.They would not even let us participate.We finally got a chance to try our hands at it.The theme of our Rangoli was 'Reaserch at IISc',as you can see in the picture-it was 'music+coffee+nature=proofs of theorems'.We got a consolation prize,which was good enough,as compared to the 2nd prize.We were pretty pleased with our efforts,though they might not have got us the best results.Its fun to work as a team,and create something close to modern abstract art.As the prizes were bieng distributed,we were told that,having 'Rangoli' at ones doorstep,helps eclipse negative energies.And in general adds color to the household.It was a great experience,even though the 2nd prize was a disappointment.
Getting back to Holi at IISc,as I said before it was my first experience...and it was awesome,except for the fact that those jerks used dye to color people.Had to almost scrape my skin off to get rid of the color.
The fun began after lunch,was told that there was holi activity going on at the mess...I managed to get myself safely into the mess,with not a drop of color on me,I felt an air of jubilation at fact that I managed to get away from those 'coloring guys',however I could not manage to keep on to it for long.
That afternoon I was supposed to meet my guide(each student has to work under a Prof,whom they call 'guide' or 'boss' outside private circles!!!),my meeting wasn't scheduled though,however was planning to tell him after lunch.As I was leaving the mess,there came this guy running after me,was pretty obvious what plans he had for me...so I started running too(This is one instant where jogging regularly helps!!!),I outran him,but then thought it was poor spirit to behave like this on a festive occasion like this,so I stopped waited for him and then told him politely why he should not color me...luckily the man had a heart(besides brains!!!),he believed me,and just to make up for the energy he spent in chasing me,wished me with his colored hands.So far so good.I go a little far,and then there comes another fellow,this one turned out to be a rascal...put color on me without any warning.Now I had some soul searching to do,I had two desires within me,one to chicken out,just wash my face and go and meet my guide,this did not seem exciting,the other more manly and gallant was to stay on and have my own victims of color!!!which I did!!!At the end my face was colored beyond recognition....we looked like creatures from Pandoras.I left midway(after satisfying myself that I had accomplished what I stayed back for),went to my room immediately,and scrubbed my face for 30 odd minutes to get the dye off me.
Then went and met my guide...and hence got both my desires fulfilled.
In all it was a wonderful experience.It is supposed to be The festival of colors.We sometimes get so lost in our daily chores,that we hardly realize how colorful life is,and occasions like these remind you about this fact.The energy you see in people who celebrate is awesome,its great fun.
If you missed it this time...don't worry,in the coming year bond with people who celebrate and you too can have a great time...a great time it is!
Getting back to Holi at IISc,as I said before it was my first experience...and it was awesome,except for the fact that those jerks used dye to color people.Had to almost scrape my skin off to get rid of the color.
The fun began after lunch,was told that there was holi activity going on at the mess...I managed to get myself safely into the mess,with not a drop of color on me,I felt an air of jubilation at fact that I managed to get away from those 'coloring guys',however I could not manage to keep on to it for long.
Then went and met my guide...and hence got both my desires fulfilled.
In all it was a wonderful experience.It is supposed to be The festival of colors.We sometimes get so lost in our daily chores,that we hardly realize how colorful life is,and occasions like these remind you about this fact.The energy you see in people who celebrate is awesome,its great fun.
If you missed it this time...don't worry,in the coming year bond with people who celebrate and you too can have a great time...a great time it is!
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!!!
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!!!
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