Float freely in the world of numbers

2017-11-17T17:31:00.001+05:30

Ramblings of a Bohemian

The whispering infection

South Point High School in seventies was a different place to study. I am not aware how it was done, but our HS registration applications were sent in such a way that the entire lot of XI-D found ourselves sitting next to each other at Jagabandhu High School. Girls were not there as their HS seat were somewhere else. On the first day, it was Bengali exam and we found that barring four boys from some other school, our room was only class XI D and so immediately we were comfortable.

The fun started just after the invigilator showed up, parents with their worried but at the same time encouraging faces (a feat that can only been achieved by parents of HS examinees, worries, concern, fear, encouragement, confidence all such conflicting emotions get displayed on their face at the same time!!!) were shooed away and so it was us and four hapless students at four corners of the room and the poor invigilator only in the class room.

The invigilator received the first shock when Amlan found that the fan above his head was showing tremendous inertia of going from a state of rest to that of motion. So Amlan decided that application of the proviso of Newton’s First law is necessary and with his voice that has as much sweetness in it as in a dry sand paper, he commanded the invigilator to get a bamboo and to give suitable motivation to the fan to set it in motion. Such was the authority in his voice, the poor invigilator obliged. That set the tone in the exam hall that we are the master and the invigilator should be available at our beck and call. After we are all South Pointers, that too XI D!!!

There was a gap of about one hour or so between the first and second paper when we were met with not only guardians but also the teachers from school who had equally worried faces. It was rumored that Arup Ratan Gupta’s parents had rented a room next to Jagabandhu where he used to disappear for the last minute study for the second paper. I am not sure about the veracity of the rented room but it is a fact that Arup was nowhere to be seen during this one hour. For the rest of us, it was a feast of our favourite snacks. Like for me it was two massive gulab-jamuns with Lassi laced with green mango syrup. We would be prodded in vain by our mothers to take a look at whatever they felt needed to be looked at but we were too busy chatting amongst ourselves.

Pradip was sitting next to me and just behind me was Sumantra Sen. In front of us were Arup Ratan Gupta and probably Pradipta. English second paper translation landed me into trouble, it was a passage about the vagaries of farmers. Most probably I didn’t know the word plough or my memory had failed me. PD was doing some other passage. I asked him for help but I think memory had failed him too. So what I got from some unintelligible utterings, which was, nowhere near something used by a farmer. I still remember my brilliant (?) improvisation of calling a plough “agriculture instrument”!!!!

South Point had turned all of us into paper guzzler. My physics paper script was 30 plus pages for each paper. But the unbeatable one was Madhujit. He was consuming paper at a speed of one extra sheet, which is four pages every two minutes. His handwriting had come to two words per line and three lines per page. I think a forest must had have been fell to supply all the paper we consumed during those six days.

The last day, it was Mechanics, was fun. Specially the second paper in the afternoon, when we could see the end of the long and tedious journey of last three years and the final end the school days and beginning of what we thought to be our freedom. So the scene in the exam hall became more of chat and less of exam. The discussions ultimately landed into what movie to be seen based on what movie someone else had seen already. The two most discussed one were Jana-Aranya and Kabhie-Kabhie. So the interpretation of various scenes of Jana-Aranya was being given. I recall the most discussed one was an alarm clock shown in the movie. The incisive analysis of the presence of the clock, its inner meaning and interpretation of the hour and minute hand of the clock and their relative position probably would have befuddled the film maestro himself making him wonder whether he had thought of such deep end of the presence of the clock.

Discussion on Kabhie-Kabhie was even more interesting. One can recall that it was one of those complicated movies not on a love-triangle but on a love-marriage web, like X is in love with Y but marries Z who is in love with W who marries U who wanted to marry Y. To make matters worse, the makers of the movie made such an entanglement spanning over two generations with a cross-connection of intra-generation. So for the scientific minds of SPHS XI D it was a challenge to be thrown at each other to see the deciphering ability of the other person. The invigilator was initially looking very happy; after all he was getting a very multi-perspective review of the movies from brilliant minds like ours, which no newspaper film critic will ever give. But then he realized that the matter is getting a little out of hand and tried to stop us and make us get back to mundane stuff like solving motions of particles and accelerating or decelerating trains.

The Midas touch of SPHS authorities by making us sit next to each other did not result in purely pleasant experience for all of us. It had its pitfall too. That happened in the First paper of the Maths exam. There was this problem where they give you some number power upto some other number and ask you to calculate the number of digits of this contraption. All you have to do is to take the logarithm and take the integer part called characteristic and add one to that. Now I never could remember whether to add or subtract. So I always used a trick: take log of 100 to the base 10 and that’s 2 and 100 has three digits so add one!

Now all of us landed with characteristic of 20, which is pretty neat. Sumantra whispered from behind “Boss, the answer is 19 right!” Ok we got 20 and he says 19. So we didn’t think and wrote the answer to be 19. PD heard the same whisper and wrote 19. The whisper spread like infection and all of us landed with 19.

Exam over, and before going out and facing our parents proudly that all of us have done 100 out of 100, we milled around each other. Madhujit, who had this odd habit of always tucking his shirt end just below his elbow using one hand, came towards us with his tucking speed doubled and grinning widely and said “That answer is 21 isn’t it?” Now Madhujit’s seat was up there in the front a little away from the other rows and on his other side was that nondescript student from a nondescript school and so he was a little isolated acoustically from us. So he was unpolluted from the infecting whisper and came out with the right answer. Our jaws dropped. I mentally did what always I did and didn’t at the most crucial moment: log of 100 is 2 and 100 is 3-didgit so add one. “OOPs!!!! 5 marks gone”. Our dream of 100 out of 100 shattered.

We rapidly went into damage control mode. Result is three months away and lot of water will pass under the bridge in the meantime. So result is not the crisis but our mothers were immediate threat. So quick correction on the question paper where we used to jot down the answers with pencil and an unspoken “omerta” (code of silence). So when we stepped out, for our parents everything is hunky-dory.

But eventually it leaked out at least to Shyamadas babu. My poor cousin who was one year junior to me and had landed in the Madhyamik trap, came to me seven days after the exam. He whispered to me, “You have screwed up 5 marks?” I was horrified and asked him how he had come to know of it. It seemed that Shyam babu has found another new gimmick to drive home that one needs to be added by saying in the tutorial of class X Additional maths “Pradip Dutta has made this mistake! Arup Ratan has made this mistake! Debasish Som has made that mistake!”

We have added another missile in Shyam babu’s arsenal and all for that infectious whisper of Sumantra Sen!!!

My Sojourn with Mathematics

It was the first week of June 1982. My father was posted in Midnapur. I was staying there and was waiting eagerly for my Civil services Result. I was reasonably confident that I will make it to IAS despite that being my first attempt. Accessing the result from Midnapur was a challenge. Somehow around 4 pm we managed to get our connection via urgent trunk call (it was 1982; STD was rare, mobile and internet was very very in the womb of future) with someone at PIB in Kolkata. I kept on listening to this guy with increasing incredulity as he rattled off names after name but without any mention of my name. When it was mentioned I had realized that whatever service I might land up with, it was not IAS. I have missed the bus that year. I replaced the receiver on the cradle and with a broken voice, tear in my eyes looked at my parents and broke the news. For the next one hour, I sat shattered smoking cigarettes one after the other. My parents left me alone though I could feel the disappointment of my mother hanging in the air. My father was far more steady and kept on explaining that competitive examinations are like this and there is nothing to get shattered about.

By early evening I had got over the shock. I felt mentally down, battered and bruised but I was gradually recovering. Three of us had tea together and with a chuckle, I told my mother that she is the most foresighted one. After all, despite my serious objection, she had made me fill out the UPSC form and the admit card for the Prelims which was ten days away was already in her almirah. I had felt that filling up of the form was an indication of my lack of self-confidence. I never realized before that day that it was a folly and what my mother did was the smartest thing possible.

That was not surprising also. It was because of my mother's insistent motivating push that had induced me to explore the path of Civil Services Examination, despite my deep love for digital communication. I already had appointment letters from MAMC and CMC through campus placement, had topped Engineering Service examination jointly with my classmate of many years (IIT and Hindu School), Amit Haldar and had four or five offers from Central PSUs like ONGC, NTPC, SAIL where I have appeared for the tests after applying through Newspaper advertisements just for fun and had bagged offers as Management Trainees. So Civil Service Examination was an ambition which had to be scaled but not the only option.

My mother's determination of making me an IAS officer was not a recent one either. It had started seven years back in 1974. One may recall that in 1974, the state government engineers had gone a long strike. One of the demand was that engineers have to be treated at par with IAS officers. My father was one of the engineers who had participated in the strike. It is not that he had any ideological inclination or sympathy for the cause but not participating would have been an act of renegade on fellow colleagues and so he joined. The eldest maternal uncle of my mother had visited us one day when my father was home as strike was going on. Exchange of usual pleasantries ultimately took turn towards the ongoing strike. My father explained the demands of the engineers. My maternal cousin grandfather commented that whatever may be the demand of the engineers, parity with IAS officers is an impossibility as no way engineers can be compared with IAS officers who according to him were kind of supermen. The word he actually used was a Bengali proverb that "Muri" and "Murki" cannot be compared as the later is much superior, metaphorically putting engineers as "Muri" and IAS as "Murki". This statement infuriated my mother. She vowed that day after the departure of her maternal uncle that her home would be endowed with both "muri" and "Murki". The old man had hardly realized that by making a statement, probably very casually from his experience of seeing ICS officers in the pre-partition India from a distance, he has changed the destiny of a school student.

I was then in class ten. I made it to IIT and during the summer vacation of 1980 when I was in my fourth year, my plans for having a nice time along with the summer training was shattered when I was handed over a thick bundle of cyclostyled sheets by my mother. They were the study material from some study center and I was supposed to read them in the evening. They had the usual general studies stuff. The general studies frenzy was in abeyance in my final year as I was busy with my project works but immediately after that I was seriously into studies of general studies along with preparation for engineering service and Physics for Civil services exam.

Any way ultimately all these culminated into my appearing in 1981 and the results came out in 1982 June with me landing with some service but IAS.

I had appeared in 1981 with Electrical Engineering and Physics as optional paper. Electrical Engineering had sections meant for Electronics Engineers and so it was manageable. Physics was my most favorite subject in school and I really excelled in that. I was in love with Physics too. So it was a natural choice.

But falling in love with a subject and exploiting that for an exam six years down the line is like a having infatuation for a girl classmate in school and then meeting her after six years and hoping that she is the same old flame is a little too much to expect. So I read the books that I felt like reading in school: Feynman's Lectures in Physics, Berkeley Physics Course (all five volumes), Atomic Physics by Max Born and so on. They are great Physics books, but they don't tell you how to write answers to Physics questions or solve problems. I was having this uneasiness creeping all over me and tried to tell my parents that I am having some difficulty. My articulation of the specific nature of difficulty was very poor and vague. So the conversations always took an ugly turn; I would be saying something like, "I can't understand up to what depth I should read." My father's response would be , "What do you mean by depth, read whatever is there." My mother would be furious, "only excuses for not studying...".. the typical response of bong mother.

And I would clam up. That was the end of discussion.

So finally when I landed up in the examination hall for the Physics exam, I found that for writing the answers my knowledge is limited to what I have been taught by Anjan Babu in South Point with the deductions being done with elementary calculus. I could explain the theoretical questions but when it came to problem solving, in some cases I just could not solve them properly.

I wont say I came out disappointed but I didn't also exactly walking on seventh heaven. My ignorance was literally a bliss.

But on that fateful evening of June, when I introspected I realized that my handling of Physics paper was just not up to mark and I had to do something about it the next time.

It was about 11 pm or so when I made my declaration, " I am not going to take Physics as optional, I am going to take Maths." The silence that followed was deafening. Then my mother broke the silence, " How much of the syllabus you have covered in Engineering?"

Well, the fact is virtually zero. In IIT we have done Applied maths and this is Pure Maths.

"I know the stuff; but the approach is a little different" was my response hoping the discussion will stop there. But NO!!!!

My mother told me to get the syllabus and made me go over item by item and tick or cross what I knew and what I didn't. When I was done, there were more crosses that ticks and the horror on my mother's face was as if the ghosts from the near by cemetery is doing a tarantula dance in front of her.

The next three to four hours should go down in history as the unique case study on negotiation; every arsenal my mother had at her disposal, cajoling, psyching, sentimental pressure, anger, despondency, desperation, threat of hunger strike everything was used to dissuade me from what she though was a suicidal attempt by adopting maths. Calendar was brought, days till mains were counted and all kinds of calculation by allocating time for the different subjects was done; another case study of optimal allocation of resources can be made out of the exercises that was done to prove that I am proposing an impossibility. But somehow I stuck to my point and finally at 4 in the morning, my father who was sitting impassively listening to this epic negotiation and puffing his pipe gave his verdict.

Maths is a go.

Why I did it? I had a secret agenda too and a source of strength as well. The strength was Prof. G C Giri of Midnapur College, a gold medalist of Calcutta University (MSc in Pure Mathematics) who was doing his Phd at IIT Kharagpur. I had befriended him during my journey from Midnapur to Kharagpur where he was a daily commuter. I knew he would be able to guide me.

My secret agenda was to learn mathematics as this will help me in my pursuit of Digital Communication, one of the most Maths intensive subject of Engineering.

Two days later I went to meet my mentor, philosopher and guide, Prof J. Das. I told him of my decision to change to Maths as optional. He was OK with that but he had other concerns. He asked me "Do you propose to ever become a Professor?" On a very strong negative reply from me, he said in Bengali "Don't travel with your legs on two boats". It is a Bengali proverb meaning being a fence sitter and pursuing two different objectives. So his advice was to go full throttle no holds barred with Civil Services preparation and to give up pursuing MTech which I was doing and was going to be in second year.

Again it was a watershed decision but it was easier one to take. So I left M.Tech course and became an idea jobless unemployed young layabout.

The day after the prelims, I was gifted with a small blackboard by my father which was hung up behind my chair on the wall. On top of the blackboard was written "120 days". Everyday that number will get reduced by 1 and that many days I had at my disposal to learn mathematics.

My day started at 8 am and by 8:30 after having my tea and morning formalities, I will be at my desk. My father's orderly Sambhu-da will bring two packets of Charminar Gold (packs of twenty cigarettes) and I will be at it. A lunch break for an hour and a tea break for half an hour around 5:30, dinner break of half an hour at about 10 pm were the only breaks. I had a collection of Ananda Shankar musics which were constantly playing on the stereo system. My bed time was any where between 3 am to 4 am everyday.

But every week, on Friday a night show movie at the movie hall Mahua next door was a must.

But the days were fun. I was learning mathematics. There about in total 650 to 700 theorems and more than 1000 problems covering the syllabus. Most of it was new stuff for me. A substantial part needed conceptualizing so that it could be internalized. So many times my mother will find me smoking a cigarette and looking out of the window at the expanse of the huge ground with cows grazing with my foot up on the table and almost a lost look on my face. Initially she thought that I was about to go asleep but later realized the importance of those trances.

Prof Giri was of great help. He suggested me books, most of it from some publishers at Meerut or Delhi and those books were like what K. C Nag used to be during Higher Secondary days. Problems were annotated with the years they have appeared in the Civil Services exam. Later I think, when I had about 35 days left on my blackboard count downer, he started setting up mock question papers and I have to answer them in exactly 3 hours. He will then correct it and my marks initially was very poor in the range of 170-180 out of 300. Gradually it started improving and in the final days it reached almost 270-280 marks.

On 120th day I had to stop studying Maths and get back to study General Studies and revise Electronics.

My 120 days sojourn with Maths was over.

The movie we never saw:

I joined as SDO Rampurhat in September 1985. It was my first posting. Rampurhat is one of the oldest subdivisions of West Bengal; a completely rural subdivision with 8 blocks and 4 police stations. The Subdivisional Police Officer was G M P Reddy of 1982 batch, who later became DG.

In the academy, there have been lot of discussions about the friction between SDO and SDPO and one of the most contentious issue, we were told, was the relative sitting position in a jeep. The custom is the senior officer sits on the outside and the junior guy sits sandwiched between the driver and the senior guy; the securities sit in the back. So Reddy and I decided that we would improvise and beat all the pundits of the Academy hollow; it was decided by following a simple protocol that on one way he will drive and the other I will drive and driver will be relegated to the backside and there is no conflict.

Till the time GMP was SDPO in Rampurhat, we followed this and it was a great thing.

It was just after the Puja of 1985. Both of us were living as forced bachelor and the offices were closed. So it was a slow day. We were sitting at Reddy’s Bungalow and were having whatever lonely forced bachelors normally have in the evening of a holiday. At about 7:30 pm we decided that we should go for a movie. The only movie worth seeing was running in the movie hall of Mallarpur, 15 km away from Rampurhat. It is a block headquarter but not a PS Headquarter. So we drove down; I think I drove. After reaching we found that the next show was going to start after one and half hour. So we decided to take a walk incognito.

We strolled as ordinary people and at a road crossing, came across a tea stall. We had advised our security guards to maintain a distance so that nobody recognized us. We sat on the wooden bench of tea stall and ordered two cups of tea. The old stall-owner gave us tea and looked quizzically at us and asked, “Are you guys new here? Never saw you before?” We told him that we are indeed new to that place but work there. “Oh! Do you work at the bank?” We did not want to lie and so gave a vague reply. Both of us were enjoying tremendously at our playing the modern avatar of Haroon-Al-Rashid.

Finishing tea, we walked some more but also asked our security to get the jeep so that we could return to the movie hall quickly whenever we wanted. We were walking down a dark road with a high wall with a steel gate on our right side. Suddenly we saw a truck coming out of the gate with all lights (both headlight and side light) switched off. To us it appeared to be a suspicious move. So we waved the truck to stop and called our security to ask the driver to come down. The driver gets down from the vehicle and Reddy with his cop voice asked what he is carrying and where are his papers. The driver could not produce any paper and said he was carrying oil. The high walled compound apparently was an oil mill. So we asked guy to reverse and get inside the compound and we followed him inside.

We went around and called for the people in oil mill and started asking questions. While Reddy was quizzing the guys, I looked around and came across some container carrying some oil, which did not at all look like mustard oil. These people claimed that it was palm oil.

Now at that age, one is an eager-beaver officer always trying to right all the wrongs and the world is full of crooks, who need to be caught and punished. Ideology and all those lectures of academy still fresh in mind, we were determined that we were the last crusaders fighting all evil. And here is an evil act of adulteration being committed, which needed to be punished. So we declared that we are seizing the truck which was carrying the same white looking oil of indeterminate origin, which we were sure being used for nefarious purpose and also all the containers in the mill carrying the same oil.

So I told GMP that lets make the seizure list. GMP looked distinctly uncomfortable and said that he has to summon the Circle Inspector. I asked him why he would need the CI. He whispered back, “Som, I don’t know how to make a seizure list under the Essential Commodity Act. I need the CI to make one!” So he radioed Rampurhat and asked the CI to report to Mallarpur immediately. We sat on the footboard and bonnet of our jeep and smoked waiting for the CI to arrive while the mosquitoes had a delicious time feeding on us. The people of the oil mill was rounded up under the watchful eye of the securities as we were sure that they were the worst possible villains and but for us would have created a huge black spot on the history of Human race.

The CI arrived with some more cops after one and half hour and took over. It was 10:30 in the evening by then.

We didn’t go to the movie that evening.

I don’t know what happened to the truck and those people either!!!

Evolution of my Library

Back in 1973, when we lived in a Government Bungalow called Canalvilla, situated at princely location on the corner next to Chitpur Bridge, my books, all being school textbooks, were accommodated in a small wooden bookshelf. Behind the books, I used the keep stuffs like storybooks hidden from the eyes of my parents.

In that year, we shifted to our new home at Ballygunge Place and next year I joined South Point. Sometimes in April/May, I visited Anjan Babu at his home….his bookshelves full of Physics books kind of started a simmering desire to have lot of books. Physics was the subject I fell in love..and Anjan Babu introduce me to the world of foreign authors…Gamow: Physics Foundations and Frontiers, Isaac Asimov: Understanding Physics, Greene: Physics, White: College Physics. With interest grew my urge to buy books…it was in Class X and XI, I bought Glasstone: Physical Chemistry, AJ Mee: Physical Chemistry, Piskunov, Berkley Physics Course Vol I at a princely sum of Rs 10.75, Resnick and Halliday, both the volumes,Scientific American Compiled Papers 3 volumes of Physical Science…so the bookshelf was looking respectable. Along with that grew my habit of scoring the railings of Presidency College, the bookshop on Dover Lane, Oxford (those days they kept both science , mathematics and Engineering books).

By the end of the fourth year and in final year of IIT Kharagpur, I had fallen in love second time: with Digital Communication. That was the beginning of my Digital Communication library…with Taub and Carlson, then Communication Circuits by Clarke and Hess, Jayant: Waveform quantization and Coding, IEEE. I got Dixon's Spread Spectrum Systems IEEE, Ash: Information Theory as a gift from an aunt who was a resident of USA.

By the time I was due to leave for Academy to join IAS, my library has grown to a respectable one almirah and one bookshelf full of books, about 40% from the various subjects of B.Tech curricula like Millman-Halkias, Millman-Taub, Taub-Schilling etc but along with that books on Physics (my first engagement with Civil Services Examination) and Mathematics (my second and final engagement).

My job kept me away from my quest of books and learning but in 1994, when I came back to Calcutta and joined WBSEB, I had brought back from Balurghat a Science and Technology encyclopedia. In WBSEB, amongst engineers many of whom were academically excellent people, my old passion for communication theory got rekindled and my library started growing in size. By that time, I have been allotted the mezzanine floor room for my library and my parents even sponsored a couple of very decent bookshelves to be built for keeping my books.

It was around this time probably in 1995, I met Arabindada of Dasgupta Publishers, who became a constant encouragement and supplier of books. He got me my first copy of Courant's Calculus and Weyl's Space, Matter and Time, max Born's Atomic Physics and umpteen books on Digital Communication and Spread spectrum. On one trip to Hyderabad, I went to a bookshop where I almost went crazy: so many books which I have only read about in the bibliographies… I borrowed some money from my fellow colleagues and bought a suitcase full. Those days in Hyderabad airport one had to walk on the tarmac from the terminal to the craft and while I was walking, the straps of my suitcase weighing several kilos broke; oops….dragged the beast somewhere.

During my tenure in KMC, I first bought books from Amazon. One librarian in British Council where I have gone on some program and landed in the library searching for Delta Modulation by Steele, told me about Abebooks.com. Money was problem; my father being a strict disciplinarian and manager of my money ( YES!!: He managed my money and I was only given a pocket expense when I was controlling crores of government money as I didn't have the time and inclination to manage anything other than my job) will not allow my book expense beyond a point. Not that the salary was so princely as to afford matching my hunger for books….but nevertheless I managed to buy books at regular frequency. The two bookshelves were no more sufficient so came third, fourth and the fifth…

Oh! Sometimes in 1999, I was told by a friend of mine working for Prentice Hall of India that they have marked more than 5000 books for destruction (yes destruction…they tear off the title page and the book as per their accounting standards become valueless!!!) and these books are stored in the garage of their MD at his house in Bansdroni. One saturday I went down there, it was like two garages and the books were stacked without any space to even walk between the stacks….so I took off my shoes and spent some four hours going through rummaging the stacks and had about 150 books. They were loaded in the boot of my ambassador staff car, the car's backside sagged; I had to give up loading when my driver told me that the car could not be driven if more are loaded….what books my God!!! Rare, relevant, hardcover, original US edition …..its a treasure trove.

Tryst with Mathematics

My love for mathematics started growing when I appeared for civil services examination in 1982 with Maths as optional. However the love remained dormant for many years but came out of hibernation around 2009. I had been thinking of doing MSc in Mathematics in 2004 and had even obtained permission of the State Government for appearing in the exam as a private candidate. But it never happened due to work commitments. But in 2009 when I started looking for opportunities to do MSc, I found that the norms have changed. One needs an undergraduate degree in Mathematics for doing post graduation. I couldn't find any that allows pursuance of an MSc by an Engineering graduate. IGNOU has MSc in Mathematics and Computer Applications but the course content did not appeal to me. It was closer to Computer Application than to Maths. I enrolled for MA in Economics at IGNOU. I was then working for an Infrastructure Consultancy company and thought a grounding in Economics will be of a lot of help to me. With vigour I started reading microeconomics, which to my delight was completely mathematical. However this effort fizzled out as the examination dates of the first year coincided with the Board meeting date in he new job I had joined just recently. That was the end of the MA in Economics. Moreover some of the subjects I did not like as it involved long essays. So the appeal and excitement was not much in any case.

The next two three years I floundered academically. There was no definitive direction of my study; i was wandering in the alleys of mathematics like a rudderless and directionless boat, reading, studying mostly things I liked and avoiding things I abhorred. Then suddenly one day browsing the net I saw Netaji Subhash Open University eligibility criteria for doing MSc in Maths to be only graduate in any science /engineering subjects. Bingo!!! I tried to enroll but hit a roadblock. The online (and you could apply only online!) format wanted Madyamik marks. Apparently they never foresaw an old man like me from a prehistoric period when Madhyamik exam was not even in existence applying!!! I called the Higher Education Secretary, Vivek Kumar who was few years my junior and told him about my predicament. He chuckled and told me that He will request the Vice-Chancellor to speak to me and to sort out the issue. Any way Dr. Sarkar, the Vice Chancellor was very kind and I was enrolled.

I received the Course material and started studying. The first year was a little boring as I was reading all the stuff I had studied during my civil services examination. But a huge shock was waiting for me. When I started solving problems, I found I didn’t have a clue where to start, what to write, how to build the logic of solving the problem. Last time I had done that kind of thing was almost three decades back and I had lost the edge. Staring from scratch, I gradually built up my skill and confidence over couple of months. More importantly, I gave up most of my boozing activity specially the customary chilled beers on Sundays and Saturdays as they played havoc with my wakefulness post-lunch. So hard drinks was substituted with cold water. My daughter was studying in Great Lakes at Mahabalipuram at that time. So our trips to Mahabalipuram and stay at hotel was with the accompaniment of books on real Analysis. Even on the day of cataract operation of my mother, I had taken Algebra by Prof. Mapa to the Nursing home and solved problems while my mother recuperated.

In 2014 was the first year examination. It was fun. The exam center was at New Alipur College. The exam was in August/September and the weather was saltry, warm and humid. I am habituated in working or studying out of an air-conditioned room, used to writing on decent exercise books with roller ball pen which does not smudge. my study hours have been spent on a comfortable well cushioned revolving chair. The exam center environment was just the opposite in all respects. I was sweating profusely, my fingers were sweaty and after few minutes the pen was slipping. So I had to exert extra force to hold my pen. The sitting was on wooded bench as contrasted to cushion support for my backside and the answer script was getting black smudges on the other side. The paper was like a blotting paper and was sucking ink hungrily and leaving black marks all over. So my handwriting, of which I am somewhat proud of, went for a toss and it did not look like any handwriting that I have ever seen in my life. I was guzzling water from the bottle I carried mostly to recreate the environment of study room (that was the closest resemblance I could manage) and to stop from getting dehydrated. But even then it was fun.

I must say what happened on my Mechanics paper. I loved the subject, had prepared with gusto and was very confident that it will be a cakewalk. Now first problem, I made a wrong start. What ought to have been done in half a page, went for three pages and I landed with an equation with sixteen terms on each side and started struggling. This was not what I had ever done with that problem!!!! It was probably a Poisson bracket deduction. I went out for a smoke and tried to cool down, bring my panic level down by telling myself that it hardly matters as I am doing all these for fun. But I was unnerved and had a partial brian-freeze. So by the time it was over I knew I have badly screwed up and possibility of failing in that paper kept on lingering in my mind!!!

The other fun part was the reaction of my co-examinees. They couldn’t figure out exactly what kind of an animal was I. I was not a teacher, old enough not to be an aspirant for the post of teacher and they were at a loss to figure me out. I saw lot of furtive glances full of curiosity and decided that it was time to have some fun. So I opened some cryptic dialogue with some of them. But the most disappointing thing happened when the young girl co-examinees started calling me “uncle” and I realized that I have started really looking old…..

The second year became even more exciting. I started learning new subjects like Topology, Tensor analysis, differential geometry (geometry of manifolds), Topological groups, topological vector spaces and so on.

I had trouble with Topology. For some peculiar reason, the concept was not getting clarity in my mind. I recalled having a telephone conversation with Mr. Samar Ghosh, ex-Chief Secretary when he had mentioned “He loves Topology”. So I called him one evening and told him that I was having difficulty in Topology understanding. He suggested that I read A textbook of Topology by Dr B C Chatterjee. That was a wonderful suggestion….the book was like a poetry and opened up the inner beauty of Topology to me.

The other person who helped me again over phone was Prof. U C De. On the sufficiency of proving diffeomorphism, I called him and sought his advice. “Which book you are reading from?” When I told him, he told me that for a beginner that book might be difficult and suggested Differential Geometry of Manifold which he has co-authored. That truly is one of awesome books I have ever read. Even today when I study differential geometry, that book is my constant companion.

The other amazing thing that happened to me was with computer programming. I had always been very weak in this; the grammar and syntax of a language always eluded me. We were supposed to do fifteen hour of computer practical on five Saturdays. It was in New Alipur College. The practical word is a misnomer. They give us few problems and also the program. So one has to type out the program, debug it and then run it with the given input and compare with the output that is also given. But what happens it, suddenly you start getting the meaning of various symbols you have to type in as a prefix, which indicates it as a constant or a variable and so on. After you have done a couple of them you start getting hang of it and debugging mistakes starts getting fewer and fewer. I found it very interesting and back home I loaded it on a window laptop, I almost got addicted to it and started writing programs that gave out stupid results, like the primes in the number range from 1 to 10000000 and the list went on and on. Then started count of the primes from different number range and was trying to get a hang of frequency of occurrence of primes (You know Riemann’s Hypothesis is partly about it!!!!!). However I landed with good mark in computer programming, which I did not know anything about earlier and have worked on only for couple of weeks.

The exam of the second year was a non-event excepting due to some other examination it was delayed by couple of weeks and almost got close to Pujas!!

It was during one of the afternoons I was studying Differential Geometry, that an idea occurred to me. I had stopped studying and was contemplating the walls and windows, peeling painting, the garbage, the kind only school students dump of South Point. The concept of charts and atlas of a manifold started giving me an idea of looking at a spread spectrum signal through frequency windows like one does in case of wavelet. I felt that a deep connection exists between differential geometry and Communication theory and wondered whether someone has explored it ever. I searched the net and came across a name Prof. Shunuchi Amari and it seemed he had not only written a number of papers on the subject but also did his doctoral dissertation on the same subject. That was the beginning of my study of Information geometry, Compressed sensing and Differential Geometric method of Statistics which I am pursuing now.

In February 2016, one of my co-examinees sent me a cryptic message “Result is out”. I had an idea that my marks will be decent but results are results and even now hands tremble, knees weaken while I search for my marks on the web despite it hold nothing for me except being an ego-booster. Nobody else cares a damn about how I fare. I saw 824 against my name. 824!!!! Nobody has ever got 824. I browsed the site and came across someone who has got 819.

Later one gentleman who is aware of things as he teaches students told me that nobody has ever got in the range of 700 even with Pure mathematics. Applied Mathematics is much more scoring but not Pure. He called it a miracle!!! I doubt the miraculous nature of the mark but attribute it to something akin to beginner’s luck!!!!!!!

Anyway finally I was a postgraduate at the age of 56.

CAT: measuring brain power

I always wondered whether my mental agility is going down with age or not. It was difficult to assess with the normal chores of life, as any change will be incremental and hard to detect. Any measurement will imply comparing with someone who has the highest mental sprightliness at its prime. The most suitable place to find such best brains will be what is considered to be one of the toughest exams CAT. I also thought it will be great fun to sit there and to solve some challenging problems raking my brain in a new environment.

In 2008, my daughter was planning to appear for CAT as a dipstick test before she appears fully prepared. I kept on telling her you don’t have to prepare with some exam like CAT; you just go and solve it and that’s all about it. Of course I was in a minority. If you look around and browse the net, you will find that people prepare for more than a year and there are so much research on CAT, you feel scared and terrified about the test. So the other purpose was to break this myth if not to the world, but at least to my daughter and family that its no big deal. You just go and write it. So I filled out the form along with my daughter and sent it.

The admit cards came as scheduled and the exam center was at Pailan. So two days before the exam, I went on a reconnaissance trip with a friend of mine so that the driver knows where to take us without a hitch on the appointed day.

So we reached the hall on the date. But my daughter was feeling so self-conscious about having her father tagging along not to the exam center but to the hall and that too not as a guardian but as a candidate, she flatly told me before getting down from the car “From now on I don’t recognize you…I find it so awkward”. Great!!! We were in the same hall and she stubbornly looked the other way whenever I looked at her and tried to wink to humor her!!!

It was the last CAT with paper and OMR sheet. From the next year it was all computerized. So the moment I got the paper, I started solving the quant. To my horror, I was stuck at the first problem. Then the second one too!!! And the third…. This was not something I had bargained for. So I sat there and tried to solve them with all the brain computing power at my disposal but I was missing something. Twenty-five minutes had passed by. I longed for a cigarette; my brain screamed for nicotine. So I requested for permission to go out.

One of the invigilators, a short plump middle-aged gentleman had earlier come to me and told me, “Sir, I know you. You were commissioner Kolkata Municipal Corporation.” Ouch!! I requested him not to advertise that. So when I requested for permission to go out, he came to me and said “Sir, after five minutes.”

I eagerly waited. After five minutes this guy signaled and I walked out of the hall and lit up. Two drags and the solution of the first problem that had eluded me so long, clicked in place in my mind. Few more drags and the others followed suit. I finished my cigarette and came back and started solving the problems.

2008 CAT paper was one of the most beautiful papers of CAT. It had lot of nice challenging problems. Anyway I had lost twenty-five minutes and was hard pressed for time already. So I did the paper not entirely to my satisfaction. I came back home and after lunch with chilled beer started solving the remaining of the problems. They were all gems. Some of them were really challenging and needed lot of firepower. I enjoyed solving them.

I landed with a percentile of just under 95.

I was not happy with the experiment. Lack of nicotine seemed to have distorted the output. So another experiment was necessary. In 2010, again I filled up the form along with my daughter.

The exam center was just behind Great Eastern hotel. It was a known place for me as I had been there to chat with Vishnu Mohta, one of the directors of Venkatesh Films, whose office was on another floor of the same building.

My daughter had the same scornful attitude about lugging along a parent who refused to behave and act as a guardian, a befitting role for someone of his age but playing havoc with all sensibilities by being a candidate with boys and girls half his age. As we descended form the car and started getting onto the footpath and the gate, a security guard stopped me and told me that guardians are not allowed beyond that point. My daughter simply waved her admit card and vanished inside the gate without even bothering to look back to check what happened to her poor father. A very understandable reaction from her: if the father is denied entry, fine; he can play the guardian and if allowed to enter, then he is another candidate without any acquaintance with her let alone family ties.

I patiently waved my admit card to the security guard who looked at it, looked at me and still had a huge doubtful look on his face. I could feel he was wondering whether to give a shout at the cops that someone is masquerading as a candidate in trying to get entry. There was a continuous flow of dialog exchange going on simultaneously which is like this:

“Sir, guardian allowed nahin hain”

“Mein guardian nahin, candidate hun!”

Finally he took a last careful look at my admit card, my id proof of retired Government officer, made sure that I am the same person and not someone in disguise or something and allowed me to enter.

Then there was this counter where they take your photograph, check admit card, id proof, take fingerprint almost akin to processing of a criminal at a US Precinct.

The gentleman who was checking these documents looked at my id proof, looked at me and again gave the id proof a hard look and decided a loony is at hand. However he sounded respectful and processed me!!!

I proceeded upstairs and decided that it is time I fill my blood stream and brain with enough nicotine to last at least three to four hours to avoid a repetition of last time when nicotine deficiency screwed up my experiment of measurement of mental agility against a proper benchmark. So I smoked three to four cigarettes in quick succession and felt the nicotine making me sufficiently high. I felt that two more measurements might be necessary, one when one sits for CAT after consuming two bottles of chilled beer and another with two large pegs of single malt. That experiment is still pending!!!

Before entering the hall, one team with one gentleman and one security asked me to handover my mobile, cigarettes, my lighter, pens, watch, purse and put them in a pouch. I got peeved of being deprived of things, which are my constant accompaniment and asked the gentleman whether he also wants my shirt, trouser and the undergarments too. He looked even more peeved at my suggestion that these apparels can be of great assistance in adopting to unfair means and therefore the candidates should be asked to shed them too.

My daughter was nearby in the queue of the female candidates and I was not talking particularly sotto voce. So I saw her glaring at me and mouthing instructions not exactly a daughter gives her father rather it is the other way round asking me to shut my trap.

The gentleman refused to take my suggestion and I made it to the hall fully attired and found myself sitting across my daughter. They make you to sit in front of a terminal, a keyboard and a mouse; the terminal had nothing on the screen only a blue background. There were cardboard pieces on the sides and on the front to prevent your neighbor looking at your screen and the person sitting opposite you to talk to you in sign language or lip-talk with you. So it was a kind of lonely setup where you have nothing to do but stare at a blue screen.

I tried to shut my eyes and tried to sleep. It was difficult as people were clamoring around you. So I opened my eye and started whistling. Now I am not at all great at whistling and whatever comes out is neither loud nor has any specific tune in it. But the girl who was sitting across me behind the cardboard in front of me screamed at me that I should stop. I tried to peer at her through the gaps and found a young girl whose nerves are clearly taut as the piano string. I told her not to be so high strung as that will impact her performance but she told me to shut up.

This wait was for almost an hour and after that there was some fanfare about explaining the way it should be answered etc. etc. Probably there was a short tutorial also.

The test happened without any event. I missed singing like I normally do for challenging and interesting problems, while I was solving the problems lest I am screamed at again. Then it was over and we all signed off on our screen.

But they won’t let us stand up and let go. We have to wait. My feet had cramped and I longed for stretching it. So I stood up and asked permission to visit the restroom. I was denied permission as for some stupid reason you can’t leave your seat until something God knows what happens. So I asked whether it was OK if I kind of relieved myself in the hall itself under my table. That rattled the invigilator guy to some extent. To convince him further, I took my hands to my zipper and made movements to convince him that the zipper is about to start its downward motion. He said “OK!! OK! Go!” The moment I started, few more hands went up and he allowed everyone to visit the loo. So much for a stupid rule and all you have to do to prove it to be stupid, you have to put them in a difficult untenable position.

The only downside of all these was my daughter refused to speak to me during the delicious lunch we had with Chhole bature at a restaurant next door and complained bitterly to my mother that I was a crack pot and expert in creating embarrassing situation.

This time I had another point to prove. My daughter had, against my advice, had enrolled herself in one of the tutorials for CAT. I had told her it was a stupid proposition and she should know how to solve the problems from first principles. Solving quant problems by logic, in my opinion, is the quickest and smartest way. My daughter vehemently disagreed with me. At home we used to have our competition with my mother as arbitrator and in most of the cases shortcut formula lost to logic.

I took a look at the shortcut formula given by the tutorial and was aghast. They ran pages after pages. You needed another shortcut to remember shortcuts. An example is like this: What is the last digit of 7 to the power of 4007. Shortcut: divide 4007 by 4 and if the remainder is 0 then 1, if 1 then 7, if 2 then 9, if 3 then 3”. No explanation, no reason as to how such profound wisdom of shortcut has come by. No mention that the last digit starts repeating as you keep on raising the power of seven. All these shortcuts said were if this is that, then you do this otherwise you do that and so on.

They were taking away the beauty of the sums and turning the students into automatons. If you forget the shortcut in the exam hall, it is like a short-circuit of a robot. It stops, as it doesn’t know what to do. It is so mindless. It was utterly a sham.

I landed with a percentile of 98.92 with a quant percentile of 99.84. So my brain was working OK without any degeneration worth mentioning.

Secondly I was glad that my love for logic and first principles and my support for them are vindicated at least to my daughter.

My daughter landed with a percentile of 85 and a quant percentile of 75. She gave up the tutorial and started the old fashioned logic. After couple of months she confessed to me that this shortcut is all bogus and there is no substitute of arithmetic logic and working out from first principles. Next year she landed a very decent percentile and did her MBA with brilliant result.

The other thing they keep on telling in these tutorials that you have to be very quick and you don’t have time. This is also entirely bogus. If one works steadily and slowly like the proverbial tortoise or to use a more recent analogy of Robocop in the Robocop movie, you don’t have any dearth of time. Both the times I never felt I was short of time and the first time though I had lost twenty-five minutes, I did nit feel the time pressure. It is another myth.

The Internet sites and the various forums create an unnecessary panic situation of these examinations. Nobody tells the kids that if you have a strong fundamental knowledge, a logical bend of mind and analytical skills, you don’t have to prepare for CAT. You just walk in with a free mind without any tension and write the exam; have fun while writing it and you will come out with brilliant result.

The intent of this test is to test who you are, what your real capability is and not what kind of a zombie a tutorial has turned you into. So be yourself and walk in with head held high…but alas….nobody absolutely nobody tells that and in the process our kids are misguided and business worth crores flourish in the name of these tutorials.

Evolution of my library

2016-06-23T18:13:00.003+05:30

It was around this time probably in 1995, I met Arabindada of Dasgupta Publishers, who became a constant encouragement and supplier of books. He got me my first copy of Courant's Calculus and Wyl's Space, Matter and Time, max Born's Atomic Physics and umpteen books on Digital Communication and Spread spectrum. On one trip to Hyderabad, I went to a bookshop where I almost went crazy: so many books which I have only read about in the bibliographies… I borrowed some money from my fellow colleagues and bought a suitcase full. Those days in Hyderabad airport one had to walk on the tarmac from the terminal to the craft and while I was walking, the straps of my suitcase weighing several kilos broke; oops….dragged the beast somewhere.

In 2007, when I was about to leave government service, my parents agreed after a lot of cajoling that the library has become much bigger to be accommodated in the mezzanine floor room and books need more space in house. So the first floor flat was designated to be the library. with some more new shelves the library in its current form started blossoming….years went by….9 years….more books, more interest in Mathematics and well I have now shortage of space…yes Shortage….every conceivable wallspace has now bookshelves and there is no more wall….I need some more space for my books….

Bregman Divergence

2016-06-21T13:07:00.002+05:30

Learnt a new mathematical concept: Bregman divergence. Knew about Kullback-Leibler divergence but this one I didn't know about. The concept of dual space is very interesting. the following is from Wiki page.

Definition[edit]

Let be a continuously-differentiable real-valued and strictly convex function defined on a closed convex set .

The Bregman distance associated with F for points is the difference between the value of F at point p and the value of the first-order Taylor expansion of Faround point q evaluated at point p:

Properties[edit]

Non-negativity: $D_{F}$ p q0 for all p, q. This is a consequence of the convexity of F.
Convexity: $D_{F}$ p q is convex in its first argument, but not necessarily in the second argument (see ^[1])
Linearity: If we think of the Bregman distance as an operator on the function F, then it is linear with respect to non-negative coefficients. In other words, for $F_{1} F_{2}$ strictly convex and differentiable, and $λ 0$ ,

Duality: The function F has a convex conjugate $F^{}$ . The Bregman distance defined with respect to $F^{}$ has an interesting relationship to $D_{F}$ p q

Here, and are the dual points corresponding to p and q.

Mean as minimizer: A key result about Bregman divergences is that, given a random vector, the mean vector minimizes the expected Bregman divergence from the random vector. This result generalizes the textbook result that the mean of a set minimizes total squared error to elements in the set. This result was proved for the vector case by (Banerjee et al. 2005), and extended to the case of functions/distributions by (Frigyik et al. 2008). This result is important because it further justifies using a mean as a representative of a random set, particularly in Bayesian estimation.

Examples[edit]

Squared Euclidean distance $D_{F}$ x yxy2 is the canonical example of a Bregman distance, generated by the convex function $F x x^{2}$
The squared Mahalanobis distance, $D_{F}$ x y12 xyTQ xy which is generated by the convex function $F x \frac{1}{2} x^{T} Q x$ . This can be thought of as a generalization of the above squared Euclidean distance.
The generalized Kullback–Leibler divergence

is generated by the convex function

The Itakura–Saito distance,

is generated by the convex function

Marriage of two Completely different ideas

2016-06-17T17:08:00.004+05:30

It was alate afternoon and I was studying Differential Geometry of Manifolds. I was smoking a cigarette and just simply introspecting on what I had just learnt: Concept of charts and local neighborhoods on a manifold. A tiny idea started idea gradually germinated in my mind…an n-dimensional coordinate space and in communication we have n-dimensional signal space …can they be similar or rather can there be some kind of cross-germination…Next time I was on my computer, I did what everyone does….Google….a little bit search and I come across the name of a gentleman called Shunuchi Amari who has written few papers back in 1960s on geometric analysis of communication system… frantic search in the net but these papers are not available. Email to Prof. Amari and in 36 hours his assistant sends me a treasure trove….four papers going in the same direction as I had thought and An Idea was born…..

Today thats what is the subject of my Doctoral Research…it is somewhat uncharted territory but I have a lighthouse…a subject called Information Geometry…Prof Amari can be called the father of the subject which is a beacon in my journey….may be that will make me reach my destination.

It has been a long time…..

2016-06-17T16:45:00.001+05:30

It has been a long time since my last post. In the meantime, I have fallen in love….with Differential Geometry. I don't know how it happened….but it has. I have also acquired my M.Sc degree in Pure Mathematics..so logically can call myself a Mathematician now along with a Digital Communication Engineer. My two years sojourn into the world of structured study of Mathematics while studying for the 20 papers that M.SC degree entailed made me learn a lot of things which left to myself I would have never learned…Topology, Topological Vector Space, Graph Theory and believe me…C Programming and Numerical Analysis. They are all wonderful things but somehow on my own I would not have made myself to learn it unless forced which happened.
Writing the exam was also a great fun. The weather was sultry, mid July to mid September, No air-conditioning, sweaty hands, supervisory eye of the invigilator, small benches which now my backside hardly fitted…..a sense of deja vu prevailed. Weirdest part was being called by my co-examinees "Uncle"…augh…oops…trimmed my mustache so that the whites show their minimum, took deep breaths to suck in the paunch but to no avail…."Uncle…"Huh ..! I later figured out that I was also an enigma to them…I am not a teacher, nor I am looking for job of a teacher then what the hell am I? They wondered..Nobody could imagine that I am so crazy a nut that I am doing my M.SC which I need not do..nothing forcing me to go through the grueling process..but I was doing it..and It was great fun.

Loney's Coordinate Geometry Solutions: Some problems on straight Lines solved

2013-04-17T13:44:00.000+05:30

Papers published by me

2013-01-14T13:57:00.003+05:30

1. Debasish Som, “Noise Immunity Study Of Hermite Polynomials In Digital Transmission In A Multi-User Environment”. Proceedings of the All India Seminar on ‘Multi-Dimensional Advancement in Telecommunication and their Global Importance’, 09-10 September 2008, Electronics & Telecommunication Engineering Division, The Institution of Engineers.

2. N. C. Som & Debasish Som, “A Retrospect of Lapses in Disaster Management – An Overview” Proceedings of the 3^rd International R&D Conference 2000, 29 February – 3 March 2000, Jabalpur, India, Central Board of Irrigation and Power, New Delhi.

3. Debasish Som & N. C. Som, “Cyclone Vis-à-vis Cyclone Warning In Disaster Management: A Case Study”. Proceedings of the 2^nd International R&D Conference 1997, 21-24 October 1997, Vadodara, India, Central Board of Irrigation and Power, New Delhi.

4. Debasish Som & N. C. Som, “Flood Management In A Border District Of West Bengal: A Case Study”. Proceedings of the 2^nd International R&D Conference 1997, 21-24 October 1997, Vadodara, India, Central Board of Irrigation and Power, New Delhi.

5. N. C. Som & Debasish Som, “Disaster In Urban Areas: Strategy Of Management”. Proceedings of the International Conference on Urban Engineering in Asian Cities in the 21^st Century. Organized by School of Civil Engineering, Asian Institute of Technology, November 20-23, 1996, Bangkok, Thailand.

6. N. C Som & Debasish Som, “Review on the preventive measure for reduction of impact of Cyclone and Flood in coastal area of Bay-of-Bengal- A case study”, Hydrocast 95, Workshop on water related problems in low lying coastal areas, 13-17 November 1995, Bangkok, Thailand.

2012-12-31T17:14:00.001+05:30

The following sum has a history:
Volume created by revolving the arc of a parabola from the vertex to one extremity of the latus rectum about the corresponding chord is [{2*5^0.5}/75]times pi times a^3: prove.

It came in the Civil services maths second paper in 1982 when I wrote it. I was stuck and it was the last problem. I decided to take a smoke break and sat on the staircases outside the exam hall. First cigarette gone... no solution...lit up the second... and the invigilator comes out and asks me : aren't you going to come in and complete the paper?" I shooed him away... and suddenly I had it figured out.... went back and the volume came out smoothly....

Nostalgia I guess... so I tried it... last night.. it is from Das & Mukherjee..(bless the oldie and goldie..) ....and hooray.... I could do it but it took me thrice the time it took me in 1982 inclusive of the two cigarettes that I smoked....

The solution to the problem :
Volume created by revolving the arc of a parabola from the vertex to one extremity of the latus rectum about the corresponding chord is [{2*5^0.5}/75]times pi times a^3: prove.

1981 IIT Comm

2011-03-08T12:52:00.003+05:30

Complex Domain

2010-06-21T16:18:00.000+05:30

The shortest route between two truths in the Real Domain passes through the complex Domain.
Hadamard

Contour Integration

2010-06-18T11:17:00.000+05:30

Recently I started reading complex analysis again. I remember Feynman once saying that he never understood contour integration but he loved doing integration (the tough ones) by applying the differentiation under integration rule. I found a nice exposition on the same in the Advanced Calculus by Woods, a book that Feynman said he read in his early days. One of the excellent books on Advanced Calculus I have come across. It is a pity that the Publishers (with the exception of Dover Publication) prints these old classics.
I was even surprised when I started searching the book on Complex Variable by E T Copson and found that the book has gone out of print. My enquiry with the Publishers (Oxford University Press) was met with a smug reply that the book is OP. I wonder whether the publishers even have an appreciation the value of these oldies and goldies.
By the way coming back to Contour integration, one limitation I am finding that it is inadequate to solve indefinite integrals. The beauty of the world of complex numbers is the real analysis world transgresses into simpler models once seen through the prism of the Complex world.

Letters of Feynman

2010-03-08T10:28:00.003+05:30

Recently I got a book edited by Michelle Feynman, RPF's daughter. The book contains letters written by RPF during his entire life. It is an impressive collection and provides an excellent window to the personality of one of the greatest physicists of all times. If "Surely you are joking.." gives a glimpse to RPF's passion for science and life, this book gives an undiluted feel of his persona.

More photographs of my library: It should also act as a reference list and bibliography

2010-01-10T22:45:00.005+05:30

Pi : One of the most mysterious numbers of the Universe

2009-12-17T16:04:00.003+05:30

To 100 Decimal Places
Here is Pi with the first 100 decimal places:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...

Dreams shattered

2009-12-11T15:44:00.002+05:30

Today I visited an Institute of repute and met the Director. Pandit Nehru and Dr B. C Roy laid the Foundation stone of the Institute in early 50s with the dream that social welfare will ensure more prosperity and consequential growth of business. Today the Institute has not reached anywhere near these dream. To the contrary I was provided in the name of vision, mision and road-map a scenario which I found to be depressing. Any area of interest I discussed was in the womb of future. The vison is obfuscated, mission lacking clarity, road-map hotch-poth. The Social welfare stream does not address needs of Rural Development, Nothing on the Millenium Development Goals, Business Mangement does not have any industry interaction and updation of curriculum based on industry requirement and present environment. I felt very saddened and deppressed that a premier Institution with so much potential is just fading into irrelevance because the peopel who could have taken it from height to height are so satisfied and compalcent with what they are doing that they has just stopped even listening to new ideas.
I FELT LIKE SCREAMING MY HEADS OFF BUT WHO WILL HEAR?????

Stephen Hawkin

2009-12-11T07:51:00.000+05:30

The apparently inconceivable marriage between the astronomy and quantum mechanics has been achieved by him! While we always thought that quantum mechanics can be understood by common sense as it deals at subatomic levels but that in the science of large bodies the theory can be seamlessly integrated can be termed only the work of a genius! We can only admire him, personally I worship his intellect!!!!
D Som

Quotes by eminent persons

2009-12-09T19:04:00.000+05:30

Quotes by eminent persons of great repute & Nobel Laureate

1. Albert Einstein, (1879-1955) physicist. In 1905 He published his theory of Relativity.

When I read the Bhagavad Gita and reflect about how God created this universe, everything else seems so superfluous. We owe a lot to Indians who taught us how to count, without which no worthwhile scientific discovery could have been made.

2. . George Bernard Shaw, (1856-1950) a vegetarian and Nobel Laureate in Literature.
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.

The apparent multiplication of gods is bewildering at the first glance, but you soon discover that they are the same GOD. There is always one uttermost God who defies personification. This makes Hinduism the most tolerant religion in the world, because its one transcendent God includes all possible gods. In fact Hinduism is so elastic and so subtle that the most profound Methodist, and crudest idolater, are equally at home with it.
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3. Annie Besant { Annie Wood Besant (1847-1933) was an active socialist on the executive committee of the Fabian Society along with George Bernard Shaw.
After a study of some forty years and more of the great religions of the world, I find none so perfect, none so scientific, none so philosophic, and none so spiritual as the great religion known by the name of Hinduism. The more you know it, the more you will love it; the more you try to understand it, the more deeply you will value it. Make no mistake; without Hinduism, India has no future. Hinduism is the soil into which India's roots are struck, and torn of that she will inevitably wither, as a tree torn out from its place. Many are the religions and many are the races flourishing in India, but none of them stretches back into the far dawn of her past, nor are they necessary for her endurance as a nation. Everyone might pass away as they came and India would still remain. But let Hinduism vanish and what is she? A geographical expression of the past, a dim memory of a perished glory, her literature, her art, her monuments, all have Hindudom written
across them. And if Hindus do not maintain Hinduism, who shall save it? If India's own children do not cling to her faith, who shall guard it? India alone can save India, and India and Hinduism are one.
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Nobel laureates

4. Niels Bohr, (1885-1962) Danish nuclear physicist who developed the Bohr model of the atom. His received the Nobel Prize in physics in 1922, for his theory of atomic structure
I go into the Upanishads to ask questions.

5. Werner Heisenberg
After the study of Indian philosophy (derived from Vedas), some of the ideas of Quantum physics that seemed so crazy, suddenly made much more sense (father of Quantum Physics Werner Heisenberg).

6. Erwin Schrödinger (1887--1961) Austrian theoretical physicist, was a professor at several universities in Europe. He was awarded the Nobel prize Quantum Mechanics, in 1933. During the Hitler era he was dismissed from his position for his opposition to the Nazi ideas and he fled to England. He was the author of Meine Weltansicht

This life of yours which you are living is not merely apiece of this entire existence, but in a certain sense the whole; only this whole is not so constituted that it can be surveyed in one single glance. This, as we know, is what the Brahmins express in that sacred, mystic formula which is yet really so simple and so clear; tat tvam asi, this is you. Or, again, in such words as "I am in the east and the west, I am above and below, I am this entire world."

The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. In 1925, the world view of physics was a model of a great machine composed of separable interacting material particles. During the next few years, Schrodinger and Heisenberg and their followers created a universe based on super imposed inseparable waves of probability amplitudes. This new view would be entirely consistent with the Vedantic concept of All in One.

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

Nirvana is a state of pure blissful knowledge.. It has nothing to do with individual. The ego or its separation is an illusion. The goal of man is to preserve his Karma and to develop it further – when man dies his karma lives and creates for itself another carrier.
There is no kind of framework within which we can find consciousness in the plural; this is simply something we construct because of the temporal plurality of individuals, but it is a false construction....The only solution to this conflict insofar as any is available to us at all lies in the ancient wisdom of the Upanishad.

The multiplicity is only apparent. This is the doctrine of the Upanishads. And not of the Upanishads only. The mystical experience of the union with God regularly leads to this view, unless strong prejudices stand in the West.

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7. Alfred North Whitehead
Science in the most advanced stage now is closer to Vedanta than ever before -- (Alfred North Whitehead)

8. Romain Rolland (1866-1944) French Nobel laureate, professor of the history of music at the Sorbonne and thinker.·
If there is one place on the face of the 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....For more than 30 centuries, the tree of vision, with all its thousand branches and their millions of twigs, has sprung from this torrid land, the burning womb of the Gods. It renews itself tirelessly showing no signs of decay.

9. Octavio Paz (1914-1998) was awarded the Nobel Prize for Literature in 1990.
The Hindu genius is a love for abstraction and, at the same time, a passion for the concrete image. At times it is rich, at others prolix. It has created the most lucid and the most instinctive art. It is abstract and realistic, sexual and intellectual, pedantic and sublime. It lives between extremes, it embraces the extremes, rooted in the earth and drawn to an invisible beyond.
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10. Dr. Carl Sagan, (1934-1996) famous astrophysicist.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.
The most elegant and sublime of these is a representation of the creation of the universe at the beginning of each cosmic cycle, a motif known as the cosmic dance of Lord Shiva. The god, called in this manifestation Nataraja, the Dance King. In the upper right hand is a drum whose sound is the sound of creation. In the upper left hand is a tongue of flame, a reminder that the universe, now newly created, with billions of years from now will be utterly destroyed.

A millennium before Europeans were wiling to divest themselves of the Biblical idea that the world was a few thousand years old, the Mayans were thinking of millions and the Hindus billions.
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11. Julius R Oppenheimer- (1904-1967--Father of Atom bomb)Scientist, philosopher, bohemian, and radical. A theoretical physicist and the Supervising Scientist for the Manhattan Project, the developer of the atomic bomb. Graduating from Harvard University, he traveled to Cambridge University to study at the Cavendish Laboratory.

Modern Physics is an exemplification and a refinement of old Hindu wisdom- contained in Vedas

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

The general notions about human understanding… which are illustrated by discoveries in atomic physics are not in the nature of things wholly unfamiliar, wholly unheard of or new. Even in our own culture they have a history, and in Buddhist and Hindu thought a more considerable and central place. What we shall find [in modern physics] is an exemplification, an encouragement, and a refinement of old wisdom.

The juxtaposition of Western civilization's most terrifying scientific achievement with the most dazzling description of the mystical experience given to us by the Bhagavad Gita, India's greatest literary monument.

CALCULUS by Spivak

2009-12-09T14:52:00.002+05:30

Yesterday I have got this book. I read in a blog that this is one of the best books on Calculus. I scarcely believed the guy who wrote it. After all, there are so many excellent books on Calculus but on reading the book or rather browsing through it, I am amazed at the depth and at the same time the simplicity with which many issues have been written. Reading the book gives one a feel of reinventing Calculus, concepts of Limit, Continuity, differentiation etc. I read the chapter which the author said to be a digression and the chapter is on Keppler' Laws of planetary motion and their derivation from Newton's law of Gravitation. Apparently elementary stuff; taught at senior school level, but here the teatment is so intersting and unique.I wish we had acces to this book when we learnt Calculus and I wish the publishers will come up with an edition that can afforded by the students. More so because the problems and the examples provides an insight which I have not come across elsewhere.

Beauty of mathematics

2009-12-03T21:09:00.000+05:30

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn't it?
And look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

Now, take a look at this...

101%

From a strictly mathematical viewpoint:

What Equals 100%?
What does it mean to give MORE than 100%?
Ever wonder about those people who say they are giving more than 100%?
We have all been in situations where someone wants you to
GIVE OVER 100%.
How about ACHIEVING 101%?

What equals 100% in life?

Here's a little mathematical formula that might help
answer these questions:

If:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.

If:

H-A-R-D-W-O- R- K
8+1+18+4+23+ 15+18+11 = 98%

And:
K-N-O-W-L-E- D-G-E
11+14+15+23+ 12+5+4+7+ 5 = 96%

But:
A-T-T-I-T-U- D-E
1+20+20+9+20+ 21+4+5 = 100%

THEN, look how far the love of God will take you:

L-O-V-E-O-F- G-O-D
12+15+22+5+15+ 6+7+15+4 = 101%

Therefore, one can conclude with mathematical certainty that:
Fine , while Hard Work and Knowledge will get you almost there, with the right Attitude one can actually reach the desired point /position ............................................

BUT IT IS "LOVE OF GOD" that will put you over the top!

--
LIVE LIFE KINGSIZE :-)

D Som

Is Global Warming and rIse in the level of sea is a myth?

2009-12-03T20:59:00.000+05:30

Global warming will cause polar ice to melt and so the sea level will rise. If that is so, then the paradox is if ice submerged in water melts, water level does not rise!!! Then how the sea water level rises?
The other explanation can be rise in temperature causes the water to expand leading to level of rise in water!
The most important and interesting problem is earth is spherical and holds the water on its surface! How can we mathematically model this or carry out experiment on a model? How do we make a model!!!!
D Som

My library

2009-12-03T18:32:00.002+05:30

Can Traffic Flow can be modelled in the same manner as a Streamline flow of Hydrodynamics

2009-12-03T18:13:00.002+05:30

Can we model traffic flow with a streamline hydrodynamic model. The volume of traffic is equivalent to mass of fluid, velocity being the same, width of the road representing the conduit area, and traffic density as pressure? Has anybody really tried this?????

What is happening to Science education???

2009-12-03T13:41:00.002+05:30

Why today the education system does not show the interconnection between the various streams of science: Biology can be taught not merely as biology but as part of physics, mechanical engineering, computer system, instrumentation, pattern recognition etc??? Why we don't tell students that invention of DNA structure was not merely an off shoot of bio-chemistry, but it had lot to do with x'ray diffraction of crystals perfected by Pauling!!! And the double helix structure could be explained with Bessel functions!!! How many of physics or mathematics students have read Watson's paper announcing the double helix structure? Why they are not encouraged to do it? When calculus is taught, why do we only look at physics problems but do not state economic applications of calculus!! Why the authors also provide such a narrow focus when they write??? Why don't excite the students in school with game theory problems and show its applications?
WHY CAN'T WE MAKE STUDENTS SEE THE INTERCONNECTION BETWEEN ALL STREAMS OF KNOWLEDGE AND MAKE EDUCATION MORE EXCITING AND FUN??????

Why Call it Float freely

2009-12-03T13:09:00.002+05:30

When my daughter was in class X, I started teaching her physics and Mathematics. Our favourite way to study was what we called 'Float freely". We will start with one topic and from there seamlessly move to a related topic, say I was teaching her laws of motion and so we will start looking at how to draw a graph of velocity vs time and then start figuring out how to find out the area under the curve which turned out to be the distance travelled. The next natural step was to let her figure out why it is so!!! Once she has done it, I will try to show her that integration actually does it!!!!! Or that the area for a uniformly accelerated particle is an area of a trapezium. When we started talking of a trapezium, we will try to figure out that sum of an Arithmatic progression series of numbers can be found by the same formula as that of a trapezium. So somewhere we had connected lot of apparently disconnected things and that was the result of float!!!!!!!

I wish I Could do Maths in such good handwriting!!!!

2009-12-02T22:41:00.001+05:30