Movies and Careers

Movies play a big role in our lives. They make us think beyond the known, they uncover truths, they inspire us, they entertain us - They shape the way we look at things. But I feel that it is sad to believe the are 'the way'. They are never larger than life.

Recently, I have been to a movie which had a character that was close to mine... the clash between career interests and parents' opinions! Then flies a comment that I would make my parents sit and watch that movie... to explain to them that I would like to do something else (What was so nice of them was that they were thinking about this when the movie was going on!). That was one of the most shocking comments I have ever heard. May be I was and am over-reacting but that's the way it is.

What I couldn't figure out was - why I would need a movie to tell my parents that I love something. I love nuclear physics , cardiology, neuroscience, robotics, rural development and many more but I never got interested in them after reading a book or watching a video. I started loving them when I could contemplate something that was fascinating or something which raised lots of questions. To the best of my knowledge even my parents know that I like them (because I keep explaining them whatever new I learn). I couldn't succeed in convincing them that I can have a good career even in those fields. That is my failure!

When my love for something is true, it would definitely help me convince people around... I wouldn't convince my parents that I want to go into nuclear physics by showing them a 3hr video, I would better do a research project and show that. It is true movies give me the energy to keep going but I don't like the idea that a movie would decide a son-father relationship. My little mind can't accept it.

--buddi
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28 - 12 - 2009

The story behind a dice game

COMBINATORICS

0. Combinatorics – The story behind a dice game

Every day we come across passwords. Passwords for computers, passwords for ATMs (commonly referred to as pin number), number locks, and so on. All of these are combinations; some are combinations of alphabets while others are combinations of numbers and still others use symbols; in some cases the passwords are case-sensitive, sometimes they are not.

Among other examples of combinations we can think of – how your teachers come up with the time table, how a metallurgist tries different combinations of elements to come with up an alloy of desired properties, how a linguist examines the meanings of combinations of letters in an unknown language and so on. All of these visibly 'different' applications come under one roof called combinatorics. Combinatorics (or combinatorial mathematics) is a field of mathematics that deals with problems of how many different combinations can be built out of a specific number of objects.

This field has its origin in the gambling games that played a large part in the European high societies in the 16th century. Whole fortunes were won or lost in a game of cards or dice; something very similar to how the Pandavas lost all their fortunes in a game of dice in the Mahabharatha! In how many ways can a certain sum in throws of two or three dice be scored (haven't you played Ludo?), in how many ways is it possible to get two kings in a card game and other similar problems in a game of chance gave the initial push to develop combinatorial mathematics and the theory of probability.

Italian mathematician Tartaglia was among the first to list the various combinations that can be achieved in a game of dice. His list showed the number of ways 'x' dice can fall. However he failed to take into account the fact that the same sum can be achieved in different ways. For example, if we are using 2 dice and we want a sum of 7, the various combinations are (1,6), (2,5) and (3,4).

In the 17th century, Chevalier de Mere, an ardent gambler, had sort the help of his friend Pascal to determine the division of the stakes of an interrupted game of chance. This marked the first theoretical investigation into the problems of combinatorics. Fermat, a contemporary French mathematician, was also working on the same problem. Their work was followed by valuable contributions from Bernoulli, Leibnitz and Euler.

Combinatorics is extensively used in the field of statistics, cryptography, discrete mathematics, linear programming, group theory, non-associative algebra... the list is unending. Most of the names given above might sound new and not of your understandability. However, it is interesting to realise that the mathematics involved in all of them is the same as in a game of dice. Through a series of articles we will travel with Kabani (a student like you) through the field of combinatorics. We will learn to solve problems from the simplest to the toughest, and enjoy the beauty of mathematics. The only thing that you need to know is how to play a game of dice!

Food for thought -

Simplest Question – In a class, every student is to be given a 2-digit roll number. What is the maximum number of students that can be given the roll number?

Toughest Question – There is a queue of x + y persons at a ticket counter of a cinema theatre. x have Rs20 note and y have Rs10 note. Each ticket costs Rs10 and the cashier has no change to start with. In how many ways can the people line up so that the line keeps moving and no one has to wait for change?

Get the dice rolling... try solving the above problems. Correct solutions will get prizes.

Reference – “Combinatorial Mathematics for Recreation” by N. Vilenkin. Translated from the Russian by George Yankovsky

Great Discovery, Humble Beginning…

NUCLEAR PHYSICS

1. Great Discovery, Humble Beginning…

The 19th and the 20th centuries were the time for the most breath-taking discoveries and inventions of modern science. What was once considered fiction and everything that was ever dreamt of - flying machines for carrying people non-stop from continent to continent, submarines which could travel under water from Pole to Pole even under ice, rockets to carry us to the other worlds in the universe, apparatus to make it possible to converse over long distances without wires, and what not.

The development of science and technology outran the fantasies of the writers and the dreams of the scientists. One of the miracles of the era was the discovery of a mysterious chemical, a matchbox full of which could produce enough energy to propel a large ship for several years! The secret to its vast energy lies deep inside the matter that surrounds us.

At the turn of the 20th century, little was known about the structure of matter. Not all elements had been discovered, however it had been established that all matter was made of atoms. Atoms were believed to the smallest, and hence indivisible, particles of matter. J J Thomson then discovered the electron, the smallest particle of negative charge and soon Robert Millikan determined the mass of an electron to be 1836 times lighter than an atom of hydrogen, the lightest of all elements. In 1898, Thomson proposed that the indivisible atom was a uniformly distributed positively charged sphere, in which electrons were embedded. This proposal couldn't answer several of the questions raised about the plausibility of positively charged particles, stability of the atom and so on.

Becquerel's Mistake

The phenomenon of the luminescence of certain substances when exposed to sunlight is called fluorescence. The French scientist Henri Becquerel spent many years studying this phenomenon. Once he had observed a photographic film wrapped in a black paper and kept in a drawer was exposed. There was no way this could have happened because the substance (sulphate salt of potassium and uranium) he used could have fluoresced in the darkness of the drawer. When he studied more carefully the reasons for the same, he could establish that the binary salt of uranium and potassium emitted invisible rays that could expose the photographic film even in darkness. Thus, 26 February 1896, marked the discovery of a new physical phenomenon which became the starting point of the whole of new physics of the 20th century. It is interesting to note that all of the physics that followed started from this accidental observation. More to come in the articles to follow…

3 People, 3 Lessons Learnt

3 People, 3 Lessons Learnt

These are my experiences as a student and as a teacher. Inspired by the Dead Poets Society, there was no better name I could think of..

To start with, the three biggest lessons I learnt and the people behind them..

1. Being more than a teacher - Mr. Keating, the teacher from "Dead Poets' Society". He is the teacher, friend and the person to whom everyone looks upto. The one who is ready to stand up for his students but at all times wishes that his students explore their real interests and live for them... Truly one teacher I would like to be!

2. Value what people have - Mr. N G Bhat, my mathematics teacher. An inspirational figure in my life... one person who valued what ever each of us could afford and glorified what ever little we could do. He was the teacher who had taught me to enjoy and appreciate what I study, the person who did things for the satisfaction rather than the benefits we get out of the results. He was appreciative of the smallest of efforts... once everyone in the class got sweets because I cracked a problem, his beautiful solution sheets (with funny comments) for the problems we put in the drop box, his special classes (I was the only student!) for 8 months to help me solve some maths olympiad paper, his vast library, encyclopedic knowledge... To put it in short no one ever has influenced me so much in my life and no one has ever made me feel so proud of whatever little I could do. What ever I am today.. I am still walking in his shadows, trying to imitate him in his clarity of thought, his insights into the subject and tenderness with which he used to handle a topic. Now-a-days after every class I am dragged into a thought of how he would have taught that... I know I can never figure that out!

3. Expectations should have boundaries, never impose them - Blessy Joseph, once my student (even now!) and now a dear friend. She wouldn't quite agree that she had taught me this but it was one of the biggest lesson from my teaching experiences. Probability is a topic of immense interest for me... and a horror show for her and the class. My drive to push the class out of misery of that mathematical dynamite pushed people to the limits of breaking down. That was a big mistake I was doing... imposing expectations! My intentions though good weren't helping much, then I had realised that if I had to impose something - I had to do so gently.

What I have experienced can never be written down, but these are attempts to acknowledge the efforts of all the people involved. I hope one day I will be a teacher I wish to be..

--buddi

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04 - 12 - 2009