A few days ago, I read an article about a poor Kolhapur Dalit boy Sridhar Kamble, who, owing to his single minded dedication to astronomy, had landed a NASA scholarship. This news piece and the one in TOI were both really heartening to read; they made me happy with the thought that true scholarship paid off. This was rural India making a statement. The voice and will of the oppressed triumphs. The article mentioned the numerous hardships the boy's poor farmer father had to endure to make his son study. In spite of selling more than half of his land, the boy was short of meeting his travel expenses and I was satisfied to read that the state had intervened with a scholarship to fund his expenses.

But the words jumping the gun could not have been more ominous. The first CNN-IBN article that hit my face this morning was about the entire business of Sridhar going to NASA being a fake and a case of deceit and forgery. He probably did have a genuine interest in astronomy, but he had faked documents starting from his 10th marks to his correspondence with NASA, in order to get funds from the government. Unfortunately, this momentary lapse of the boy (who is all of seventeen and cannot be guilty of dreaming high) is going to extract a heavy price on his future career and education.

Selective abortion in nature

A Danish researcher proposes an incredibly intriguing hypothesis - that the sex of the progeny is related to the stress levels experienced by the expecting mother during her pregnancy. Based on data collected from surveys that were administered to nearly 8000 expecting mothers between 1989 and 1992, the researcher arrived at a startling correlation- the more stressed a mother had been, the less chance she had of having given birth to a boy.

Most of us are statisticians enough to appreciate that correlation does not imply causality. However, the goal of scientific investigation is to look at possible causal structures that manifest themselves through final correlation. The investigator believes that if at all there is such a causal mechanism that directs the sex of the baby according to the stress experienced by its mother, the reasons are likely to be adaptive rather than pathological.

But all said and done, in spite of being a Darwinist at heart (not a social one though), I cannot say I am not surprised (even amused to an extent) when I read paragraphs such as these:

That is because the chances are that a daughter who reaches adulthood will find a mate and thus produce grandchildren. A son is a different matter. Healthy, strapping sons are likely to produce lots of grandchildren, by several women—or would have done in the hunter-gatherer societies in which most human evolution took place. Weak ones would be marginalized and maybe even killed in the cut and thrust of male competition. If a mother's stress adversely affects the development of her fetus (as it is likely to do) then selectively aborting boys, rather than wasting time and resources on bringing them to term, would make evolutionary sense. That, in turn, would explain why women in rich countries, who are less likely to suffer from hunger and disease, are more likely to give birth to sons.

- From The Economist

In so much as the contextual premises that such arguments are based upon, they seem perfectly reasonable. But there is still a part of me that feels something clinically lacking in these reasonings. A lazy disposition holds me back from thinking further in the present moment, so I'll leave it for the record.

Our sweetest songs

We look before and after,
And pine for what is not:
Our sincerest laughter
With some pain is fraught;
Our sweetest songs are those that tell of saddest thought.

Yet, if we could scorn,
Hate and pride and fear,
If we were things born
Not to shed a tear,
I know not how thy joy we ever should come near.

- From To a skylark by Percy Shelley

jumping the gun?

Being a part of my generation of Indians, there are sometimes when I feel lucky and gratified to find myself a witness to a propitious phase of rapid economic development in my city. That the scent of this 'progress' has not permeated beyond the urban epidermis into the rural landscape of my country will be of some concern in the near future, with buzzwords like 'inclusive growth' keeping the thinkers and planners busy.

But in an interesting NDTV article, a grad student questions whether these current metrics of growth are reasons to quote and be proud about. She doesn't get into developmental economics and analyze what these metrics really reflect; she is rather blunt in asking us Indians whether we have any reason to be proud about the direction our country is taking. It's not a crime to be 'confident' she says, but fears that this confidence is changing too quickly into arrogance in some quarters - arrogance, that neither has any basis in reality nor advances the interests of 'Brand India' in any way.

In the true spirit of Monty Python, we Indians like to always look on the bright side of life. When we have master campaigners in parties like the BJP, it isn't difficult for most to live under the delusion that India is 'shining':

For instance, if you challenge the idea of a rising India with the dogged optimists by pointing out the Gujarat genocide, you are immediately reminded that Gujarat is also one of the most industrially advanced and administratively efficient states in India. If you point to the fact that most of our engineering graduates are not employable you are immediately reminded that India still produces the highest number of engineering graduates in the world.

If you suggest that Indian democracy is so criminalised that it has killed good governance you are told that no other country sends a billion people to the ballot box. This is the new half-full approach to life but it tends to gloss over anything that points in the other direction and brands anyone who says so as a skeptic and a kill-joy.

I would still like to question the author's premise which made her conveniently assume the naive homogeneity of the Indian voice over these issues. But I cannot help but acknowledge the bitter truth in the following words, where she harpoons this ineluctable diatribe against a nation she believes is counting its chickens much too early referring to our collective dream of becoming a South-Asian superpower:

But a great power is fundamentally supposed to be able to positively influence events, something we can't do even in our own backyard at the moment. Afghanistan is a mess, Pakistan is losing control over itself, Bangladesh can't decide when to have elections, Nepal is in transition and Sri Lanka in civil war.

India has little or no control over events in its own neighbourhood, let alone projecting its power around the world. Besides even when the chance arose, India could not take a bold stand. It refused to condemn China on its actions in Tibet and it did business with the Burmese junta at the height of the crackdown on pro-democracy protests.

Anecdotes-IV

Probably the last or the second-last in this series. The process is getting too monotonous :-). Following are some Albert Einstein stories.

10. Einstein, who fancied himself as a violinist, was rehearsing a Haydn string quartet. When he failed for the fourth time to get his entry in the second movement, the cellist looked up and said, "The problem with you, Albert, is that you simply can't count".

11. Einstein was attending a music salon in Germany before the second world war, with the violinist S. Suzuki. Two Japanese women played a German piece of music and a woman in the audience exclaimed: "How wonderful! It sounds so German!" Einstein responded: "Madam, people are all the same."

12. In 1946 a South African child, Tyffany Williams expressed in a letter her surprise that Einstein was still alive. He answered: "I have to apologize to you that I am still among the living.There will be a remedy for this, however."

13. An American women's organization protested Einstein's visit to America (1928) on political grounds. Einstein replied: "Never have I experienced from the fair sex such an energetic rejection of all my advances; if it *has* happened, it was never by so many at once."

Anecdotes - III

7. Today's serving shall involve three stories of the extraordinary Hungarian mathematician John von Neumann (1903-1957)

The following problem can be solved either the easy way or the hard way. Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown? The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances.

The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it.

When this problem was posed to John von Neumann, he immediately replied, "150 miles."

"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series." "What do you mean, strange?" asked Von Neumann. "That's how I did it!"

8.

Student: "Er, excuse me, Professor von Neumann, could you please help me with a calculus problem?"

John: "Okay, sonny, if it's real quick -- I'm a busy man."

Student: "I'm having trouble with this integral.

John: "Let's have a look." (after a brief pause) "Alright, sonny, the answer's two-pi over 5."

Student: "I know that, sir, the answer's in the back -- I'm having trouble deriving it, though."

John: "Okay, let me see it again." (another pause) "The answer's two-pi over 5."

Student (frustrated): "Uh, sir, I _know_ the answer, I just don't see how to derive it."

John: "Whaddya want, sonny, I worked the problem in two different ways!"


9. Von Neumann (like our own Srinivasa Ramanujan) supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes".

Anecdotes -II

4. More Paul Erdős

a) On one occasion, Erdös met a mathematician and asked him where he was from. "Vancouver," the mathematician replied. "Oh, then you must know my good friend Elliot Mendelson," Erdös said.

The reply was "I am your good friend Elliot Mendelson."

b) He had the habbit of phoning fellow mathematicians over the whole world, no matter what time it was. He remembered the number of every mathematician, but did not know anybody's first name. The only person he called by his Christian name was Tom Trotter, whom he called Bill.

c) This one's definitely a fabricated urban legend, but what the hell :-). There was a storm with thunder and lightening. Little Paul Erdos was in bed, frightened and fretting and his mother couldn't calm him. Then, as mothers seem to instinctively do, she found the right words. "It's all right dear", she said, stroking his shiny head, "there's always a prime between n and 2n".

After that, little Paul drifted off into a blissful sleep.

5. This is a story that I remember reading in E. T. Bell's excellent book 'Men of Mathematics'

This story is about the number 2^67-1, the 67th Mersenne number (Numbers, Mersenne had claimed to be prime, which was proven to be non-prime in 1903 by Frank N. Cole (1861-1927). In the October meeting of the American Mathematical Society (AMS), Cole announced a talk "On the Factorisation of Large Numbers". He walked up to the blackboard without saying a word, calculated by hand the value of 2^67, carefully subtracted 1. Then he multiplied two numbers(which were 193707721 and 761838257287). Both results written on the blackboard were equal. Cole silently walked back to his seat, and this is said to be the first and only talk held during an AMS meeting where the audience applauded. There were no questions.

It took Cole about 3 years, each sunday, to find this factorisation, according to what he said.

6. The mathematician G. H. Hardy was to give a keynote speech at a conference. Asked for an advance summary, he said he would present a proof of the Rieman zeta hypothesis -- but they should keep it under their hats. When he arrived, though, he spoke on a much more prosaic topic. Afterwards the conference organizers asked why he said he'd talk about the theorem and then didn't. He replied this was his standard practice, just in case he was killed on the way to the conference.

It was part of his tactics against God - in that he thought God would not allow him to die on the sea trip, because then everyone would think that Hardy had solved this great theorem. Hardy had other anti-God tactics, including always taking an umbrella, and some grading or other boring work, with him to the cricket games. For an athiest Hardy certainly spent a lot of effort against God.

Apparently Hardy's ambitions were:

1. Prove the Riemann Hypothesis
2. Score the winning play in an important game of cricket
3. Murder Mussolini
4. Prove the non-existence of God