Thursday, 29 May 2008

Classical Misrepresentations

Some years ago, when I was reading The Sign of Four, I recollect having been particularly disturbed by the description of the little dart-welding, dark skinned, deceptive Indian native that the villain, Jonathon Small, smuggles from the Andamans to carry out his nefarious plans in England. It was representative of a particular brand of racial stereotyping that was rampant in the writings of classic authors like Conan Doyle and Rudyard Kipling. Consider, for instance, this line from the Sherlock Holmes' mystery describing 'Tonga', the perfidious, snake-like havoc wreaking uncontrollable pygmy of an Indian:
"It was that little hell-hound; Tonga, who shot one of his cursed darts into him. I had no part in it, sir. I was as grieved as if it had been my blood-relation. I welted the little devil with the slack end of the rope for it, but it was done, and I could not undo it again."
Some would say that such a characterization should not be used to read too far into the author's mind and if anything, should be written off as a peccadillo subsumed under the larger umbrella of artistic freedom. Nonetheless, it is surprising how deeply progressive writers such as Doyle (someone who was singularly responsible for popularizing the methods of science and deductive reasoning) had a part of their minds that still lived in the past. And this was a time when the moral Zeitgeist was undergoing rapid progressive transformation, thanks to philosophers and visionaries in the West. This was a time when slavery had long ended in America, a time when feminism was already a significant social force in Europe, a time when philosophers like T. H. Huxley and John Stuart Mill had broke open conservative traditions through critical reasoning. Three years after the publication of The Sign of Four, Swami Vivekananda's speech at the Parliament of Religions in Chicago would be greeted by a thunderous applause by a prominently white audience.

But my thoughts in this vein were rekindled today, not by Conan Doyle's works, (which in spite of being masterful are filled with such racial innuendos) but by one of the most innocuous of authors in the English literature- the master comedian P. G. Wodehouse. While most of us fancy Wodehouse as light reading, I read Wodehouse carefully for I find his wit unparalleled and worthy of emulation. At the same time, his writing is pregnant with incredible perception and satirical irreverence of English orthodoxy. Dawkins' tells us how Wodehouse's writings were filled with extremely smart and appropriate biblical allusions (See The God Delusion):

P G Wodehouse is, for my money, the greatest writer of light comedy in the language, and I bet fully half my list of biblical phrases will be found as allusions within his pages. (A Google search will not find all of them, however. It will miss the derivation of the short story title, 'The Aunt and the Sluggard' from Proverbs 6: 6.) The Wodehouse canon is rich in other biblical phrases, not in my list above and not incorporated into the language as idioms or proverbs. Listen to Bertie Wooster's evocation of what it is like to wake up with a bad hangover:

I had been dreaming that some bounder was driving spikes through my head — not just ordinary spikes, as used by Jael the wife of Heber, but red-hot ones.

Coming back to what whetted my appetite to write a post was a growing consternation at regular negative allusions to the 'tropics' and the 'natives of the subcontinent' in Wodehouse's classic bestseller, Life at Blandings. In an otherwise hilarious racket of a series, these instances seemed like bad notes spoiling a well-woven melody. The first instance that I quote is from Summer Lightning(1929), when Millicent discusses Schopenhauer with Sue Brown, who is posing as Miss Schoonmaker in Blandings Castle.

Schopenhauer says suicide's absolutely O. K. He says Hindoos do it instead of going to church. They bung themselves into the Ganges and get eaten by crocodiles and call it a well-spent day.

For all his mystical infatuations with the wisdom of the east, I am pretty certain that Arthur Schopenhauer would not have made a statement that even suggested a practice similar to that described above. But while The Sign of Four was published in 1890, Summer Lightning was published much later in 1929, sixteen years after Rabindranath Tagore had won the Nobel Prize in Literature and ten years after Srinivasa Ramanujan had left Wodehouse's country after one of the most successful collaborations in the history of mathematics with England's most famous mathematician then. In less than a year's time, India would have its first Nobel laureate in Physics - C. V. Raman. Gandhi was already world-famous and highly respected in England. Yet, Wodehouse's representation of India is reminiscent of the arrogant Maculay and James Mill (who is said to have written the first 'authoritative' history of India) as opposed to the likes of his own contemporary writers like E. M. Forster. As an other example, consider the following statement of Colonel Horace in Something Fresh(1915) when he speculates what must be wrong with Rupert Baxter's disposition:

It's a well known form of insanity. Paranoia- isn't that what they call it? Rush of blood to the head, followed by a general running amuck. I've heard fellows who have been in India talk of it. Natives get it. Don't know what they're doing, and charge through the streets taking cracks at people with dashed whacking great knives.
I was surprised to find not two but five or six instances throughout the Life of Blandings where the tropics were used with great dexterity and with to make fantastic allusions to degrees of madness and insanity that can manifest themselves in humans. I was far from outraged when I read these things :-). However, they invariably led me to reflect upon the biases that writers carry in spite of not wanting to be labeled as such. My only take-home from this is that in the process of being funny and witty, one just ends up being squarely obnoxious and unjust to a largely heterodoxical culture, worthy of kinder words. Such misrepresentation is more of an indicative verdict on the intellectual limitations of the author as compared to being defamatory on the an entire culture/community. I still stand by my love for Wodehouse and Conan Doyle - they are to me, the greatest comedy and mystery writers respectively and absolute masters of the English language. No reader can miss the feeling of a rejuvenated ability to write and speak after reading a single chapter of any book by either of them. But a writer must exercise caution; it is easy to get carried away forgetting that there is a thin red line separating satire and stupidity.


I made an honest confession to myself yesterday- I suck at math puzzles. Unless the puzzle has a familiar character, attacking the conundrum is to feel like a monkey trying to pluck a banana using two long wooden sticks. To begin with, he feels confident and sophisticated thanks to the impeccable machinery in possession- sticks and opposable thumbs. But he soon realizes that neither of the sticks is long enough to reach the banana and finds himself unable to conjure a successful contraption with the tools at hand. Incapacity turns into frustration and the monkey begins to gnaw his teeth in exasperation. And finally, he ends up doing what he always wanted to avoid- break the entire creeper with his might for that one measly banana. That's the (similar) feeling that this monkey gets when all intuition fails and one has to resort to the savage way of doing puzzles. And when out pops an elegant solution from a smarter friend or the answers on the back of the book or the bottom of the page, one feels really really stupid.

I spent a nearly half an hour trying to write down the solution to a pretty looking problem that was suggested by Onkar yesterday morning- Given any group of 6 people, prove that you can always find a sub-group of three individuals that has one of the following properties - (a) Everybody knows everybody in that group (b) Nobody knows anybody in that group. (Also, assume that only two kinds of relationships exist between a pair of individuals- they either know each other or they don't; eliminating one-sided acquaintances). I have this infatuation with generalization. Naturally I started playing with variables, started writing comprehensive combinatorial possibilities, applying PHP and doing all sorts of tortuous things that only made life more difficult. Ultimately, I arrived at a solution that I knew was far from elegant as soon as I had finished it. A complicated solution is worth the effort if it leads to new insights about the problem- (say) like what should be the minimum number of people to make the same statement about groups of four, five, etc. But my solution was a mess; brute, lacking any new insight and boring.

But I still felt the relief of solving a problem; or to rephrase, this was how I felt until I heard the solution from Onkar, after which I felt incredibly stupid, like a monkey who's outsmarted by a smarter monkey in the banana game. The elegant solution proceeds like this. Imagine you are one of those five people. Then (convince yourself) that there will be (at least) three people, all of whom are either your acquaintances or completely unfamiliar. Assume without loss of generality that it is the former case (for if it is the latter, the arguments are completely analogous). Now among the three people who are your acquaintances, if you can find two persons who know each other then, combined with you, we have a group of three individuals, all acquaintances of each other. If this does not happen, then we have three individuals, all strangers and we have the required set. Complementary arguments apply if the original set of three are complete strangers to you and it can be trivially seen that one can always find a set of three individuals satisfying either of the two properties required. Incidentally, one needs a minimum of seventeen people (I haven't checked this yet) to be assured of having a sub group of four individuals who are all acquaintances or complete strangers.

Well, I have reconciled myself to this fate of mine- I suck at math puzzles. However, there have been a handful of times when I have felt the bulb glow in my head while working on a puzzle/problem and those times have been memorable. But the great thing about these puzzles even to someone who is fairly mediocre at solving them like me is that solutions often contain brilliant insights that stretch your intuition. In spite of possessing fairly competent analytical skills, people often get their intuition wrong with these puzzles. The best examples come from those involving probabilistic reasoning involving variable change (or conditional probability). I shall quote two examples:

1. The first is the often mentioned Monty Hall Problem or The Game Show Host problem- You are playing a game show where the host shows you three shut doors (A, B, C) and asks you to select one. In one out of the three doors lies the sports car of your dreams while inside the other two, sits a goat each. You select 'door A' because your mother's name starts with the letter 'A' and you think that will bring you luck. The host the opens door 'C' that contains a goat, and asks you, "Mr. K, so would you like to stick with door A or would you like to switch your choice?". The question is, what must you do to maximize the chances of winning the car? Stick or switch?

There used to be a show called 'Khulja Sim Sim' on television some years ago with the same format. And whenever confronted with above question, most people used to stick to their choices. There is a certain sense poetic justice, a moral high ground that people associate with following a set of ideals and that makes them avoid caprice. I am not aware of the statistics of the show but I won't be far from the truth if I claimed that two out of three people who would have stuck to their choices would have ended up with the goat. That's what simple probabilistic bookkeeping tells us. Though I cannot remember the exact details, I think I was properly bowled by this question when I had heard it first as a kid. It is very likely I would have felt that the prudent (and moral) thing to do is to stick to your choice.

Now that I know the solution to the problem (if you switch, you are likely to win the car 2 out of 3 times), I know what was wrong in my thinking so. But since the time I understood the problem, I have posed this question to many people and I have observed that it shocks most of them. It was just yesterday when I communicated the problem and explained its solution to an acquaintance and while he acknowledged the solution he kept wondering that there was some 'deep mathematical flaw' in the reasoning. It is not surprising that when Marilyn vos Savant posed the problem and the solution in 1984, many people, including PhD graduates and professors disagreed with her solution. In spite of the fact that the mathematical reasoning was as clean as a virgin's honeypot (and not terribly difficult either, one had to simply account for the conditional probability) vos Savant arguments had to be validated using computer simulations and mock trials in classrooms. I shall not bother writing down the solution here; it can be looked up online in hundreds of sites.

2. The other problem is called the double toss problem and is much more straightforward compared to the earlier one. The problem goes as this: I have tossed a coin (assume unbiased) twice and I tell you that one of the tosses turned out to be a head. I ask you the probability that the other toss was also a head.

Most respondents (primarily non-mathematicians) tend to answer half as the probability. Their reasoning is simple yet specious - since the tosses are independent why would the outcome of the other toss depend upon this one. While this is true in the literal sense, the context of the problem asks you to go a little deeper. To make a small digression, suppose I told you instead that my first toss was a head and asked you what is the probability that the second toss turned out to be a head. Many people cannot differentiate between this and the original problem. Yet they are fundamentally different.

Let us look at the set of possible outcomes of the two tosses - TT, TH, HT, HH, each with a probability 0.25 with H denoting 'head' and T denoting a 'tail'. Now when I say that 'one of the tosses turned out to be a head', this confines us to the sample space - TH, HT, HH. Now the only case where both the outcomes were a head is the case 'HH' but since it is one of three possible outcomes, the chance associated with it is 0.33. But when I say that 'the first outcome was a 'head'' as in the second case, the set of possible outcomes are - HT and HH. In this case, the probability is 0.5.

Interestingly, even this problem created a lot of controversy leading to lot of experimental validation in spite of a clean mathematical explanation. But the funny part is that the problem was not posed in this form in its original version. The original problem went something like this : You meet a person who confesses to having two children. If she tells you that one of them is a boy, what is the probability that the other one is too. Incidentally, survey forms were dispensed to mothers known to have two children of whom one was a boy to calculate the chance that the other one was too. The survey results showed that 35 % of respondents had a second boy-child, a figure that is close to 33% than to 50%. But it is nonetheless funny that such an experimental validation had to be carried out to resolve a clean mathematical argument (assuming of course that the sex ratio was 1:1).

While I often despair my lack of the fast mathematical intuition to penetrate such simple yet confounding problems, I am happy to know that I can fairly easily grasp the arguments that explain these riddles. I refer to the feeling as 'enjoying artificially sweetened sour grapes' :P.

Tuesday, 27 May 2008

Article on Predatory growth in India

The Economist recently speculated that the inflation rate could hit 10 percent, stated a CNN-IBN article that I came across yesterday. This is despite the fact that this year, India is all set to register a record growth rate. Those of us who commonly cite the Chinese model of economic growth might want to know that both India and China have suffered this paradoxical phenomenon- a high rate of growth going brothers-in-arms with increasing economic inequality among classes.

The problems of welfare and developmental economics are really deep and complex. Many (including me) cannot even get their dialectic parlance beyond commonalities like 'free-market economy', 'socialism', 'demand elasticity' or 'marginal utility'. And I couldn't disagree more with G. B. Shaw who insinuated that the economists were a group who if laid end-to-end, could not reach a conclusion. They are a set of people I have come to deeply respect for their ability and courage to articulate these problems so well. But I often wonder whether the ability to penetrate conventional wisdoms to disinter latent insights ever translates into good public policy.

I came across this article yesterday and it was one of the most deep and perceptive essays that I have read in recent times. Only after finishing the article did I find out that the author was an emeritus professor at JNU, Delhi (such thoroughness and erudition can come only from an academic) by the name of Amit Bhaduri. On the problem of China/India growth-inequality paradox, Bhaduri delineates:

A central fact stands out. Despite vast differences in the political systems of the two countries, the common factor has been increasing inequality accompanying higher growth. What is not usually realized is that the growth in output and in inequality are not two isolated phenomena. One frequently comes across the platitude that high growth will soon be trickling down to the poor, or that redistributive action by the state through fiscal measures could decrease inequality while keeping up the growth rate. These statements are comfortable but unworkable, because they miss the main characteristic of the growth process underway. This pattern of growth is propelled by a powerful reinforcing mechanism, which the economist Gunner Myrdal had once described as ‘cumulative causation’. The mechanism by which growing inequality drives growth, and growth fuels further inequality has its origin in two different factors, both related to some extent to globalisation.
I strongly recommend the article to anyone who, like me, has felt the paralysis from old cliches and the lack of fresh perspectives while discussing these issues. With the UPA brandishing the increasing growth rate as the natural panacea to all the socioeconomic inequalities that continue to affect nearly a quarter of our population, with evangelical platitudes like "high growth will soon be trickling down to the poor" being constantly mouthed, this article analyzes the apparent Indian economical dilemma- is product growth going to really solve the problems of inequality in India?

Bhaduri's critique of 'predatory growth' can be summarized by a quote forwarded to me by Anirudh Patil (who incidentally was responsible in leading me to this article) - Growth for the sake of growth is the ideology of a cancer cell.

Monday, 26 May 2008

McCain can?

An excerpt from an article describing Senator John McCain's health reports:

The doctors also said McCain has occasional momentary episodes of dizziness when he suddenly stands up, high cholesterol, blood in his urine from an enlarged prostate and kidney stones. Additionally, McCain had his most recent colonoscopy in April, when six benign polyps were removed.

He also suffers from degenerative arthritis in his joints from broken arms, legs and shoulders suffered when his plane crashed in Vietnam.

His medical records revealed that he takes simvastin to control his cholesterol, hydrochlorothiazide for kidney stone prevention, aspirin for blood clot prevention, Zyrtec for nasal allergies and a multiple vitamin tablet.

If McCain is elected (personally I hope he doesn't for I have reasons to fear the Republicans), he would become the oldest President in the history of the United States. Apart from what is mentioned above, the article stated that the Senator's history puts him at increased risk of skin cancer. He also recently underwent treatment for a 'minor skin cancer in his leg'.

But in true Monty Python style, the same article concludes:

However, McCain’s age is not a problem for voters, according to recent national polls. Now that the medical records are also in the open and do not reveal worrisome health conditions, he is more than ready to compete.

Inscrutable is our appetite for contradictions and absurdity!

Kaifi aur main

He often finds himself in the society of things that leave him overawed and humbled. He can locate his position in many of these situations; a mute witness to an unconquerable, brilliant expression of art. And like Salieri, he curses God to have given him the longing but denied him the talent. All his vanity and hubris are uprooted mercilessly and flung beyond the horizons of his imagination. His identity thins beyond recognition and the only place he finds solace is in the gentle indifference of the world that has accommodated his mediocrity long before finding a place for him in its vast bosom. Nothing defeats a person like a beauty that he can sense but cannot conquer. Nothing makes him feel more human.

I saw a play in Urdu yesterday. On recollection, I cannot help but think that every moment of that play was pure gold and I am yearning to catch it once again. Bearing the yoke of an unfamiliar language was certainly a severe limitation, yet the feeling that I experienced was that of a wanderer who had fortuitously arrived into a foreign land where, despite the atrophy of language, he could understand the feelings of the native culture better than those of its own. The machinery of expression was more friendly and even without resorting to sophistication, it was pregnant with the inconceivable variety of human experience.

I am reminded of Jack Kerouac immortal lines (Source: On the road):

"..and I shambled after as I've been doing all my life after people who interest me, because the only people for me are the mad ones, the ones who are mad to live, mad to talk, mad to be saved, desirous of everything at the same time, the ones who never yawn or say a commonplace thing, but burn, burn, burn like fabulous yellow roman candles.."

However I try, I can simply not get myself to write a part by part review of the play. It suddenly seems a task too formidable and it would be presumptuous of me to make a half-hearted attempt. I shall refrain.

Saturday, 24 May 2008

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.

Friday, 23 May 2008


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!"


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".

Wednesday, 21 May 2008

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


Thanks to Vaibhav Devanathan, I have a huge notepad file filled with wonderful anecdotes of scientists and mathematicians albeit in a very haphazard manner, with parts of text transposed from one part to another. To add to my travails, most anecdotes need to be set into prose too; many of them are just points exchanged in e-mails. Nevertheless, some of these anecdotes (or urban legends) are truly remarkable and I feel they are worth the effort of deciphering. But since the task is formidable, I am going to do it bit by bit; so this should be a 3-4 part series starting the current one.

1. A mathematician bought bread once a day from his local baker. The bread was supposed to weigh 1 kilo but afer a year of record keeping the mathematician found a nice normal distribution with mean 950 gr. He called the police and they told the baker to behave himself. One year later the mathematician reported to the police that the baker had not reformed. The police confronted the baker and he said "How could that dastardly math guy have known that we always gave him the largest loaf?

The mathematician then showed the police his record for this year which was again a bell shaped curve with max at 950 gr. but truncated on the left side. The mathematician was none other than Henri Poincare.

2. The Hungarain mathematician Paul Erdos, one of the most prolific mathematicians in history was always making jokes about how old he was. (He said, for example, that he is two and a half billion years old, because in his youth the age of the Earth was known to be two billion years and later was known to be 4.5 billion years.)

He observed one day that the audiences at his talks had been getting larger and larger, to the point where they filled halls so big that his old and feeble voice could not be heard. Erdos speculated as to the cause of this. "I think," he said, "it must be that everyone wants to be able to say "I remember Erdos; why, I even attended his last lecture!"

3. Paul Erdos had his own peculiar language. The following is the glossary of terms that he employed and what they actually meant.

  • Supreme Fascist = God (Also abbreviated as SF. A person who hides Erdös's socks, glasses, Hungarian passport and kept the best equations to himself)
  • straight from the book = beautiful, elegant proof (book of the SF)
  • boss = woman
  • slave = man
  • captured=married
  • liberated = divorced
  • recaptured= remarried
  • epsilon = child, or a little
  • to preach = to deliver a math lecture
  • to exist = to do math
  • to die = to stop doing math
  • trivial being = someone who does not do math
  • Joe (USSR) = for Joseph Stalin
  • Sam = USA
  • Sam and Joe show = international news
  • On the long wavelength = communist (red)
  • On the short wavelength = fascist (opposite of red)
  • noise = music
  • poison = alcohol
  • my brain is open = I am ready to do mathematics
  • when was it alive? = what kind of meat is that?

From the journal of misapplied anthropology

This, is by far one of the best polemics against Creationism that I have read in recent times. Aah, I wish that I could imbibe some of this razor sharp wit and the skill to hit the nail on the head with precision! As usual, for people who don't want to read the entire thing, I shall leave some excerpts.


Two gentlemen, both with what one might term a mild delusion -- they are deeply involved with people who don't exist. Both spend a lot of money on this obsession. Both can recite, at length, the putative words, thoughts, and deeds of their fictional obsessions. Both have allowed the ideals expressed by these non-existent beings to shape their lives, and both proudly proclaim their allegience in a sect of followers. Despite this odd obsession, both men hold down jobs, have families, pay taxes, and commit no more than trivial crimes, such as jaywalking, or speeding, or ripping the tags off of mattresses. One of these men, though, has a serious problem -- he won't acknowledge the fictious nature of his fantasy friend. The other one has no such difficulty distinguishing between reality and fantasy.

Yet, in our society, the former is considered normal and healthy -- while the latter is, at best, a figure of mockery, at worst, a reviled outcast.

The former man, you see, is a 'Christian', and the fictious being he admires is called 'God'. The latter is a 'Trekker' and his fictional focus is called 'Mr. Spock'.


Given how unhealthy and destructive religious beliefs are, you would think fandom would be lauded and praised. No fan of Star Trek ever went to court to demand that warp drive theory be given 'equal time' with the theory of Relativity, as Creationists have done with Evolution. No matter how vicious the Internet flame wars between fans of Star Wars and Star Trek, no one has yet been burnt at the stake for heresy. Not even the most fanatical follower of Mr. Spock would voluntarily limit himself to sex once every seven years (if the opportunity for more frequent matings ever arose), yet thousands of followers of Jesus voluntarily suppress the most fundemental, basic, human urge for their entire lives. Some women even claim to be the BRIDES of this fictional being, living forever in an unconsummated relationship with a man who does not exist. Compared to that, two Trekkers getting married in Klingon garb is postively wholesome. At least the 'Klingons' will probably have sex at some point.

3. This one is my personal favourite:

Religion is needed to inspire men to do good deeds? If a man chooses pacifism because Yoda said that anger is the path to the dark side, rather than because Jesus told him to turn the other cheek, is he any less of a pacifist? Marcus Welby undoubtedly inspired many to become doctors;Perry Mason, many to become lawyers. The usefulness of incarnate ideals to serve as our guides and inspirations is beyond doubt -- but there is grave danger when we forget these incarnations are just the creations of other men.

Tuesday, 20 May 2008

Shāntatā! Court Chālu Āhe

Where Abraham Lincoln emphatically proclaimed that "this nation shall have a new birth of freedom — and that government of the people, by the people, for the people, shall not perish from the earth" more than a hundred and fifty years ago, interesting questions are being raised while debating the exact role of the judiciary in a democracy in 2008. Understandably, dissenters against the recent Californian lift of the ban on gay and lesbian marriages see the decision as "symptomatic of judicial activism that thwarts the will of the people and their elected representatives". This, I guess definitely raises a higher question, one that is often repeated during the course of history - Should the state machinery enact decisions that are against popular public opinion but which, according to it, are morally expedient? Or should it let the public zeitgeist take its own course? Interestingly, even the supporters of gay and lesbian marriages have "questioned the wisdom of the court intervening when public opinion is shifting toward support of gay marriage in any case".

See this op-ed article in Washington post for some interesting bits of history on the legacy of court rulings in America where the entire nation awakens to an inquitous social institution remembering "the principles of the Declaration of Independence which are guaranteed by the Bill of Rights and the Fourteenth Amendment . . . that all human beings have equal rights . . . and that the right to liberty and the pursuit of happiness is inalienable".

So is such judicial intervention a blessing or a curse to the positively evolving moral zeitgeist in a modern democracy? The author succintly concludes:

So was last week's ruling an impetus or impediment to that process? My hunch is that by basing the case for the right to intra-gender marriage so clearly and forcefully on the doctrine of equal rights, the court situated gay marriage not only in an established body of law but also within the essential definition of America. Opposition to gay marriage is most commonly rooted in tradition, religious tradition in particular. But the ideas that all men are created equal and have an inalienable right to the pursuit of happiness are the traditions that define our nation, and by basing its decision on those premises the court did gay rights, and American ideals, a huge service.

As to what the vanguards of our judicial system have been upto, this CNN-IBN article makes some timely revelations :P

Monday, 19 May 2008

I spent the last two hours reading about this remarkable man who is confronting the worst form of iniquity in our country currently. Thanks to a recent post on a friend's blog, I learned about Dr. Binayak Sen, a public health specialist of international repute and the national vice-president of the People's Union of Civil Liberties (PUCL) , Chhattisgarh. Dr. Sen was arrested in May 2007 for alleged links with Maoist groups under the CSPSA and UAPA provisions, that allow for arbitrary detention denying the right to appeal. Dr. Sen had been actively involved in criticizing the unlawful encounter killings of several adivasis in the state through government controlled civil militia under the pretext of eliminating Naxal activities. The following statement was issued by Dr. Sen a few months before his arrest:

we are seeing all over India - and as part of that in the state of Chhattisgarh as well - a concerted programme to expropriate from the poorest people in the Indian nation, their access to essentials, common property resources and to natural resources including land and water... The campaign called the Salwa Judoom in Chhattisgarh is a part of this process in which hundreds of villages have been denuded of the people living in them and hundreds of people - men and women - have been killed. Government-armed vigilantes have been deployed and the people who have been protesting against such moves and trying to bring before the world the reality of these campaigns - human rights workers like myself - have also been targeted through state action against them. At the present moment the workers of the Chhattisgarh PUCL (People's Union for Civil Liberties) the Chhattisgarh branch, of which I am General Secretary, have particularly become the target of such state action; and I, along with several of my colleagues, are being targeted by the Chhattisgarh state in the form of punitive action, illegal imprisonment. And all these measures are being taken especially under the aegis of the Chhattisgarh Public Security Act.

According to online sources, this man has been kept in solitary confinement for the past eleven months while no conclusive evidence has been found to substantiate his alleged Maoist links. It is unfortunate that a man who has devoted himself to serve the public sphere finds himself the victim of an unlawful state, a corrupt police and an impotent judiciary. The case for Dr. Sen has found support from eminent personalities like Noam Chomsky, Amartya Sen, Ramachandra Guha, Arundhati Roy, filmmaker Shyam Benegal and the Magsasay award winning journalist P. Sainath. About a month ago, the Global Health Council announced that Dr. Sen had been selected to receive the most prestigious international honour in Global Health and Human Rights, the Jonathon Mann award. "The Mann Award is presented annually at the Global Health Councils international conference to "a practitioner who makes significant contributions toward practical work in the field and in difficult circumstances; highlights the linkage of health with human rights; works predominantly in developing countries and with marginalized people; and demonstrates serious and long-term commitment". Less than a week ago, twenty two Nobel laureates from around the world wrote India's President, Prime Minister and the Chhattisgarh state authorities to release Dr. Sen.

I strongly urge that you read about this man and perhaps think of casting a vote on this online petition form. It isn't much to be proud about but the least we can hope is that our armchair activism reaches some considerate ear that has the ability to restore a man his right to dignity and liberty.

Sunday, 18 May 2008

Divorce rates and the indian dream

Amit Varma, in his recent post, articulates on how modernization and technology have bridged the gap between the sexes in recent times. Interestingly, he titles his post 'We Should Celebrate Rising Divorce Rates' and I would imagine he does that with a tongue in his cheek. Though his thesis seems convincing on first read, some clear counterexamples came to my mind in the very beginning. One is that of Kerala, where the empowerment of women has not really been fostered by the advent of modern technology. The matrilineal system is known to have existed in the state since ages. The second counterexample is that of an Islamic country like Saudi Arabia, where, in spite of technological sustenance, the condition of women in society remains decadent thanks to the preponderance of the Shariah laws.

Mr. Varma is perhaps correct in his main thesis- that increasing divorce rates in a country like India is definitely indicative of women empowerment. But I feel he is simplifying the causal connections associated with the empowerment of women in society. For a portrait of 19th and early 20th century British society, I'd recommend a reading of Virginia Woolf's AROO, an essay that I briefly talked about in an earlier post. That said, the quality of life that women in Kerala enjoy (literacy rate of 97% against the national average of 55%; sex ratio of 1.06 as opposed to the national avergae of 0.93; highest and lowest life expectancy and infant mortality rates in India) is something that I find immensely surprising and at the same time ennobling. One finds writers like Amartya Sen (in The Argumentative Indian and Development as Freedom) and Shashi Tharoor (in his India:From Midnight to the Millenium and the more recent The Elephant, the tiger and the cellphone, a collection of essays on India) raving about the Kerala miracle. Sen, tries to articulate some reasons for these successes but I still feel there remain lessons to be learned - for Mr. Varma and the rest of us too.


Subrahmanyan Chandrasekhar, perhaps the greatest astrophysicist of the twentieth century, loved to tell the story of a visit to Princeton in the mid 1980s, where he was feted in honor of his recent Nobel Prize. At the dinner, he found himself seated next to an earnest young man. As physicists often do to make conversation, he asked his dinner companion, "What are you working on these days?" The reply was, "I work on string theory, which is the most important advance in physics in the twentieth century." The young string theorist went on to advise Chandra to drop what he was doing and switch to string theory or risk becoming as obsolete as those in the 1920s who did not immediately take up quantum theory.

"Young man," Chandra replied, "I knew Werner Heisenberg. I can promise you that Heisenberg would never have been so rude as to tell someone to stop what they were doing and work on quantum theory. And he certainly would not have been so disrespectful as to tell someone who got his PhD fifty years ago that he was about to become obsolete."

- From "The trouble with physics" by Lee Smolin

Saturday, 17 May 2008

Vanity and vada pav

Some interesting historical comments about Mumbai along with the washing of Thackeray's (or should I say Thakre) dirty linen in true editorial fashion in this HT article. The other hilarious piece of news that I heard recently was the possibility of the ubiquitous vada pav being patented by Shiv Sena as an exclusively Marathi recipe. They want to rechristen it to Shiv vada pav. Other repercussions notwithstanding, my primary concern is the collateral damage it will cause to my father's love for the mumbai ispecial delicacy. Vada pav might lose one of its more loyal connoisseurs to the brickbats of marathi chauvinism. Happily touring the US right now, my father doesn't know what's in store for him when he steps out of Sahar, oops....Chattrapathi Shivaji International airport.

Same-sex marriage

A commendable resolution from the californian judiciary as this article suggests. And while the Chief Justice's statement - The essence of the right to marry is freedom to join in marriage with the person of one’s choice- noteworthy his comparison of same-sex marriage with inter-racial union was a bit enterprising, I thought. Notice the following criticism of the resolution. And while it might have its wisdom in Christian bigotry as opposed to scientific reasoning, I couldn't help noticing that it conveyed a fundamental point:

“Sure, it works at the surface level,” Mr. Stewart continued. “But it is actually defeated by the deeper reality of marriage itself. Marriage in its deep logic has nothing to do with race and everything to do with the union of a man and a woman. To apply Perez in the genderless marriage context is actually to betray it.”

A silly question popped up in my mind by the time I was finished with the article, the latter part of which was pretty uninteristing- Is it necessary for two sexes to exist in higher forms? Is there a distinct biological/evolutionary advantage to it?

Monday, 12 May 2008

From Woolf's AROO

Thanks to Deepa Nair, I had the good fortune to read Virgina Woolf's A Room of One's Own, one of the greatest feminist essays of the 20th century. It was 'Feminism 101' for me personally, and I tried to read it dutifully suppressing any preconceived biases of what the area ought to be about. It would be an understatement if I said that I was overawed by Woolf's masterful prose that sparkled with a rare genius combining depth, vision and balance. It is beyond me to write my own views on the subject and I shall stay clear from untrodden paths. For now, I quote two passages from the essay:

1. In the first passage, Woolf emphasizes that writers, especially practitioners of fiction should consciously avoid a sexual bias in their endeavors, something humans seem to be naturally predisposed towards.

Even so, the very first sentence that I would write here, I said, crossing over to the writing–table and taking up the page headed Women and Fiction, is that it is fatal for anyone who writes to think of their sex. It is fatal to be a man or woman pure and simple; one must be woman–manly or man–womanly. It is fatal for a woman to lay the least stress on any grievance; to plead even with justice any cause; in any way to speak consciously as a woman. And fatal is no figure of speech; for anything written with that conscious bias is doomed to death. It ceases to be fertilized. Brilliant and effective, powerful and masterly, as it may appear for a day or two, it must wither at nightfall; it cannot grow in the minds of others. Some collaboration has to take place in the mind between the woman and the man before the art of creation can be accomplished. Some marriage of opposites has to be consummated. The whole of the mind must lie wide open if we are to get the sense that the writer is communicating his experience with perfect fullness. There must be freedom and there must be peace. Not a wheel must grate, not a light glimmer. The curtains must be close drawn. The writer, I thought, once his experience is over, must lie back and let his mind celebrate its nuptials in darkness. He must not look or question what is being done. Rather, he must pluck the petals from a rose or watch the swans float calmly
down the river.

2. This passage in many ways, is a microcosmic mirror of the entire essay. It captures Woolf's thesis (that a woman requires a room of her own and an income of five hundred pounds a year to be able to pursue something as transcendental as writing fiction) and her call for the emancipation of women.

‘What are the great poetical names of the last hundred years or so? Coleridge, Wordsworth, Byron, Shelley, Landor, Keats, Tennyson, Browning, Arnold, Morris, Rossetti, Swinburne—we may stop there. Of these, all but Keats, Browning, Rossetti were University men, and of these three, Keats, who died young, cut off in his prime, was the only one not fairly well to do. It may seem a brutal thing to say, and it is a sad thing to say: but, as a matter of hard fact, the theory that poetical genius bloweth where it listeth, and equally in poor and rich, holds little truth. As a matter of hard fact, nine out of those twelve were University men: which means that somehow or other they procured the means to get the best education England can give. As a matter of hard fact, of the remaining three you know that Browning was well to do, and I challenge you that, if he had not been well to do, he would no more have attained to write SAUL or THE RING AND THE BOOK than Ruskin would have attained to writing MODERN PAINTERS if his father had not dealt prosperously in business. Rossetti had a small private income; and, moreover, he painted. There remains but Keats; whom Atropos slew young, as she slew John Clare in a mad–house, and James Thomson by the laudanum he took to drug disappointment. These are dreadful facts, but let us face them. It is—however dishonouring to us as a nation—certain that, by some fault in our commonwealth, the poor poet has not in these days, nor has had for two hundred years, a dog’s chance. Believe me—and I have spent a great part of ten years in watching some three hundred and twenty elementary schools, we may prate of democracy, but actually, a poor child in England has little more hope than had the son of an Athenian slave to be emancipated into that intellectual freedom of which great writings are born.’

Nobody could put the point more plainly. ‘The poor poet has not in these days, nor has had for two hundred years, a dog’s chance . . . a poor child in England has little more hope than had the son of an Athenian slave to be emancipated into that intellectual freedom of which great writings are born.’ That is it. Intellectual freedom depends upon material things. Poetry depends upon intellectual freedom. And women have always been poor, not for two hundred years merely, but from the beginning of time. Women have had less intellectual freedom than the sons of Athenian slaves. Women, then, have not had a dog’s chance of writing poetry. That is why I have laid so much stress on money and a room of one’s own. However, thanks to the toils of those obscure women in the past, of whom I wish we knew more, thanks, curiously enough to two wars, the Crimean which let Florence Nightingale out of her drawing–room, and the European War which opened the doors to the average woman some sixty years later, these evils are in the way to be bettered. Otherwise you would not be here tonight, and your chance of earning five hundred pounds a year, precarious as I am afraid that it still is, would be minute in the extreme.

Sunday, 11 May 2008

Of the past


It's playtime.
I want to undress you
with these eyes
and play
those delightful games
that we had invented
in the past.

I hope you play your part
and help me up
whenever I fall.

do not desert me
when I am blindfolded,
helpless and alone.


Unmoved by those who suffer,
Unaffected by the chirping sparrow,
Inconsiderate of the those below,
Oblivious to the plaintive roar
pleading its way through extinction.
Our lives are
a characteristic immoderation,
anesthetically impervious
to evocation.


The colours
bled through the sky
as the twilight undressed
and disbursed
the remains of a yellow sun.
The elements descended into her
and found welcome.
They were released
that night;
with the parting
of her legs.

Improvising on a quote I heard a while ago - Activity is surgery without anesthesia; Imagination is anesthesia without surgery. Experience is what one needs :-). Clearing my gmail inbox is my way of revisiting the past these days. That is how I happened to chance upon these little friends.
All of us probably remember the time when the papers were filled with outrage from the intelligentsia following Bal Thackeray's endorsement of Adolf Hitler. The demagogue, surprisingly, stood by his admiration for Hitler even after the criticism. While this might not even be a passing thought for many of you out there, I was intrigued by the possible causes behind this 'telepathic' connection. It is true that we find it plausible that Thackeray can draw inspiration from the life of Hitler (it definitely seems more plausible than the case of Hitler himself who confessed to have been guided in his mission by the music of Wagner) but I still find that the causal connection needs to be articulated. To me, Hitler was acknowledgedly a great mobilizer of masses and a propagandist of unprecedented competence, being able to steer an entire country using his fiery speeches and idealogical harangues. On the other hand, I find myself incapable of separating this acknowledgment of Hitler from a fundamental belief that he was a psychotically deluded man to have committed the atrocities that he did. Notwithstanding his other qualities, Hitler's commitment to his belief that the extermination of an entire ethnic body could resurrect a nation from its economic and social problems is nothing but a delusion and I personally find it impossible to look at him as a role model in any mode of representation or interpretation.

Let me now quote a passage from Amitav Ghosh's essay The Fundamentalist Challenge to invoke his views on the subject of the 'telepathic connection' that I mentioned earlier (People who have read the piece will forgive me for a contrived juxtaposition. While Ghosh does not particularly deal with Thackeray's admiration of Hitler, it is I who has taken the liberty of transporting Amitav Ghosh to the present context for I believe that the views apply):

I was amazed because I could not immediately understand why extremist Hindu beliefs should translate so fluently into sympathy for a group that had no religious affiliations at all, a group whose ideological genealogy ought to have inspired revulsion in these middle-class professional men. It only became obvious to me later, reading reports from Bosnia, Croatia, Sudan, Algeria, Sri Lanka, and other strife-torn lands, that for this species of thinking, religion, race, ethnicity, and language have no real content at all. Their only significance lies in the lines of distinction they provide. The actual content of the ideology, whether it manifests itself in its religious avatar or its linguistic or ethnic one, is actually the same in every case, although articulated through different symbols. In several instances- Sri Lanka, for example- extremist movements have seamlessly shifted their focus from language to religion.

What then is this ideology that can travel so indifferently among such disparate political groups? I believe that it is an incarnation of a demon that has stalked liberal democracy everywhere throughout this century; an ideology that, for want of a better word, I shall call supremacism. It consists essentially in the belief that a group cannot ensure its continuity except by exerting absolute cultural and demographic control over a particular stretch of geography. The fascist antecedents of this ideology are clear and obvious. Some would go further and argue that nationalism of every kind must also be regarded as a variant of supremacism. This is often but not necessarily true. The non-sectarian, anti-imperialist nationalism of a Gandhi or a Saad Zaghloul was founded on a belief in the possibility of relative autonomy for heterogeneous populations and had nothing to do with asserting supremacy.
These are thoughts that must have struck many of us in some form or the other. George Bernard Shaw's following famous quote, "Patriotism is your conviction that this country is superior to all other countries because you were born in it" probably applies to every other form of identity where supremacism manifests.