Tuesday, August 31, 2010

The Great Mathematics Bazaar II: Music lectures

It came as an enormous (and pleasant) surprise when Prof. Raghunathan asked me, nearly a year ago, whether I would be willing to give a lecture or two on Indian classical music appreciation at the ICM. The idea would be to present some aspects of Indian culture to the participants, specially those from outside India, and to prepare them to some extent for the planned live concert. Accordingly I gave two lectures, one on Sunday August 22 and the second on Tuesday August 24. The vocal concert by Ustad Rashid Khan took place on August 25.

During my first lecture the sound and video (files embedded in my powerpoint presentation) worked well, and speaking in Hall 2 was a thrill since it was there that Vishwanathan Anand, a couple of days later, played simultaneous chess against 40 participants (apparently unmoved by the gratuitous questions about his Indian-ness or lack thereof).

The second lecture was held in the infinitely larger Hall 4, and like everything conducted there, was videotaped. Hall 4 was even more of a thrill given that I was on the stage where the President of India and the Fields medallists had stood a few days earlier, but for me the thrill quickly evaporated when the sound failed to work and some time was wasted getting things in order. The video of this session can be viewed by going to this page and selecting Part 3 under "24th Aug 10 Time 15:00 – 18:00 /Hall4" or you can download this flv file. Unfortunately due to the sound problem, by the end of an hour I was only 45 minutes into the talk. Since the video was programmed for an hour, it failed to capture the last 20 minutes (in which incidentally Pandit Kumar Gandharva features twice).

Now about the content of the talks. I was asked by the press unit there (= R. Ramachandran, better known as "Bajji") to send a writeup for the ICM daily newsletter, so I might as well reproduce that here.

Titled "A Mathematician's Guide to Hindustani Classical Music", this pair of talks on the musical tradition of North India has been put together specially for the ICM. The first talk presented a brief history of Indian music, which has its roots in religious chanting from Vedic times around 5000 BCE. The textbook "Natya Shastra " by Bharata, the basis for the Bharata Natyam dance form presented at the ICM on Friday, has some reference to this music, and more details including an embryonic concept of raga appear in Matanga's Brihaddeshi in the 8th century. By around the 11th century Persian and Arabic influences started to enrich the music and around this time the North and South Indian streams of music began to diverge. The present lectures focus exclusively on the North Indian or "Hindustani" tradition, which will be presented at the ICM in a live concert by Ustad Rashid Khan on Wednesday.

The nature of Hindustani music evolved during the 12th to 18th centuries, partly in response to the Bhakti movement in Hinduism, in which participatory and devotional love for the divine being (rather than formal worship of God as an idealised entity) became the principal theme. Another contributing factor was the patronage of the Mughal emperors. By the 18th century the "khayal" form of music was established. It remains an oral tradition even today, despite many books and treatises on the subject, some of which have established a rudimentary notation.

In the first of these talks, the notion of raga is introduced by playing short clips of pairs of performances, by different musicians, of the same raga. The common features between the members of a pair serve to illuminate the concept of the raga, even to a complete novice. A definition can then be built up through a series of successive approximations. In its barest form, a raga is a set of notes selected from the 12 notes of the musical scale. But then these notes must be combined into patterns following certain rules. One can emulate the definition of a topological space in mathematics by saying that a raga R={S,U,T} is a subset S of notes from the musical scale together with a collection U of subsets of S and a set T of rules for combining elements of U! But art is not mathematics, so we need to add an aesthetics clause: the rules for combination must give rise to desirable results and create an appropriate mood. It is this mood that lies at the heart of a raga, which some authors consider to be a "living entity" rather than a mere combination of proportions and form. Parallel to raga, the concept of tala (rhythm) is briefly developed.

In the second talk the notion of "gharanas" or schools of music is briefly introduced (parallels with mathematics are quite strong!) and video clips used to illustrate some of the instruments and show how they are played. This is followed by a description of the structure of a typical performance, the different types of movements (introductory, slow and fast) and the complementary role of compositions and variations. The bulk of the talk consists of audio and video clips of performances by some of the leading musicians of India (many of them sadly no more) illustrating different segments and features of a performance. In selected cases the lyrics and their significance are highlighted. The association of ragas with times of day and seasons is also briefly discussed. The talk closes with a short outline of the "lighter" forms: thumri, tappa and bhajan that are usually performed towards the end of a concert.

Monday, August 30, 2010

The Great Mathematics Bazaar

I haven't blogged in exactly two months, the longest hiatus since I started. Not sure why. Now (under pressure from my brother!) I'm giving it another shot.

I just got back from the International Congress of Mathematicians at Hyderabad. That should give me plenty to write about! It's a long conference, all of 4+4 days with a day's break in between. And it's an enormous conference -- somewhere between 3000-4000 participants. It takes place once in four years and covers "all" areas of mathematics.

First the academics. Four young (under-40 is the rule) mathematicians received the prestigious Fields Medal. It was quite a thrill to be present as the medals were announced, and the awardees came on stage to receive them from the diminutive President of India, Her Excellency Smt. Pratibha Patil, shimmering in an exquisite silk sari. With each medal, a tug-of-war ensued as the recipient tried to take it from her hands, but she grimly held on to it and gestured with her head that they should face the camera! Only after the photo-op did she allow herself an impish smile and relinquish the medal to the winner.

There were other awards including the Chern, Gauss and Nevanlinna prizes.

The awards ceremony was followed by laudatory talks, by (who else) laudators, specially chosen, each of whom lectured on the work of an awardee. Unfortunately for the most part they were marred by (i) poor transparencies in microscopic fonts, (ii) halting and uncertain accounts of the work, (iii) super-technical accounts lacking in the big picture, (iv) all of the above. Later, however, the medallists themselves gave talks on their own work (every day after lunch) and these were by and large superb. Vietnamese Ngo Bau-Chau (I'm missing half a dozen accent marks that belong to his name) and Israeli Elon Lindenstrauss won the award for work that was "purely mathematical" in nature. But the work of the other two: Stas Smirnov, a Russian working in France, and Frenchman Cedric Villani -- the latter wearing fashionably long hair and what appeared to be a bouquet of red silk ribbons on the front of his shirt -- was motivated by rather straightforward problems in physics.

To get to the latter first: Villani studied the rate of increase of entropy and the approach to equilibrium predicted by the Boltzmann equation. He also illuminated the phenomenon of Landau damping and studied optimal transport theory. The last one is described as follows in the nicely written work profile that you can find here: "Suppose you have a bunch of mines and a bunch of factories, in different locations, with varying costs to move the ore from each particular mine to each particular factory. What is the cheapest way to transport the ore?" I find it wonderful that the highest level of mathematics today still deals with problems that are relatively simple to state.

Stas Smirnov proved the existence of the continuum limit of certain lattice models (models of systems like magnets where microscopic spins sit at each site of a discrete lattice and interact with their neighbours). Physicists of course use such a limit all the time without having any proof that it is rigorously defined. Smirnov spoke very engagingly about it and I felt I understood very clearly (at the time) what it was he had done, though not in any detail how exactly he had done it.

The work of Lindenstrauss too seemed fairly accessible at least in its motivations. Ergodic theory, the study of how dynamical systems do - or don't - go everywhere eventually, originates in celestial mechanics. Number theory deals, among other things, with how many integer solutions there are to a given polynomial equation or inequality. In finding a connection between the two branches of mathematics, he made major progress on Littlewood's conjecture: on how a pair of irrational numbers can be approximated by fractions in a correlated way.

That leaves only Ngo, whose work on the Fundamental Lemma of Langlands remained rather obscure to me despite his valiant attempts. I can only say here that the Langlands programme attempts to relate automorphic forms and number theory among a wide canvas of interconnections, and that Ngo proved what Langlands had thought would be a simple result (hence the name "Lemma") that turned out to defy attempts for decades.

Since this is getting rather long I shall end this instalment here. To make the next one interesting let me mention that I gave two invited talks at the ICM (and I have an "Invited Speaker" badge to prove it!). But they were not about mathematics, nor even physics. More on that soon.

Tuesday, June 29, 2010

Waka Waka

The comedian Dave Barry once wrote about the difference between men and women in the following terms (I'm recalling this from memory so it's not an exact quote). When two men bump into each other by accident on the street, the result is this:

Man A: Watch where you're going!
Man B: No, YOU watch where you're going!
Man A: Oh yeah?
Man B: Oh yeah. I'll teach you.
(they fight)

In contrast when two women bump into each other, it goes like this:

Woman A: I'm sorry!
Woman B: No, I'm sorry, it was my fault.
Woman A: What nice shoes!
Woman B: I got them on sale.
(they go shopping together)

As a paradigm of competitive vs cooperative behaviour this is unbeatable. Somehow it came to my mind yesterday when I happened to see the amazing video of Shakira and the South African band Freshlyground performing the FIFA theme song "Waka Waka". It opens with a goalie gearing up and facing a penalty shot, then cutting to Shakira in a grass skirt, looking fresh and vivacious and singing the song with four African women dancing alongside. Then it goes back and forth between scenes of men colliding, stressing, shouting and weeping over football, and women joyously dancing together to this delicious rhythm.

I wondered why they didn't just drop the football scenes and have everybody dance instead. So much more cooperative! Imagine if instead of football championships they had huge festivals (in places like South Africa) where everyone would dance and sing together. I'm sure a lot of people would love the idea -- but of course, men wouldn't settle for it.

Thursday, June 10, 2010

The worst of American and Indian cultures

The recent judgement on the Bhopal gas disaster saddened many people including myself greatly. This disaster occurred during my first year in TIFR so its tragic aftermath has been a sort of constant through my entire career. Like so many other people, and mostly following the lead of the press, I've given it some attention in brief spurts but it's dropped off the radar for the rest of the time. Now the judgement has brought the issue back to centre-stage. Unfortunately it will fade again from the press and then from the lives of the rest of us who are not directly affected nor courageous enough to be activists.

Still I feel a few points are worth commenting on. First of all the judgement three days ago is merely the foregone conclusion of a trial for criminal negligence whose maximum sentence was two years. So the judgement can hardly be termed a "disappointment", given that this maximum sentence was handed out to all the accused. Now the reason for this low maximum sentence appears to be a 1996 decision of the Supreme Court that this case involved criminal negligence and not culpable homicide. This decision was based on their understanding of the law and without being a legal expert, I don't know how I can question it. Note that they did not "reduce the sentence" as is implied in current discussions, but merely stated what are -- and are not -- the valid charges.

The key question in this case, which no one seems to be asking, is why is two years the maximum sentence for criminal negligence? (when 7 years is the maximum penalty for eve-teasing!). It seems that the courts may be taking the rap for a failure by the law-makers. Other failures by the law-makers are of course quite visible in this case. Warren Anderson's quick repatriation in 1984 seems an obvious case of collusion and strongly suggests the Indian government at that time was anxious not to displease the US government, while the latter was anxious not to have its corporate honcho in a foreign (or domestic) jail whatever he might have done. The recent judgement eloquently blames "the synergy of the very worst of American and Indian cultures" and I couldn't agree more.

But all the talk today is about punishment. Despite its valuable role as a deterrent for the future, what possible benefit can punishment bring to victims who have lost their dear ones and their own health? Focusing excessively on this, it seems to me, results in a loss of focus on the one thing that even at this stage can help the sufferers: compensation. This issue was fundamentally lost over a decade ago when in 1989 the Indian government settled for a mere 470 million dollars in compensation from Union Carbide (compared with 350 million that Union Carbide offered on their own, and 3 billion that the Indian government claimed in its lawsuit). Why did they accept such a compromise? I don't know, but one can hardly blame the courts for it. What can be done today? Again I don't know, but baying for the offenders heads seems to be a distraction from this key issue.

There's one more relevant matter that's getting a minor fraction of the press coverage: cleaning up the site, from which contaminants are still leaking into the soil of Bhopal. Let's hope today's governments in both countries are stung by the judge's remark about "the worst of American and Indian cultures" and will effectively rehabilitate the site.

Wednesday, June 2, 2010

Boat attacks helicopters

A newspaper magnate once said that "dog bites man" isn't newsworthy, but "man bites dog" -- that is news. We now have a similar situation in the brutal world of peace activism.

The New York Times (ever the beacon of responsible journalism) has raised a subtle point about the recent struggle on board the Mavi Marmara, a ship carrying humanitarian aid for the besieged people of the Gaza strip. In a recent article a certain Brian Stelter suggests that it is difficult to determine who was the aggressor in this conflict. The article in question starts "When Israeli commandos attacked the so-called Freedom Flotilla...", which appears to resolve the issue, but spin-doctoring must be hard work and evidently Mr Stelter forgot this line while writing the rest of the article. Instead he went on to say:

"But what is missing so far from the flotilla clips on both sides is context: it is difficult to establish the sequence of events or, more simply, to determine who attacked first."

How true. Without having been on the spot, how can we know whether Israeli helicopters attacked the boat, or the boat attacked the helicopters? It all boils down to plain conjecture. Of course we do know that peace activists are aggressive by nature and their boats are equipped James-Bond-like to make gigantic leaps into the air. So my guess is it was the latter that happened - the Israeli helicopters were snatched out of the air and slammed down on the boat, caught totally unawares while they thought they were safe in "international airspace".

One feels a pang of sympathy for the Israeli government, which despite being the victim has received criticisms ranging from "deeply concerned" to "terrible". Knowing how sensitive they and their army can be, is it fair or responsible to denounce them thus? What if they get depressed and discouraged as a result?

Tuesday, June 1, 2010

Research scholars and Dr Bhabha

One realises one's age when every new occurrence brings back a memory. In this case, the occurrence was the Foundation Day lecture at TIFR this morning by His Excellency A.P.J. Abdul Kalam, former President of India. Dr Kalam started his talk by recalling how he had gone through a file at Rashtrapati Bhavan which documented an invitation from Dr Rajendra Prasad, first President of India, to Sir C.V. Raman to receive the Bharat Ratna award. In his reply Raman regretted he could not attend the award ceremony because he was guiding a Research Scholar whose thesis was due for submission. With this story Dr Kalam emphasised the importance of Research Scholars in the scheme of things, and deservedly won the hearts of those who were in the audience today (the rest of his talk was a fairly generic utopian vision of the future).

Now for the memory this brought back to me. A mere fourteen years ago, in the same auditorium, TIFR celebrated its Golden Jubilee with a glittering function that included the then chief minister, Manohar Joshi of the Shiv Sena, and the then union telecommunications minister Sukh Ram who released a postage stamp of TIFR. There were also speeches by TIFR Council Chairman J.J. Bhabha, younger brother of TIFR's late founder, and some other major figures. When about to enter the hall, I discovered that three entire batches of Research Scholars at TIFR were not allowed into the auditorium for the function, supposedly because of a lack of space. In protest I did not enter either, and watched the proceedings on closed-circuit TV in a lecture room.

Thereafter I penned a somewhat melodramatic missive to our late founder Dr Homi Bhabha and put it up on a notice board in the TIFR lobby. It was removed by the chief security officer who scolded me and warned me not to put it up again. Today he is retired (and moreover Manohar Joshi is in the political wilderness and Sukh Ram has been sentenced to three years in jail for corruption!!) so this may be a reasonable time to exhume the letter. I reproduce it below.

=========================================================
Dear Dr Bhabha

February 9, 1996

To:
Dr Homi J. Bhabha
c/o God
Heaven

Dear Dr Bhabha

I am writing to tell you about the Golden Jubilee celebration that took place at TIFR this evening. I did not enter the Auditorium, but watched the function from outside on closed-circuit TV. If they have closed-circuit TV in Heaven then you might have seen it yourself, but somehow I think you were not watching.

Dr Bhabha, this was a function on a grand scale. The elaborate arrangements would have impressed you. The dignitaries all looked suitably important and spoke with seriousness (except the Chief Minister, who looked bored but spoke with humour). And the audience contained all the important people in this Institute, in their finest clothes.

Some people were turned away at the door. They had invitation cards, so they thought that they were invited. Not so. There was a complex and subtle system to make sure that only the right people got through.

The cards came in three colours of envelope: white, blue and pink. This meant: big shot, medium shot and small shot. Then the white and pink envelopes were further divided into those with the Stamp and those without. (No, not the postage stamp, that was only worth 2 rupees! The Registrar's Rubber Stamp was priceless.) A foreign visitor to TIFR remarked that this looked like an elaborate caste system.

On a white envelope, the Stamp meant: Big Shot Plus Spouse. That went to Senior Professors, Heads of Sections and Chairmen of Committees, plus some people who did not fit in this list, but were known to be important just by virtue of their importance. It also went to hundreds of non-TIFR people, including army and navy top brass, who came with their spouses.

On the pink envelope, No Stamp meant: "You are invited, but you can't come in." It was actually a non-invitation. So these were the people who got turned away. I was standing near the door and watching their faces.

Who were these people, you might ask. The pink non-invitations were issued to second- and third-year Research Scholars, and later also to Visiting Fellows, after a protest on their behalf. They were also issued to some categories of non-academic staff. (There was still one lower category --- the first-year Research Scholars received NO invitations. They shared this privilege only with the daily-wage workers.)

In particular, Research Scholars and Visiting Fellows who have research publications at TIFR were turned away from the Auditorium. What made the Institute famous in the first place, Dr Bhabha? Sorry if I forget sometimes.

Of course, those who couldn't get in had the option to watch the ceremony outside on closed-circuit TV. But many Research Scholars chose to play cricket instead. Maybe they didn't care enough about the Institute, or maybe they were hiding hurt feelings. Who knows.

I chose not to enter the Auditorium, in sympathy with the non-invited persons. But I was very interested in the programme, and watched every detail on TV. Many of the speakers talked of the bright future of TIFR. They all said very kind words about you, Dr Bhabha. They showered generic praise on your achievements as a scientist, administrator, and man of culture. Your brother said something more precise: that you used to identify talented young persons, and give them the freedom and encouragement to become successful and eminent scientists. He asked a question: What would Dr Homi Bhabha have done if he had been here today?

At that moment a strange idea entered my head. I thought: maybe Dr Homi Bhabha, had he been here today, would have pointed out that the Research Scholars and Visiting Fellows are the future of the Institute. He might have suggested that their pink non-invitations were inappropriate. He might have insisted that the priorities be revised so that the Auditorium could accommodate the future leaders of Indian science. Perhaps he would even have politely asked senior members of the Institute to desist from bringing their families?

Maybe I am wrong, Dr Bhabha. Maybe you would have done something different. But your spirit was definitely not here today, even though most of the talk was about you. Frankly, I feel that the more we talk about you, the less we think for ourselves.

Yours sincerely,
Sunil Mukhi

=========================================================

Sunday, May 30, 2010

Obsession

A tragic news item today brought back some memories. A girl studying in an engineering college in Kelambakkam near Chennai was spotted by the college chairman (who happened to also be her relative) sitting next to a boy and - horrors - talking to him. He scolded her, whereupon she went to her hostel room and committed suicide by hanging herself.

The memory this brought back was of attending a summer school at IIT Madras in 1976. In those days, IIT's were nasty, forbidding places (at least the ones in Madras and Delhi). The organiser of our National Science Talent summer school, whom I'll call Prof. R, was a rude, obnoxious and overbearing person. Beyond all this, he had an obsession -- that boys and girls should not mingle under any circumstances. We were ordered to sit in separate halves of the class. This was unexpected and quite bizarre at least for those of us who had come from Bombay. We already knew our batchmates and since we had never received any warning about the dangers of opposite-sex fraternisation, we simply treated them as fellow students with a reckless disregard for gender.

Now what I remember particularly about Prof. R. is that his obsession for gender separation appeared to coincide with an obsession for one of the girls in the class. He would constantly try to talk to her, alone, and warn her about the dangers of fraternising with boys.

Cut to about six or seven years ago and a similar incident took place in Bombay. At this time no one (certainly in Bombay) would dare suggest that students be physically separated by gender in class. This is what happened instead: I was informed by a senior institute administrator that a certain girl was illegally staying in a boy's room in the hostel, that he (the administrator) had information that her modesty was in danger, and that in his view the authorities should raid the hostel room and "rescue" her. The entire story sounded to me quite fabricated. How did he have advance information about what was to happen to her? Apparently from a friend of the girl's parents. I then met this "family friend" who told me he had known the girl since she was a child, that she had fallen into "bad company", and that we needed to save her before something terrible happened. But to me, his tone betrayed a very questionable obsession about the girl.

The next step turned out pretty simple - I located the girl, gave her a very abbreviated version of the story and asked her if she was in any sort of trouble. She smiled brightly and said she wasn't, and that the boy she was visiting (not staying with) was her fiancé. They were soon to get married, their parents had met each other etc etc. She couldn't imagine what the problem was. Wishing I didn't have to do this, I had her call her father on my mobile and he confirmed her story. So what was this family friend getting all worked up about? (remember he had nearly brought about a raid to "rescue" her!) The young lady revealed a plausible reason. On her arrival in Bombay she had initially stayed with him (he lived alone) and had soon begun to feel uncomfortable with the way he looked at her and questioned her closely about her activities. So she moved out to her own lodgings. The "family friend" did not take this well and the above story was the result.

Back to the story I started with. Apparently the chairman of this engineering college in Kelambakkam discovered the girl was hanging out with boys when he surveyed CCTV footage of the students. I don't want to speculate on why he was surveying this footage and beyond the newspaper report I know nothing about this case, which presumably will be investigated. Let's hope it bears no analogy with the two cases I've described above.