Update on Hironaka's Proof.

As I wrote a few days ago, Hironaka claimed to have obtained a proof of resolution of singularities in characteristic p > 0. Today he completed his series of six talks.

As expected, pretty early in the series things began to go above my head. But I diligently sat through all the talks. Talking to some experts after the talks, I was given the impression that this proof, or a very precise program of a proof, is extremely promising. It is expected to work. Hironaka promised to write up the remaining part in the future which is expected to outline all the ingredients of the proof.

I guess people will be eagerly looking forward for that future publication by Hironaka.

Revealing of Secret Government Actions by New York Times is Good.

The recent publication of secret monitoring by the US of international money transfers has been discussed in depth. There is one thing that escapes my, quite possibly limited, comprehension.

The papers, particularly the New York Times, have been accused of compromising on the national security. This was no flippant charge made over coffee. The president himself suggested that the publication was disgraceful.

The idea is that now the "terrorists" know that their misdemeanors are being monitored by the US, and they will hence be little more careful next time. This line of argument is ridiculous for more reasons than one.

For one thing, as a Times editorial pointed out it is, at best, wishful thinking to suppose that terrorists did not know this already.

Moreover, this argument suggests that the government is competent to disrupt nefarious activities only when they are indulged in via anticipated routes. It is the duty of the government to deny them however they try to do it. It has no business complaining that it's job is made harder.

Most importantly, the "war on terrorism', or indeed any war against criminals, is at the most fundamental level, an attempt to prevent the crimes. Only then the question of catching the criminal arises. (There is a deeper philosophical issue here: one is not a criminal till the crime is committed.) Of course, these two objectives are tied to each other. But I think it is important to grasp the distinction.

I used to wonder why police cars when they arrive at the crime scene make their approach known to everybody (most crucially to the prospective criminal) by their loud sirens. I never found out the official reason, but I convinced myself as follows: the objective of catching the criminal is inferior to the objective of preventing the crime. So if a guy is about to shoot somebody the police sirens might dissuade him. So while he might escape, a life could have been saved.

In the same way, even if it comes as news to the terrorists that their wire transfers are being watched, it's good that they will now not use these known methods. So one route for criminality is eliminated. And the infrastructure and devotion needed to find out new routes may filter out numerous potential terrorists.

So I think the over all goals of the so-called war on terrorism are served well by this report.

Galbraith, Again.

It is not often that people misjudge their pecuniary interest over a large scale for a long time. Those who suggest otherwise show that what is called sound economics, very often, is what mirrors the needs of respectably affluent.

Again from his book Money.

Resolution in Characteristic p.

As I wrote a few days ago I met Hironaka who is also attending this conference. I just learned that he is announcing a proof of resolution of singularities in characteristic p > 0! He will talk about it in a series of six lectures beginning today.

It appears that he only has a sketch of the proof now, but it presumably contains all the ideas needed for a complete proof. If correct, this will be a truly important event in the history of mathematics.

Of course, there is the question of how many will understand it right away. Not many, by all accounts. It seems he has been explaining some of the key ideas to other experts in the conference. But many of them have confessed, quite frankly, their inability to follow him. So it will be a while before authenticity is established or some flaws revealed.

More on this as I learn it.

Drinking Up One's Fortunes.

In colonial America a plethora of goods served as money, such as tobacco, rice, grains, whisky, brandy and even cattle. Tobacco was the most used and it was the main medium of exchange for nearly two centuries in Maryland and Virginia.

John Galbraith is at his lucid best when he mentions the use of whisky and brandy as money in some states.

The use of whisky and brandy as money makes exceptionally poignant the injunctions, common through American history, against drinking up one's fortunes.

I read this in his book Money.

Nice Quote.

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation. -- G.H. Hardy

Class War Politics.

This is a nice article by Paul Krugman in New York Times on the changing trends in American politics in the last several decades. I am quoting it completely here.

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In case you haven't noticed, modern American politics is marked by vicious partisanship, with the great bulk of the viciousness coming from the right. It's clear that the Republican plan for the 2006 election is, once again, to question Democrats' patriotism.

But do Republican leaders truly believe that they are serious about fighting terrorism, while Democrats aren't? When the speaker of the House declares that "we in this Congress must show the same steely resolve as those men and women on United Flight 93," is that really the way he sees himself? (Dennis Hastert, Man of Steel!) Of course not.

So what's our bitter partisan divide really about? In two words: class warfare. That's the lesson of an important new book, "Polarized America: The Dance of Ideology and Unequal Riches," by Nolan McCarty of Princeton University, Keith Poole of the University of California, San Diego, and Howard Rosenthal of New York University.

"Polarized America" is a technical book written for political scientists. But it's essential reading for anyone who wants to understand what's happening to America.

What the book shows, using a sophisticated analysis of Congressional votes and other data, is that for the past century, political polarization and economic inequality have moved hand in hand. Politics during the Gilded Age, an era of huge income gaps, was a nasty business — as nasty as it is today. The era of bipartisanship, which lasted for roughly a generation after World War II, corresponded to the high tide of America's middle class. That high tide began receding in the late 1970's, as middle-class incomes grew slowly at best while incomes at the top soared; and as income gaps widened, a deep partisan divide re-emerged.

Both the decline of partisanship after World War II and its return in recent decades mainly reflected the changing position of the Republican Party on economic issues.

Before the 1940's, the Republican Party relied financially on the support of a wealthy elite, and most Republican politicians firmly defended that elite's privileges. But the rich became a lot poorer during and after World War II, while the middle class prospered. And many Republicans accommodated themselves to the new situation, accepting the legitimacy and desirability of institutions that helped limit economic inequality, such as a strongly progressive tax system. (The top rate during the Eisenhower years was 91 percent.)

When the elite once again pulled away from the middle class, however, Republicans turned their back on the legacy of Dwight Eisenhower and returned to a focus on the interests of the wealthy. Tax cuts at the top — including repeal of the estate tax — became the party's highest priority.

But if the real source of today's bitter partisanship is a Republican move to the right on economic issues, why have the last three elections been dominated by talk of terrorism, with a bit of religion on the side? Because a party whose economic policies favor a narrow elite needs to focus the public's attention elsewhere. And there's no better way to do that than accusing the other party of being unpatriotic and godless.

Thus in 2004, President Bush basically ran as America's defender against gay married terrorists. He waited until after the election to reveal that what he really wanted to do was privatize Social Security.

Pre-New Deal G.O.P. operatives followed the same strategy. Republican politicians won elections by "waving the bloody shirt" — invoking the memory of the Civil War — long after the G.O.P. had ceased to be the party of Lincoln and become the party of robber barons instead. Al Smith, the 1928 Democratic presidential candidate, was defeated in part by a smear campaign — burning crosses and all — that exploited the heartland's prejudice against Catholics.

So what should we do about all this? I won't offer the Democrats advice right now, except to say that tough talk on national security and affirmations of personal faith won't help: the other side will smear you anyway.

But I would like to offer some advice to my fellow pundits: face reality. There are some commentators who long for the bipartisan days of yore, and flock eagerly to any politician who looks "centrist." But there isn't any center in modern American politics. And the center won't return until we have a new New Deal, and rebuild our middle class.

Manufactured Merit.

This is a brilliant article by Praful Bidwai in Frontline. He brings out an extremely important point which was lost in the euphoria over the reservation debate.

The whole debate was centered on the preeminence of merit and why one shouldn't compromise in that regard. Even the pro-reservation side of the debate accepted this and suggested ways to ensure the continued respect for merit. However, as in all emotionalized slogan-chanting debates, none ever stopped to consider what really is "merit" and what form it took in Indian professional education. It became simply a meaningless word devoid of any significance to the situation on the ground.

Praful Bidwai has done a great service by bringing some relevance to this debate by analyzing the meaning of "merit". Aptly, he talks about "manufactured merit".

It is a pity that we have allowed our higher education institutions, located as they are in a situation of scarcity, to be filled by those who possess ... manufactured merit.

He gives two important reasons for his diagnosis.

One, more intrinsic to the structure of professional courses, is that competitive exams do not ensure a proper understanding of the principles involved in any particular science, and neither are they a reliable predictor of the prospects for future excellence. At the most basic level, they establish nothing more than a "hierarchical Brahminical notion" of merit. He insists that education has more to it this confined vision suggests.

Education is as much about understanding social processes and life in all its complexity, about respecting diversity and difference, understanding and practising citizenship collectively, and about building a learner-teacher community based on free inquiry. Such values are indispensable for all universities, not just liberal education colleges.

For instance, he says,

...for recruitment in the civil service, an understanding of India's social structure, familiarity with the agrarian situation, comprehension of the links between deprivation and crime, and above all, a public service orientation are at least as relevant as performance in entrance tests. For doctors being recruited in government hospitals, clinical ability and empathy for patients should count higher than quantitative grades.

I think this is a profoundly relevant point which must be understood before embarking on any appraisal of Indian education.

Two, and more important, is that the merit is "manufactured" in ways that suit privileged classes. It is common knowledge that medical seats are, in most instances, "bought" for ridiculous amount of money, running into tens of lakhs of rupees. It is ludicrous to suppose that such a system produces meritorious doctors and it needs to be preserved. It is also fairly common to see engineering seats bought like this in the numerous private colleges that are doing lucrative business.

According to an informed estimate, the delay [in implementing the reservation] would bring an annual windfall of nearly Rs.800 crores to non-medical private unaided institutions. If the intake of 18,000 medical seats is added, the profits would rise by between Rs.135 crores and a huge Rs.1,350 crores (depending on the capitation fee).

Another aspect is that privilege plays its role in indirect ways.

...how are most "meritorious" youth trained to develop and "demonstrate" this attribute? Why, through high-quality parental attention (available only to a few), and of course, coaching classes such as those at Kota which cost up to Rs.2 lakhs, including accommodation and food. Up to a third of all Indian Institutes of Technology seats are reportedly filled by candidates who take such tuition. For medical colleges, the proportion is probably higher.

In such an atmosphere of fragrant denial and misrepresentation of scientific notions of merit and societal values, any debate is only going to touch on peripherals and not address the substance of the issues. That is why, I think this article by Bidwai is very important.

Role of Tradition.

While watching some of the world cup matches, particularly of Brazil, a question stuck me: why is Brazil so consistently good over a long period of time? More generally, why are some countries better than the rest in different sports? (Of course, this question can be asked of any field, but here I confine myself to sports.)

This question is surprisingly potent. Why is Australia dominating cricket world for the last 20 years and why did it not do so well for some years prior to that? Similarly how did West Indies rule cricket world for two decades and then dissipate? How can Pakistanis keep producing fast bowlers, while Indians struggle? Then again, why is India is so good in producing quality spinners? Why are Russians so good at chess and East Europeans in gymnastics? Kenyans in marathon? East Asian countries in Badminton? And so on.

I admit that in all these cases there are crucial exceptions. However, in spite of their significance, the validity of my question remains. Another thing I must clarify is that each of these cases has specific explanations and there needs to be thorough research in order to understand them. I do not mean to belittle the deep sociological meaning of these phenomena.

What I am interested in is a common feature of these disparate phenomena. Notice that in every single case I mentioned above the dominance is maintained for a considerable period of time. When I think about it, the only answer I can come up with is the important role of tradition, by which I mean a wide array of cultural aspects present in a society.

I firmly believe that the potential to achieve excellence in a field is distributed randomly. It is certainly not distributed nicely along geographic lines. But I used the word potential. So when they are born, an Indian is as likely to have the potential to become a great soccer player as a Brazilian. The differentiation begins from the moment they are born. The atmosphere in which they are groomed plays a major role in how they turn out. And that atmosphere is determined by what drives the passions of that society, what defines their thinking. In a word, tradition. And yes, a major catalyst in establishing a tradition is how your country is doing at that point of time. If it's doing well, then the tradition is strengthened.

But how are these traditions created, and equally importantly, how are they broken. Well, there are all sorts of different reasons for it, and they need to be studied and understood in each case. What I wanted to emphasize here is only the importance of tradition in sustaining the success of a country in a sport.

On a lighter note, here is a satirical look at which political arrangements tend to produce successful world cup teams. It ends like this:

There's one iron law that overrides all the others. The political reality most likely to produce a Jules Rimet trophy at any given moment in history: whatever form of government has taken up residence in Brasilia that week.

Hironaka.

Today I met Heisuke Hironaka, the great mathematician famous for his proof of resolution of singularities in characteristic zero. His solution remains among the greatest pieces of mathematical work ever. Grothendieck, arguably the greatest ever algebraic geometer, is said to have claimed (orally) that "Hironaka's work is the most complicated mathematical work".

He is also a Fields medalist. (Fields medal is the biggest award there is for mathematicians.) In fact he becomes the first Fields medalist I met or saw in my life!

When my adviser introduced me to him today, the amusing dialogue went something like this:

I: Very nice to meet you, Sir.

Hironaka: Nice to meet you. Nice to meet young geniuses. [To Bernard Tessier who was present] they don't know now that they are geniuses....they will know in future.

He appeared old, but was quite lively. He is supposed to give some talks in the conference, and he asked the organizers to schedule his talks in the afternoon, because "I feel weak in the mornings. You know my grand mother used to take half an hour to get down from the bed. I am becoming like her"!

Tax Cuts and Spending.

Reducing government spending to a level where expenses for defense and law and order constitute a substantial part of it is one of the cornerstones of conservative world view. That much is clear.

How to achieve this in the constrained domain of politics driven by interest groups is not so clear.

The standard approach of the Republican governments in the last few decades has been to rely on tax cuts and appeal to the starve the beast approach. The idea is to make sure governments have not much money to spend.

Elegant as this strategy appears, there is a catch. Governments can spend the money even if they don't have it! This is familiar to everybody. Successful businesses have developed since ancient times on the assumption that human beings want to spend their future income in the present.

Needless to say, this often leads to spending which is in excess to income, even of future. There is nothing to suppose that governments will behave more responsibly. In fact, there is ample reason to suppose the contrary. Governments have little incentive to spend responsibly.

Moreover, after cutting taxes Republican presidents could feel as if they have done their bit for the conservative cause, and proceed to attend to more immediate issues of concern - such as increasing the spending to appease the various politically crucial groups that may have been angered by the tax cuts to the wealthy.

Well, this is exactly what seems to have happened. Ironically this is the upshot of a study by William Niskanen, chairman of Cato Institute, a bastion of libertarian thought.

This is a short note by Niskanen himself. Some reports in the media on this can be found here, here and here.

In Italy.

After a relaxing and largely sedentary sojourn at home in India, I am back to work (which includes blogging). The scene of my activities now is Trieste, Italy where I am attending a workshop and conference.

My month-long stay in India was tranquil and pleasurable. I stayed at home mostly, ate good food, watched cricket and read some nice books, notably this and this. Owing to the nature of my stay, busy and lazy, I did not blog. That is not to imply, however, that I did not have regular urges to pen some thoughts. I did. May be I will still write about those thoughts - if the urges persist and time permits.

Presently, I am occupied with this conference. It is very exciting and I look forward to some nontrivial learning in the coming three weeks.