Tuesday, November 29, 2011

The simplest schoolboy is now familiar with truths for which Archimedes would have sacrificed his life. -- Ernest Renan

Motion, I thought, could be simply defined as a shift in the position of a body over time – if at all there is one. Not quite a difficult concept to grasp. But this definition is too vague. Feynman said it superbly:

“Any vague theory that is not completely absurd can be patched up by more vague talk at every point that brings up inconsistencies – and if we begin to believe in the talk rather than in the evidence, we will be in a sorry state.”

Over 2300 years ago, Aristotle tried to define motion in all its complexity, including as the increase and decrease of that which can be increased or decreased. This puzzle about motion endured until Newton came onto the scene in late 1600s. Newton’s three laws of motion even apply today when we send rockets into space or design machines.

1. A body continues at rest or in motion with a constant velocity in a straight line, unless acted upon by force.

2. The change in velocity of a body is in the direction of the force acting on it, and the magnitude of change is proportional to the force acting on the body times the time during which the force acts; and is inversely proportional to the mass of the body.

3. Whenever a first body exerts a force on a second body, the second body exerts an equal and oppositely directed force on the first body.

These laws are only special forms of the more general laws when we assume that velocities are small compared to that of light and when the scale of phenomena is large compared with the atom. Yet these laws are the building bricks of Physics.

In fact, Newton solved the problem of motion as he defined it not as Aristotle considered it to be. So Newton’s definition assumes certain things and it is only in the ambit of this assumption that his laws hold. But these laws more or less embrace the usual notion of motion that we encounter.

Similarly, our speech is adapted to our daily needs or perhaps to the needs of our ancestors. We cannot have a separate word for every distinct object and for every distinct event. If we did, we would ever be coining words. In order to have language at all, many things or many events have to be referred to a single word. It is natural to say both men and horses run and even more convenient to say a motor runs.

The unity among these concepts lies far more in our human language than in any physical similarity with which we expect science to deal easily and exactly. So, it would be foolish to seek some elegant, simple and useful scientific theory of running which would embrace runs of motors or men. It may or may not be possible, but to blame Science for not having one is tomfoolery.

Friday, September 16, 2011

Though I’m not a great fan of climate models, I do believe climate change is real and has anthropogenic origins. Rick Perry, the governor of Texas, went on record saying that pouring research dollars into climate research is disastrous to the economy. Needless to say, he makes sweeping statements of disbelief among scientists about the reality of climate change. According to a 2010 study published in the Proceedings of the National Academy of Sciences, 97-98% of the world’s 1,372 scientists “most actively publishing in the field” of climate research are quite certain of the idea of anthropogenic climate change, or climate change brought about by human actions.

Climate change deniers – skeptics still have their place in my heart – take to God as an opposition to reality-based arguments about human actions. The Republican insistence on rejecting this reality for another, intangible one isn’t just bad science; it is, quite literally, bad faith.

Ten Commandments is one movie that has a special place in my heart. Of course, Charles Hesterton (who plays Moses) is not my pick for that role. Infinitely better than him in his appearance as Moses is the charming Israeli mathematician, Harry Furstenberg. In any case, the most interesting part of this long movie was how lead out of evil Egypt by Moses, the Israelites get to wait at the foot of Mount Sinai. Moses goes to the top to get the word of God. Meanwhile, the folks get restless waiting for a week and create a golden calf. So, does this mean they no longer believe in God?

Here, after all, were people who, just a few weeks before, had witnessed with their own eyes the glories of God, but, impatient with their absent leader, waited barely a month before fashioning a more tangible deity out of precious metals. In Sinai, the Israelites knew God with their minds, but not with their hearts. They realized that the Almighty was real and present, but they did not yet believe in him.

We mustn’t blame them. God is a mighty difficult idea to grasp. Proof of his existence doesn’t make it any easier. Faith is required. Because faith, Moses knows, is more than believing in things we’ll never know for certain exist; faith is also the wisdom to believe in things we know for certain do.

Which brings us back to the Republicans. The adherence of so many in the party to counterfactual narratives is often explained away by faith. Just what kind of faith Rick Perry repeatedly makes clear. In a speech in Virginia earlier this week, Perry said that his “faith journey is not the story of someone who turned to God because I wanted to. It was because I had nowhere else to turn. I was lost spiritually and emotionally.”

Perry, then, assumes that if he trusts in God, God will tell him what to do. He believes, if we take him at his word, that he is capable of interpreting the precise and unerring will of the Creator. This is the opposite of Moses’ brand of faith. For Perry, faith comes first, and proof is unnecessary; for Moses, proof comes first, and faith must follow. Perry was lost until he found God; Moses found God first and then made his people wander in the desert for 40 years, until they were ready—intellectually as well as emotionally—to embrace what faith meant.
And what faith really means is responsibility. Because we are incapable of knowing God’s mind—and by “we” I mean decent people of all political persuasions who are humbled by their belief in God—we’re left grappling with life’s greatest mysteries by ourselves. We try, like children playing a game with rules they don’t entirely understand, to make sense of what might seem, to the unbelieving, like a cruel and random existence. All we can do is our best, and our only guide is our heart and its call for compassion.

The Israelites at Sinai didn’t understand this idea at first. They yearned for a god they could grasp, a shiny golden god, a god they believed could redeem them. It took them four decades in the wilderness to learn that only they could redeem themselves, and that faith isn’t, in itself, salvation, but merely its engine

Faith follows facts. Now I get why Jews are so mightily good at exact sciences.

Thursday, September 8, 2011


The Swiss philosopher, Jean-Jacques Rousseau said that individually, four hunters can each only get a rabbit. But together, he said, they could bring down a deer if they collaborated. Yet we continue to hunt for rabbits. Why?

People come into conflict mostly due to the beliefs they hold dear. Such conflicts result in anything from awkward situations to wholesale murder. Resolution of conflicts involves sorting out issues with give and take. I will try to give two clear-cut examples: one on a more personal level of ethics and the other on a national level.

Individual-level Example

Vernon L. Smith, a 2002 Nobel Laureate in Economics devised what is called the Ultimatum Game.

Version 1

You give Ram $100 and tell him to share it with Radha. Radha has to say beforehand how much she is going to give Ram. If Ram refuses the offer, no one gets anything.

The rational offer would be to offer Ram $1. Ram should accept it because he comes out ahead. But people who are offered a low amount in these games do not accept the offer. It makes them mad and the punishment they dole out is to refuse it. Both sides lose. Most people who play the ultimatum game offer $50. This would make you think that fairness is what is going on.

Version 2

Let’s twist the game a bit. Radha now has to earn her position by scoring in the top half of the class on a general knowledge test. And Ram has to accept whatever he is offered. This is now known as the dictator game. Behaviors change. Radha becomes less generous. She no longer offers half, as she had in Version 1. If Radha thinks her identity is not known to Ram, she is again less generous. If Radha thinks the experimenter doesn’t know her identity, she is most likely not to offer any money to Ram.

These results led Vernon Smith to conclude that fairness is obviously not the motivation in these games, whereas opportunity is. Smith argues that the reason Radha acts fairly in Version1 of the ultimatum game is that she wants to maintain her personal reputation. But when her identity is not known or she has a higher status, fairness is not the issue. This goes on to prove that conflicts require people to meet head on and resolve matters with give and take, rather than tit for tat.

A Broader Example

Two nations --or let us assume neighbors-- very well know that exports will hurt each other. So each country erects trade barriers and the easiest way to do that is to impose a tariff on such imports. These tariffs will add to the cost of imported goods and thereby makes their entry into a country cumbersome. But having a free trade is mutually beneficial. Both countries will be better off if these barriers were eliminated.

But if either country were to unilaterally erase the barriers, their economies will be hurt. In fact whatever one country does, the other country is better off retaining its own trade barriers.

So, the problem is that each country has an incentive to retain trade barriers. This will lead to a worse outcome than would have been possible had both countries cooperated with each other. A country which only considers self-interest leads to a poor outcome for all.

Such conflicts of self-interest among countries cry for cooperation. But what is the way out. History may teach us some lessons.

Between the 1830s and the 1940s, Europe reigned supreme over world trade. In response to tough competition from Europe, the United States developed its industries behind literally the world’s highest tariff wall: 35-55%. This means that a European product will cost nearly 50% more in America.

But why did America do that? US pitted what is called the ‘infant industry’ argument: producers in relatively backward economies needed to be protected and nurtured through tariffs. So that they can nicely mature and can compete with producers from more economically developed countries. Later, as the US economy matured, foreign products gained more acceptance – for example, Toyota cars in 1970s and China-made products after 1990s. Again, recently due to financial crisis, the Made-in-America argument has regained ground.

Industries and factories, hard-hit by cheap Chinese goods, are being asked to revive through freshly training their workers and re-tooling their machines. This gives some amount of protection to their products in American markets. Industries that have no future are being given strictly temporary protection so that they can break up phase by phase and get liquidated.

The point in talking about all this history is this. Conflicts of national interest involve the wisdom of knowing when to hold on and when to let go. Giving in to the opponent so as to win peace always is not how conflicts are resolved nor is to hold on to your position forever. No single one-size-fits-all strategy can be applied to all conflicts.

Another Example

Joshua Greene, a neuroscientist at Harvard, conducted an extremely interesting and simple experiment.

Version 1

You are the driver of a runaway trolley, whose brakes have failed. The trolley will run over five workers who are fixing the track. But you change the course of the train by switching and turning the wheel onto a track where there is one worker. What do you do?

In this hypothetical case, about 90% of people agree that it is morally permissible to turn the trolley. The decision is just simple arithmetic: it’s better to kill fewer people.

Version 2

You are standing on a footbridge over the trolley track. You see a trolley racing out of control, speeding towards five workmen who are fixing the track. All five men will die unless the trolley can be stopped. Standing next to you on the footbridge is a very large man. He is leaning over the railing, watching the trolley hurtle towards the men. If you sneak up on the man and give him a little push, this big man will fall on the track and will stop the trolley from killing the workers. Will you push the man off the footbridge? Or do you allow five men to die?

The brute facts, of course, remain the same: one man must die in order for five men to live. If our ethical decisions were perfectly rational, then we would act identically in both situations, and we’d be as willing to push the man as we are to turn the trolley. And yet, almost nobody is willing to actively throw another person onto the train tracks. The decisions lead to the same basic outcome, yet one is moral and one is murder.

In Version 1, it seems we make a rational decision and in Version 2, we are worried about what others think about us. You can imagine many decisions in the workplace to pose such dilemmas. Not that we will kill someone at our workplace. But such dilemmas are everyday office affairs. For instance, an employee who has to stay back in office on his first marriage anniversary; or a manager who has to sacrifice an experienced team member to give a chance for new members.

All this is not to say that we are incurably bad but our innate goodness is fragile. It is not that we are good but have to remain good.

Thursday, August 18, 2011

I've come to realize that I can no longer indulge in playing around with words and derive carnal satisfaction from it. "When I use a word,' Humpty Dumpty said in rather a scornful tone [to Alice], 'it means just what I choose it to mean — neither more nor less." I do not do that. So, though this blog has been anonymous, I cannot fool my good self. That is why I've mostly picked up others words/sentences and formed a line of thought from them. So, for now, I'll continue this exercise and it may be quite long before I'll writing something by myself entirely.

Anna Hazare is a nice guy trying to turn things around. Of course, I would have been happy if Gandhi was also jailed before he went on to that fatal fast to give away most money in the already-emptying Indian treasury to Pakistan. India would have been saved so much of nuisance. And so many Brahmins would not have been massacred in Pune and around, as Godse belonged to that elite class. But after all, he was Gandhi and could get away with anything. Now, Anna wants something to be done about corruption. I do not know anything about the Lokpal Bill or rather I do not wish to know. I have got nothing to do with this third-rate society or ways to reform it.

Seeing Anna, I'm reminded of what a brilliant mathematician said about Anna's guru: "Setting all moral judgments aside, Gandhi and Hitler have been the greatest publicists of the first half of the 20th century". Anna could have congenitally acquired this trait. Somehow, I'm amazed at the youth who have turned up to support Anna. I've never known so much youthful strength come together for any movement that calls for educational reforms. Right to Education act is just a sham and will hardly reignite a culture of learning in this country. India did have this culture once. No one complains about bad teachers or rote learning. Some "experts" do complain about the coaching institutes in closed doors. Parents go on record ruing about their kids being super-stressed by exams but still coaching institutes have a gala time pounding students with knowledge that is at best superficial.

In Tel Aviv, recently, protestors pitched their tents angered over rising housing prices. They are into what is called "tent warfare". Of course, before this there were protests by the disabled, holocaust survivors and border dwellers. "And yet none ever succeeded—despite repeated attempts—at mobilizing the mass support they required to effect meaningful social change. The geographic, socioeconomic, and ethnic divides that have split Israeli society and prevent mass mobilization become clear." Of course, Israel and India share many things. Israel got its independence a year after India, but has outperformed it considerably.

The Tel Aviv protestors, mostly aged 20 to 30 years, erected tents in elite neighborhoods. "It served not merely as a provocative spectacle but also as a boost to the self-confidence of these highly self-conscious performers, who play to the cameras at every opportunity...a testimony to the fact that as much as the protesters may be trying to prove their inflated sense of self-accomplishment to the greater public, they are primarily trying to make themselves believe in their own historical import."

Indian protestors have done all this. There seems to be a sudden groundswell about an issue that can unite anyone and everyone. You can call it a culmination of years of disgust at the state of affairs. But the demonstrations are “an effort by the young to recapture an older, more egalitarian, more idealistic, country that their parents lost.” The Arab protests have given those waiting for a big change something to cheer about. But more than this, it is the protestors' own guilty conscience that has shamed them into action. Guilty for their inability to change the way things function in this country, they seems to have hoisted Anna as a facade to hide their guilt. Poor old man, he is trying his best to remain the moral rudder. I wish him all the best in this senile adventure.

India, first get your education preferences right, make space for exceptions/ underdogs/ amateurs, learn to trust people, stop moralizing...

Disclaimer: I'm not an Indian and have no interest in its fourth-rate society. Lastly, this aptly applies to India: "First rate people hire other first rate people. Second rate people hire third rate people. Third rate people hire fifth rate people." Replace 'people' and 'hire' with 'culture/society' and 'generate/create', respectively. Yes you guessed it right, its arithmetic progression.

Sunday, July 3, 2011

Misha Gromov was born during the peak of the Second World War. A difficult time indeed and "Misha decided not to speak until he was two and a half years old. By then the war was over, and Misha uttered his first words as whole sentences. At the age of six he annoyed his first grade teacher to by solving a mathematical problem given to him by mistake and intended for third graders.

"The teacher refused to believe that Misha had solved the problem without his parents' help. This especially hurt his feelings as his parents had indeed tried to solve the problem but failed. When Misha was ten his teacher told his mother that he would become a professor of mathematics. But at that time the future professors found more delight in playing with noxious chemicals than with theorems."

Does this mean you must be born a genius like Misha to turn into a world-class mathematician? May be but if someone genuinely wishes to be good at Mathematics, it is next to impossible in India to turn out into a fairly talented mathematician at least, if not a genius.

Pesi Rustom Masani, an Indian mathematician settled in America, gave a talk back in 1963 aptly titled "The Basis for Mathematical Miseducation in Indian Universities". Nearly half a century later, it still is valid today. Strange regulations of having half of the questions in an exam to be optional, no weekly assignments (meaningful and truly challenging ones) and no periodic tests "makes for a good deal of learning by rote."

"In this educational set-up the intellectually and creatively inclined students get a raw deal. The system allows no short-cut or other amelioration to the gifted...They are made to go through a grinding mill in which the cramming of barren technicalities and trivialities is emphasized, clear and imaginative thought is discounted, and intellectual initiative stifled."

Masani goes on to say that even if Srinivasa Ramanujan was reborn in Independent India, he would have suffered the same fate of failing his exam, go begging for a research stipend, become a clerk and then rescued by a British (or maybe an American) mathematician.

Masani also points at what could be the greatest lie promoted by many: that the British brought modern education and economy to India. The British education was "geared more to the production of an officialdom loyal the the rulers than to the creation of an elite of practical-critical thinkers and men of action, or to the dissemination of knowledge among the masses. [it was more to do with the] consolidation of an authoritarian bureaucracy with a disdain for manual work...". Masani also comments on what's hindering education: "rapid vitiation of youthful idealism in India".

A great physicist, Werner Heisenberg has this to say of the English-bred economy in India:

"Hotels for Europeans, railroads, everything is very poor and very expensive. Obviously, all profits are pocketed by the English, do not stay in the country, and can therefore not be used for infrastructure improvements. For instance, even in the sleeping compartments of the first class one is not provided pillows and sheets, you have to bring those yourself, and any fourth class compartment in Germany is better than first class here."

What Masani says next has a direct bearing on the mess a university, not far from where I live, can wind up into.

"There is a good deal of student unrest, but it is unintellectual and manifests itself in ploy agitation over trifling issues. There is...a small minority of intellectually motivated students, but theirs is a voice in the wilderness".

Whatever are the merits of having a separate state, university students have far more important issues to agitate for: poor labs, uneducated professors, etc. I have never heard of a protest in India about the poor teaching of professor -- if I'm wrong, then India should attract American or Jewish students, rather than the other way round.

Atle Selberg, a great Norwegian Mathematician, writes:

"One sometimes hears it said that true genius will always make its way and be recognized in the end. I do not think that is true... The most important lesson that one could draw from Ramanujan’s story about the educational system is that allowances should be made for the unusual and perhaps lopsidedly gifted child with very strong interests in one direction, at all stages of the educational system."

As my dear friend said all this can be written down in our obituary. of course, he was being too generous in including me. But I know for sure his would be the case where this nation would not even know what it has lost.

Tuesday, May 10, 2011


The questioner does not want to learn any mathematics when he asks the question "What is mathematics?".

The opposite is true: the questioner wants to rid himself of the need of learning any mathematics whatsoever. He wants to add to his conversational repertoire some brilliant answer that will permanently excuse him from any further dealings with the subject.

One cannot escape the duty of giving a nutshell answer to the question "What is mathematics?", despite the dishonesty of all short answers.

Definitions are dangerous stuff in mathematics.

Friday, April 8, 2011

I did not make my brain, but I'm helping finish it.

John Updike, in his memoir Self-Consciousness,describes the act of stuttering as the process of “trying, with the machete of the face, to hack my way through a jungle of other minds’ thrusting vines and tendrils.”

According to Updike, however, his stuttering wasn’t just an aggravating mental hiccup which got him teased in school. Instead, the affliction was responsible for his lifelong interest in words. He was hurt into writing


Though I do not really like giving entrance exams, I'm now compelled to do so. But that is tolerable, given the little torture that the United States of America is subjecting me to for entry into its Eden (of mathematics). But I cannot forget what the gifted mathematician, Vladimir Arnold had to say about GRE. After writing about the way French students are made to think in a rigid way (and turn into narrow-minded folks) to solve a problem (even an incorrectly framed one), Arnold says:

"The United States has a different danger. No Russian professor is able to solve correctly the problem they give in the Graduate Record Examination, the official entrance examination for graduate studies: find the closest pair to (angle,degree) among the pairs: (time, hour), (area,square inch), and (milk, quart).

Every American immediately solves it correctly. The official explanation for the correct response (area, square inch) is: one degree is the minimal measure of angle, one square inch is the minimal measure of area, while an hour contains minutes and a quart contains two pints.

I always wondered how it is possible for so many Americans to overcome such difficulties and become great mathematicians. One physicist in New York who
solved the problem successfully told me that he had the correct model of the degree of stupidity of the authors of such problems."

Friday, March 11, 2011

I did know that there was someone named Milan Kundera. But never knew he could get this close to describing my perennial question and nearly answering it as well...

If it is not possible to change this world which does not deserve love, then what is left to us? Not to allow to be cheated. To see and to know. To know how to see.

How can I forget Feynman...

You see, one thing is, I can live with doubt and uncertainty and not knowing. I think it's much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of certainty about different things, but I'm not absolutely sure of anything and there are many things I don't know anything about, such as whether it means anything to ask why we're here, and what the question might mean.