Category Archives: social perspectives

Math and Indians!

I was reading this wonderful new book on math econ by Kamran Dadkhah published by Cengage Learning. He has this amazing introductory chapter on history and philosophy of math and using math in economics. I have rarely come across such an exciting introduction to mathematics, especially in an economics oriented text. The later chapters are also well written and book also tries gears you up to use software like MATLAB and MAPLE to solve problems. If I were to teach a course I would definitely give this book a try.

Having said this, I have to admit that I was bothered by one thing. The name of Indians and their contribution to mathematics was almost conspicuous by absence in the introductory chapter!

Well, I knew one thing for sure- the numerals and zero that we use today is courtesy the Indians. However, is that all that is to our contribution? At the risk of sounding jingoist, I decided to dig a bit deeper and guess what, the search was not in vain! The internet was full of pages on Indian mathematics and in what follows are just a few highlights of what I found. If your appetite is rightfully whetted after reading through feel free to click on the links listed below!

To start with there seems to be a long history of substantive contributions starting with pretty sophisticated standardized weight measures from the Indus Valley civilization (2500-1900 BCE) to geometry, trigonometry, algebra and astronomy in the later periods.

Indians thought about the Pythagoras theorem in Budhayana’s Sulbha Sutras dating back to 800 BC (Pythagoras comes sometime in 569 BC). Budhayana also gives the value of square root of 2 till five decimals among other things. Around 4th century BCE, Panini wrote his Sanskrit grammar which is a context free grammar and happens to be an example of early use of Boolean logic and the null operator. It is also thought of as a precursor of the Backus–Naur form (used in the description programming languages).

Around this time we also see important contributions from Jain mathematicians that include simple algebraic equations and the first use of word shunya to refer to zero. They also anticipated the combinatorial identity, Pascal’s triangle and Bernoulli coefficients.

The classical period of Indian mathematics is said to be the period between 400-1200 ACE. Aryabhata, Varahamihira, Brahmagupta, Bhaskara I, Mahavira, and Bhaskara II are some of the prominent names in this period. This period sees major ground breaking mathematical activity in the history of Indian mathematics. Aryabhatta in his Aryabhatiya comes up with first ever tables for sine and cosine values. He talks about quadratic equations, gave the value of pi till 4 decimals, whole number solutions to linear equations, performs astronomical calculations for solar and lunar eclipses and also proposes that the planets revolve around their own axis and also around the sun. This was way before Galileo’s time and surprisingly nobody wanted Aryabhatta’s neck for proposing the theory!

Bhaskara II (11 century ACE) anticipated and conceived the concept of derivative, stated Role’s theorem and derived the differential of the sine function and contributed to development of Algebra and Trigonometry. His book Leelavati is a well known text among the Sanskrit scholars.

The Kerala School of mathematics between 1300-1600 ACE gave important results before they were rediscovered by the European world. Infinite geometric series, Taylor series, proof by induction and so on to name a few were discovered by this school.

If you want to know more click on the following links:

1. Indian Mathematics on Wikipedia
2. Indian Mathematics Index

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Manglore and Cultural Policing

There are few times when I agree with GPD. This seems to be one of those. It is a write up on the Manglore incident-certainly insightful and written in a good taste. A must read!

For those who do not know what happened in Manglore, follow this link.

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Race and financial deregulation

Policies can have unintended consequences and most of the time if we talk about them they are negative. However, financial deregulation in US might have had a favorable one; that of reducing the wage gap between whites and blacks. This weeks Economic Focus from the Economist comments on two papers which argue that it was indeed the case.

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Is Obama really that different?

If Obama wins the elections tonight, it indeed would be a historical moment. But what does this mean for other nations? Will the rise of Obama significantly alter the way the world sees US? Will US ever refrain from mindless meddling in other nation’s affairs under the pretext of “war on terror”? Will it ever stop touting 9/11 as the only deplorable act of terrorism in the world? Will it ever stop to think that people who see American planes bombing their homeland actually see it as act of terror?

This article in the Economic and Political Weekly uses the words of Obama from his book, The Audacity of Hope, to speculate about what exactly we might have in store when Obama becomes the President of the US.

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Supreme Court, Hussain & Hindu Morality

The recent Supreme court’s stand on M F Hussain’s nude portrayal of Bharat mata as being a piece of art could come as a surprise to some. Of course the so called “Hindutva” brigade is not at all happy and the so called left- secular lobby could not but betray a smile!

Now are Hindu’s really not used to having their gods and goddesses scantily or not clothed at all? The answer is no. Through out history we as people living beyond the Sindhu river have never been moralizing about nudity or overt displays of love and sex. We celebrated love, life and bodily pleasures. Look at the walls of Khajuraho or Konark temples or the various statues of fertility goddesses. To have a glimpse of how common people viewed these things read Gatha Saptashati. Now I know this is gross simplification and also anachronism, but you get the point right!

Hindu values (or the way VHP and likes would like to think about it) have changed a lot in the last two centuries and now resemble more the Victorian ideals of morality. So are they not real? Actually they are- we as Hindus today believe in Victorian ideals of morality as being the essence of being a Hindu. There is no problem with that. The problem is believing that it has always been like that or allowing politicians in fooling you to believe that way.

So is M F Hussain wrong in painting Bharat mata nude? As I said, some three hundred years back we would not have thought of it as wrong. But today we are different and we would react in a different way. Would every body join the bandwagon? I do not think so. There are still some people who see things differently or a have a more balanced perspective because of reading history.

Having said that, it is also notable that M F Hussain has never used his artistic expression to portray Islam or Christianity. It would be interesting to see how he would do it and how these religious groups react to it.

The so called left liberals and secularists are a different creed altogether. For e.g., I did not read any news about the secular brigade criticizing the Christian response to Dan Brown’s Da Vinci Code in India. So its the art of politics that they have mastered or what we would call engaging in selective empiricism!

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Caste Discrimination in Urban India

Does caste discrimination express itself in terms of difference in salaries and wages in urban India? I am afraid the answer is a qualified yes; qualification being it seems to depend on the level of aggregation we are addressing the issue. There seems to be some evidence for discrmination in the overall urban sector but little or no evidence in software and call industry in particular.

Madheswaran and Attewell use National Sample Survey (NSS) data and find that employees from SC/STs in urban salaried jobs in 1999-2000 received wages that were about 30 per cent lower on average than those of other castes. About 15 per cent of this differential could not be explained by the measures of education and work experience available in the NSS data. Of course, how much of this unexplained differential acutally can serve as an evidence of discrimination will depend on how finer the measures of education and work experience are in the NSS data.

In yet another paper Banerjee and his coauthors find less dicrimination in the call center industry and no discrimination in the software industry. So now the interesting question is why does discrimination persisit in some industries and not in others. It would be intersting to see a model where employers choose to discrminate in equilibrium conditional on some factors.

Banerjee, A, M Bertrand, S Dutta and S Mullainathan(2007): ‘Caste and Religion in India’s ‘New Economy’:Evidence from a Field Experiment on Labour Market Discrimination in Delhi’, Mimeo.

S Madheswaran & Paul Attewell (2007), Caste Discrimination in the Indian Urban Labour Market: Evidence from the National Sample Survey, Economic and Political Weekly, VOL 42 No. 41 October 13 – October 19.

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D D Kosambi Birth Centennial Issue

Here is the link to the D D Kosambi Birth Centennial issue of the EPW. For those who want to know who this guy was, visit this link for some biographical information.

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Bomb Blasts in India

As regrettable the recent bomb blasts in India are, there is also something new about them. The responsibility is being claimed by an obscure group called “Indian Mujaheddin” and does not seem to have a definite objective. Of course, any such kind of violence is destabilizing and creates an environment of mistrust and religious tensions. This article in the NY times gives a good summary of what happened and what is the current state of investigation.

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India and its Left!

The showdown ulitmately yeilded a coalition government that may be standing on even more tenuous grounds than before! But yes, the Leftists are out of the government now. What are the gains? Will the nuclear deal come through in time before Prosident Bush’s term expires? Well that needs to be seen and any cynicism on this front would not be completely out of line. Nevertheless, it remains clear that anything that augments energy capabilities of India should be welcomed.

What becomes of the Left in India? It certainly is not dead. Having continuously ruled a couple of states for quite some time now, they are anything but dead. However, the confidence vote is definitely a setback to its efficacy. The economies of the states that it rules are also not in great shape. West Bengal lost its industrial leadership long back and never really recovered since. Kerala has an amazing record of human development but probably survives on remittances more than any local economy. So there is not much to show in terms of economic success for the Left. As the EPW rightly (and finally!) argued, if the Left wants to have any chance of dominating the central politics it has to have a backing of a successful model. Unfortunately, this is not the case; neither in India nor anywhere else in the world.

Notwithstanding this, one successful contribution of the Left has been in the area of public debate on important economic and social aspects of the Indian economy. And this is surely an important one. If such debates have prolonged the much needed economic reforms, they also have helped avoid unnecessary pitfalls. For example, the left winged economists in India argued against allowing capital mobility long before the mainstream economists started seeing sense in such a policy. The Left intelligentsia has long supported the peoples struggle against poorly executed mega projects like the Narmada Dam.

But apart from such successes, it is indeed true that the Left has much less to offer in terms of economic success. And so long as that remains, it would be difficult for them to contribute meaningfully to politics and governance in India.

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Ashis Nandy and the tragedy of the Argumentative Indian

Ashish Nandy is an influential political psychologist and has written sensibly so far. However, he is being legally persecuted for writing an allegedly provocative piece in the Times of India. His article is been touted as an assault on national integration and hence, its claimed, that he should be tried under the Indian Penal Code. An NGO claiming to deal with civic liberties has filed the case.

First question is where was this NGO during the riots? We do not have to go into the details of who started the riots and for how much of it is Modi government responsible. It would be reasonable to expect that a NGO which finds Nandy guilty of writing a provocative piece should also find Modi government guilty of not being able to control the riots or mishandling of the relief work post riots. Is this failure of Modi government not a violation of civic liberties or detrimental to national integrity? And does not it deserve the same treatment as has been doled out to Nandy?

Well, we know that when actions are politically motivated it is kind of hard to expect fairness. Having said this the important question still remains. Is Nandy’s article detrimental to national integrity? It is definitely not. Is it provocative? I think the only thing that it provokes is thought! But isn’t that is what the written word is supposed to do?

It is indeed high time we question the divisive politics that seems to be catching a significant number of people by fancy. So yes there is a need of continuous efforts to educate people about games that the politicians play. And to this end we need thousand times more of Ashis Nandys writing in all sorts of languages and forms and debating on all sorts of forums. Through reason we progress and see things which emotions try to cover up or at least color up.

If you still disagree with what Nandy has written put your thoughts in words. There is a reason why the system of writing to the editor of a news paper came to exist. With internet it has infact become even easier to use. You can comment then and there itself. The fruits of technology should be used to harbor social cohesion and not division. And cohesion will arise only through dialogue and exchange of views. It definitely cannot come through frivolous lawsuits launched by even more frivolous organizations. I would be more than happy to see BJP condemning the law suit and hope that it sincerely does so. It should do it despite the fact that Nandy accuses most of Sangha Parivar for the divisive politics. It would signal that it is open for dialogue and arguing its case rather than flexing muscles through organizations like Bajrang Dal.

Even I do not agree with some points that Nandy makes. In having a penchant for voilence he clubs Bengali babus, Maharashtrian Brahmins and Kashmiri Muslims together. While mentioning countries as maneaters he forgets to mention Chinia (we have not forgotten Tianmen square) and USSR. He also fails to mention the Maoist factions of left having a penchant for violence. By blaming Sangh parivar for radical Islam he absolves all the fundamentalist Islamic groups in India of any responsibly for their actions. I think these are good examples of gross simplification and selective empiricism. It can actually amount to distortion of history and Nandy of all the people should not be engaging in it.

However, I do agree with his objection to the role of the media. News papers in general and regional news papers in particular have failed to play their role as educators of the society. In catering to market demand they seem to be more than happy to role out pages of crap, bland and sterile psycho babble.

With all these agreements and disagreements the point still remains-pen it down and let people respond to it! Common man, as is often supposed, is seldom a fool.

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