Category Archives: social perspectives

gender gap and test score distribution

A number of people have been talking about the gender gap in math in the US recently. The debate was most likely initiated by Larry Summer’s comments on the small number of female researchers in hard sciences in the top US schools. So much so that there might also be some policy initiative to address the problem.

There, of course, has been some careful analysis of the gender gap phenomenon. Steve Levitt’s this paper is an example.  However, there are some people who just tinker with the distribution of the test scores to infer something about differences in abilities between male and female students.

So the important question is can we use the distribution of  test scores for male and female students to infer something about the difference in their abilities? My answer is a straight no. Technically there would arise what we call an endogeneity problem. Existence of social bias and the ever pervasive gender stereotyping has a great influence in shaping the preferences and development of certain abilities among male and female students. If this is the case, the resulting distribution would reflect these cultivated differences and hence any inference based on it about the gender gap is going to be obvious. It is like we planted one avocado and one mango tree a while back and then after some time infer that they give completely different fruits.  How stupid would that be?


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Demise of the bilingual intellectual!

One of the exciting things about Diwali, the festival of lights, in my homestate was reading the special issues brought out by variety of publishing houses. These special issues are called “Diwali Anka”. However, oflate we have found that the wirteups seemed to be loosing steam with every Diwali. So much so that last Diwali we did not get the special issues at all!

Same is the story with marathi news papers. In the race to appear as flashy and colorful as possible, most of these papers have lost substance. They pander to the smug middle class sensibility which is typically non confrontational and prefers status quo over almost all important issues. Unfortunately they form the major chunk of the market and running a newspaper is more of economics than promoting debate and intellectual stimulation.

The newspapers in English, on the other hand, have done quite well in terms of having a balanced mix of entertainment and substance. I always wondered why is this so. Fortunately, Ramchandra Guha provides an interesting answer in this very well written article in a recent issue of the Economic and Political weekly.

He very aptly points out the decline of the bilingual intellectual from the Indian social scene and suggests that as a reason for the deterioration of intellectual discourse in the regional languages in India.

I completely agree with his assessment. Let me know what you think!

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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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