Further points on how to understand modern India (from the comments)

Good post.

There are a few other topics that can serve as useful handles to “understand” India.

1. Study the folk history of the popular Indian pilgrimage sites –

For a lot of people, Hinduism is associated with abstruse metaphysics, mysticism, Vedanta, and Yoga. And this obsession with the high falutin theoretical stuff, means that many students of Hinduism don’t pay as much attention to the pop-religion on the ground. And this religion is best understood by actually understanding the few hundred important pilgrimage sites scattered across the country. Each of these sites is ancient and has a “legend” associated with it. (the so-called Sthala Purana). The civilizational unity of India is largely accomplished because of the pan Indian reverence for these pilgrimage sites. Be it Benaras in the North, Kolhapur in the west, Srirangam in the south, or Puri in the East. A nice way to get started on this is Diana Eck’s book – “India – A Sacred Geography” where she makes a strong case for the theory that the idea of one India is one that is primarily stemming out of the pilgrimage experience of Hindus.

This study of pop religion will be messy and frustrating for people from an Abrahamic monotheistic background. But there is no better way to understand what makes Indians tick spiritually, and why every Indian is a millionaire when it comes to Religion.

2. Study of the history of Indian mathematics –

This may seem like an odd handle to understand India. But in my view it is useful, because Indian mathematical tradition that goes back to roughly 700 BCE, is one that is highly empirical, algebraic, and averse to theorizing and rigorous proofs. So it tells you a lot about the Indian mind. Which is very different from the Greek mind, in that it places a very very low premium on “neatness”, and a high premium on “improvisation”.

Unlike the Greeks, Indian mathematics is not that big on geometry. And also not that big on “visualization”. While someone like Euclid leveraged diagrams to make his point, Indian mathematicians like Brahmagupta and Bhaskara I/II, just stated results in 2-line or 4-line verses.

The Indian mathematical tradition is arguably the greatest Indian contribution to human civilization. Particularly the decimal number system, infinite series, and the algebraic orientation in general (markedly different from the Greek emphasis on geometry). The tradition includes Sulba Sutras (700BCE), Aryabhata (400CE), Varahamihira (400CE), Brahmagupta (500-600CE), Bhaskara I (600CE), Bhaskara II (1100-1200 CE), and ofcourse the famed Kerala school of mathematics (14th century). Madhava from the Kerala school approximated Pi to 13 decimal places. In more recent times, the most distinguished mathematical mind is ofcourse Srinivasa Ramanujan, very much a man in the Indian tradition, who disdained proofs and conventional rigor, and instead relied on intuition and heuristics.

3. Study of Indian poetry and music and its emphasis on meter

This is something that is again uniquely Indian – the very very high emphasis on meter. Which is a consequence of the Indian oral tradition and cultural aversion to writing. Which continues to this day. The emphasis on meter and rhyming was partly an aid to memorization and rote learning. And this emphasis begins with the Vedas (the earliest religious literature, preserved orally for some 1500 years before they were written down in the common era) And you see this in Indian poetry and even Indian film music to this day! Bollywood songs are characterized by their metrical style and perfect rhyming, which you don’t always see in western popular music. In that sense, the metrical legacy of the Vedas is still alive in popular culture.

That is from Shrikanthk.

Comments

What is a good way to study the history of Indian mathematics?

In English, the seminal work is the five volume "Census of the Exact Sciences in Sanskrit" by the late Prof. David Pingree of Brown University. This was published in 1970 though so the scholarship has probably advanced since them. Pingree's contribution to the History of Indian Literature (Volume VI, fasc 4: Jyotihshastra, Astral and Mathematical Literature) gives a decent birds eye view.

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And what's a good way to study the future of Monet's sunrise?

Be there tomorrow morning?

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Thanks for sharing.

Additional remark on the third point - the emphasis on meter has not always been beneficial in its effect. In fact the meter obsession is one reason why a lot of Indian literature is in verse form, and often difficult to follow because several buffer words are introduced in the texts to meet the requirements of the meter.

This has also meant multiple names for the same individual in legend or history to meet the requirements of the meter while discussing them in poetry. So a particular character in an epic poem will have a dozen synonymous names - which are used interchangeably to meet the meter requirements in a given verse!

So unless one has the complete cultural context, reading Indian epic poems in the original can be a very hard exercise.

If you are reading epic poems in the original (I assume you mean Mahakavyas, the "epics" such as Ramayana and Mahabharata are almost entirely written in one, very simple meter.) you will have one or more commentaries to explain all this stuff. It is inconceivable in the traditional mode of study to not have a commentary.

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This definitely happens in Greek and English epic poems too.

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In general, it's difficult to get much of an intellectual handle upon India, in contrast to the way dynastic history provides an opening to developing a modest amount of familiarity with China.

Are there any major controversial theories about India that would be useful, the way that arguing over the Marxist theory of Europe provides a cognitive foothold?

One way to think of Indian civilization is that it represents the "unity of the elites" - there is considerable civilizational unity at the elite level even if you traverse areas as dissimilar from each other as Punjab is from Kerala. But relatively less unity at the level of the lowest denomination.

And this "unity of the elites" has existed for atleast 2000+ years. The effort over the past 2000 years has been to percolate this sense of unity to a greater and greater section of society. One can call this process - "Sanskritization" - a term coined by the sociologist MN Srinivas in a more limited sense to describe caste mobility. But it is also reasonable to use this term more broadly to describe the general process whereby the brahminical world view percolates and engulfs the whole of society slowly and gradually.

This process has been, at best, a partial success. Because unlike in the case of Islam or Christendom, force was not widely employed in India to facilitate this percolation. The elites of India had an evangelical instinct, as well as an exclusionary instinct to withdraw into a shell. And these two instincts have counteracted each other, thus preventing aggressive and fast nation building. So after 2000 years of half hearted lukewarm evangelism, we have a loosely held yet distinctive civilizational entity that can be called India. (as opposed to merely South Asia).

Thanks.

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IMO the big conceptual struggle in Indian thought has been between the householder/ritual-oriented/this-worldly viewpoint versus ascetic/liberation-oriented/other-worldly with one or the other gaining the upper hand at various times.

Thanks.

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All excellent points!

As an Indian, the first one definitely resonates with me. Pilgrimages is one of the primary reasons for Indians to travel all across the subcontinent. If it weren't for pilgrimages, most South Indians would really have no cause to go North, and vice versa. The point about the algebraic mentality is also interesting. On this note, it's good to remember one of the first grammars to be ever published was Panini's Ashtadhyayi, which was a deep and technically complete grammar of the Sanskrit language. Another hint that there was something rule-based/algebraic in the Indian mindset.

One thing I would add: You cannot understand modern India without understanding the Indian Railways. These are the arteries and veins of our country. The best way to do this is to take a long train ride—Chennai to Kolkata is a particularly good route. So is Mumbai to Kolkata. Try to travel second-class, i.e., in a non A/C coach. This way you can open the windows and see and smell the country. You'll get to taste a lot of local food, because hawkers bring in food at stations. Your co-passengers will usually be interesting people and might also have some great food to offer you (families often bring lots of home-cooked food on long train rides.) You might also be harrassed by many Hijras... which is educational. Most importantly, the speed of the trains and the distances travelled will give you a sense of the ambient timescales and lengthscales of Indian life. Of course, you can always pick up a book and read about the Indian railways. Unfortunately, I don't know a good one.

Re: travelling 2nd class

Be sure to use the toilets [vestibules between carriages*] for the full 'Indian' experience

* why rail in the Indian Railways network only lasts five years [vs twenty, in countries with actual toilets in the carriages]

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Regarding #3, FWIW, some years ago football players at Wesleyan U (Connecticut) would take a course in solkattu – a system of syllables and hand gestures used to study rhythm in South India – offered in the music department. It seems they thought it helped them with coordination.

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Underlying Indian mathematical thought and central to many other areas of Indian learning is the grammatical tradition of Panini and others.

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If you've read any of my previous comments at MR you know I'm not a fan of Marxist distortions of Indian culture and history. But this doesn't mean I approve of Nationalist distortions either. Shrikanth, alas is guilty of the later. I find two basic faults in his presentation.

The idea of "Indian mathematics" as a stand alone thing. The Indian concept is Jyotish. This covers the Western concepts of Astrology, Astronomy, and Mathematics. This is not to say that Indian astronomical and mathematical work was not "scientific" (i.e. rational and observation-based) but astrological predictions were the "killer app." If it seems the ancients disdained proofs and theory it is because they weren't really doing mathematics beyond what was practically needed to calculate calendars cast horoscopes or build accurate sundials. The much ballyhooed "Kerala school" for instance were actually a group of interrelated Brahmana astrologer families of Kerala and their findings were not disseminated outside their own circle let alone the rest of India. The shulva asutras are another area where practical needs led to mathematical innovation. They are a genre of Vedic ritual works that deal with the building of elaborate fire altars (agnichayana) for the more important Vedic sacrifices. I don't know why Shrikanth would think Indians were not big into geometry. The shulvasutras are all about geometry including a pre-Pythagorean version of the Pythagorean theorem. (Remember the word geometry means "measuring the earth.") Yet another area as Sid mentions is Sanskrit grammar which at a very early date was formalized in an algebraic form. The basic texts on meters also employ a similar scheme which could also be considered a form of binary counting. The key point is none of these were Mathematics for the sake of Mathematics which it seems to me is an exclusively Greek idea. Perhaps because we have so many other kinds of mysticism, we never got into the Pythagorean/Neoplatonic style number/shape mysticism which powered Greek science.

Second, the Nationalist narrative underestimates how much Indian sciences owe to foreign sources. It is ironic that there is a lot of talk about "Vedic astrology" when Jyotishis actually jettisoned the Vedic cosmological model in favor of the Greek epicyclic theory of e.g. Ptolomey. The new basis was in five Sanskrit works called Siddhantas. One is called Romaka siddhanta which should tell you something right there. (Romaka actually refers to Egyptian Alexandria, the major intellectual center and East-West meeting point in antiquity not Rome.) Another Paulisha siddhanta is thought by many scholars (though others contest it.) to be a translation or paraphrase of a popular late-Roman empire Greek astrological compendium by Paulus of Alexandria. One principal Jyotish work is called Yavana jataka ("birth charts of the Ionians (e.g. Greeks.) I should assure any offended Indians that we did not merely copy. Later authors take the epicyclic theory to greater heights of accuracy than Ptolomey ever did though of course eventually it turned out to be a dead end. And the Greeks were fascinated by "Indian wisdom" too. Figures such as Pythagoras, the Neoplatonist Apollonius of Tyana and even Jesus by some accounts all went to India to learn from the sages.

This cultural exchange continued during the Muslim era too mainly via central Asia. (the art of reading omens from physiognomy is called Tajik for instance.) I have a copy of a Sanskrit translation of Euclid's Elements which was based on an Arabic version. Again it was two way, the most famous example being "Arabic" numerals. I am told the Arabic word for astronomy is sindhind which comes from siddhanta.

Contact with the west even prior to colonial times brought along new innovations such as the telescope and mechanical clocks which led to a flurry of new writing and reinterpretion in Sanskrit. Nowadays calendrical and astrological calculations are mostly made according the astronomical almanac not the siddhantas.

And this I think is the real insight that the history of mathematics gives into the Indian character. The adaptability, the willingness to consider new and foreign ideas and assimilate them into the existing framework.
Three times Hinduism completely changed its cosmological model but there doesn't seem to be any Indian Galileo type martyred for "science" by an inflexible church. I think that's pretty impressive and a better source of pride than assuming everything was invented in Holy Bharata.

Jaldhar - I don't entirely get your comment.

I don't think I was thinking of nationalism or politics while making the comment. It was an entirely apolitical musing on certain handles to better understand India.

I am never going to deny the Greek and Roman influence on Indian Astronomy. It's just that I didn't find it necessary to talk about it in this brief comment. Nor did I categorically say we did no Geometry. I was just emphasizing the penchant for algebra in India.

Also I think you are wrong about Kerala school. Their period of peak activity is 14th to 16th centuries. And a lot of their work has nothing to do with Vedic altar preparation. Their immense work on Infinite series for instance definitely is mathematics for mathematics sake. "Yuktibhasa" by Jyeshtadeva of the Kerala school is a proper mathematics textbook complete with many proofs. The work of the Kerala school is several miles ahead of the ancient Vedic age Shulba Sutras - where the mathematics was clearly intended to serve a practical need of facilitating Vedic ritual. But then a lot of water had passed under the bridge between 8th century BC and 16th century CE. Kerala school is hailed very highly as arguably the pinnacle of the Indian mathematical tradition for a very good reason.

I'm talking about cultural nationalism just as we can talk about cultural Marxism without necessarily meaning the dictatorship of the proletariat. Your comments may not have been meant that way but they fit into the long-standing "Hinduism is the most scientific religion." narrative trope. It's a trope that reflects more of the cultural anxieties of contemporary Indians than an accurate account of history. Take this Kerala school for instance. The very word obscures the fact that they were related by blood not just a body of knowledge. How are they representative of "Indian" mathematics when their work was not known outside of Kerala in contrast to say Varahamihira or Bhaskara who were studied across the country. How can any description of them fail to notice they were primarily Astrologers? But typically when an Indian talks about the "Kerala school" none of these facts are mentioned.

As for the contents of yuktibhasha I can't say because it was written in Malayalam which I don't know. This is another sign it was not meant for widespread dissemination.

You talk as if Malayalam is a secret code of sorts. It is the language of the people and definitely more accessible to the people of Kerala than Sanskrit. Also besides Yuktibhasa the rest of the works in the Kerala school are authored in Sanskrit.

Also there is no conclusive proof that all members of the Kerala school were related by blood. Nor is it clear that they were all astrologers. Melpathur, the last member of the school, was a theologian and composer of Narayaneeyam, a condensation of the Bhagavad Purana.

Nor is it a conclusion that the works were not disseminated. In fact even transmission to Europe has been speculated upon. Moreover the Portugese incursion in Kerala had a deleterious impact in 16th century and contributed to the demise of the tradition.

I think you are just probably letting arguably some prejudice against Kerala or keralites to skew your judgments

Malayalam may not be a secret code but it is a foreign language to anyone outside the immediate environs of Kerala. As far as I'm concerned it might as well be Klingon. We can indulge in all kinds of speculation but the fact remains that this particular tradition never made it outside of a very restricted (even by Indian standards.) circle. Shankaracharya for instance was from Kerala and I don't have any "prejudice" against him. He is an example of someone who actually had a pan-Indian influence. The writers under discussion did not.

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The fact that they did not, has a lot to do with their timing (16th century) and the history of the next few centuries characterized by a lot of turmoil, political and cultural. In a more stable Hindu India, I would've expected the works of the school of Madhava to gain greater popularity across India in later centuries.

One member of the Kerala school, Nilakantha Somaiyaji, also wrote a bhashya on Aryabhatiya if I am not wrong. Which is clearly a pan Indian text. I don't know why he would do such a thing if this were intended to be just a Namboothiri affair.

A work like the one below by Nilakantha - translated by an East India official in early 1800s, suggests that the works were very much accessible to even Mlecchas like CM Whish -

https://en.wikipedia.org/wiki/Tantrasamgraha

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Also the later Kerala school includes men like Sankara Varman, who was a prince, and not even a brahmin, leave alone a Namboothiri.

https://en.wikipedia.org/wiki/Sankara_Varman

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"a better source of pride than assuming everything was invented in Holy Bharata."

I didn't even come close to saying anything as bizarre as that!!

All I said was that the math is arguably the one area where Indians have contributed the most relative to other Indian contributions. I didn't say that Indian math > Greek math (though one can make an intelligent case for that) or that all good things in math originated in India.

You misread my comment :)

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Do you have any thoughts as to the origin of the Indian aversion to writing things down which lead to such intricate oral traditions?

Thanks for your comment --

best,
Marc

This forces one to speculate!

Indians definitely had a script atleast from the middle of 1st millennium BCE and possibly even earlier. However for the sacred Vedic literature, the preservation was oral (father to son transmission), It is usually believed these weren't written down till the common era, though they were composed in the middle of second millennium BCE. The Marxist take on this is - that the Brahmins (priests) wanted to preserve their power and didn't want to write down scriptures and democratize them which would reduce their leverage and influence.

But that's the Marxist view. Traditionalists argue differently. For them, the Vedic songs were important and sacred for the sounds they created and preservation of the exact pronunciation of the original bards was necessary for the prayers to have their efficacy. Hence the oral tradition.

I lean towards the traditionalist view. But I think a third reason is the problem of durable writing material. Palm leaf was the most commonly used material for writing. Which isn't as durable as perhaps Vellum (not used in India due to cultural reasons). That probably contributed to the aversion to writing.

However I do see the aversion to writing to this day. My Indian colleagues in office hate writing descriptive e-mails and prefer oral conversations as opposed to my western colleagues.who like to write things down on paper or mail.

Traditionalists argue differently. For them, the Vedic songs were important and sacred for the sounds they created and preservation of the exact pronunciation of the original bards was necessary for the prayers to have their efficacy. Hence the oral tradition.

Sounds quite plausible. You may be on to something here. I've read that no one today know exactly how classical Latin used to be pronounced by its early Roman speakers. Perhaps Latin's rich written tradition is to blame for that?

However I do see the aversion to writing to this day. My Indian colleagues in office hate writing descriptive e-mails and prefer oral conversations as opposed to my western colleagues.who like to write things down on paper or mail.

Not in my experience. But my interactions have been with Indians in grad school or in companies where Indians are not in preponderance (i.e., the IT services/outsourcing companies.) But if you do observe this phenomenon, it could be partly because of the inferiority complex many Indians have w.r.t. proficiency in the language. They might feel unable to write English using all the proper vocabulary and grammar to match native English speakers, and so prefer to interact verbally. Grad students whose business it is to write papers don't have the same issues (or lose them over time.)

"Perhaps Latin’s rich written tradition is to blame for that?"

Yes, Sanskrit has a rich written tradition too. But coupled with an even richer oral tradition. The pronunciation of of both Vedic and non vedic mantras / scriptures by priests and the like today not all that different from how it was pronounced 2500 years ago.

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Most Indians historically have been illiterate but the various groups that were literate were not averse to writing things down. Traditional Brahmanic education does emphasize memorization (as did Medieval western scholasticism) but it is memorization of discrete texts not an oral tradition. My Guru compared using books to a wheelchair. Nothing wrong with it if you are disabled but it is ridiculous for an able-bodied man to use one. The sentiment didn't stop him from owning a large library.

The big exception is the Vedas which must be learned and chanted with extreme precision. I'm currently teaching a portion of the Vedic mantras to my son. As a third-generation Gujarati-American he would find it difficult to read Devanagari or Gujarati even if he wanted to (he is learning though.) But his pronunciation is as good as anyone in India. Even so, there are Vedic manuscripts some of great age so writing them was not exactly taboo. There are other sacred texts which are used in ritual or as objets d'art explicitly in written book format. Here for instance is a page from the Victoria & Albert Museum about Jain illuminated manuscripts. http://www.vam.ac.uk/content/articles/j/jainism_illuminated_manuscripts-and-jain-paintings/

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I am a little skeptical about the aversion to writing. There are Indian languages that have even 56 alphabets and sounds that are often missing in English.
In Tamil there is an alphabet ( "zha") which i cannot pronounce and generally it is held that cannot be pronounced by those who don't know Tamil , even those of neighbouring states.
Such complicated alphabets cannot develop in a culture with aversion to writing.
Yes, Shrikant's point below about the materials used is correct but although he wouldn't agree , there was a strong casteist preservation of knowledge in the oral tradition. Though one cannot deny that the cadences that arise in chanting cannot be captured in the written word alone.

In India Sanskrit holds the same place that Latin held in Europe. And the battles to bring the Prayers into popular lanaguages from Latin , held true in India as well.

When poets wanted to translate the Mahabharata from Sanskrit to the more popular languages there was a belief that they will die due to the wrath of the Gods.
Translating from Sanskrit to Telugu ( the second most spoken language , though most are not aware of it) , the poet Nannaya died after translating 2.5 Chapters.
The next poet did not dare to start in the unfinished Chapter 3 , but went from 4 through 18 , the end.
And it took a century more for a third poet to complete the unfinished chapter (famously starting with the style of the first and transitioning to the style of the second) .
Yes , literacy was low and writing a rare phenomenon but wasn't that true of Europe as well before the printing press?
https://en.wikipedia.org/wiki/Kavitrayam

The analogy to Latin is forced. Latin was the lingua franca of the learned classes of Western Christendom but it was not sacred in of itself. As I understand it, the quarrel between the Catholics and the emerging Protestant movement was mainly over authorization for making translations not the idea that the Bible couldn't be translated from Latin. It is after all originally in Hebrew and Greek. By contrast Sanskrit is intrinsically sacred. Translating a mantra into another language would destroy its essence.

There were no battles to bring prayers into vernacular languages. You have always been able to do so. The literature of most modern Indian languages begins with translations of Mahabharata, Ramayana etc. Sometimes there were other issues. For instance there is a story that when Goswami Tulsidas was writing his famous Hindi translation of the Ramayana, Ramacharitamanasa, he came under heavy criticism from the Pandits of Kashi. But the objection seems to be that Hindi was a "vulgar" tongue (and that of the Muslim oppressors who had done a lot of recent damage in Varanasi) not to the idea of translation itself. In the end Tulsidas is vouched for by no one less than Swami Madhusudan Saraswati the dean of orthodoxy of his generation which is telling.

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The strangest thing about Indians is how they crave (for lack of a better word) moreness, whether that be in terms of color, thalys, gods, traffic, multi-person debates, huge family gatherings, etc. Borges once commented that often the most cherished strands of a national culture develop as a sort of antibody to mitigate a people's dominant psychological tendencies, so for example with sober England you have highly emotional Shakespeare, in closed-minded Germany you have cosmopolitan Goethe, etc. I often suspect that the meditative strand of Indian religion developed as a sort of escape from the craving for *more* that seems so prevalent in India. I say this based on my experience of being married to an Indian, having many Indian friends, visiting a few times, reading a fair number of the canonical books, etc.

Interesting comment. Never thought of it that way. Very often the "moreness" is part of the ecology and hard to get away from.

May also have something to do with "private spaces" versus "public spaces." I have seen huge mansions in villages , where still a child may not have a private bedroom, in the western tradition.

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Sincerely, I don't think "more" traffic in India is the result of our higher levels of craving for more traffic. It's just that we (most of us) have a much lesser need for personal space and a much higher tolerance for chaos and adhocism (for lack of a better word; perhaps "jugaad" comes close.) And also, if you've grown up with "more", you really can't imagine what "less" is like, so there's little drive for change. I agree though that people who go off into meditation (or "sanyaas") are looking for an escape from all the craziness around them.

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Anyone have recommendations on getting into understanding Indian meter? Are there introductory books or must one for a more practical approach.

I have a bit of Sanskrit, Hindi and familiarity with some sung devotional traditions.

Must one study music to really get it?

No expert on this. But the classical authority is Pingala and his Chanda shastra, the fundamental book on Sanskrit prosody. I think it is in sutra form and requires study with a commentary.

https://en.wikipedia.org/wiki/Sanskrit_prosody

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Hello Prof Cowen,

One could figure some bit of India via its banking history as well. I have tried to show names of Indian Banks have evolved with changing political and economic conditions in India: http://www.livemint.com/Sundayapp/szg4AHalBBbujaCyGUfamN/Whats-in-a-name-Ask-banks.html

Thanks,

Amol

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