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Friday, October 30, 2009


Evanescent Dharma -How is our cultural and religious corrosion catalysed?

Note: I am referring to bharatiya culture and sanathana dharma in this context.


असतो मा सद्गमय
तमसो मा ज्योतिर्गमय
मृत्योर् मा अमृतं गमय
ॐ शांति शांति शांति
( बृहदारण्यक उपनिषद् 1.3.28)
Day by day, the Kali yuga proceeds and the foresight of the rishis unfold in a very predictable fashion. In the name of freedom, people live as examples of "nrupasu", meaning man who is equal to an animal. This article talks about the various factors which slowly are invading the hindu society to cut it off from its roots, which is sanathana dharma(or "eternal dharma"). These are the ones I wish to concentrate in this post, while several others might also be the reasons.

1 The Christian Missionary activity and Islamic terrorism.
I would like to start with Kanchi paramacharya's quote on the stupidity of certain important tenets of these abrahamic religions.

"We cannot, however, help asking whether their belief is right. People who do not follow either Christ or the Prophet, are they really condemned to hell? A little thinking should show that the belief that the followers of Christianity or Islam have an exclusive right to salvation cannot be sustained. It is only some 2, 000 years since Jesus was born and only about 1, 400 years or so since the birth of the prophet. What happened to all the people born before them since creation? Are we to believe that they must have passed into hell? We are also compelled to infer that even the forefathers of the founders of Christianity and Islam would not have earned paradise. If, like Hindus, all those who lived before Christ or the Prophet had believed in rebirth, we could concede that they would have been saved: they would have been again and again until the arrival of Christ or the Prophet and then afforded the opportunity of following their teachings. But if we accept the logic of Christianity and Islam, according to which religions there is no rebirth, we shall have to conclude that hundreds of millions of people for countless generations must have been consigned to eternal hell."

These untenable religions have such claims which cannot be even reconciled among themselves. Now, they start "saving" the world with their"peaceful" religions. While I acknowledge that there might have been people who were motivated towards humanitarian endeavors because of every religion, the violence in the reference texts are way beyond any acceptable limit.

Exodus 35:2 -- For six days, work is to be done, but the seventh day shall be your holy day, a Sabbath of rest to the LORD. Whoever does any work on it must be put to death.

Dueteronomy chapter 7 : Talks only about violence towards other nations and nothing else.

Ephesians 6:5 --- Slaves, obey your earthly masters with respect and fear, and with sincerity of heart, just as you would obey Christ.

Numbers chapter 31---ridiculously eulogises violence. (For eg, verse 17-18 goes like... Now kill all the boys. And kill every woman who has slept with a man, but save for yourselves every girl who has never slept with a man)

Dueteronomy 21:18-21--If a man has a stubborn and rebellious son who does not obey his father and mother and will not listen to them when they discipline him, his father and mother shall take hold of him and bring him to the elders at the gate of his town. They shall say to the elders, "This son of ours is stubborn and rebellious. He will not obey us. He is a profligate and a drunkard." Then all the men of his town shall stone him to death. You must purge the evil from among you. All Israel will hear of it and be afraid.

This list is much longer. Some more verses as ready examples are Collossians 3:22-24, 1 Samuel 15:3 , Judges 15:8 , Luke 12:49, Matthew 10:34-39 etc. With inspiration from such a scripture, the missionaries who followed the sailors literally burnt off cultures on their path.

The consistency of the missionary behaviour is a giveaway regarding the influence of their religious text on their actions. Christianization of Europe roughly extending over a period of 700 years from 350 AD to 1100AD was one of the most violent in terms of religious conversion. The Ancient greeks were tortured beyond imagination to give up their faith. Many important intellectual works were destroyed in the conversion frenzy. The medieval inquisition and witch hunt are sad episodes in the world history. Millions were killed. The inquisition in fact spread its roots even till Goa in India. Deigo de Landa burnt thousands of books of the Mayans and tortured them endlessly for following their faith. The South American native civilizations also perished in a similar way. African colonization and christianization attempt is another brutal episode. There are few places where they have not left their bloody footprint. (Of course, In India they tried more of an intellectual approach to conversion compared to violence)

Though the vedic religion survived because of its inherent strength and bhagawan's grace, the darker side of the truth is conspicuous. The Dalai Lama during his visit to one of the Kumbha melas(that has been recorded and released as a CD titled 'Shortcut to Nirvana') said that conversion is an outdated concept. I agree. Ancient India had a practise of philosophical debates to initiate conversions. Of course that shows a mature way of dealing with things. However, such fine practices are unknown to the missionaries, who lurk around in every place even now and start preaching whenever it is possible. There is absolutely no need of any new religions in India. The need of the hour is reforms in the age old tradition, to bring the wisdom of the dharmic religions to the masses.

As far as the other monotheistic religion, Islam, I have nothing to say here, because it would consume much of my post. I personally checked out a copy of Quran from my university library. It had been translated by 2 faithful Muslim scholars. To me the text appears to be just a political violence manual. In fact according to some statistics, 61% of quran talks only about violence towards non-believers. Check this out for yourself in the following link(Extremely interesting)

http://www.thereligionofpeace.com/Pages/Quran-Hate.htm

No wonder The Muslim people and Kings in India for a 1000 years destroyed countless temples and killed millions of Hindus. The best part is the hindus are blamed if they retaliate at some point when the issue goes out of control. Ridiculous!

Let us wake up and read the most important treasures of our civilization, which is of course, the vedas, itihasas, saatvika puranas, dharmashastras, pasurams of azhwars and sri sookthis of Acharyas. Let us not be ignorant of our shastras. I encourage the Buddhists and Jains also to be thorough with their religions because though there are clear philosophical and ideological differences among all the Indian religions, they all emphasize a common concern for life, peace and freedom. Otherwise how can one expect to see hundreds of sub sects in the subcontinent even two thousand years ago? 

2.Neo-hinduism and NRMs

There is a dangerous group in India from the distortion point of view of classical ideas. It consists of self-declared swamijis. Swamijis includes many 'anandas' who simply start preaching the greatest myth of all times "All religions are same", which is a statement that cannot be more farther than truth. (I will deal with this great myth in a separate post). Hinduism for that matter does not preach that all religions are same. When a religion declares "kill the non-believers" or condemns all non-believers to eternal hell, how can it be ever equal to sanathana dharma, which teaches us a path to moksham via a dharmic life?

The NRMs are the New Religious Movements. Eg, Arya samaj, ISKCON, art of living, Oneness temple(flowering heart) etc. They often have no direct spiritual lineage to relate to right from the time of vedas or leave out important parts of our scriptures. Many join the new-age gurus to propagate the myth"all religions are same" which is a lie. ISKCON, on the other hand has a track record of miserable failure in the America of the '70s due to inherent flaws. It enforces strict near ascetic life for each and everyone irrespective of their backgrounds. This is impossible for the common folks who then start going astray after sometime. This resulted in the sexual abuses in the iskcon gurukulas of the '70s. Also the much debated "Acharya succession" issue reflects the lack of authentic tradition. These gurus and institutions adapt the teaching to market their discourses to suit their audience's tastes. This contrasts with classical works whos authors never knew us and hence are a good source of our true dharma. While Swami Dayananda did the most important work to re-establish the supremacy of vedas and give them a symbolic interpretation, he rejected the archa form of the lord much to everyone's dismay. The Arya Samaj also does not accept any other later scripture as authentic which is akin to discarding a library consisting of lakhs of books while retaining just 4 books(though of supreme importance).

3. Decline of sanskrit studies.


The masses have become so money oriented that anything that improves one's spiritual life has become a mere mockery for most people in the present generation in India. We can safely assume that atleast 75% of hindus today belong to a modified charvaka matham.(the materialistic school of ancient india). Sanskrit study is not encouraged by many people, parents or the academicians. Since sanskrit, deva bhasha is the key to the vedas and all the associated literature and proper understanding of hinduism, without it most of us miss the profound teachings of our rishis and acharyas and get swayed by superstition and ill-informed malign indologists and cheap-gimmick gurus.

The 'spoken sanskrit' has taken on a huge importance these days. I am not against this trend but i feel that this is insufficient for any great purposes. It is the trend now to go to crash courses and learn to speak sanskrit in 10 days or 20 days but no deep analysis of the written texts are possible with such shallow knowledge.

4. The entertainment epidemic.

Obscene,outdated movies and profane songs full to the brim with tamo gunam and rajo gunam including their trash lyrics seem to be the order of the day. I do not quite understand how any civilised person with a good thinking can spend all their leisure time on such junk and waste away their precious human life without some form of pursuit of sprituality. Most of the Indian movies(especially tamil ones, because i was indirectly forced to listen to such trash lyrics, thanks to those, with such pathetic tastes, surrounding me wherever i go) well gel with the foregoing description. People declare proudly that they are about to watch this movie or that and end up paying huge amounts in the state of art theatres, while not spending even one tenth of such amounts to ancient wisdom or national cause. The media is so bad these days that almost any program except a few can be easily said to be trash. Good movies and songs do exist, but get drowned in the ocean of the above said lot. While it is good to relax with these, it is a grave mistake on anyone's part to spend one's life on it.

I accept that personal tastes vary among the populace but I feel that at least some portion of each one's leisure time should be spent on contemplating about spiritual problems and consulting the solutions of our Ancients. I am pretty sure that there will be guilt in these people for wasting away their youth years in such paltry entertainments. Here is a short article about how we support vulgarity in the media:

http://www.satyavidya.org/component/content/article/52-miscellaneous/1-how-we-support-the-growth-of-vulgarity

5.The rat-race.

Many of us have given up almost all of the nitya karmanushtanams like sandhyavandhanam, aradhanam etc. which do not take huge amounts of time. While we seem to have time for gossip and all the utterly useless things in our life we "do not have time" for such karmas which are the prescriptions of bhagawan krishna.(Remember that it has been repeatedly emphasised that one is unfit for any further karmas if he does not perform sandhya daily. So there is no meaning in these people doing 'pooja' to deities on every occasion). The rat-race for money, comforts and 'hep' lifestyle which were the things precisely avoided by our ancestors (for excessive money leads to attachement and all related evil) , has assumed huge importance. The peer pressure rules our decision regarding any minute thing we do and we are all slowly getting burned out at younger ages due to work pressure. Michel Danino states aptly,

"Western civilisation, not even three centuries after the industrial Revolution, is now running out of breath. It has no direction, no healthy foundations, no value left except selfishness and greed, nothing to fill one's heart with. India alone has preserved something of the deeper values that can make a man human and the world will surely be turning to them in search of a remedy to its advanced malady"

The only thing that differentiates a man from any other animal is his adherence to dharma.

"Aharanidrabhayamaithunam ca samanyametat pasubhirnaranam
Dharmo hi tesamadhiko visesah dharmena hina pasubhissamanah"

(Meaning: Human beings and animals have the same urges. They eat and sleep and copulate and besides, the feelings of fear are common to both. What, then, is the difference between the two? It is adherence to Dharma that distinguishes human beings from animals. Without Dharma to guide him man would be no better than an animal.)

6. The NRI myth.

A common myth about the NRIs is that they are culturally and religiously more pious than their Indian counterparts. While this may accurately describe a few, the general case is not so. The NRIs contribute to erosion of Indian knowledge and heritage in their own unique way. Most of them in their student phases do not even care for what their parents had to say, leave alone what Ancient India had to say. Let me take America for instance. They try to mimic what they consider 'fashionable'. This happens in various ways. Their language,behaviour and body language changes altogether in a few years. Many Brahmins start eating non-vegetarian foods, including beef, become at least half drunkards and consider it to be "modern", "fashionable" etc. This denouncement, which also exists among the Indian college students(discussed later in this essay) is a very etchy problem. Francois Gautier,a Paris-born political analyst who lived in India for 30 years, mocks India's elite intelligentsia's obsession with the west and all things western and asks them:

" O members of the Indian intelligentsia! You think that reading the latest New York times best seller, speaking polished english and putting down your own countrymen, especially anybody who has a hindu connection, makes you an intellectual. But in the process you have not only lost your roots, you have turned your back on a culture and civilisation that is thousands of years old and has given so much to the world. You are forgetting what a privilege it is to be born an Indian-and a hindu at that-inheritors of a spirituality that accepts that God manifests himself under different names, at different times, when today the world's two biggest monotheistic religions still think their god is the only true one and it is their duty to convert everybody by guile or force."

When they settle down and start having children, suddenly knowledge "dawns" upon them and they start behaving slightly better. I have personally spoken with ABCDs(i.e., children of the NRIs) and feel that they are not responsible for the terrible accents when they speak their mother tongues. How does anyone expect them to know deep facets of Indian culture?.(Infact I am not implying here that the Indians are not plagued by these problems, but am trying to analyse the NRI situation). Progressively, as generations go, they can declare proudly that they belong to "Indian" lineage but they have not even seen India . If they expect to learn about India and her culture from their text books, it is just the distortions that they will learn.(Eg, California textbook case where Hinduism was portrayed in a very negative manner due to the bias of the writers towards judeo-christian traditions.).

Most of the NRIs are not prepared to leave their big materialistic life styles to go back and take care of their ageing parents. I know of atleast three elderly women in my extended family who are loners just because their sons choose to visit them only once every two or three years. Sending back money is not the be all and end all of this issue.

I am able to observe the thinking and interests of the general NRI group since I am myself a temporary NRI until I return for good. While I am not targeting someone just for living outside India, what I am really targeting here is the myth that NRIs are somehow closer to their culture. My conviction has been strengthened after observing the people around me. The attitude and goals of most of the NRIs are no different than an average Indian. Only that they happen to live elsewhere. They are as materialistic(if not more) as Indians living in India and arrange a get together for festivals and parties. An additional feature of a NRI family is that the children usually after five years of age, are out of touch with their ancestral land, culture, language and their kinsmen.( Arguiung that culture is something that is in constant flux and hence cannot be defined etc just hints at escapism. While we know that time changes everything, we can definitely ensure that we do not go too far from what we have inherited from the previous generation. Inspite of knowing this, the present generation just seems to give excuses to carry on their easy life).

7.Political manoeuvring.

Caste and religious play is a common feature in Indian politics. More so in Tamilnadu, where the asuric forces(as of 2009) have taken over the government and interfere in many aspects of Sanathana dharma. They try to give wrong facts about the basic texts and also interfere in temple activities,which have an already well-established agama shastra and needs no one's attention. There is absolutely no need for reservation for minority religions because if they have talent then they can compete with others and establish their positions. All these factors turn some hindus against their own religion. They view their own dharma as inferior or sometimes convert to other religions for gaining entry into educational institutions etc.
Update: The New chief minister Jayalalitha was elected in 2011 and hopefully the situation should improve.

8 Self-declared 'Indologists' and their Indian pet-dogs.

Starting with Max Mueller and his "(mis)interpretations" of Rig Veda, this group of so-called scholars have done more damage to Indian and hindu literature and culture than everyone else put together. They worked hard with colonial and christian missionary work in their minds to degrade Indian culture and deem it as primitive and foreign. The Aryan Invasion theory for eg, has been decisively proven to be false. There was no invasion whatsoever and Our great rishis were the original inhabitants of the Indian subcontinent. for a thorough arguement, see:

http://www.archaeologyonline.net/artifacts/aryan-harappan-myth.html
http://folks.co.in/2009/09/harappan-civilization-is-vedic-civilization/

The damage they have done is so deep that it will take a long time to heal. Schools in India still teach this outdated and false invasion theory. The indologists also belittled the vedas and other scriptures and tried to instill a negative image into the Indian mind. Their straight descendents still exist for eg, Michael Witzel, a Harvard professor in indology. He holds on to his pet theories with no basis and was given the right treatment by Indian scholars when he could not answer their questions. Frits Staal, Wendy Doniger, Jeffrey Kripal are some more examples in this category. However there is the other lot of westernised and marxist historians like Romila Thapar, writer Meera Nanda who wag their tail to people like Witzel and denounce their own culture. The ineffeciency of these indologists to interpret any vedic scripture ia aptly discussed along with some myths about vedas here:

http://agniveer.com/vedas/myths_vedas/

The other important source of misinformation is popular sites like the wikipedia. While it is true that wikipedia might give reliable information on scientific facts, it is not so for religion or history. The group of "specialists" behind wikipedia is so rigid and hopeless that they do not welcome any suggesions or alternative readings of certain facts and theories in history and religion. They still give outdated information on for eg, Rig Veda but have no scope for improvement. So, my advise to whoever reads this post is "do not rely on wikipedia for sanathana dharma and indian history"

9. The pathetic Indian student.

The 'college culture' if there is anything like that in Indian colleges are as incorrigible as it can be. Students waste away their precious years on computer games that are of null value towards anything one can imagine(health,spiritual growth,material growth,knowledge etc.). In fact it is damaging to each of these. I am from BITS,Pilani. So I will put down what I have gleaned about this corrosive counter-culture from this place. "Oasis" is supposed to be a cultural festival of BITS. In my opinion, parts of it can be better termed as 'acultural festival' as it has no culture whatsoever in it. Some Students lose their inhibitions and freely give themselves away to drugs, sex and other vices. Others who are more sensible, restrain from these but are addicted to rock and third rate music. While taking a break in the form of a fest is perfectly fine, the song-mania almost never ceases and continues through all other times too. None of these reflect even an iota of concern for Indian culture, tradition or values. Drinking and smoking become a part and parcel of their lives for many.

The birth day celebration is another big joke. The birthday person is beaten up and he cannot even move his limbs the next day. Some groups take it to the level of breaking eggs on the person against his own desire. If one successfully puts up with all these uncouth behaviour, then he is acknowledged as "cool dude". Else he is banished from the group.!! Students often have booze parties and go to the level of puking,singing and dancing while drunk and brag later that they have had the best times in their lives(so called memories....huh!) little realizing how much time they have wasted . (It was surpising to me how much time and effort youngsters spend in uploading videos of their friends taken while they are blabbering after getting drunk).

This list of college behaviour is endless. Ragging and continuous watching of pornography are other instances for example. These self-declared free-thinking and modern youth are in fact more stubborn and biased regarding their ill-informed views that they are totally unfit to question traditional wisdom(because they do not even know what their scriptures say). In summary, students care least about other fellow human beings, their parents' feelings, Indian culture and their religion and contribute so effectively for degradation of our dharma.

10. the ubiquitous materialism in educational institutions.

The educational institutions are no less worse. They do not impart any proper moral education from a young age. While students are taught 'about' religion, they are never offered even electives on religious topics(schools as well as colleges). The management is after money and nothing else is important for the administrators. Students are encouraged to study just science for material benefits and other fields of creativity are ignored. Hence they share the role in the widespread guilottine of culture. The result of this as well as neglect on the part of the masses themselves to know their religion is best expressed by the following anecdote from the book Hindu Dharma.

The following is a part of translator's note:

"More than 20 years ago, I said in an article in The Illustrated Weekly of India that "Hindus know less about their religion than Christians and Muslims know about theirs". Wanting to verify the statement, my editor Sardar Khushwant Singh asked my colleagues (most of them were Hindus), in schoolmasterly fashion, to name any four Upanishads. For moments there was silence and it was a Muslim lady member of the staff who eventually responded to the editor's question by "reeling off" the names of six or seven Upanishads""



Thursday, September 17, 2009

Hwal' Bay Nyu Wa- A land to inspire our Spirit
(Home of the hualapai)
(painting of the canyon by Bruce aiken)
Grand canyon- one of the earth's most powerful inspiring landscapes-overwhelms our senses. Its story tells of geological processes played out over unimaginable time spans as a unique combination of size, colour and dazzling erosional forms: 446 km long, upto 29 km wide and 1.6 km deep. Its rugged landscape hosts a fascinating variety of plant and animal communities, from the desert next to the colorado river deep in the canyon to montane forests atop its north rim.
Humans have also played their part in the history of the canyon as evident from the archaeological discoveries.
The journey

I live in Tempe, Arizona presently. This belongs to the phoenix area, which is the capital of arizona state, known for its distinct Native indian population. We reached grand canyon through flagstaff, a town which is a 2 hour drive from here.
(USA-Arizona highlighted)
Grand canyon shown on google map (click to enlarge)

Our first trip was to the West rim of the canyon.

(The group)
This place is best known for its skywalk, a major attraction from couple of years back.
This is the best we could capture the skywalk(side view in the background) as we were not allowed cameras there. They had a system of capturing our picture while on the skywalk but charge us a humongous 30 dollars. So, we opted out of it. For a sake of feel of the skywalk I borrowed a couple of pictures from elsewhere in the web.
This is basically a glass bottomed, horse shoe shaped cantilever bridge which has been engineered using the state of art techniques. As you walk on it you can see through the bottom of the bridge to what is 4000 to 5000 feet of the depths of the canyon's wilderness. It is a scintillating experience. You are just a glass plate away from 4000 feet of free fall!
A nice video of the skywalk from national geographic

http://news.nationalgeographic.com/news/2007/03/070328-skywalk-video.html

60 dollars is what puts off people who go to the west rim. On the other hand what i suggest is that it is worth the trip if you consider that you pay 20 dollars for the skywalk and 40 more to enter the area to see the grand views of the grand canyon. The eagle point is the same place as the skywalk but the eagle formation in the the rocks is a natural wonder.
If you observe closely the background in the above picture, you can see the dip in the rock formation and there it resembles the eagle's body and the sides resemble its wings spread out.
(An oblique view of the eagle)
(The edge of the canyon facing the eagle)
The other good view point in the west rim is the guano point. The colarado river cuts its way meandering all over the place.

The above view shows a small hill on the other side of which the canyon turns around from the left side to the right side. The grandness of the canyon is infinite to be captured by the tiny camera!

Near the earlier mentioned skywalk we also saw some model Native american huts. It was an interesting view.

These settlements belong to the hualapai tribe, which also privately owns the grand canyon. The hualapai along with a dozen other Indian tribes especially the yavapai and the havasupai descend from the ancient anasazi tribe who inhabited the ancient southwest america more than 4000 years. They speak the languages belonging to Yuman-Cochimí language family.

The europeans directed by the hopi(another famous tribe of arizona) first had a glimpse of the canyon in 1540. It was not until 1775 that fransiscan friar fransisco garces explored upto the colorado river on foot and horseback. 'colorado' meaning "rusty-red" in spanish is the name that caught on. After some minor explorations, a major undertaking was in 1869 by Major john wesley powell and his crew of eight. He encountered the wilderness of the canyon on its face and gives us a graphic description.

"The cyclopean forms which result from the sculpture of tempests through ages too long for man to compute, are wrought into endless details, to describe which would be a task equal in magnitude to that of describing the stars of the heavens or the multitudinous beauties of the forest..."
(.....A testimony of time)

South rim

Our next day trip was to the south rim which is generally a busier outpost compared to the west or the north rim. The first point there was the manther point.
This view is curious for a different reason. The peaks in the background here are named after Hindu and other ancient deities. For eg, there is the vishnu temple,shiva temple, buddha temple, Isis temple(ancient egyptian goddess). 'Temple' means a peak here.

Interestingly enough, the basement rocks of the canyon are called as vishnu basement rocks, which i premise to be a tribute to the almighty whose shariram(or the cosmic body) forms all of the manifested worlds.

Yaki point is another important view point in the south rim. We felt that here a more wider view(about 180 degree) is available.
(A view from yaki point)

Now on to some geographical information..........

The canyon is the old world marvel consisting of several layers of rock formation.

Five broad stages can be recognised in the ultimate formation that we witness at the moment. They are as follows:

Stage 1: Vishnu basement rocks

Tectonic plates move slowly across the earth's surface. Almost 2 billion years ago a plate carrying island arcs and the plate that became North America collided. Heat and pressure from this process changed those existing rock layers into dark metamorphic rock, the basement of the canyon. Molten rock then squeezed into cracks and hardened as light bands of granite.

Stage 2: Grand canyon supergroup
The red shale, fossil-algae bearing limestone and dark lava of the grand canyon supergroup are revealed only in a few areas. The many strata of the supergroup accumulated in basins formed a s the landmass pulled apart. The expansion caused blocks to rotate, tilting the supergroup layers.

Stage 3:Paleozoic Sedimentary rocks
Nearly horizontal layers of sedimentary rocks comprise the upper two-thirds of the canyon walls. These rocks formed near sea level and at the edge of a continent. The remains of marine life accumulated on the ocean floor to form limestone. Rivers deposited sediments in swamps and deltas that then became mudstones. Dunes solidified into sandstone.

Stage 4:The colorado plateau rises

About 70 million years ago the rocky mountains began to form, pushed up as the North American plate overrode the pacific plate. In the process a large section of what is now Utah, northern arizona, western colorado and a corner of new mexico rose from sea level to elevations of thousands of feet, forming the colorado plateau. This uplift occured with remarkably little tilting or deformation of the sedimentary layers. The stage was set for the carving of the canyon.

Stage 5:Canyon carving
By five or six million years ago, the colorado river flowed across the colorado plateau on its way from the rocky mountains to the gulf of california. Each rain washed sparsely vegetated desert soils into the river. A steep gradient and heavy sediment loads created a powerful tool for erosion. The river's volume varied seasonally and over time. As the las tice age ended 12000 years ago, the volume may have been 10 times today's volume.

As the river cuts down, the canyon deepens. Tributaries erode into the canyon's sides, increasing its width. Erosion carves faster into the softer rock layers, undermining harder layers above. With no foundation these layers collapse, forming the cliffs and slopes profile of the canyon. Erosion wears away the ridges separating adjacent side canyons, leaving buttes and pinnacles.
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(Another elegant mark of the river)


Yavapai observatory point is a point that was chosen by geological and other experts to be one of the points where we can have the grandest view of this nature's wonder. Therefore the point has an observatory. The formation process of the canyon is explained there with various models similar to musuems. There is also a book shop available at the place.
(Yavapai observation station)

Exciting things to do at south rim

Helicopter ride, rafting and various trails are the different things you can engage yourself in, at this place. The helicopter ride seems costly at 150 dollars per person for just 25 to 30 minutes of the ride. We had a glimpse of how rafting would be at the yavapai observation station. Since we went as a group which had a small child, we could not attempt rafting.


This is an informative video on the first explorers and white water rafting.
There is an Imax theatre which hosts a short movie of about half an hour on the grand canyon. It was an amazing one which took us to the depths of the canyon upto the colorado river as well as gave us the bird's eye view too(the person who had flown in between the canyon walls to take a video of it did a brave and excellent job). We also learnt a bit about the people who had inhabited it and the explorers who discovered it.

Flora and fauna in the canyon
For this grand and colossal a place,the canyon teems with wildlife but it is difficult for a visitor to see most of it. I purchased a coffee table book about the canyon and it had some nice national geographic quality pictures of wildlife of the area.

Some of the fauna......
(Click to zoom in)
Some flora...
The colorado river has done the consistent work of carving the canyon. So it occupies the pivotal position in its history. Some paintings depicting the colorado river...

Grand canyon also has its share in the legends and imaginative accounts of people. What came to my mind immediately is the "Road runner show" which i used to watch in the cartoon network more than 10 years back. The coyote makes repeated tries to catch the road runner but in vain. I thought a snapshot from the cartoon was a nice way of representing it here.
(The coyote hatching another one of its 'would be failure' plots to catch the road runner)
(The coyote has a 90 degree fall into the canyon depths as a result of backfiring of its plans)

The Havasupai Indians have their creation story in relation to the grand canyon.

Before there were any people on earth there were two gods. Tochapa of goodness and Hokomata of evil. Tochapa had a daughter named Pu-keh-eh, whom he hoped would become the mother of all living. Hokomata the evil was determined that no such thing should take place, and he covered the world with a great flood. Tochopa the good felled a great tree and hollowed out the trunk. He placed Pu-keh-eh in the hollowed trunk and when the water rose and flooded the earth she was secure in her improvised boat.
Finally the flood waters fell and mountain peaks emerged. Rivers were created; and one of them cut the great gushing fissure which became the Grand Canyon.
Pu-keh-eh in her log came to rest on the new earth. She stepped forth and beheld an empty world.
When the land became dry, a great golden sun rose in the east and warmed the earth and caused her to conceive. In time, she gave birth to a male child. Later a waterfall caused her to conceive and she gave birth to a girl. From the union of these two mortal children came all the people on the earth. The first were the Havasupai, and the voice of Tochopa spoke to them and told them to live forever in peace in their canyon of good earth and pure water where there would always be plenty for all!’.
We can see that the great floods is nothing but the pralayam from which Lord sriman narayana rescued the vedas and sapta-rishis by taking the matsya avataram. We find that the same story trickles through to the stories of various cultures including the much later written Noahs story.
Some other myths revolving around the place are its possible link with the not-yet-proven atlantis civilization or with the Egyptian civilization.
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"The canyon is its own answer. It fills the soul of all responsive persons with awe. It allures, attracts and holds those who have gazed into its mysterious depths."
--- George wharton James, 1910
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Wednesday, July 15, 2009

Vedantabijam (वेदान्तबीजम्) or 'Seed of vedanta'



Vedantam has been the undercurrent of life in Bharata desam from time immemorial. It has been reviewed, re-reviewed and commented upon, translated for thousands of years. It is the purport of our 2 grand epics Mahabharata and Ramayana. Following the footsteps of our fore fathers, i have summarised to the extent of my knowledge, the meaning of a very important verse from a very important upanishad in the following post:

http://venetiaansell.wordpress.com/2009/07/13/vedanta-bijam/

Read and provide your comments.

Tuesday, March 10, 2009

Upto Calculus in India: A review of important elements of calculus found in Indian mathematics till the 17th century-- PART I


यथा शिखा मयूराणाम् नागानां मणयो यथा |
तद्वद् वेदांगशास्त्राणाम् गणितं मूर्धनि स्थितं ||

( लगध : वेदांग ज्योतिषं :4) before 3500 B.C
[Like the crest of the peacocks, like the crest-jewels of the serpants, so does the lore of the mathematics stand at the head of all the lores forming the auxiliaries of the vedas]

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The Newton-Leibniz feud over priority of discovery of calculus is a famous episode in modern western mathematical history. That these two men, despite having many other inventiones/discoveries to their credit, fought over calculus itself lends an idea as to how important a discipline it is. Many of us, whose disciplines involve mathematics in some way,have experienced the utility of calculus during our education. It is almost an ubiquitous mathematical technique.

In this blog which i divide into 2 parts, I intend to summarise from various sources about how Indian mathematicians over the ages came very close to discovering calculus. In fact, they did use calculus, but in a limited sense of astronomy and did not extend it to general functional analysis.Due credit must be given to them for some of the greatest ideas they introduced for the first time in the history of mathematics like infinite series and error associated , numerical integration and infinitesimals. The euro-centric view tries to cast aside these as a mere footnote. This is a ridiculous situation.

While I provide the details about various mathematicians in the following paragraphs, I stick to the dates in history given according to modern research, by V.Lakshmikantham and S.Leela as opposed to euro-centric dates which always tries to push all Indian dates into A.D and hence prove that Indians learnt all things from greeks(although it should be appreciated that there was interaction and mutual learning between indians and greeks to some extent over the ages) .

For more information on this view of indian history see:
http://www.vnn.org/editorials/ET0003/ET14-5679.html

Though there are so many contributions to the field of mathematics by Indians, in this blog i concentrate only on those aspects that involve calculus ideas. Astronomy was the main discipline for Indians although right from Aryabhatta's time we see chapters exclusively dedicated to mathematics too. In the course of tackling various problems in astronomy, elegant mathematical techniques were developed.

In this first part i will outline details about our mathematical history upto the point of Bhaskaracharya II. In the second part we will take up the medieval Kerala school of mathematics and their contributions.

Ideas of zero and infinity
These two important concepts in mathematics were known from time immemorial in India in sanathana dharma (eg, anantam) and emphasised more by the later indian religions namely, buddhism(from c.1800BC) and jainism. The infinite brahman(ananta) as well as infinite cycle of yugas were the fundamentals of upanishads. zero was the part of the place value notation indicated in the vedic literature.

Buddhism's 'sunyavadham' and Jainism's five kinds of infinities also developed these concepts further. The idea of infinitesimals and limits often involve a variable approaching these two entities.

Aryabhatta (born 2765 B.C) was one of the very important early mathematicians/astronomer who influenced later mathematicians for over the following 4000 years. He gave the value of π (pi) to be 3.1416 and mentioned that it is an approximate value. This value was remarkable for his age. Though it is not very clear as to how he arrived at this value, there are theories that he used a 256 sided polygon as an approximation to the circle. This has been disproved in a subsequent paper. There is also a theory that he used a 384 sided polygon ('crest of the peacock:Non-European roots of mathematics' and 'Geometry in Ancient and Medieval India'). These indicate that Aryabhatta had the insight of the limiting value of the perimeter of a N-gon to be the circumference of the inscribed circle.

He also introduced the notion of tatkalikagathi(instantaneous motion) while talking about the motion of moon and planets and expressed the instantaneous velocity of a heavenly body in the form of a basic differential equation. Aryabhatta and Brahmagupta(born 30 B.C) gave the formula pertaining to instantaneous motion as
where u,v,w are the true longitude, mean longitude, mean anamoly respectively at any particular time and u' , v' , w' are the values of the respective quantities at a subsequent instant and e is the eccentricity or the sine of the greatest equation of the orbit. This was later expounded fully by Bhaskaracharya who writes:

'to find the instantaneous velocity in longitude of the planet, the kotiphala is to be multiplied by the time rate of change of anomaly and divided by the radius, and the quotient thus obtained is to be added to or subtracted from the mean velocity of the planet according to its position in the six signs from the beginning of cancer or capricon'. Expressed in modern notation,

where the symbols have their meaning like true longitude,mean longitude,anamoly,radius of epicycle,kotiphala etc.(which cannot be easily understood without a deeper knowledge in astronomy)

While dealing with this type of equation, Manjula(c.900 A.D) hit upon an important result in differential :

where (w'- w) is small.

Virasena(710-790A.D) uses the method of exhausion to find the volume of frustum of a cone in his Dhavala. If a and b are the diameters of the bigger and smaller bases, then he removes a cylinder of diameter b from the solid and cuts open the solid to form a wedge kind of solid. He then removes smaller and smaller pieces from it and through series summation arrives at the result. This is akin to techniques that Archimedes uses for the quadrature of parabola and other figures.

Bhaskaracharya(b. 1114 A.D)-(486A.D according to Lakshmikantham and Leela)-(well known as Bhaskara-II)gives the geometrical proof of the above result and uses it to calculate "the angle of position"(an important parameter in determining the position and velocity of planets).

In modern notation it is as follows:
Bhaskara-II expressed other important ideas of differential and integral calculus in his texts. He had a primitive notion of limit. In the second chapter 46th verse of Lilavathi, his well known mathematical treatise, he poses the following question and answer:

'What number is it, which multiplied by cipher and added to half itself and multiplied by three, and divided by cipher, amounts to the given number sixty three?'

The question may seem strange for a modern reader for we were all taught that dividing by zero is not allowed in operations. Here if we take a look at the answer given by bhaskara and the method he adopts to arrive at it, we can compare it to the notion of limits that we have today.

The answer given by him is 14. Let us look at the method. Do not operate with the zeros until the end. Write the expression and we finally cancel the zeros as shown.

This is akin to:
The following two important results , which are wrongly attributed to later day european mathematicians such as Rolle were given by Bhaskaracharya.

1. When a variable attains maximum value, its differential disappears.
2. When a planet is either in apogee or perigee, the equation of the centre vanishes, hence for some intermediate position, the increment of the equation of the centre(ie, differential in modern term) also vanishes.

The second one is the celebrated intermediate value theorem.

Bhaskara has up his sleeve some very ingenious numerical integration methods to find the volume and the surface area of a sphere. He first gave the correct formula for the volume of sphere in the indian subcontinent.

Methods Surface area of a sphere:

1. The first method is to divide the surface of the sphere into thin strips by drawing circles of increasing radius keeping one of the poles as the centre. This will result in latitude kind of circles on the surface. (See below)

Now area of each strip is found out by considering it as a rolled up trapezium.(Note that dimensions of the trapezium are known because while we draw the circles we measure the increasing radius in terms of arcs of sine, the table of which exists right from Aryabhatta's time).
This totalled up gives the surface area. Bhaskara concludes through explanation here that the area can be generalised as (circumference x diameter). The essence of this method is the idea of integration, though not presented in a numerical rather than the general way.

2. The second method is by dividing the sphere into lunes (vapras) as shown below and adding the areas.

The way Bhaskara indicates this method is interesting. He asks us to divide the sphere into parts that resemble natural divisions on the amalaka(myrobalan) fruit. Even through this method the consistent result of (circumference x diameter) is concluded. I do not wish to go into details here but a comprehensive description can be found in Sarasvati amma's book 'Geometry in Ancient and medieval India'.

Volume of sphere:

In the words of Bhaskara , " Consider on the surface of the sphere pyramidal excavations, each of a base of an unit area having unit sides and of a depth equal to the radius of the sphere, as many as the number of units of area on the sphere. The apices of these pyramid meet at the centre of the sphere. The sum of the volumes of the pyramids equals the volume of the sphere".

This idea is a 3 dimensional extension of the method to find circle's area when it was divided into triangles.

The next part will concentrate on Post Bhaskara II mathematics,mainly on the Kerala School of mathematics which gave some of the most brilliant results ever to humanity.

COURTESY: Various issues of Indian journal of history of science, 'Geometry in ancient and medieval india' by Saraswati Amma, 'Crest of peacock', 'Origin of mathematics'