Saturday, August 07, 2010

The trigonometric tables of the Brahmins

One of my favourite pastimes is to dip into Google Books and scan through books concerning India and published 250-300 years back by the British when they were slowly and steadily gaining control over the vast territory. The area was relatively new to them and they were in an exploratory mode. Their penchant for meticulously recording their observations resulted in many, many books which, thanks to Google, we can access easily now.

This is my 37th post under the label, “Britindia” and I find that, even given the general poor readership of this blog, the series has attracted the least attention. To my dismay, my wife told me yesterday that if she finds the tag “Britindia’, she gives that post a miss.

Be that as it may, I shall carry on bravely…..

In an earlier post, I had linked to a report on the mathematical discoveries of the school of Madhava and their knowledge of the infinite series. In another post, I had linked to a book published in the year 1799 that had provided proof that the Hindus were aware of the binomial theorem.

To add to above, the “Transactions of the Royal Society of Edinburgh” published in the year 1798, contains on page 83,  a chapter titled, “Observations on the trigonometric tables of the Brahmins”. The author provides evidence of the existence of well laid-down trigonometric principles in India, 2000 years before the Europeans arrived at the same conclusions.

In the second volume of the Asiatic Researches, an extract is given from the Surya Siddhanta, the ancient book which has been long, though obscurely pointed out as the source of the astronomical knowledge of the Brahmins. The Surya Siddhanta is in the Sanscrit language: It is one of the Sastras, or inspired writings of the Hindoos, and is called the Jyotifh, or Astronomical, Sastra. It professes, to be a revelation from heaven, communicated to Meya, a man of great sanctity, about four millions of years ago, toward the close of the Satya Jug, or of the Golden Age of the Indian mythologists ; a period at which man is said to have been incomparably better than he is at present ; when his stature exceeded twenty-one cubits, and his life extended to ten thousand years.

Interwoven, however, with all these extravagant fictions, this singular book contains a very sober and rational system of astronomical calculation ; and even the principles and rules of trigonometry, a science of all others the most remote from fable, and the least susceptible of poetical decoration.

It is not a little singular, that we should find a table of versed sines in the Surya Siddhanta; for neither the Greek nor the Arabian mathematicians, had any such, nor had we, in modern Europe, till after the time of Petiscus, who wrote about the end of the century just mentioned. I think it might fairly be concluded, even if we had had no knowledge of the antiquity of the Surya Siddhanta, that the trigonometry contained in it is not borrowed from Greece or Arabia, as its fundamental rule was unknown to the geometers of both those countries, and is greatly preferable to that which they employed.

If we were not already acquainted with the high antiquity of the astronomy of Indostan, nothing could appear more singular, than to find a system of trigonometry, so perfect in its principles, in a book so ancient as the Surya Siddhanta. The antiquity of that book, the oldest of the Sastras, can scarce be accounted less than 2000 years before our era, even if we follow the very moderate system of Indian chronology laid down by Sir William Jones. It is remarkable that the Hindoos should have been thus led, at so early a period, to put in practice a method which has been but lately suggested in Europe as an important improvement in trigonometrical calculation.

If these are claims made by Indians, I would discount them immediately, prone as we are to making exaggerated assertions on our glorious past. But, these conclusions were arrived at by British scholars after a fairly rigourous and impartial analysis, and so carries more credibility.


Anonymous said...

Thank you sir, for bringing to light such an important topic, I think you are doing a great job by publishing such information so that next generation readers such as myself are kept informed.

i don't think you should put off writing anything just because the stats might seem low today, Maybe in a few years time your blog would be well read by readers who notice the importance of such a subject.


Anu said...

Raj, I read with interest all the BritIndia posts and if someone happens to be nearby, I read parts of it aloud to them as well :) Lack of comments does not mean lack of readership. I myself would not have the patience to plough through the entire volumes but thankfully you can always be relied upon to give us the most interesting excerpts.

Agoglife said...

so what do we do about these glorious past? what's the impact of that and your writing on the present and future? shouldn't we publish these for a wider audience? social engineer so that the common man gets to know the truth about our past and try to carry on the intelligence and not while away in western junk like KFC?

Ranjit V, Srivatsaa said...

Raj, by your post I observe you to take pride in our past but at the same breath you disparage them by saying "exaggerated assertions on our glorious past" your phrase itself is contradictory to start with. It has to be either exaggerated or glorious both should not figure in the same phrase! Let me add that these comments are not meant to criticize but my earnest desire that Indians should start taking pride in their past and not to fall prey to claims that our ancestors were liars. A convenient tool used by missionaries to convert.

I am more appalled at your veneration of the Brits though , From when did the British become purveyors of truth. WMD in Iraq was their last big "truth", I suppose. Any way Let me add what Dr Satya Pal Singh, Commissioner of Police, Nagpur had to say ( I suggest you read his blog in full and probably create a link to your post.

Quote: ...."Most foreign scholars and Indologists believe that Indians taught and learnt their lessons verbally, without the aid of any written material. .....

Let us also know the fact that McCaulay did not know even one Indian language but he commented on all Eastern wisdom, James Mill never visited India but he wrote on Indian history. None of the foreign Indologists like Max Muller, Winternitz and Griffith had any knowledge of Vedic grammar , astronomy, metre (chhand) etc but they all translated Vedas and assumed the status of authorities.

As per Vedic time computation and tradition, the age of creation is 4.32 billion years, and the sankalp mantra 'Om tatsat adhay bharamano dutya parardhey swetvarahakalpe saptmein vaivasvat manvantare astahvinsatitame kaliyuge kaliprathme charne _____ gatabde'. They have kept intact the history of the time of creation and the advent of man on earth till today. Man arrived on earth exactly 1,97,29,49,108 years ago (approximately two billion years ago). Some Vedic scholars also believe that man was created on earth only in the seventh manmantar of Vaivasvat Manu. The sun, planets, stars, earth, sea, vegetation, flora and fauna were created in the earlier six manmantars in a very scientific manner. If we accept this theory, then man was born about 12,05,33,108 years ago. At least this much is certain, that the history of mankind is indeed very long.

Indians always knew the art of writing. The Rig Veda (10.71.4) says speech has two forms .........

Ignorance in faith

The foreign scholars and their Indian followers who have spread the mythological canard that Ram and Ramayana are historically untrue, figments of imagination and only a fable are no more responsible than some of our Indian poets and writers. .........

Analysis and conclusions

1. Can our saints and seers, who have from birth till death spoke the truth, acted with truth and preached only the truth, become the liars today and their writings unbelievable and false, whereas the foreign scholars and their native modern followers are truthful? Were our ancient visionaries and authors like Rishi Valmiki, Muni Vyas, Kalidas, Bhas, Bhavbhooti, Ashvaghosh, Samarth Guru Ramdas, Guru Govind Singh, Swami Dayanand, Swami Vivekanand, the leading lights of Buddhist and Jain traditions, etc were liars, selfish and believed in the imaginary, whereas today's professors and scholars of our colleges and universities, writing about history and culture are more learned, committed to truth and missionaries of humanism?


Raj said...

Srikanth, thanks, that was re-assuring.

Anu, thanks. I hope that you are not reading out the passages loud to others, to put them to sleep!

Arun, fair question, I have no answers. In fact, any talk of 'glorious past' normally puts me off. What's the point in taking pride in the past, if we had lost the momentum and not evolved further? To use a stock market cliche, past performance is no guarantee for future success. All the same, knowledge that our ancestors could produce such good stuff in the same environment may inspire some.

Raj said...

Ranjit, that was an awesome comment even if you didn't agree with me. My response:

1) I do not know Sanskrit. This is a handicap while trying to read up on ancient scripts.

2) The few translated works that I have read tended to mix mythology, history and science together, leaving me confused.

3) An example of exaggerated assertion is that since there is mention of "Pushpak Viman' in Ramayana, it is proof that Indians had knowledge of aeronautics". This kind of meaningless claims can put a rational thinker off. In the process, some genuine claims may get lost.

4) I concede that I am more likely to believe western scholars. I have been conditioned by western methods of teaching. It had good points of scientific rigour, etc. It may have a flip side of blinding our eyes to other approaches.

5) There are hundreds of books that you will find on Google, from the period 1750 onwards, dealing with India. Some British writers were undoubtedly too critical of anything Indian. Especially the Missionaries. But the beauty of the British system was that it encouraged several freelancers, scholars to come here on exploratory trips, make their own observations and draw independent conclusions.Many of them have been awestruck by the country's history and knowledge base, and have written rich eulogies. Overall, there is a good balance.

6) The British took pains to understand Indian culture and folklore. Warren Hastings had a conference of Hindu priests in Calcutta to hear out their version of Indian history. Another Englishman ( I forget his name), while investigating claims that Ayodhya mosque was built where a temple was, went deep into the lineage of Rama's ancestors as well as his descendents and drew up the entire chain.

7) Thus, Google Books can help you find what you want to find. If you want to find evidence that the British were tyrants and maniacs, you can. If you want proof that some of them were benevolent, fair and keen observers,you can find it.

Ranjit.V.S said...

Warren Hastings did that because an astrologer predicted one of his near relatives (don't remember which) would die (and die that person did as predicted), he threatened that poor astrologer with death if his prediction came unstuck. So much for his 'broad-mindedness'! In 1773, Warren Hastings wrote ...: "These Sannyasis appear so suddenly in towns or villages that one would think they had dropped from the blue. They are strong, brave, and energetic beyond belief." Evidently, they had resolved to sacrifice their lives for the protection of Hindu religion and culture which, they thought, were in great danger. The Mutiny of 1857 was, in many respects a legitimate successor of the Sannyasi revolt, exploding in a wider and more violent outburst. — Based on Dr. Jadugopal Mukhopadhyaya's 'Viplavi Jivaner Smriti', written in Bengali.

Those guys were forced to accept greatness (after their initial barbarism) of this Punya Bhoomi had elevated souls and powerful Deities after experiencing them first hand (Thanjai Mariamman Koil, Madurantakam Tank, Tirukoilur, Munro's talk with Shri Raghavendra in his samadhi etc)

I did not write about your knowing or not knowing Sanskrit, it was those Indologists I referred to, whom you hold in such great esteem (none of whom deserve any respect leave alone veneration). In any case we don't need to learn
from them about ourselves.

How can you say, Pushpaka Vimanan did not exist, just because your mind refuses to believe that it could not have existed,(admit your mind cannot comprehend certain things). Today the almost science (with so many theories and yet mest of them proved) of astronomy is accepted just because no one
understands it fully. You say "I am more likely to believe western scholars. I have been conditioned by western methods of teaching. It had good points of scientific rigour, etc" If that is so how can you believe that man landed on the Moon when even now we don't know if any air conditioners will work on the moon even today in near vacuum! (since conduction and convection cannot happen in vacuum) or biscuit tin thick moon buggies could stand
cosmic radiation? So please change your opinion on the West and start re-examining all of your beliefs on these motivated writers and give more credence to our own.

If History can repeat itself why not Science? How many of the so called albino history talks of flying or oil-less lamps much before they were invented! Why should we Indians get intoxicated, everytime some white skin writes about us whether in praise or mostly when they disparage us, why can't otherwise sane people not understand the underlying tone of their writings.

My grouse is - When their (West) culture is all about spreading falsehoods, (Biblical nonsense whom Brits peddle as the TRUTH) why cannot 'educated' Hindus understand their real motives? BTW It was the English who generally upheld and enforced a mutated version of the traditional Hindu caste system, which led to outright segregation

In 1784, the (in)famous Indologist Sir William Jones wrote to Sir Warren Hastings, "....As to the general extension of our pure faith in Hindoostan there are at
present many sad obstacles to it .......... and the history of the Divine Person (Jesus) is predicted, were severally made public and then quietly to disperse the work among the well-educated natives." (Asiatic Researches Vol. 1. Published 1979, pages 234-235. First published 1788).

theja said...

@ Ranjit:
1) I must say, you have put forth a well structured argument, though I'd differ with you.
2) How can you say, Pushpaka Vimanan did not exist, just because your mind refuses to believe that it could not have existed Are you asking someone to prove non-existance of a thing?
3) I'd rather follow a structured approach (you might call it Western) wherein the proofs are based on any/combination of the five senses (i.e., see,smell,hear,touch & taste) rather than have a leap of faith and assuming that there existed a Pushpaka Vimana which used to fly & have space for n people where n->oo
4)Btw, have you heard of the phrase 'God of the Gaps'. The wiki link (though improperly written) can give you an idea.
5)@Raj: Fabulous job 'digging' out the history and the adjoing commentry. Bring more on BritIndia series.


Balajisblog said...

Raj - Your braving on with Britindia, inspite of your wife giving it a go by....could it be because of your shortened name ?

As for Ranjit's views that Indians must take pride in the past - no second thoughts, but, when I see folks spitting in Jalianwala bagh, and letting out their dongs on temple walls to relieve themselves - I deeply worry about the future !


Raj said...

Ranjit, I think our frames of references differ. So, it will be difficult to convince each other.

Theja, thanks.

Balaji: Maybe I persist because wife doesn't like it?

About the second para, Indians have never had any sense of history.

Sathish Mayil said...

Raj, I believe I got answer to my comment, posted an hour ago in a different post. Going by the comments for the post, you must have understood that there is a cerain amount of readership to your blog as well as Brit India series. We love this, keep it going.

@Ranjith - Raj doesn't just post whatever is being said of India in a good manner. He posts things which are worth mentioning only. I believe what is important is the content and not who writes them. For the matter, we can't accept there was a Pushpa Vimana even if a Brit writes out an article saying that they where there.

Raj said...

Sathish, thanks.

A sad part about Indian history is that we never ever paid importance to written records. Passing on knowledge verbally from one generation to next was the norm, and often this created serious distortions and even got mixed up with mythology.