Friday 28 February 2014

Restoring India's calculus crown

Tuesday , February 25 , 2014 |

Restoring India's calculus crown

Ananthakrishnan G.
A digital image of Madhava drawn up by the Madhava Ganitha Kendram, a voluntary association working to revive his works, with inputs provided by descendants of the mathematician-astronomer
Thiruvananthapuram, Feb. 24: George Gheverghese Joseph is on a mission to reclaim India's pride of place in the world of mathematics. An emeritus professor at Manchester University in the UK, his book, The Crest of the Peacock; Non-European roots of Mathematics, has challenged the status quo and persuaded the West to acknowledge that a 15th century Kerala mathematician-astronomer named Madhava (Madhavan, in local dialect) had worked on the fundamentals of calculus — a vital tool for measuring time, making almanacs and finding directions at sea — almost two centuries before Sir Isaac Newton and his German counterpart Gottfried Wilhelm Leibniz were credited as its founders.
Kerala-born Joseph has some reasons to conclude that the southern Indian state may have served as a conduit for the transmission of Indian mathematics to Europe through Jesuit priests, though the evidence available is more circumstantial.
Joseph played an important role in purging the South African mathematics curriculum of its racial overtones post-apartheid but rues that the "colonial mindset" that "denigrated native contributions" and "politics" had clouded India's efforts to honour its heritage.
The Telegraph caught up with Joseph at his holiday home near the Kovalam beach resort here. Excerpts from the interview:
Question: How did the West react to the conclusions in your first book, The Crest of the Peacock; Non-European roots of Mathematics?
Joseph: The perception of the West was a very pleasant surprise. I did not expect so many people to be so receptive to ideas. I think the reason they had not touched upon it earlier is because they did not have the information. The book received over hundred reviews by all sorts of groups. Not just maths educators, even activists reviewed it. What particularly moved me was the extent to which African Americans and Blacks took up some of the things in it after they realised they had a very rich history. For instance, the earliest mathematical artefact is available right in the middle of Africa, but nobody knows. It's called the Ishango bone which is a type of lunar calendar and dates back to 22,000 BC, much earlier than anything of that sort found anywhere in the world.
There were a few critics, but nobody took me on on the maths in it. It was mostly the interpretation. There was criticism that I was devaluing Newton, Leibniz and the Greeks. But all I was saying was that there is that part of history which has been ignored and we need to reflect on. And also, how some of the ideas travelled to the West to, in fact, create the scientific revolution.
George Gheverghese Joseph
People who disappointed me were the Indians. Part of colonisation involves a form of brainwashing where you end up defending something because you think you have invested time and emotion in it. I was awarded a Royal Society Visiting Fellowship to deliver a series of lectures in Indian universities. But a number of those I met didn't either want to know or were very critical. Subsequently, I also noticed that academics has been highly politicised in the country. So I suddenly find my views and conclusions either being approved by the Right who say, look here is a book that shows India is great, or being criticised by the Left, who claim that the book panders to the other side and contains not much of material analysis.
Q: What spurred your interest in Madhava?
Joseph: I always felt that from the little I knew, the mathematical tradition outside the European tradition was neglected. Even in Africa where I taught for a long time, children would ask me if there was any African link to the evolution of the subject and all I could point out to them were some Egyptian connections. But then the children would say Egypt is not Africa.
Later, when I became interested in the work of the legendary Srinivas Ramanujan and had gone to Cambridge in this connection, I met an eminent Newton scholar, Tom Whiteside. He asked me if I had come across the Kerala school of mathematics. I said no. He then referred me to a footnote by him of an earlier Indian researcher who had with his collaborators written extensively on the work done in Kerala on the infinite series. Whiteside suggested that I explore it further and that's how I discovered the work of Madhava and his disciples.
Q: What exactly was Madhava's contribution to mathematics?
Joseph: His works laid the foundations of the Kerala school of mathematics which flourished between AD 1,300 and 1,700. But he was only part of the wider Indian school founded by Aryabhata who wrote the masterpiece Aryabhateeyam in AD 499. There are still differences over Aryabhata's birthplace, whether it was in the north or the south of the country. Madhava's contribution was his work on the infinite series. Though Newton and Leibniz are credited with the discovery of calculus, the fact is one of its critical strands had been developed in Kerala more than two centuries before that. The West has now recognised this and accordingly renamed certain results relating to the trigonometric series, previously known as the Newton, Gregory and Leibniz series, as the Madhava-Newton, Madhava-Gregory and the Madhava-Leibniz series, respectively.
The irony is that we still don't know much about Madhava, the man himself. An eminent mathematician from Oxford, Marcus Du Sautoy, recently made a series of television programmes on the history of mathematics. I was consulted on those programmes relating to the history of Indian mathematics, including the remarkable work in Kerala. He was particularly interested in finding the physical location of Madhava and his main disciples to add some footage of film. When he asked me I was clueless and somewhat embarrassed. But now I'm told that he hailed from Sangamagrama, a medieval town in present-day Irinjalakuda in Thrissur district. It is a shame that there is no memorial plaque at the place which would certainly attract maths tourists.
Q: How do you suggest the knowledge from Indian shores reached Europe?
Joseph: That was the subject of my third book, A passage to infinity — Medieval Indian Mathematics from Kerala and its Impact. I had undertaken a project on the topic and what I concluded was that a lot of the knowledge may have reached Europe through the Jesuit priests. We looked at a lot of archives in Rome and Lisbon, mostly Europe. There was no direct documentary evidence to prove this, but this may be because the documents may have been destroyed. A lot of Jesuit papers were destroyed by the Catholic Church at one stage and also there was an earthquake in Lisbon. However, there is strong circumstantial evidence as these priests were sent out with the brief that they should find new ideas on stellar astronomy, how to use the stars for calculations, how they would be of use for navigation. And India, as we know, was at that time much advanced in these areas through works of people like Aryabhata and Bhaskara. These priests used to move around in the court circles in Kochi whose royal family too boasted of astronomers like Sankararaman.
Q: Has India been fair to its mathematicians?
Joseph: The question to ask is if India would have recognised the work of Ramanujan, a failed college student from a relatively poor background, if he had remained in India.
Q: How did you get involved with the curriculum revision committee in Africa?
Joseph: Our family had moved to Kenya from Kerala when I was nine years old and I had my schooling there before we shifted to the UK. In Africa, I realised that the curriculum was much affected by racial bias. For instance, Black students were not expected to learn calculus because the apartheid government felt it was too abstract for them. Just before Nelson Mandela became President, a group of us were invited, including me, to help in the reform of the school and university curriculum.
Q: What ails maths education in India?
Joseph: Firstly, there is too much stress on examinations, that the exam becomes the end in itself and knowing the subject is not so important. Secondly, there is limited opportunity for people to do a PhD in maths (and, even worse, history of mathematics) which is why even the best minds opt for an MBA or move to the IT field. Thirdly, there is not much of an inspiration coming from the teachers because they are dealing with large classes and, in a number of cases, engaged in tutorial work after work. Also, the system of teaching is too didactic — that there is only one right answer and only one right way of doing a problem.




Calculus (CK Raju Oct. 2005)

Posted

-- 
S. Kalyanaraman

__._,_.___

                                          ( hari krishnamurthy K. HARIHARAN)"
'' When people hurt you Over and Over
think of them as Sand paper.
They Scratch & hurt you,
but in the end you are polished and they are finished. ''
யாம் பெற்ற இன்பம் பெருக  வையகம் 
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गुलदाऊदी- Gladiolus

गुलदाऊदी

- गुलदाऊदी या सेवंती के फूल बहुत सुन्दर होते हैं। छोटे फूलों वाली गुलदाऊदी के औषधीय गुण अधिक होते हैं।
- इससे घर का वातावरण भी अच्छा होता है . घर में इसके दो तीन पत्तों पर देसी घी लगाकर कच्चे कोयले पर जलाएं तो नकारात्मक ऊर्जा खत्म होती है।
- हृदय रोग के लिए गर्म पानी में इसकी पत्तियां डालकर दो मिनट बाद निकाल लें। फिर उस पानी को पीयें।
- मासिक धर्म अनियमित हो या दर्द रहता हो तो इसके फूलों व पत्तियों का काढ़ा पीयें।
- पेट दर्द होने पर इसके फूलों का रस शहद या पानी के साथ लें।
- कहीं पर गाँठ हो गयी हो तो इसकी जड़ घिसकर लगायें।
- kidney stone हों तो इसके फूलों को सुखाकर उनकी चाय पीयें। Urine रुककर आता हो तो इसकी चार पांच छोटी छोटी पत्तियों में काली मिर्च मिलाकर , काढ़ा बनाकर पीयें।

                                          ( hari krishnamurthy K. HARIHARAN)"
'' When people hurt you Over and Over
think of them as Sand paper.
They Scratch & hurt you,
but in the end you are polished and they are finished. ''
யாம் பெற்ற இன்பம் பெருக  வையகம் 
follow me @twitter lokakshema_hari

Thursday 27 February 2014

மகா சிவராத்திரி நாளில் நடந்தவை!


மகா சிவராத்திரி நாளில் நடந்தவை!

1. ஈசன், லிங்கத்தில் பிரசன்னமான நாள்.
2. அடி& முடி தேடிய விஷ்ணு மற்றும் பிரம்மா ஆகியோருக்கு சிவனார் காட்சி தந்த நாள்.
3. பார்வதி வழிபட்டு அர்த்தநாரியான நாள்.
4. பாற்கடல் கடையும்போது வெளிப் பட்ட விஷத்தை சிவனார் உண்ண... அதை விழுங்கா வண்ணம் தடுத்தார் பார்வதிதேவி. இதனால், நீலகண்டன் நஞ்சுண்டன் ஆகிய பெயர்களை, சிவனார் பெற்ற நாள். (இப்படி விஷம் உண்ட மயக்கம் தீர சிவபெருமான், பார்வதிதேவியின் மடியில் பள்ளி கொண்டார். இப்படிப்பட்ட காட்சியை கருவறையிலேயே காணலாம். எங்கு தெரியுமா? ஆந்திராவில் சுருட்டப்பள்ளி என்ற ஊரில்).
5. அர்ஜுனன் தவம் இருந்து பாசுபதம் பெற்ற நாள்.
6. பகீரதன் ஒற்றைக் காலில் கடும் தவம் இருந்து கங்கையை பூமிக்கு வரவழைத்த நாள் (இந்த தவக் கோலத்தை புடைப்புச் சிற்பமாக மாமல்லபுரத்தில் காணலாம்)
7. மார்க்கண்டேயனுக்காக, எமதர்மனை சிவனார் சம்ஹரித்த நாள் (திருக்கடையூர்).
8. கண்ணப்பன் தன் கண்களை சிவனுக்குக் கொடுத்த நாள் (காளஹஸ்தி)
9. மகா பிரளயம் உண்டானபோது மீண் டும் உலகைப் படைக்க பார்வதிதேவி சிவ பெருமானை நோக்கி தவம் இருந்த திருநாள். 
_ இப்படி, புண்ணியம் மிகுந்த நிகழ்ச்சிகள் பல நடந்தது இந்த சிவராத்திரியில்தான் எனக் கூறப்படுகிறது.
                                          ( hari krishnamurthy K. HARIHARAN)"
'' When people hurt you Over and Over
think of them as Sand paper.
They Scratch & hurt you,
but in the end you are polished and they are finished. ''
யாம் பெற்ற இன்பம் பெருக  வையகம் 
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7 Reasons Vegetarians Live Longer

7 Reasons Vegetarians Live Longer

The latest study shows that meat abstainers have lower blood pressure

Benefits of a vegetarian diet

Recently an article was published that listed various scientific benefits to a vegetarian diet. Here is one point from the article:

A 2012 study randomly split participants into three diets: all-meat allowed, fish-only, and vegetarian no-meat. The researchers found that after two weeks, the people on the vegetarian diet reported more mood improvements than those onthe other two diets.

There's nothing wrong with eating meat if you're doing so in moderation (I for one, will never give up the occasional cheeseburger), but research does show that vegetarians tend to be healthier overall, and even live longer.

Now there's another health perk vegetarians can boast about. A new study published in the journal JAMA Internal Medicine looked at data from seven clinical studies and 32 other studies published between 1900 and 2013 where participants kept a vegetarian diet and found that vegetarians have lower blood pressure compared to people who eat meat.

Here are some other reasons vegetarians may outlive meat-lovers.

1. Low blood pressure: 

In the latest study, researchers found that not only do vegetarians have lower blood pressure on average, but that vegetarian diets could be used to lower blood pressure among people who need an intervention.

2. Lower risk of death: 

A 2013 study of more than 70,000 people found that vegetarians had a 12% lower risk of death compared with non-vegetarians. With none of the saturated fat and cholesterol that clogs arteries, vegetarians may be at a lower risk for chronic diseases overall.

3. Better moods: 

A 2012 study randomly split participants into a three diets: all-meat allowed, fish-only, and vegetarian no-meat. The researchers found that after two weeks, the people on the vegetarian diet reported more mood improvements than those on the other two diets.

4. Less chance of heart disease: 

Another 2013 study of 44,000 people reported that vegetarians were 32% less likely to develop ischemic heart disease.

5. Lower risk of cancer: 

Researchers at Loma Linda University in California studied different versions of the vegetarian diet and cancer risk among people at a low risk for cancer overall and discovered that a vegetarian diet may have protective benefits. 

Although the study is not the final say on the matter, vegans had the lowest risk for cancers, specifically cancers most common among women, like breast cancer.

6. Lower risk of diabetes: 

Studies have shown that vegetarians are at a lower risk for developing diabetes. While the diet won't cure the disease, it can lower an individual's risk by helping them maintain weight and improve blood sugar control.

7. Less likely to be overweight: 

Research shows that vegetarians tend to be leaner than their meat-eating counterparts, and that they also tend to have lower cholesterol and body mass index (BMI). 

Some data suggests that a vegetarian diet can help with weight loss and be better for maintaining a healthy weight over time.

People who don't eat vegetarian can still be very healthy, and a vegetarian diet comes with its own health risks. 

For instance, research has also shown that vegetarians are at a higher risk for iron deficiencies, and some experts question whether children who are raised vegetarian get the right amount of nutrients for their growing bodies. 

Making sure you get the right amount of nutrients is important, and keeping your physician in the loop about your eating habits can make sure you're meeting all the requirements for good health.

MORE: 

Vegetarians May Live Longer

...


                                          ( hari krishnamurthy K. HARIHARAN)"
'' When people hurt you Over and Over
think of them as Sand paper.
They Scratch & hurt you,
but in the end you are polished and they are finished. ''
யாம் பெற்ற இன்பம் பெருக  வையகம் 
follow me @twitter lokakshema_hari

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