Kerala School And Eurocentrism

Mail Today, Sunday, January 25, 2009

Page 10

COMMENT

WHY DOESN’TTHE WORLD KNOWABOUT OUR ILLUSTRIOUS ASTRONOMERS WHO MAYHAVE MATCHED COPERNICUS OR GALILEO?

Who is in charge of the nukes here? LET it be said upfront: India is not taking its nuclear weapons state status seriously enough. What else would explain the complete absence of a command structure when it comes to controlling the nuclear button? The prime minister is the chairman of the Nuclear Command Authority, and by definition, the person this nation trusts to decide if India needs to use nuclear weapons to defend itself. Now that the prime minister is incapacitated due to surgery, what does the Indian establishment do? In one word — nothing. Even the presumed successor, External Affairs Minister Pranab Mukherjee, has not been told clearly whether he is acting prime minister or not. In contrast, in the US, if the President is incapacitated for some reason, the VicePresident takes over. If that person is also unable to take decisions, the Speaker of the House, the Secretary of State, Defense Secretary, in that order, are the next in line to be responsible for the nuclear weapons. While it is true that we follow the different Westminster model of hierarchy, this can be no excuse for disorder. The absence of Plan B clearly leaves the country vulnerable to attack, since the adversary knows decision making would be slow. India also needs to build an effective protocol to ensure that everyone in the nuclear weapons chain is aware of who is in charge. For instance, when President Barack Obama was being inaugurated on January 20, Defense Secretary Robert Gates was present at a command bunker to ensure that the country was run smoothly, and that someone had a finger on the nuclear button, just in case. The prime minister’s health condition gives the Indian establishment just the right circumstances to put this protocol in place — better late than never.

Settle the matter CHIEF JUSTICE K G Balakrishnan should act rather than be a mere party to the debate on disclosure of assets by judges. Also, his regular public statements on the issue do little to resolve the debate when, as the head of the judiciary, people expect to hear the last word from him. After sticking for quite some time to his argument that there was no law making it mandatory for judges to disclose their assets, he has now indicated that a meeting of all judges would be convened to discuss the issue. It is believed that this stems from the criticism he has faced from various quarters. It is also being reported that several Supreme Court and High Court judges want to disclose their assets to put an end to the controversy. On being confronted with this, the CJI said judges with such an inclination had his consent. However, he did not spell out how judges would be able to declare their assets when there is no mechanism in place for the purpose. The CJI’s initial stance of there being no law on the matter, reiterated in at least two interviews by him, was not convincing as it was the Supreme Court itself which had directed disclosure of assets by politicians contesting elections — this was done to fill a vacuum in law. Besides, the CJI’s statements came when an appeal in this regard was pending before the Delhi High Court.

Focus on essentials WE must confess to some amusement at the Delhi High Court striking down the ban imposed by the government on smoking on screen. As needs no reiteration, this has been Union Health Minister Anbumani Ramadoss’s hobbyhorse, leading him to public spats with Bollywood personalities who saw in the move an attempt to stifle creative freedom. While there are no two ways about Mr Ramadoss’ stance that the consumption of tobacco needs to be seriously discouraged, what isn’t certain is whether banning smoking on screen would help the cause significantly. For, the jury is still out on to what extent life follows art. On the other hand, as the HC judge remarked, art mirrors society and must reflect its realities if it is retain its power and relevance. Mr Ramadoss would be doing his job better were he to concentrate on health issues on which there is no dispute: quality health care for all, infant and maternal mortality, the list is long.

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O commemorate the International Year of Astronomy in 2009, P Govinda Pillai, a Communist Party of India (Marxist) ideologue, in an article in the Malayalam newspaper Mathruboomi, examined the legacy of Copernicus, Galileo and Kepler. He also brought up an important topic — Eurocentrism in history writing — due to which we know about the work done on telescopes by Galileo, Hans Lippershey and Roger Bacon, but almost nothing by the Muslim scientist al-Hassan. Mr. Pillai stopped there. He wrote nothing about the contributions of mathematicians and astronomers from his state, Kerala, in developing the heliocentric model and calculating planetary orbits. It is not Mr. Pillai alone who is at fault. This apathy, this ignorance, this refusal to acknowledge Indian contributions — all point to a deep malaise in our historical studies. For perspective on this issue, we need to understand the contributions of Indian astronomers and decide if we should be like Confucians during the time of the Ming dynasty or 21st century Peruvian archaeologists.

Kerala In 1832, a paper, “On the Hindu quadrature of a circle”, was read at the Royal Asiatic Society. This paper by Charles M. Whish of the East Indian Company Civil Service described eight mathematical series quoting from a text called Tantra Sangraham (1500 CE) which he had discovered in Kerala. These series were also mentioned in Yukti Dipika by Sankara Variyar and Yukti-Bhasa by Jyestadevan; both those authors had learned mathematics and astronomy from Kellalur Nilakanta Somayaji, the author of Tantra Sangraham. Some of those series were linked to Madhavan of Sangramagramam (1340-1425 CE). These mathematicians who lived between the 14th and 16th centuries formed the Kerala School of Mathematics and were proof that Indian mathematics did not vanish after Bhaskaracharya. The importance of the Kerala school can be appreciated only by understanding the Copernican revolution. The contribution of Copernicus was two fold: first he improved the mathematics behind the Ptolemaic system and second, changed the model from geocentric to heliocentric. The heliocentric model was proposed as early as the third century BCE by the Greek astronomer Aristarchus of Samos and so it is the maths that made the difference. In his Tantra Sangraham, Nilakanta revised the Indian planetary model for the interior planets, Mercury and Venus and for this he formulated equations to find the centre of the planets better than both Islamic and European traditions. He also described the planetary motion in which Mercury, Venus, Mars, Jupiter and Saturn moved in eccentric orbits around the Sun, which in turn went around the Earth. Till Nilakanta, the Indian planetary theory had different rules for calculating latitudes for interior and exterior planets. Nilakanta provided a unified rule. The heliocentric model of Copernicus did not alter the computational scheme for interior planets; it would have to wait till Kepler (who wrote horoscopes to supplement his income). In their propensity to solve astronomical problems, mathematicians of the Kerala school developed concepts like Gregory's series and the Leibniz's series. The hallmark of earlier texts, like those of Madhava, were instructions and results without proofs or explanations. It is believed that the proofs and explanations were passed orally and hence rarely recorded. Yuktibhasha, the text written by Jyesthadeva, contains proofs of the theorems and the derivations of the rules, making it a complete text of mathematical analysis and possibly the first calculus text. Our education system, based on content from Western textbooks,

Eurocentric chronicling may be one of history’s bigger lies by Jayakrishnan Nair have rarely questioned Western accomplishments. But Peruvians thought differently. When Peruvian archaeologists revisited the history written by the victors they discovered that the romantic tales woven by the Conquistadors were — well, tales. According to the original story, Francisco Pizarro, a Spaniard, arrived in Peru in 1532 with a few hundred men. A few weeks after their arrival, in a surprise attack, they killed the Inca king Atahualpa and took Cusco, the Inca capital. Four years later the Inca rebellion attacked Cusco and the new city of Lima.

Peru On August 10, 1536, while Copernicus and the Kerala school were revolutionising the world of astronomy half a world away, Francisco Pizzaro watched as tens of thousands of Incas closed in on Lima. With just a few hundred troops, Pizzaro had to come up with a strategy for survival. The Spaniards led a cavalry attack and first killed the Inca general and his captains. Devoid of leadership the Incas scattered and once again the Spaniards won. Recent archaeological excavations found a different version of this story. Out of the many skeletons found in the grave near Lima, only three were found to be killed by Spanish weapons; the rest by Incas. A testimony by Incas who were present in the battle was found in the Archive of the Franciscans at the Convent of San Francisco de Lima, which mentioned that it was not a great battle, but just a few skirmishes. Pizzaro was helped by a large army of Indian allies and the battle was not between the Spaniards and Incas, but between two Inca groups. It was also found that the strength of rebels was not in tens of thousands, but in thousands and there was no cavalry charge. Thanks to the work of native archaeologists dramatic accounts of a small band of heroic Europeans subduing the Incas has a new

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narrative. Instead of following such examples and popularising the work of Indian mathematicians, we have been behaving like Confucians at the court of the 15th century Ming emperor Zhu Di who erased evidence of the large fleets that sailed as far as the Swahili coast. While the world knows about the accomplishments of Europeans like Vasco da Gama, Columbus, Magellan and Francis Drake, little is known about Zheng He who arrived in Calicut eighty years before da Gama commanding a fleet of three hundred ships carrying 28,000 men; Vasco da Gama arrived with three ships and less than two hundred men.

China Between 1405 and 1433, Zheng He's fleet made seven voyages — three to India, one to Persian Gulf and three to the African coast — trading, transporting ambassadors, and establishing Chinese colonies. Following the death of the emperor who commissioned these voyages, the Confucians at the court gained influence. Confucius thought that foreign travel interfered with family obligations and Confucians wanted to curtail the ambitious sailors and the prosperous merchants. So ships were let to rot in the port and the log books and maps were destroyed. The construction of any ship with more than two masts was considered a capital offence. A major attempt at erasing a proud chapter in their history was done by the natives themselves. The goal is not to diminish the accomplishments of Copernicus or Galileo but to note that no less important accomplishments were achieved by the Kerala school either before or around the same time. Interestingly in the West, the Copernican revolution was considered a movement into science to which the Church, obstinate in religious dogma, would take umbrage. In India no one was burned at the stake or put under house arrest for proposing a heliocentric model. Instead of accepting the astronomical concepts of the Church on faith, Galileo investigated them and found new truths. Extrapolating that to historical studies we need to critically examine the Eurocentric history like the Peruvians and popularise the work of our ancestors. In this International Year of Astronomy, if we do not inform everyone about our great astronomers, who will? Postscript: In the midst of all this Eurocentric history, as a surprising exception to the norm, the only educational institution where one can take an elective course in The PreHistory of Calculus and Celestial Mechanics in Medieval Kerala is Canisius College, Buffalo, New York. The writer is an engineer based in the United States