Personalities

Nehru and the USSR …

Posted on November 17, 2017. Filed under: Personalities, From Russia with Love |

https://thewire.in/197484/jawaharlal-nehru-russian-revolution/

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Maj Gaurav Arya addresses the British Parliament …

Posted on November 9, 2017. Filed under: From a Services Career, Pakistan, Personalities |

http://www.republicworld.com/s/11213/delivered-in-the-british-parliament-major-gaurav-aryas-speech-will-make-every-indian-proud

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4th Bn Sikh Regt – SaraGarhi – Sam n More …

Posted on November 7, 2017. Filed under: From a Services Career, Personalities |

4 SIKH is a very Great Battalion but which, in my opinion, has had singular BAD LUCK. For instance in the 1962 War, two of its coys were airlifted to Walong where it did singularly well but due to a communication failure two coys were air dropped in Along.

See https://improveacrati.wordpress.com/2010/11/18/the-battle-of-walong-oct-21st-nov-17th-1962/

Again in the 1965 War, this great unit went into the PAK POW Bag when things did not quite work out as planned.

See https://improveacrati.wordpress.com/2011/05/20/the-1965-war-a-khem-karan-sector-story/

And here is where it earned eternal Glory.

“DEFENCE OF SARAGARHI POST.”. Camperdown Chronicle (Vic. : 1877 – 1954). Vic.: National Library of Australia. 5 December 1907. p. 6. Retrieved 1 September 2014.

DEFENCE OF SARAGARHI

The Tirah campaign of 1897 teemed throughout with thrilling incidents of gallantry and heroism. After a space of years, perhaps none is remembered with more enthusiasm, or takes a more conspicuous place in the annals of the Indian Army, than the heroic defence of Saragarhi Post by a mere
handful of Sikhs against an attacking force of the Orakzais tribe, 6000 strong.

The magnificent defence of the native soldiers for nearly nine hours, until totally annihilated, was unparalleled in the events of the frontier war of ten years ago, and is now historical. September 12 is therefore a day memorable in the history of the Indian frontier regiments.

Up on the sun-baked frontier stations the memory of the brave men who fought until death for the honour of the British service is kept alive by a general holiday on every anniversary of the defence.

Saragarhi post, the scene of this thrilling fight, was nothing more than a small signalling station situated on a barren, wind-blown hill-slope between, Fort Lockhart and Fort Cavagnari on the Santana range of hills. Within its walls on.the night of September 11, 1897, were gathered twenty-three Sepoys and one follower, detached from the gallant 36th Regiment of Sikhs.

All was still and tranquil in this inhospitable outpost. The night was dark and starless. Meanwhile, in the darkness, the Pathans were gathering together at the foot of the ridge, silently and slowly. The whole plain was alive with moving bodies. Inside the little fort on the summit the sentries walked patiently to and fro during the small hours, unconscious of the danger at hand. As yet the presence of the enemy was unknown.

The quiet peacefulness of the fort, however, was soon to be disturbed. Down in the valley the wily leader of the Orakzais gleefully took in hand the placing of his men. The operations were to be a huge joke. What, indeed, could be more humorous? On his right lay Fort-Lockhart; on his left, Fort Cavagnari,, both full of Sahibs and Sepoys. But here, right in the very palm of his hand was a mere handful of Sepoys, entrenched possibly but surely not very terrible,without a British Sahib to encour-
age and command them. He would catch them unawares, take the place by assault, batter down the walls, and then pass on. Dawn was advancing and he would begin at once.

Up in the fort the sentries saw a flash In the darkness. Then came the crack of a rifle and a shot hurried harmlessly over the fort. The attack on Saraghari had commenced.

The sleeping Sepoys were quickly awakened. rifles clicked, bandoliers were filled. with ammunition. What was happening they sleepily wondered. Evidently a sniping party of tribesmen intent on giving trouble were at hand.

When daylight came the brave men within the walls of Saragarhi Fort saw that they were preposterously outnumbered. Undismayed they returned the enemy’s fire from the loop-holes of the walls. If they could keep back their assailants for a few hours, help would come from Fort-Lockhart.

By helio they informed the garrison of the danger of their position and a cheering message of encouragement flashed back across the hills to them. Fort-Lock-hart was sending all the men that its slender garrison could spare. The day advanced, and the fort was subjected to a constant fire, but the men of the 36th Sikhs fought stubbornly on. ‘The enemy began to close in around them.

Surely help would soon be at hand. Fort-Lockhart would save them. They did not know that the Pathans had already outflanked the relieving force, whose frenzied efforts of rescue were checkmated by the overwhelming forces of the enemy.

The little garrison of Saragarhi fought desperately for their lives. they had now been besieged for six hours. The construction of the fort, alas, was faulty in the extreme. At the corner of the flanking tower there was a dead angle, or, in other words a part of the wall could not be defended from any part of the parapet or loop-holes.

The enemy were now to take advantage of this weak spot in the building. The splendid efforts of the soldiers had so far kept them at bay. Again and again their bullets had driven back the Pathan mountain men. Their leader decided that the garrison must be rushed. All through the fight the Sepoy signalmen up on the parapet kept in constant communication with
Fort-Lockhart by heliograph.

The distracted commanding officer in that fort, with every detail of the fight before him, knew that the gallant little force in Saragarhi was doomed. He could do nothing to check the attack of the enemy or assist the garrison.

The crisis came at last. The Orakzais brought an unceasing hail of bullets to bear on the besieged fort. Intoxicated with fanaticism and the desire to kill, they advanced up the hill with a rush. The signalman
did not desert his post until at last he was driven to defend himself.

The enemy were now beside the dead angle in the flanking tower and battering a hole in the walls. Soon an opening was made and the Pathans crowded into the: fort. The brave men of the 36th Sikhs determined to sell their lives dearly, and retired to an inner enclosure. Here they gallantly fought until reinforcements of the enemy, climbing the walls on all sides, swarmed into the fort, when they were cut up to a man.

A wounded Sepoy lying on a bed shot four of the enemy before he was killed himself. The last surviving man barricaded himself in the guard-room and accounted for twenty of the Pathans.

Up on the frontier the defence of Saragarhi and the brave men who did their duty and died at their posts in the Frontier war of ten years ago will not be forgotten while British rule in India remains.

On September 12, 1897. the 36th Sikhs covered themselves with undying glory — Pall Mall Gazette.

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And here is an extract from an Article on Sam Manekshaw on his 100th Birth Anniversary by Hamid Hussein which has lots re 4 Sikh ….

“He ie Sam, followed the routine of spending one year of probationary period with a British regiment; 2nd Battalion of Royal Scots after commission. He then joined the elite 4/12 Frontier Force Regiment (FFR).

This battalion had evolved through its one hundred and fifty year history going through various reorganizations which changed its name. It started as 4th Sikh Local Infantry after First Sikh War in 1846. In 1901, it became 4th Sikh Infantry and in 1903 became 54th Sikhs. The 1922 reorganization changed it into 4th Battalion of 12 Frontier Force Regiment. The 1957 reorganization gave it its present designation of 6 Frontier Force (FF).

The original designation of the force deployed on the frontier of newly acquired territories in 1849 was Punjab Irregular Frontier Force (PIFFER). Till today those who join Frontier Force Regiment are known as PIFFERS.

Young impressionable cadets in the Academy see their instructors as role models and the caliber of an instructor may be a factor when a cadet chooses his battalion.

Lieutenant Colonel Jimmy Carter of 4/12 Frontier Force Regiment was a first rate officer and then instructor at Dehra Dun (he later commanded the battalion in 1942 when it was being reorganized into a reconnaissance battalion at Ranchi). He may have been responsible for two cadets of the batch joining the 4/12 FFR; Sam and Atiq-ur-Rahman, nick named Turk.

In the Second World War, Sam then a captain was leading Sikhs of Charlie company of 4/12 FFR in Burma.

A small group of Japanese soldiers surprised the troops and sneaked into the perimeter of the battalion at night. This caused panic and a number of soldiers bolted from the scene. Sam’s Sikhs firmly stayed in their positions. Sam had threatened them that he will personally distribute ‘bangles’ if any of them moved from their position.

xxxxxxxxxxxxxxxxxx And –

When Major Shabbir Sharif of 6 FF got the highest gallantry award of Nishan-e-Haider fighting from Pakistan side, Sam wrote to his old British Commanding Officer (CO) of 4/12 FFR in England that he was so proud that an officer of ‘his battalion’ got the honor although Sam’s forces were fighting against Pakistan.

In 1973, when he came to Pakistan for post-war negotiations, he requested that dinner be served in the silverware of his parent battalion. 4/12 FFR (6 FF) was then stationed in Okara and cutlery of the battalion was carefully packed and sent to Lahore where Sam was entertained. During his 1973 visit to Pakistan, Sam was given a lunch at Station Artillery Mess in Lahore. Sam went around looking at the impressive array of trophies in the mess. He stopped by a trophy and asked what a trophy of 54th Sikh (4/12 FFR) was doing in the artillery mess. One Pakistani officer confided that the trophy was brought to the mess for the special occasion.

In March 1973, when Sam visited England, he hosted a dinner where all serving and retired officers who had association with 54th Sikhs and 8th Gorkha Rifles were in attendance.

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The Importance of being S Gurumurthy …

Posted on November 1, 2017. Filed under: Personalities |

The Importance and Unimportance of S. Gurumurthy bY PARANJOY GUHA THAKURTA – Paranjoy Guha Thakurta is an independent journalist.

The accountant-cum-ideologue is believed to have played a key role in many of Narendra Modi’s economic policies, such as demonetisation.

Many contend that while the move was announced suddenly in order to take everyone by surprise, it was nevertheless premeditated. Importantly, it is said that the decision to demonetise 86% of the currency in circulation in the country was based on inputs from a few close advisers of the prime minister, notable among whom was Swaminathan Gurumurthy.

Whatever the truth of note bandi’s provenance, today, however, the 68-year-old chartered accountant and ideologue of the Rashtriya Swayamsevak Sangh, is a chartered accountant by qualification and well-known mediator in corporate disputes involving families. Gurumurthy is a columnist by vocation and an activist too – he is co-convenor of the Swadeshi Jagaran Manch, which espouses economic nationalism, Hindutva-style.

He belongs to a small group of thinkers whose views are given considerable importance by the prime minister. His association with Modi goes back to the early-1990s, when he apparently acted as an adviser to him and to Amit Shah.

His proximity to Modi may be inferred from the email correspondence of former additional advocate general of Gujarat Tushar Mehta in the wake of the 2002 communal riots that was presented in the Supreme Court by advocate Prashant Bhushan in October 2015.

Gurumurthy, who was born in a poor family in Tamil Nadu’s South Arcot district and obtained a scholarship to study for a bachelor’s degree in commerce, often criticises professional economists in general and foreign-educated economists in particular. He sees himself as an ardent proponent of “Indian economics” and believes in the virtues of economic “self-reliance”.

One of the favourite issues he engages with is “jobless growth”. He has often railed on this issue by citing numbers contained in the employment survey report by the National Sample Survey Organisation collated by the then Planning Commission.

Sources in the BJP who spoke on condition of anonymity say that of late, Gurumurthy has been defensive about the fact that job creation has not taken place during Modi’s term in office. In fact, government data indicates that there has been an absolute decline in employment between 2013-14 and 2015-16, perhaps for the first time in the history of independent India.

Within the Sangh parivar, it is believed that Gurumurthy was among those who advised the prime minister to set up a new body in place of the Planning Commission. This change was announced in August 2014. In January 2015, he provided inputs during the drafting of the mission statement of the NITI (National Institution for Transforming India) Aayog in January 2015.

The cabinet note for the formation of the NITI Aayog stated: “The new institution has to zero in on what will work in and for India. It will be a Bharatiya approach to development”. This statement echoes the words of Gurumurthy.

He is a firm believer in the ability of the country’s 50 million-odd small and micro enterprises to create jobs and transform the country’s economy.

Sources say that the government initiative MUDRA – or the Micro Units Development and Refinance Agency – that was announced in the February 2015 Union budget was identical to what Gurumurthy had suggested and prescribed. They add that he not only helped conceptualise, design and draft the MUDRA scheme, he subsequently endorsed his own idea once it was adopted.

MUDRA essentially advocates relaxation of risk norms and greater generosity in lending to small and medium businesses.

Between April 2015 and May 2016, the RBI under its governor at the time, Raghuram Rajan, was concerned about growing non-performing assets (NPAs) in the banking system and was averse to the idea of reducing/relaxing risk weights applicable to banks while lending to small and medium enterprises.

It is claimed that Gurumurthy was opposed to Rajan’s move to get banks to adopt stricter norms for recognition of non-performing assets.

While delivering a speech in Chennai last month, Gurumurthy was quoted as saying the government “grievously failed to implement MUDRA first” before demonetisation which was the “original strategy”. What he didn’t say was whose original strategy this was.

During the speech delivered at the Chennai International Centre, Gurumurthy remarked that the establishment of the MUDRA Bank “was stopped by the Reserve Bank, which did not want to give up monetary control” and “control over financing smaller players…

Hence, aggregate consumption and job generation have stagnated and the informal sector borrows at 360-480% interest rate.” He claimed that the “RBI and the department of financial services (in the Ministry of Finance) are insensitive, and this will hit growth badly.”

The MUDRA scheme has not really been a grand success.

Official statistics suggest that the number of loans for the self-employed has not gone up significantly. BJP sources alleged that when the MUDRA scheme failed to take off, there was an effort by various individuals, including Gurumurthy and BJP MP Subramanian Swamy to discredit Rajan and not give him the customary extension of term.

Soon thereafter, on June 18, 2016, Rajan announced that he would not seek an extension of his term as RBI governor.

Four days later, Gurumurthy wrote an article explaining why Rajan was not given an extension of his term as RBI governor and explicitly argued that high denomination notes were fuelling growth of gross domestic product (GDP).

In that article, he predicted that there would be a new RBI governor soon who would agree with the government’s new ideas after which the “war on high denomination notes will begin”.

Gurumurthy’s article, which appeared on June 22, 2016, was either remarkably prescient or he had an inkling of the prime minister’s interest in demonetisation of high-denomination currency notes.

Incidentally, Swamy and Gurumurthy were both involved in the anti-corruption movement in 2011 that was led by Anna Hazare and Arvind Kejriwal. Gurumurthy and Ajit Doval (now national security adviser) hosted Swamy at the Vivekananda International Foundation, a right-wing think tank. Swamy was then still a member of the Janata Party.

Gurumurthy apparently convinced the BJP to take Swamy into the party in 2013 before the Lok Sabha elections.

On November 8, 2016, Modi announced the scrapping of the Rs 500 and Rs 1000 currency note. Gurumurthy then backed the government’s decision and explained the rationale for demonetisation.

He argued that there was too much cash in the economy and that there was a pressing need to extinguish such excess liquidity. An otherwise reticent and publicity – shy individual, he granted three television interviews in quick succession and even responded to former prime minister Manmohan Singh’s trenchant criticism of demonetisation in an article in the Hindu.

Gurumurthy currently seems more than a bit disappointed with the impact that demonetisation has had. He seems to be targeting the RBI and the Ministry of Finance for the negative consequences of notebandi. He talks of a lack of communication between the finance ministry and a “confidential cell” that allowed black-money holders to get away.

He even attacked the Supreme Court for “wanting” riots to take place after demonetisation.

Here are a few quotes from his September 22, 2017 speech in Chennai that have been taken from news reports published in the Hindu and the Hindu BusinessLine:

“I have a feeling we are hitting the bottom now. There is no way this situation can continue. Because the government has to take a decision whether to have this whole lot of NPA regulations, the MUDRA decision; if these two-three decisions are taken in the coming six months, the economy is poised to take off.

‘I have faith that given the right policy input, the economy will pick up immediately…

‘Too many disruptions, too soon. This is one of the things which a government in urgency is doing. Demonetisation, NPA rules, bankruptcy law, GST (goods and services tax), thrust against black money — everything at one stretch; commerce cannot absorb all this…

‘It is a corrective step. I consider demonetisation as an investment… One of the key successes of demonetisation is that nearly 30 crore bank accounts were opened, and brought huge savings into the banking system. One of the fallouts of demonetisation is it brought unmonitored money into the system…

‘Irresponsible monetary management has been stopped, tax base has risen by about 20 per cent and advance tax for 2017-18 has increased by nearly 42 per cent… Today, it is not possible to bring black money to invest in land, gold or equity on the scale that used to happen in the past.

‘I have not come here to defend the government … despite its many benefits, demonetisation was implemented badly… . due to a communication error between the Finance Ministry and a confidential cell, black money holders escaped the demonetisation dragnet.

‘… withdrawal of cash crippled the informal sector, which generated 90% of jobs and satisfied 95% of its capital requirements from outside the banking system….

‘… political pressures on the government had reduced the many objectives of demonetisation to one: of ending the circulation of black money….The demonetisation scheme had a big hole. It was because there was no coordination within the government.

‘The advice the government of India received was that demonetisation and the income disclosure scheme should be announced simultaneously. Because of the communication gap within the system, income disclosure was announced first and demonetisation, later.

‘Demonetisation became a gas chamber. That was the first major strategic fault…Instead of collecting the tax in advance, the government is now chasing the black money to collect taxes…GST is a welcome measure, but it is too ambitious. It wants to formalise the Indian economy in one go. It’s not possible. It has to be a calibrated formalisation of the Indian economy.’

‘The media is failing, economic think-tanks are not doing original work for India because they are still on a one-size-fit-all model… (After demonetisation) the media wanted riots, the Supreme Court wanted riots. The people did not riot. It goes to prove the psychology of India as a peaceful nation…”

Gurumurthy is said to be a great networker. His contacts cut across classes and regions. Among the clients of the accountancy firms with which he has been associated have been companies controlled by the Chhabria family and liquor baron Vijay Mallya.

In 2003, he played a key role in resolving a dispute over the control of assets and businesses between the families of Rahul Bajaj and his younger brother Shishir Bajaj that had gone on for more than six years. More recently, Gurumurthy is believed to have played a role in brokering the deal between Russia’s Rosneft, the Oil and Natural Gas Corporation and the Essar group.

He was a great confidante of the late Ram Nath Goenka who founded the Indian Express group of publications. In 1986, he co-authored (together with Arun Shourie) a series of articles against the Reliance group of companies, then headed by Dhirubhai Ambani.

In 2003, Gurumurthy, on behalf of the SJM, demanded a criminal investigation into the controversial Enron power project in Dabhol, Maharashtra.

In 2010-11, he was among the convenors of a task force on black money set up by the BJP. In 2012, he gave a clean chit to Nitin Gadkari (who was then BJP president) when allegations of financial misdemeanour were levelled against his Purti group of companies.

Gurumurthy has been editing the Tamil magazine Thuglak after the demise of its founder Cho Ramaswamy.

Among his close friends is Revenue Secretary Hasmukh Adhia who moved from the Gujarat government to North Block in Delhi as secretary, financial services in the Ministry of Finance. Adhia is a trusted confidante of Modi. It is said that Adhia was introduced to yoga and the finer nuances of Hinduism by Gurumurthy.

Adhia holds a doctorate degree in yoga from Swami Vivekananda Yoga University in Bangalore. Besides Adhia, another officer of the Indian Administrative Service (IAS) to whom Gurumurthy is said to close to is T V Somanathan in the Prime Minister’s Office. In fact, he is said to have recommended his appointment.

India Today magazine ranked him in 30th place in its 2017 list of “India’s 50 Most Powerful People”. He was the subject of media attention in 1997 when he accused two senior government officials of acting as American “moles” without directly naming them. Later, in 2006, in a newspaper article, he named the people he was accusing: V.S. Arunachalam and Naresh Chandra Saxena.

Of late, Gurumurthy’s relations with Swamy seem to have changed somewhat. In a tweet sent on September 22, Swamy remarked: “Spin talk can never cure our economic ailments. In fact it ends up in tailspin. CAs and laymen must know macro economics is complex Maths”. CAs, in this instance, presumably means chartered accountants.

I have known Gurumurthy for quite some time. In 1997, he appeared on a television programme that I used to anchor for CNBC-TV18 and vigorously participated in a debate on “swadeshi economics” with Bibek Debroy, who currently heads the Prime Minister’s Economic Advisory Council.

Before writing this article, I wanted to speak with Gurumurthy to seek certain clarifications from him on the record. But I was not successful.

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Macaulay’s Best …

Posted on October 25, 2017. Filed under: Books, Great Writing, Personalities, The English |

Lays of Ancient Rome, a series of very popular poems about heroic episodes in Roman history which Macaulay composed in India and published in 1842.

The most famous of them, Horatius, concerns the heroism of Horatius Cocles. It contains the oft-quoted lines:

Then out spake brave Horatius,
The Captain of the Gate:
“To every man upon this earth
Death cometh soon or late.
And how can man die better
Than facing fearful odds,
For the ashes of his fathers,
And the temples of his gods?”


PS As a rival you might enjoy

https://improveacrati.wordpress.com/2008/03/15/ulysses/

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Tolstoy …

Posted on October 25, 2017. Filed under: Books, From Russia with Love, Personalities |

Tolstoy’s Classics Are Still Fresh a Century and a Half Later -Henry James called ‘War and Peace’ a ‘loose, baggy monster.’ Count me a fan of monsters. By Benjamin Shull

I read Tolstoy this year to plug a literary gap unbefitting a book -review editor. Getting started was no easy task. His two pre-eminent novels, “War and Peace” and “ Anna Karenina, ” clock in at more than 1,200 and 800 pages respectively, the former so massive that Henry James called it a “loose, baggy monster.”
Count me a fan of monsters.

Published in 1869, “War and Peace” nominally centers on Napoleon’s 1812 invasion of Russia, but it more broadly surveys the effects of Europe’s early-19th-century conflicts on several Russian families.

Its scenes shift from the landed estates of Moscow and St. Petersburg to the battlefields of Austerlitz and Borodino. Its main characters include Pierre Bezukhov, by turns an illegitimate son, Freemason and Napoleon’s would-be-slayer; Andrei Bolkonsky, the sardonic and military-minded prince; Natasha Rostova, the young woman who comes to love both; and of course, Bonaparte, le petit caporal himself.

“Anna Karenina” came eight years later. It relates the trials of its title heroine, a strong-willed woman who has an affair with the charming Count Vronsky, bearing his child and the wrath of Russian society in turn.

“Anna Karenina” has its own cast of unforgettable characters — “Stiva” Arkadyich Oblonsky, Anna’s jaunty, epicurean brother; and Konstantin Dmitrich Levin, the idealistic landowner (and Tolstoy’s self-modeled proxy).

Like Bob Dylan’s “Visions of Johanna,” the settings and people that populate these two books have conquered my mind. It’s a common experience for readers of great literature.

In last year’s “Books for Living,” Will Schwalbe recounts how he sobbed after he’d read “David Copperfield” for the first time, distraught that he’d miss the characters so much. Later in life, when asked if writing a book about his late mother would give him closure, Mr. Schwalbe remembered reading Dickens as a teenager and realized that closure wasn’t necessary when you could continue to talk with the deceased and the fictional alike.

“Just because someone is gone,” Mr. Schwalbe observes, “doesn’t mean that person exits your life. I remember vividly the day during that hot summer when I finished David Copperfield. But my engagement with David and Little Emily and Steerforth and Dora . . . had just begun.” So it is with Pierre and Prince Andrei and Anna and Stiva.

Though there’s plenty of heartbreak in “War and Peace” and “Anna Karenina,” each is also enormously life-affirming. Before Anna’s tragic fate crescendos, we find Levin and his wife, Kitty, at the bedside of his dying brother, Nikolai. Levin dreads death, but his remarkably poised wife helps him face it with courage.

As Nikolai drifts away, Levin (in Richard Pevear and Larissa Volokhonsky’s translation) manages to keep his gloom at bay:

“In spite of death, he felt the necessity to live and to love. He felt that love saved him from despair and that under the threat of despair this love was becoming still stronger and purer.”

Nary a paragraph later, Nikolai since passed, Kitty learns she is pregnant, as one mystery of life supplants another. Thinking about this scene has been a comfort for me since.

Both works are in every way “books for living,” rife with guiding principles for life. Themes of magnanimity and forgiveness figure prominently in each.

In “War and Peace” there is a remarkable scene toward the end of the book in which Prince Andrei is wounded at Borodino. At the field hospital he finds the also-wounded Anatole Kuragin, whose attempt to seduce Andrei’s fiancée, Natasha, had led her to break off the engagement.

Andrei had wanted revenge, but in the blood-soaked camaraderie wrought by war—Anatole ultimately has his leg amputated — Andrei feels nothing but love for his former enemy and fellow man.

Though Tolstoy colorfully renders the battle scenes of “War and Peace,” he still manages to make war seem insignificant.

The book notably departs from its narrative at times to showcase its author’s meditation on history and the course of human affairs. Tolstoy’s conception of a historical process driven not by great figures but by the interplay of countless interconnected phenomena has influenced my own convictions about the world.

Because the forward march of history is so incomprehensibly beyond our grasp, in Tolstoy’s telling, it seems to throw our own freedom into doubt. He writes in his epilogue (again, courtesy of Mr. Pevear and Ms. Volokhonsky): “For history, freedom is only the expression of the unknown remainder of what we know about the laws of human life.”

That’s a humbling thing to read after spending 1,000 pages living with these iconic literary figures.

These books may well change the way you look at the world. The characters, settings and messages will stay with you for as long as you want them to.

Mr. Schwalbe must have had Tolstoy in mind when he wrote that books “are uniquely suited to helping us change our relationship to the rhythms and habits of daily life.”

It’s on that note that this humble editor recommends you read “War and Peace” and “Anna Karenina.”

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S Chandrasekharan – Indian Scientist …

Posted on October 20, 2017. Filed under: American Thinkers, Indian Thought, Personalities |

Professor Subrahmanyan Chandrasekhar Why Google honours him today?

In his honour, Google is changing its logo in 28 countries to a doodle, or illustration, of him and the Chandrasekhar Limit.

Described as a “child prodigy” and hailed as the first astrophysicist to win a Nobel Prize for his theory on the evolution of stars, Diwali on Thursday would have been Subrahmanyan Chandrasekhar’s 107th birthday.

But in his lifetime, the Indian American astrophysicist was not always recognised for his achievements. This is his story:

Born in Lahore in 1910 to a Tamil family, Chandrasekhar was home tutored until age 12. In his autobiography, Chandrasekhar referred to his mother as “My mother Sita was a woman of high intellectual attainments”. His uncle, Sir CV Raman, won the Nobel Prize in Physics in 1930. Also in 1930, Chandrasekhar completed his bachelor’s degree in physics at the Presidency College in Madras, India (known today as Chennai).

Chandrasekhar was then awarded a scholarship by the government of India to pursue graduate studies at the University of Cambridge in the UK. He completed his PhD studies in 1933.

Married to Lalitha Doraiswamy in the southern Indian city of Madras, Chandrasekhar praised his wife’s “patient understanding, support, and encouragement” and called those the “central facts of my life”.

Working as a researcher at Cambridge University, Chandrasekhar made his most significant discovery, which became known as the Chandrasekhar Limit. But his colleagues were sceptical of his discovery and sought to discredit it. According to the Open University, English astronomer Sir Arthur Eddington persuaded Chandrasekhar to present his findings at the Royal Astronomical Society in London on January 11, 1935.

At the astronomical society, Eddington then gave a lecture to “demolish the young researcher’s calculations and theory, dismissing it as mere mathematical game playing”.

More than 30 years later, in 1966, scientific research with computers and the hydrogen bomb gave credit to Chandrasekhar’s calculations. Black holes, central to Chandrasekhar’s theory, were identified in 1972. His calculations contributed to the understanding of supernovas, neutron stars and black holes.

In 1937, Chandrasekhar emigrated to the US and started working at the University of Chicago. During World War II, he was invited to join the Manhattan Project at Los Alamos to make a nuclear bomb, but delays in the processing of his security clearance prevented him from joining.

Chandrasekhar contributed to the war effort, working for the Ballistic Research Laboratory in Maryland. In 1953, 16 years after he came to the US, Chandrasekhar was granted US citizenship. He died in Chicago at the age of 85.

In his book, Truth and Beauty, he offered his advice to aspiring scientists, “What a scientist tries to do essentially is to select a certain domain… and see if that takes its appropriate place in a general scheme which has form and coherence; and, if not, to seek further information which would help him to do that.”

In his autobiographical sketch for the Nobel Prize ceremony, he described what motivated his scientific quest, “When, after some years of study, I feel that I have accumulated a sufficient body of knowledge and achieved a view of my own, I have the urge to present my point of view, ab initio, in a coherent account with order, form, and structure”.

In an interview, Chandrasekhar praised the US, “I have one advantage here in the United States. I have enormous freedom. I can do what I want. Nobody bothers me. What a scientist tries to do essentially is to select a certain domain … and see if that takes its appropriate place in a general scheme”

When Chandrasekhar was 43, he was awarded the Gold Medal of the Royal Astronomical Society. At the age of 56, he was awarded the National Medal of Science for his numerous contributions to stellar astronomy, physics and applied mathematics.

At the age of 61, he was honoured with the Draper Medal from the US National Academy of Science for his leadership in, and major contributions to, the field of astrophysics.

In 1983, at 73 years of age, Chandrasekhar shared the Nobel Prize in Physics with William Fowler for his “theoretical studies of the physical processes of importance to the structure and evolution of the stars”. That is, how shining stars eventually become “black holes” or “white dwarfs”.

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Clinton on Grant …

Posted on October 15, 2017. Filed under: American Thinkers, Personalities |

GRANT By Ron Chernow – reviewed by Bill Clinton.

This is a good time for Ron Chernow’s fine biography of Ulysses S. Grant to appear – as we live with the reality of Faulkner’s declaration, “The past is never dead, it’s not even past.”

We are now several years into revisiting the issues that shaped Grant’s service in the Civil War and the White House, from the rise of white supremacy groups to successful attacks on the right of eligible citizens to vote to the economic inequalities of the Gilded Age. In so many ways “Grant” comes to us now as much a mirror as a history lesson.

As history, it is remarkable, full of fascinating details sure to make it interesting both to those with the most cursory knowledge of Grant’s life and to those who have read his memoirs or any of several previous biographies.

It tells well the story of a country boy’s unlikely path to leadership, his peculiarities, strengths, blind spots and uncanny powers of concentration and courage during battle. It covers Grant’s amazing feats on horseback at West Point, where in jumping hurdles “he exceeded all rivals,” clearing the bar a foot higher than other cadets.

His mediocre grades have long obscured his interests and abilities: He was president of the literary society, had a talent for drawing and was trusted by classmates to mediate disputes.

His service in the Mexican War is covered briefly, but it contributes to our understanding of his later military and political life. Grant’s often harrowing experiences and extreme efforts to care for the wounded still on the battlefield taught him both about the conduct of war and about war’s political implications.

He believed that the victory over Mexico, with its huge territorial gains, intensified disputes over slavery and led directly to the Civil War.

The major encounters of the Civil War are deftly included, as are the business failures and bouts of drunkenness — never proved to have happened during major military campaigns, despite what his enemies often asserted.

Chernow, the author of “Alexander Hamilton” and other biographies, judiciously quotes from Grant’s own memoirs, and he also shows how they were a miracle of sorts, produced by a dying man racked with pain from throat cancer, in a final effort to leave his family some amount of financial stability. “Somehow,” Chernow writes, “in agony, he had produced 336,000 splendid words in the span of a year.”

“The Personal Memoirs of Ulysses S. Grant” ends shortly after the surrender at Appomattox Court House, and as Chernow states in his introduction, many biographies of Grant skip over his presidency as an “embarrassing coda” dominated by multiple scandals.

As Chernow puts it, “It is sadly ironic that Grant’s presidency became synonymous with corruption, since he himself was impeccably honest.”

For all its scholarly and literary strengths, this book’s greatest service is to remind us of Grant’s significant achievements at the end of the war and after, which have too long been overlooked and are too important today to be left in the dark.

Considered by many detractors to be, as a general, little more than a stoic butcher, Grant, in the written terms of surrender at Appomattox, showed the empathy he felt toward the defeated and downtrodden — conditions he knew from harsh personal experience.

The terms presented to Robert E. Lee carried “no tinge of malice” and “breathed a spirit of charity reminiscent of Lincoln’s Second Inaugural Address.”

He notably allowed the exhausted and starving Confederate regulars to keep their mules and horses, knowing from the rough experience of his failed Missouri farm (Grant presciently named its log cabin “Hardscrabble”) that only by putting in a crop as soon as they returned home would these destitute farmers — and their families — have a chance to survive the coming winter.

Grant also knew that if the country had any chance of being brought back together, it needed something other than a harsh peace. In making national healing a priority, he — like Lincoln — took the long view.

Grant’s tendency toward empathy with the downtrodden and defeated would return again and again, and not always to his advantage or credit.

He didn’t hesitate to appoint family and friends far above their abilities, and to remember even the smallest favor done on his behalf while he was a struggling civilian.

There’s a wonderful exchange in the book when Grant as president offers a political appointment to a friend from his prewar days in St. Louis, when he was broke and dependent on his slave-owning (and openly contemptuous) father-in-law. Grant reminded the friend that “when I was standing on a street corner … by a wagon loaded with wood, you approached and said: ‘Captain, haven’t you been able to sell your wood?’ I answered: ‘No.’ Then you said: ‘I’ll buy it; and whenever you haul a load of wood to the city and can’t sell it, just take it around to my residence … and I’ll pay you for it.’ I haven’t forgotten it.”

After Appomattox, and the assassination of Lincoln, Grant moved to what he then called Washington City to lead the Army through the war’s aftermath. Chernow notes that, as a general, Grant had nearly always fought on unfamiliar ground, which required a kind of concentration that could support a state of continuous reassessment.

Washington was also unfamiliar ground, and continuous reassessment was just as vital to political success as it had been to victory on the field. Grant proved a quick study, even after he had professed to be “no politician.

For example, he saw early on that the new president, Andrew Johnson, who many feared would be much harsher on the South than Lincoln would have been, had begun to lean hard — and dangerously — in the opposite direction.

“Mr. Johnson,” Grant writes in his memoirs, “after a complete revolution of sentiment, seemed to regard the South not only as an oppressed people, but as the people best entitled to consideration of any of our citizens.”

Needless for Grant to say, this favor of Johnson’s fell to white Southerners only. He began to bring the weight of the presidency down on the side of those who championed what became the infamous Black Codes, designed to force freed slaves to continue to work on plantations in conditions much like those before emancipation.

As Grant’s and Johnson’s political differences grew wider, Grant, as General of the Army and immensely popular, began to suffer the ire of the increasingly besieged Johnson, who demanded fealty and, when frustrated and convinced of disloyalties real or imagined, tended to lash out.

“It grated on Johnson that Grant,” Chernow says, “a mere subordinate, had been endowed with … godlike powers over Reconstruction.”

Contrary to Johnson’s claim, the power Grant had to oversee the fate of the postwar South was hardly godlike. A former social club named for the Greek word kuklos, or circle, the Ku Klux Klan had begun “to shade into a quasi-military organization, recruiting Nathan Bedford Forrest as a leader” — and vowing “to ‘support a white man’s government’ and carry weapons at all times.”

By the time of Grant’s election as president in 1868, the Klan was targeting black voters and their supporters with “murders and mutilations in a grotesque spirit of sadistic mockery.” The Union that Grant had been instrumental in saving as a general was splintering anew even before he took his oath of office.

As Chernow writes, “If there were many small things Grant didn’t know about the presidency, he knew one big thing: His main mission was to settle unfinished business from the war by preserving the Union and safeguarding the freed slaves.”

And there was a very real chance Grant, and with him the country, would fail.

For that new mission, Grant needed cabinet members, staff and advisers every bit as masterful as his wartime lieutenants. His choices were notably hit-and-miss, but his very first appointee from a Confederate state proved to be one of his best. Amos T. Akerman of Georgia, Grant’s second attorney general, was “honest and incorruptible” and “devoted to the rule of law.”

When Congress created the Department of Justice the same week as his appointment, the attorney general became overnight the head of “an active department with a substantial array of new powers.”

Those powers were sorely needed to fight the Klan and what Chernow appropriately calls “the worst outbreak of domestic terrorism in American history.”

Grant signed three bills, collectively known as the Enforcement Acts, to strengthen federal powers in combating Klan terrorism, which had already claimed thousands of lives – the vast majority of them black. After the laws were in force, “federal grand juries, many interracial, brought 3,384 indictments against the K.K.K., resulting in 1,143 convictions.”

Almost as important as the convictions was the message they sent. As Akerman told his district attorneys, “If you cannot convict, you, at least, can expose, and ultimately such exposures will make the community ashamed of shielding the crime.”

By the end of his first term, scandals had begun to take their toll, but at the same time the Klan — at least in its original incarnation — had been essentially destroyed.

“Peace has come to many places as never before,” declared Frederick Douglass, an ally and admirer of Grant’s. “The scourging and slaughter of our people have so far ceased.”

However short-lived, it was an important victory not only for an enlightened version of Reconstruction but also for the beneficial use of the powers of the federal government to promote the general welfare and safety of all Americans – not just some.

As president, Grant appointed a record number of African-Americans to government positions all across the board, including the first black diplomat. Douglass once noted “in one department at Washington I found 249” black appointees, “and many more holding important positions in its service in different parts of the country.”

Early in his presidency and at the height of his popularity, Grant had also been a booster of the 15th Amendment, giving former slaves the vote, and many believe his support was key to its ratification by the states, which was far from guaranteed.

Grant himself minced no words in describing the magnitude of the amendment’s passage, saying in a message to Congress upon its ratification, “The adoption of the 15th Amendment … constitutes the most important event that has occurred, since the nation came into life.”

He knew the right to vote is the heart of democracy and did not hesitate to defend it, a legacy today’s Supreme Court and Republicans in Washington and across the country should embrace, not abandon.

Chernow shows a fine balance in exposing Grant’s flaws and missteps as president, and the ill-fated turn that Reconstruction took after a promising start, while making it clear that Grant’s contributions after Appomattox were as consequential to the survival of our democracy as any that came before.

As Americans continue the struggle to defend justice and equality in our tumultuous and divisive era, we need to know what Grant did when our country’s very existence hung in the balance.

If we still believe in forming a more perfect union, his steady and courageous example is more valuable than ever.

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All about an Officer …

Posted on October 6, 2017. Filed under: From a Services Career, Personalities |

An Article by Col Abhay Gupta.

I was all of 48 yrs when I was superseded in my present rank. At a social-do, I was asked by this pretty girl, “Just 48, and the end of the road for you! What has Army really given you? You’ve never been paid well in the Army. And see what they have done to you now!”

I appraised her top to bottom. I must confess she was a pretty sight. What I told her was this,

“The Army, my dear, is a way of life. It is not about making a living. As far as supersession is concerned, lady, that is the way of army life. You can’t complain just because your personal interest, as you perceive it, has not been looked after.

‘The Army has a wonderful, time-tested and evolved systems.
You don’t fight personal battles for the heck of it. And it is about unselfishness, dear – Service Before Self is our motto. Remember it is a Service (seva).There are no expectations of rewards in Seva, for Seva is considered its own reward.

‘What has Army given me?, you asked. It has given me a glimpse and understanding of dimensions you, in the civil sector, can only wonder and feel over-awed about. Have you any idea of camaraderie? When you see a soldier brave the shower of artillery shrapnel’s to rush to rescue his bleeding colleague wounded in the shelling – then you KNOW the meaning of the word ‘camaraderie.

‘When you are lying in a hospital on a DI List and there are 20 blood donors of your blood-group spending the cold night in the verandah of the hospital, just so that any emergency call for blood to save your life may be attended to, that is camaraderie.

‘Camaraderie implies selfless help and support to someone who is not necessarily a friend. You have to cross Banihal to understand all this. Do you know the holy significance of the word ‘command’?
It is a sacred word.

‘And who can know the meaning of it other than a person in uniform?
Even the CEO of a Fortune 500 company can’t comprehend the significance of this sacred word. When you are in ‘command’ you are God.

‘Can you comprehend what being God can be like? It is not about the authority, it is about responsibility. The authority comes into play after you have rendered your part of the deal of unflinching loyalty displayed towards your subordinates.

‘Now when you signal him – not ask him or tell him or order him – to dash down-crawl – observe – fire, and in the process subject himself to imminent death, he does so without a second thought. This is when you REALIZE what is so sacred about command.

Even before you can move your hand to the door of the gypsy, the driver jumps from his seat and beats you to the door, your door is what command gets you. Such are the rewards of command.

Do you know the meaning of ‘being a gentleman’? In the last thirty years in uniform one has witnessed a proliferation of designations in the civil environment.

There have been Executive Officers and there have been Managers – General Mangers, Assistant Managers, and a whole spectrum. Then there are CEOs and Vice Presidents. In the Army we have only ‘Officers’.
Some are General Officers and some just Officers. At the induction level we have Young Officers.

What it means to be an ‘Officer’ is something you can’t comprehend. Hollywood tried to bring about a differentiation, calling the phenomenon, ‘An Officer and a Gentleman’, little knowing that being a gentleman is inherent when you are an Officer. Being a gentleman is his primary nature, not second-nature.

His behaviour is bhadra – i.e. kalyan-kaarak swabhav, guna, aur karma.
The Army imbibes this peculiar quality in us when we are as young as 17 to 20 years only. I’ll explain with an example. An officer once held the door open for a particular lady. She, trying to be smartly polite said, “You don’t have to hold the door open for me, just because I’m a lady.” He replied, “Ma’am, I’m not holding it for you because you are a lady, but because I’m a gentleman.”

We may appear to be ruthless and egoistic, but we are enlightened ones. In the corporate world have you ever come across the word ‘honour’? In uniform we serve only for honour, and never the ‘package’. Naam, Namak, Nishan – are alien words in the corporate world.

You know what it means to serve for honour? When a subordinate, who already has a bad ankle, is told of a mission which entails 12 hours of walk in the most rugged terrain; and when he expresses reservation on account of his current physical condition, is told that if we can’t do it, it will be a smudge on the Regiment – AND THERE IS NO ONE TO REPLACE HIM. He says he’ll do his bit.

That is for honour. The Army has commanders at every level – langar commander, section commander/ detachment commander, platoon commander/troop commander, and up the chain to Brigade Commanders, and General Officers Commanding in Chief.

What is implied by the term ‘commander’? Maybe something most people will never know. To be a commander implies responsibility – complete responsibility. As a commander you are responsible for every aspect of your command – right from his morning cup of tea, his toilet facilities, his professional training, his mental makeup, his family’ well being and his spiritual requirements.

In the Army we first train young boys, and now even young girls, to be an Officer and then to be a Commander.

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Indian Math and Music …

Posted on September 26, 2017. Filed under: Indian Thought, Personalities |

Prof. K. Ramasubramanian from IIT, Mumbai, delivered a lecture titled “Glimpses of Indian Mathematics: Sutra Style to Paragon of Poetry” at MIT on Sunday, August 13, 2017.

In this talk organized by Samskrita Bharati Boston and MIT Samskritam, Prof. K. Ramasubramanian offered an illuminating view of Indian Mathematics over the ages, its unique approach based on poetry rather than prose, the need for such an approach, and presented many surprising facts about mathematical results ranging from algebra and trigonometry through calculus, that were discovered in India much before the West.

For example, Fibonacci numbers are described in Bharata’s Natya Shastra. Prof. Ramasubramanian mostly used the work of Pingala (prior to 300 BCE), Bhaskara (12th century CE) and Nityananda (17th century CE), mathematicians from three different periods of history to illustrate his ideas.

It was fascinating as well as amusing to learn how complex ideas in Math were taught and transmitted over the millennia via the medium of delightful poetry, in effect giving a musical character to Mathematics! Here are highlights from his talk.
Music in Mathematics

In most of the world, technical literature is written in prose, while poetry is reserved for subjects involving fantasy and feeling. However, a significant corpus of scientific and mathematical literature in the Indian tradition have been composed in Sanskrit verses that can set to melodious music.

This approach was driven by compulsion, because the Indian learning tradition was an oral tradition where ideas are captured and transmitted via sound rather than the written word. There was an element of choice also to this approach because structuring a concept as musical poetry makes it fun and easy to memorize.

For example, this verse (link to recitation) captures the date of its composition in musical form (in a meter known as “shaardUla vikriiDita”). The chanted verse actually describes the following set of simultaneous equations: y=m2, t = y/2, v= t x 3, b = v/2, that when solved will yield the exact date of the verse’s composition (April 25, 1629)!

This musical method of conveying ideas in Math has been used for representing numbers, specifying the value of pi and representing it as an infinite series, specifying expressions for sums of series, and even computing the derivative of a quotient, among other things!

The earliest shaastras were composed in sutra style, for example Panini’s grammar, and Bodhayana’s shulba (measurement) sUtras – see “Pythagorean” theorem above. A sutra is a pithy aphorism and its length is not uniformly regulated, and is not really constrained by any metrical discipline.

The rules of prosody (chandas shaastra) were composed later in the 2nd century BCE by Pingala-naga (though Prof. Ramasubramanian believes that Pingala may have predated Panini, based on the coarser style of the sUtras used in chandas shaastra), and consists of two classes of meters, one based on number of syllables (varNa vRRittaH), and another based on the number of beats (maatraa vRRittaH).

The later shaastras were set to these poetic meters, and are more musical to hear than sutras. Use of a meter restricts the choice of words that can be used in a verse, and therefore created challenges in conveying mathematical ideas. This resulted in some innovations such as the “khyughRRi” representation invented by Aryabhata, and the number naming system of “bhUta sa~Nkhyaa”.

The khyughRRi notation for instance used vowels to denote powers of 10 and consonants for other numbers (e.g., ka=1, ki=100, ku=100000), and created new (but difficult to pronounce) words such as “khyughRRi” (=4.32 million) for numbers used in astronomical calculations. The “bhUta sa~Nkhyaa” approach employs representative ideas to stand in for numbers that these ideas are typically associated with.

For example, the word “eye” (netra) represents the number two (we have two eyes), “veda” represents the number four (there are four vedas), and “aakaasha” (space – is empty) the number zero. Further a composer can choose from any of the numerous synonyms of these words which may each have a different number of syllables to meet metrical requirements in a verse. For example, “kham”, “vyoma”, “aakaasha” are all synonyms for “sky” but with different number (1, 2 and 3 respectively) of syllables.

An example of “bhUta sa~Nkhyaa” may be found here, where bhU” (earth) represents the number one, and “baaNa” (arrows of manmatha) represents the number five.

Meters based on syllables and beats lead to innovations that are today known by the names of scientists in the West who also discovered them much later. For example, Pascal’s triangle, which captures binomial coefficients in a triangular array of numbers, is described by the concept of “meru prastaara” (arrangement in the form of a mountain), the construction of which is described by a Sanskrit verse composed by Halaayudha.

Prof. Ramasubramanian presents this verse and its translation here. Each level of the “meru prastaara” captures the number and types of meters that are possible for a given number of syllables. When the number of beats is fixed instead of the number of syllables, and a rhythm is constructed either using a set of ‘laghu’ (1 beat long) or ‘guru’ (2 beats long) units, determining the number of rhythms possible leads to the discovery of what is known as the Fibonacci sequence in the west.

Prof. Manju Bhargava from Princeton University, the young winner of the 2014 Fields Medal (considered by many as the Nobel Prize equivalent in Mathematics), who as a tabla player encountered this problem of number of rhythms given a fixed number of beats, popularized the fact that this problem has been solved before Fibonacci (1202 CE) by an Indian Mathematician known as Hemachandra (1150 CE).

Fibonacci numbers are now also referred to as “Hemachandra numbers” by many. Prof. Ramasubramanian pointed out that there are mathematicians even before Hemachandra, such as Virahanka (600 CE), Pingala (200 CE), and Bharata (100 CE) who described the same idea.

In fact, these numbers are described in Bharata’s “naaTya shaastra”. To add to the fun, the Hemachandra numbers can be derived from the “meru prastaara” by adding along the diagonals.

Prof. Ramasubramanian also presented verses from Bhaskaracharya’s Lilavati, that has problems at the level of high school algebra expressed as poetry. One verse dealt with a problem involving a single variable linear equation.

This verse expresses what would now be called a “word problem”, but with a poetic touch and describes a collection of bees split divided into various fractions groups. Here is a link to the recitation of the verse. Another verse described a “word problem” involving a quadratic equation.

The problem uses a setting in the “Mahabharata” war and deals with the number of arrows that Arjuna needs to discharge to kill Karna on the battlefield (link to recitation).

A more interesting verse (link to recitation) specifies not only the sum (sankalita) of the first ‘n’ natural numbers (1+2+3+…+n = n(n+1)/2), but also the sum (sankalitaikya) of such sums: (1 + (1+2) + (1+2+3) + … (1+2+3+…n) = n(n+1)(n+2)/1.2.3).

Trigonometry was important for astronomical calculations. Prof. Ramasubramanian described the work of Nityananda, who was a brilliant astronomer in the court of Mughal Emperor Shaj Jahan, and the author of the monumental treatise “Sarvasiddhaantaraaja” (1639 CE).

In addition to original contributions, Nityananda also absorbed ideas from various sources including Arabic Astronomy and Mathematics, and incorporated them into his Sanskrit works.

Nityananda devoted 65 verses to trigonometric sine formulae, provided a summary of Arab mathematician Al-Kashi’s method for determining the sine of 1 degree, and an original procedure to solve the cubic equation that arises in Al-Kashi’s method, all in verse form. The sine formulae that he describes includes the well-known expansion for sin(a+b) = sin(a)cos(b) + cos(a)sin(b), but in verse form.

Prof. Ramasubramanian also mentioned the work of other earlier Indian mathematicians who came up with methods of computing sines, such as Aryabhata’s recurrence relation and Bhaskara’s approximation function, He also pointed out how infinite series expansions for trigonometric functions and pi – the ratio of the circumference to the diameter of a circle, and the idea of a derivative defined in calculus appear in the work of Indian mathematicians a few centuries before Newton and Leibniz.

Prof. K. Ramasubramanian is at IIT Mumbai in the Cell for Indian Science and Technology in Sanskrit, Department of Humanities and Social Sciences. He holds a doctorate in Theoretical Physics, Bachelors in Engineering, and Masters in Samskritam. His research interests include Indian Science and Technology and other disciplines such as Indian Logic and Philosophy.

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