India’s anger exposes gormless leaders and media


A 23-year old girl, raped and beaten to pulp by half a dozen goons, battled for life in Delhi’s Safdarjung Hospital for almost thirteen days; a day before the end she was flown to a Singapore hospital in a vain last-ditch attempt to save her life. She died early in the morning of December 29. Her injuries were so severe that an ordinary person may not have survived even for a day, but ‘Nirbhaya’ as a section of the media began to call her, wanted to live. Nirbhaya in Hindi means fearless, not the hallmark of the current political class and their media minions.

The candle light vigils and prayers for the young student of physiotherapy were a major protest to make life safer for women. The goons are already behind bars and the judiciary will have to handle this one very carefully. The government has already announced two inquiry commissions, one to look into women’s safety and another to speed up trial and conviction in rape cases.

Sensing trouble during the week-long mass protests, the administration and Delhi Police bared their fangs with mindless violence and restriction on the movement of citizens. Using water cannon in freezing Delhi, they somehow managed to disperse the protesters and yet they kept coming to India Gate, President’s House and the homes of senior leaders. The National Police Commission’s lengthy eight volume report published from 1979 to 1981 in which there were many important recommendations on handling rape cases as well as public issues are still gathering dust.

Normally, Christmas to New Year is a raucous week, but not this time. It’s been quiet and solemn. Many are quietly shedding tears, young and old alike.

 The pompous pontificating of major western media [BBC, CNN, Fox, etc] projecting sexual harassment as a way of life in India was gross propaganda and purposive dysinformation. Has the BBC ever uncovered the paedophiles masquerading as brain dead ruling Elites in British society? Has CNN and Fox done anything  to unravel why San Fernando valley is home to global pornography where thousands of unsuspecting women are lured into drugs and sex and disposed off like dregs of the society and no one notices it? Has the New York Times exposed the porn industry in which some US Senators have major shareholding? Has any newspaper reporter exposed the fact that woman Peace Corps volunteers from prestigious US universities in Cambodia sleep with 12-14 year old poor girls?  

 And despite the powerful feminist movement in Anglo-Saxon countries, are women safe there? Their conviction rate is as bad as India’s but I’d like to see a mass protest there when a raped girl dies as we have seen here. Europeans don’t have a monopoly to civility and being do-gooders.

 When Sextus Tarniquinius raped Lucretia in ancient Rome, Lucretia committed suicide. Sextus was son of the King Tarquin of Rome. Lucretia’s dead body was paraded through the streets of Rome. People revolted and banished the King and his son from the Kingdom paving the way for what eventually became the Roman Empire.  

 The dull, brainless western and Indian mainstream media’s sole responsibility now is not to state the truth as it is, but to project a criminal ruling class as do-gooders. It could have reformed today’s closely integrated global society; instead it shamed and discredited our profession. Since these rogues have chosen to be the minions of the ruling class, many more young girls and minor children and many more nations will be violated.  

by Arun Shrivastava

Delhi gang rape victim dies in Singapore hospital


At about 3.21 am on Saturday the super speciality hospital in Singapore announced the death of the 23 year old gang rape victim.

Hospital chief executive Kelvin Loh told the BBC that she had passed away due to multi organ failure due to “serious injuries to her body and her brain.”. He also added that “she was courageous” in fighting for her life for so long” against the odds “but the trauma to her body was too severe.”

According to hospital authorities she had been sinking ever since she had arrived in Singapore. In fact the doctors in Delhi, who had been attending to her told DNA on the request of anonymity that shifting her had led to further trauma to her. The journey had proved to be hazardous and she had suffered another seizure in the special aircraft while enroute to Singapore.

On December 26, she had suffered two cardiac arrests and Dr Naresh Trehan had been rushed to Safdarjung Hospital secretly to assess her condition. She had started having multi-organ failure and an infection to her brain had started spreading.

Doctors also told DNA that she had been put on a ventilator as soon as she landed in Singapore as her capacity to breathe on her own had collapsed.The Indian High Commission alerted itsaa superiors in New Delhi at 3.30 am as soon as the news was officially communicated to them. According to the Singapore hospital officials the girl’s family was with her when she breathed her last.

The Delhi Police immediately announced strict measures to restrict movement out of fear that protests would erupt. In fact, the union cabinet had decided to fly her out of Delhi after spontaneous protests broke out in the heart of Delhi. Last week had seen several surges of protests when protesters marched to South and North Block that houses the Prime Minister’s Office and the union home ministry as well as Rashtrapati Bhawan.

Arrangements are being made to fly her back to India.

HIGH ALERT IN DELHI

All roads leading to India Gate, Rajpat and Vijaychowk, where violent clashes broke out over the last weekend in the wake of the brutal assault, were barricaded, have been closed. The Delhi Police tightened security across the national capital on Saturday as soon as the news of the death of the victim reached.

The Delhi traffic police posted a tweet early this morning: “Entire central Vista including Rajpath, Vijay Chowk and all road leading to India Gate will be closed for general traffic, Kamal Attaturk Marg also closed. All travelers (sic) are advised to avoid these roads..”

10 metro stations have been closed. These include Rajiv Chowk, Barakhambha Road,

PM’s CONDOLENCE MESSAGE

PM Manmohan Singh condoled the death of the 23-year-old medical student. His message:

I am deeply saddened to learn that the unfortunate victim of the brutal assault that took place on December 16 in New Delhi has succumbed to the grievous injuries she suffered following that attack. I join the nation in conveying to her family and friends my deepest condolences at this terrible loss. I want to tell them and the nation that while she may have lost her battle for life, it is up to us all to ensure that her death will not have been in vain. We have already seen the emotions and energies this incident has generated. These are perfectly understandable reactions from a young India and an India that genuinely desires change.

It would be a true homage to her memory if we are able to channelize these emotions and energies into a constructive course of action. The need of the hour is a dispassionate debate and inquiry into the critical changes that are required in societal attitudes. Government is examining, on priority basis, the penal provisions that exist for such crimes and measures to enhance the safety and security of women.

I hope that the entire political class and civil society will set aside narrow sectional interests and agenda to help us all reach the end that we all desire – making India a demonstrably better and safer place for women to live in. I pray for the peace of the departed soul and hope that her family will have the strength to bear this grievous loss.

SIGNIFICANT BRAIN INJURY

The Singapore hospital said earlier that the woman had suffered “significant brain injury” and was surviving against the odds. She had already undergone three abdominal operations before being flown to Singapore. Protests over the lack of safety for women erupted across India after the attack, culminating last weekend in pitched battles between police and protesters in the heart of New Delhi. New Delhi has been on edge since the weekend clashes. Hundreds of policemen have been deployed on the streets of the capital and streets leading to the main protest site, the India Gate war memorial, have been shut for long periods, severely disrupting traffic in the city of 16 million. Commentators and sociologists say the rape has tapped into a deep well of frustration that many Indians feel over what they see as weak governance and poor leadership on social and economic issues. Many protesters have complained that Singh’s government has done little to curb the abuse of women in the country of 1.2 billion.

A global poll by the Thomson Reuters Foundation in June found that India was the worst place to be a woman because of high rates of infanticide, child marriage and slavery.

New Delhi has the highest number of sex crimes among India’s major cities, with a rape reported on average every 18 hours, according to police figures.

Government data show the number of reported rape cases in the country rose by nearly 17 percent between 2007 and 2011.

Saikat Datta

Delhi gang-rape survivor’s condition worsens


Mount Elizabeth Hospital
 

The condition of the 23-year-old victim of a gruesome gang-rape in Delhi, admitted in a super-speciality hospital here yesterday, has taken a “turn for the worse” tonight with signs of severe organ failure.

“As of 9 pm (6:30 PM IST), the patient’s condition has taken a turn for the worse. Her vital signs are deteriorating with signs of severe organ failure,” Dr Kelvin Loh, Chief Executive Officer, Mount Elizabeth Hospital said in a statement.

“This is despite doctors fighting for her life including putting her on maximum artificial ventilation support, optimal antibiotic doses as well as stimulants which maximise her body’s capability to fight infections,” the CEO said.

“Her family members have been informed that her condition has deteriorated and they are currently by her side to encourage and comfort her,” he added.

The statement said the hospital’s medical team continues to “provide all possible treatment and care”, to the victim, who was air-dashed from the Safdarjung Hospital in Delhi for specialised treatment.

He said the the High Commission of India is with her and her family at this critical time.

The girl was gang-raped and brutally assaulted in a moving bus on December 16, triggering massive protests across India and prompting the government to airlift her to the leading multi-organ transplant speciality hospital.

She had undergone three surgeries at the Safdarjung Hospital in Delhi, where she remained on ventilator support during most part of the treatment. Doctors removed major part of her intestines which had become gangrenous.

Earlier in the day, the security was tightened at the hospital, favoured by well-heeled patients, with each visitor screened before being allowed into the ICU.

The victim’s father, who flew in with her, said he was reassured that the best is being done for his daughter.

The High Commission of India has assigned a liaison officer with the family.

The girl was shifted to the hospital here following what the Indian government said a “purely a medical decision” taken by doctors.

The unknown side of Hinduism


Hinduism is a whirlpool of knowledge, that which cannot be understood at first glance. To be a Hindu is not just about being gifted, but it’s an experience we need to live out in accordance with the Shastras.

Walking through a temple might be an overwhelming experience, where we would believe the superior powers are embedded within the deity. Sure enough, but how did this power get there? How did the idol get a life and how are we sharing this power? Or rather…what is this power that we define as “the ultimate truth”?

The power of the stone is not generate within the stone itself but is generated through the mystical diagram that defines the nature of the deity enclosed within the shrine. Various “bija mantras” attributed to the deity are embedded within this mystical diagram. For now this is just a copper/gold plate that carries the lines that define the true nature of the deity.

dwajastambhaThe real play starts at the dwajastambha, the main pillar in front of the temple. The fire of life is ignited along a darbha grass rope that connects the main dwajastambha to the shrine within the sanctum. The dwajastambha itself is a complex flag post, which contains designs all of which are attributed of the enclosed deity. Fire and ghee ignite the life of the mystical diagram placed within the sanctum followed by a series of hymns that are sung rhythmically along the cardinal directions within the shrine chamber. The mystical diagram comes alive when the fire with the burning ghee falls on its metal surface.

After this ritual the deity is placed over the metal plate and sealed to the floor using a mixture known as “ashtabandhanam”. The idol, made of a specific black stone is the carrier of this energy. This energy is maintained and enhanced by constant worship. Worship includes the bathing of the idol with water, milk, sandal wood, fruit mix, honey, oil, ghee and the like. Food is offered in the form of incense, flowers, fruit and rice to the deity.

The inner power of the idol is maintained by constant “pradakshinam” or circumambulation around the main shrine chamber and various prakaras. Only oil lamps should light the interior chamber and electricity is strictly prohibited. Flower garlands should be strung with banana fiber and not thread. Every thing that is offered to the deity is in its purest form. Hence the power of the deity is maintained.

What is the real nature of this “power”?
The nature of this power is strangely electrical, meaning it can produce anything from a mild shock near your elbow to making you shiver if you cannot cope with it.
The point is, we need to be ready to receive this power and for that the body and mind need to be prepared. Hence the various philosophies of detachment and zero desire so that we can concentrate on the Self instead of getting distracted by the world around us.

I know I made this sound really simple but this is belief as it stands today and no, Western science cannot prove this in a hurry.

10 Most Popular Books of 2012


“A room without books is like a body without a soul” said Marcus Tullius Cicero. There are certain books that are shelved as ‘must read’ and each year so many such books are published. Here are 10 popular books that were published this year, as listed by goodreads.com. These books are certainly a must read!

 

The Fault in Our Stars by John Green:
The Fault in Our Stars is the fourth solo novel by John Green and was published in January 2012. The story is narrated by a sixteen-year-old cancer patient named Hazel, who is forced by her parents to attend a support group, where she later meets and falls in love with the seventeen-year-old Augustus Waters, an ex-basketball player and amputee. Green stated on his Tumblr blog and his YouTube vlog that “the title is inspired by a famous line from Shakespeare’s play Julius Caesar (Act 1, scene 2). The nobleman Cassius says to Brutus, ‘The fault, dear Brutus, is not in our stars, / But in ourselves, that we are underlings.'”

 

Pandemonium (Delirium, #2) by Lauren Oliver:
Pandemonium is a dystopian young adult novel written by Lauren Oliver, which was published in February 2012. It is a sequel to the 2011 book, Delirium. Pandemonium follows Lena, the series’ central character, as she explores the Wilds outside the walled community she was raised in.

Fifty Shades Freed by E.L. James:
Erika Leonard, better known by the pen name E. L. James, is the British author of the bestselling erotic novel Fifty Shades of Grey. Fifty Shades Freed is one of the popular books published this year. It is the third book in the Fifty Shades of Grey series. It was published on April 17 this year. The book is a mix of fate and spite combined to make Anastasia’s worst fears come true. Anastasia is the female protagonist of the trilogy. She is the primary love interest of Christian Grey, with whom she finds true love.

 

Insurgent (Divergent, #2) by Veronica Roth:
The second novel Insurgent in the trilogy ‘Divergent’ was released in May 2012. Divergent is the debut novel of American author Veronica Roth. Roth said that the idea for the series was born while she was studying in college. The third book in the series will be released in the fall of 2013.

The Casual Vacancy by J.K. Rowling:
The Casual Vacancy is another ‘must read’ novel which was published this year. It is a tragicomedy novel by J.K. Rowling. The book was published worldwide by Little, Brown Book Group on 27 September this year. It was Rowling’s first publication since the Harry Potter series and her first novel for adults.

 
The novel is set in a suburban West Country town called Pagford and commences with the death of Parish Councillor Barry Fairbrother. Major themes in the novel are politics, class and social issues like that of drugs, prostitution and rape. The novel was the fastest-selling in the UK in 3 years and had the second best-selling opening week. It became the 15th best-selling book of 2012 in its first week of release. Within the first three weeks itself the book’s total sales topped one million copies in English in all formats across all territories. The book is being adapted into a BBC television drama and will be released in 2014.

 

City of Lost Souls (The Mortal Instruments #5) by Cassandra Clare:
City of Lost Souls is the fifth book in the Mortal Instruments series by Cassandra Clare and was published this year. It follows the books City of Bones, City of Glass, City of Ashes, and City of Fallen Angels. The next book in the series is City of Heavenly Fire which will be the final book in the Mortal Instruments, closing the series. City of Lost Souls was released on May 8 this year.

Bared to You (Crossfire, #1) by Sylvia Day:
Bared to You is a 2012 New York Times bestselling erotic romance novel by author Sylvia Day. It focuses on the complicated relationship between two people with equally abusive pasts. The novel was initially self-published on April 3, 2012 by Day, with Berkley Books re-publishing the book on June 12 this year with an initial print run of 500,000 copies. Day said that Bared to You will be the first novel in her Crossfire trilogy, with the follow-up novel Reflected in You published in October 2012. Bared to You was declared Penguin UK’s “fastest selling paperback for a decade” and Penguin Group (USA) reports that Bared to You is Berkley’s largest breakout book of 2012.

 

Cinder (Lunar Chronicles, #1) by Marissa Meyer:
Cinder is the debut novel of New York Times bestselling author Marissa Meyer, and published by Macmillan Publishers through their subsidiary Feiwel & Friends. The story is freely based on the classic fairytale “Cinderella”.

Quiet: The Power of Introverts in a World That Can’t Stop Talking by Susan Cain:
Quiet: The Power of Introverts in a World That Can’t Stop Talking is a non-fiction book by Susan Cain published in 2012. Cain argues how modern Western culture misunderstands and undervalues the behavior and capabilities of introverted people, leading to “a colossal waste of talent, energy, and happiness.”  The book presents a history of how Western culture altered from a culture of character to a culture of personality in which an “extrovert ideal” dominates and introversion is seen as inferior or even pathological. Stating that temperament is a core element of human identity, Cain cites research in biology, psychology and evolution to demonstrate that introversion is both common and normal.

 
Quiet reached the number 1 position on the NPR Bestseller List, number 3 on the Los Angeles Times Best Seller list and number 4 on The New York Times Best Seller list.

 

Gone Girl by Gillian Flynn:
Gillian Flynn is an American author. She has published three novels Sharp Objects in 2006, Dark Places in 2009, and Gone Girl in 2012.

Delhi gang-rape: PM’s wife expresses outrage, calls for severe punishment


The prime minister’s wife Gursharan Kaur on Monday joined the people in expressing outrage over the gang-rape of a young girl and said severe punishment should be meted out to the culprits.

She, at the same time, said any protest against the “ghastly” crime should be peaceful as it would yield more results than violent demonstrations.

The December 16 incident in a moving bus in Delhi was a “very bad incident” and that she was at loss of words in expressing her condemnation, she said.

“We all are very sad at this incident but if they (protests) are conducted in a peaceful manner, they will yield more results,” Kaur told reporters on the sidelines of the release of a book Sikh Heritage Ethos and Relics in Delhi.

“This is a horrible crime…Such incident need to be condemned in the strongest possible way,” she said.

Kaur said severe punishment needed to be handed down to the accused and that there was a need for fast-track courts to deal with such cases.

Matisse stolen 10 years ago found in US


Portrait of Henri Matisse 1933 May 20

Portrait of Henri Matisse 1933 May 20 (Photo credit: Wikipedia)

Photo: AFP

On July 16, a plane from Mexico City landed in Miami Airport. One of the passengers was a woman holding a bright-red tube that contained a rolled canvas of Henri Matisse. She left the airport for what would turn out to be a meeting with the law.

A few days later news emerged that an FBI operation in Florida had successfully retrieved a painting by Henri Matisse that had been stolen from a Venezuelan Art Museum in 2002. The hunt took almost ten years, and only last week two suspects were arrested when trying to sell the “Odalisque In Red Pants”.

Undercover FBI agents arrested Miami resident Pedro Antonio Marcuello Guzman, 46, and Maria Martha Elisa Ornelas Lazo, 50, of Mexico City when they were trying to sell the painting. The dealers did not even conceal the fact that the canvas had been stolen, thus explaining their incredibly low asking price. Despite the fact that Matisse’s painting was estimated at $3 million, they were ready to sell it for only $740,000. Now, the unfortunate black market art dealers are facing long-term prison sentences.

One would think that the crime had been solved, and that the investigators can head home job well done – but things are not that simple. The history of the theft of the painting is, in fact, rather complex. The “Odalisque In Red Pants” painted by Henri Matisse in 1925 was purchased by the Museum of Modern Art in Caracas in 1981 from a New York gallery for half a million dollars.

The picture was long considered one of the gems of the museum’s collection, but in 2003 information appeared that the “Odalisque” was for sale on the black market. After a close examination it turned out that the painting in the museum’s collection was a forgery. Obviously, unidentified criminals had stolen the original painting replacing it with a fake so skillfully made that museum specialists had not been aware of the swap for quite a long time. The investigators failed to establish the exact time of the crime, but it was most likely committed in 2002.

Now a comprehensive examination is needed in order to figure out whether the picture obtained in the FBI operation is the original stolen from Caracas, or if it is yet another high-quality forgery.

The search for stolen art objects often takes many years, and it is not only the robbed owners that become victims in such situations, but also the new owners of the paintings. For example, not so long ago, Niko Pirosmani’s painting the “Black Lion”, stolen back in 1993 from the house of the former rector of the Georgian Academy of Arts Apollon Kutateladze, was discovered in Moscow. A major scandal broke out, but it turned out that the painting was legally purchased at an auction. After the new owner of the paintings became aware of its criminal past, he went to Tbilisi and re-bought the picture, which is considered to be one of the best works by Pirosmani, from the family of the artist Apollon Kutateladze.

Armen Apresyan

Russia-India: a new chapter of cooperation


Russia-India: a new chapter of cooperation

Russia and India have established a relationship that could be described as a “special and privileged partnership”. A statement to this effect was made by President Vladimir Putin during his current official visit to New Delhi. The year 2012 marks the 65th anniversary of diplomatic relations between Russia and India.

The agenda of the talks focused on expanding bilateral trade and economic ties. Trade between Russia and India has increased by nearly six times since 2000. Vladimir Putin commented on prospects for further cooperation.

“Mutual trade amounted to nearly $9 bln in 2011. We expect it to hit $10 bln in 2012 and to increase twofold over the next few years. About 50% of exported and imports goods on both sides are produced on the basis of high technology. This year, the supply of Russian-made cars, equipment and chemicals to India has increased by 40%. Russia and India have agreed to increase mutual investments. A memorandum between the Russian Direct Investment Fund and the State Bank of India which was signed on Monday will create more incentives for ramping up mutually beneficial cooperation, including between small and medium-sized businesses.”

Nuclear energy projects occupy a particular place on the Russia-India cooperation agenda. According to Indian Prime Minister Manmohal Singkh, his country appreciates Russia’s assistance in building the Kudankulam Nuclear Power Plant. President of Russia’s Rosatom Corporation Sergei Kirienko says the Russian side has made a particular breakthrough in the Kudankulam Project.

“The Kudankulam Project meets all ‘post-Fukushima’ requirements and has passed ‘stress tests’. If it had been somewhere near Fukushima at the moment of the disaster, it would have withstood the earthquake and the tsunami, thanks to the high level of its nuclear safety.”

Mutual investments make up yet another important chapter of bilateral cooperation between Russia and India. The Russian Direct Investment Fund and the State Bank of India clinched an important deal to this effect in New Delhi. The Fund’s President Kirill Dmitriev comments.

“Each party will invest up to $1 billion in joint projects. We expect bilateral trade to increase by $10bln – $30bln over the next three years.”

Russian companies are taking part in projects to build metal-working plants in Bhilai, Rourkela and other cities of India. Russia’s Severstal is a partner in a joint project to build a full-cycle metalworking facility in India. Russian insurance companies Ingosstrakh and ROSNO are tapping the Indian market as well. In addition, Russia and India have signed a number of important agreements on cooperation in defense and technology.

Russia and India are also set on bolstering cooperation within the framework of international organizations, including the BRICS group, the Shanghai Cooperation Organization, the RIC group which comprises Russia, India and China, and the G20.


Russia, India sign package of agreements

Russia and India have signed a package of cooperation agreements in the framework of Vladimir Putin’s visit to New Delhi, according to the Voice of Russia correspondent.

The two countries have specifically signed a memorandum of understanding between the Russian Direct Investment Fund and the State Bank of India. The two will invest in joint projects one billion dollars each.

The Russian and Indian Ministries of Culture have signed a cultural exchange programme for 2013 through 2015, while the Ministry of Education and Science of the Russian Federation and the Ministry of Science and Technology of India have signed a memorandum of cooperation in the field of science, technology and innovations.

An agreement was also concluded on the sidelines of the summit on setting up a joint venture by the Helicopters of Russia Company and India’s Elcom Systems Private Ltd. 


Moscow, Delhi in Syria dialogue call

Russia and India call on world powers to comply with the Syria resolutions of the UN Security Council and the decisions of the Geneva conference on Syria. They believe there is no way out of the Syrian crisis other than a national political dialogue.

President Vladimir Putin and Prime Minister Manmohan Singh said this in a joint statement issued after their talks in New Delhi on Monday.

According to the United Nations, the Syrian conflict has claimed 20,000 to 30,000 lives since first erupting 21 months ago.

The Syrian government says foreign-backed terrorists are at work. 


Russia, India to foster military ties

Russia and India have made a commitment to foster bilateral military and technical cooperation, Russian President Putin has said in the wake of his Monday meeting with PM Manmohan Singh.

“We have agreed to step up Indian-Russian cooperation in military and technical spheres, to work on new projects through joint ventures and know-hows exchange,” Mr. Putin said.

He cited the fresh deal between a Russian state-run chopper maker and India on exports of helicopter units and equipment.

India has agreed to purchase 71 MiG-17B-5 helicopters worth 1.3 billion dollars. Russia is also to deliver to India 1.6-billion-dollar plane units to organize the licensed assembly of Su-30MKI jet fighters.

The legacy of Srinivasa Ramanujan – Celebrating his 125th Birthday


His work has had a fundamental role in the development of 20th century mathematics and his final writings are serving as an inspiration for the mathematics of this century

On a height he stood that looked towards greater heights.

Our early approaches to the Infinite

Are sunrise splendours on a marvellous verge

While lingers yet unseen the glorious sun.

What now we see is a shadow of what must come.

Sri Aurobindo, Savitri, 1.4

THEF_26_SRINIVASA_R_874273gMathematician Srinivasa Ramanujam

The story of Srinivasa Ramanujan is a 20th century “rags to mathematical riches” story. In his short life, Ramanujan had a wealth of ideas that have transformed and reshaped 20th century mathematics. These ideas continue to shape mathematics of the 21st century. This article seeks to give a panoramic view of his essential contributions.

Born on December 22, 1887 in the town of Erode in Tamil Nadu, Ramanujan was largely self-taught and emerged from extreme poverty to become one of the most influential mathematicians of the 20th century. How did this transformation come about? Though it is difficult to pinpoint any precise causes for this transformation, one can delineate several significant events in his life that enabled this to come about.

Ramanujan cultivated his love for mathematics singlehandedly and in total isolation. As a child, he was quiet and often kept to himself. Those that knew him were impressed by his shining large eyes, which were his most prominent features. He had a prodigious memory, and at school he would entertain his friends by reciting the various declensions of Sanskrit roots, and by repeating the value of the constant ‘pi’ to any number of decimal places. This was a foreshadow of what was to come, since later in life he would write a monumental paper that would connect the computations of the digits of ‘pi’ to modular forms, a theory developed largely in the 20th century. It is a theory which is definitely at the forefront of modern mathematics today and we will expand on this theme later in this article.

At the age of 12, he borrowed from a friend a copy of Loney’s book on Plane Trigonometry, published by Cambridge University Press in 1894. This book goes far beyond high school trigonometry and also deals with the rudiments of calculus. But the book that changed his life was Carr’s book titled, A Synopsis of Elementary Results in Pure and Applied Mathematics. This book is a compilation of 6,165 theorems, systematically arranged but with practically no proofs. It is not a remarkable book, and Ramanujan’s use of it to propel himself to the centre stage of 20th century mathematics, has made the book remarkable. It was largely used by students of Carr who were preparing for the entrance examination in mathematics at Cambridge University. Ramanujan used the book to master all of 18th and 19th century mathematics. He set about to demonstrate each of the assertions of the book, using only his slate to do the calculations. He would jot down the formula to be proved, and then erase it with his elbow, and then continue to jot down some more formulas. In this way, he worked through the entire book. People used to speak of his “bruised elbow.” Sadly, he took Carr’s book as a model for mathematical writing and left behind his famous notebooks containing many formulas but practically no proofs. Many mathematicians have made it an industry to prove these formulas that Ramanujan had scribbled into his notebooks since he left no hint as to how he got them.

In college

In 1903, Ramanujan entered the Government College in Kumbakonam. Unfortunately, he failed in the examination since he neglected his non-mathematical subjects.

Four years later, he entered another college in Chennai, and the same thing happened. Finally, in 1912, he secured a job as a clerk in the Madras Port Trust Office. Here, his duties were light and so he could devote a lot of time to his mathematical discoveries — which he recorded in his now celebrated notebooks. As luck would have it, the manager of the office, S.N. Aiyar, was also a mathematician who took kindly to Ramanujan and encouraged him in his mathematics. It was he who suggested to Ramanujan that he write to G.H. Hardy, a famous mathematician at Trinity College, Cambridge University.

In his famous 1913 letter to Hardy, Ramanujan attached 120 theorems as a representative sample of his work. Some of these formulas Hardy had already seen in the course of his own research work. But many of the other formulas, he had not. It took over two hours for him to analyse the letter in order to determine if it was written by a crank or a genius. He consulted with his eminent colleague J.E. Littlewood, also of Trinity College, and together they sat down for three more hours. Finally they concluded that it was the work of a genius. Hardy wrote: “They must be true, because if they were not true, no one would have had the imagination to invent them.” With this certificate of approval, Ramanujan was invited to come to Trinity College to work with Hardy.

To England

Ramanujan sailed to England in March 1914, just a few months before the outbreak of the First World War. From 1914 to 1917, Hardy and Ramanujan collaborated on more than half a dozen research papers. At the same time, Ramanujan published more than 30 research papers in three years. The most notable of these collaborations involved the partition function. This function counts the number of ways a natural number can be decomposed into smaller parts. Hardy and Ramanujan developed a new method, now called the circle method, to derive an asymptotic formula for this function. If one analyses Ramanujan’s first letter to Hardy, we already find a hint of the method in his work done in India while at the Port Trust Office. This method is now one of the central tools of analytic number theory and is largely responsible for major advances in the 20th century of notoriously difficult problems such as Goldbach’s conjecture, Waring’s conjecture and other additive questions. The circle method and its refinements constitute a very large area of current research and will probably continue to be so in the 21st century.

Another fundamental paper of Hardy and Ramanujan concerns what is now called the “normal order method.” This method analyses the behaviour of additive arithmetical functions. In their paper, Hardy and Ramanujan showed that a random natural number usually has about log log n prime factors. Their paper led to the creation of an entirely new field of mathematics called probabilistic number theory. In the 20th century, it was largely developed by P. Erdos, M. Kac and J. Kubilius.

Landmark paper

But the paper that really changed the course of 20th century mathematics was the one written by Ramanujan in 1916, modestly titled “On certain arithmetical functions.” In this paper, Ramanujan investigated the properties of Fourier coefficients of modular forms. At that time the theory of modular forms was not even developed. However, Ramanujan enunciated three fundamental conjectures that served as a guiding force for the development of the theory.

Indeed, the first two of his conjectures led to the development of what is now called Hecke theory, formulated by E. Hecke in 1936, twenty years after Ramanujan’s paper. Many would have heard of Fermat’s last theorem and how this was solved in 1994 by A. Wiles. But few will know that Wiles used Hecke’s theory in an essential way in his solution of the problem.

However, it was the last of the three of Ramanujan’s conjectures that created a sensation in 20th century mathematics. This conjecture, later called Ramanujan’s conjecture, came to play a pivotal role in the towering edifice known as the Langlands program, a far-reaching program articulated by R.P. Langlands in the 1970s. This program connected two seemingly different fields of mathematics, namely representation theory and number theory. But the proof of Ramanujan’s third conjecture came about through another route connecting algebraic geometry to number theory in the framework of general conjectures of A. Weil concerning the number of solutions of equations over finite fields. The Weil conjectures were settled by P. Deligne in 1974 and he was awarded the Fields Medal (the mathematical equivalent of the Nobel Prize) for this work. Ramanujan’s third conjecture turned out to be a special case of the Weil conjecture. Ramanujan’s conjecture is now seen as a spectral line of a larger spectrum of conjectures, now called the generalised Ramanujan conjecture.

Last letter to Hardy

If Ramanujan’s 1916 paper created a sensation by heralding the development of the theory of modular forms, his last letter to Hardy, written literally on his deathbed in 1920, outlining a new theory of “mock theta functions,” is now creating a greater sensation in the development of 21st century mathematics. Indeed, Ramanujan’s theory of mock theta functions was largely ignored for much of the 20th century and was discussed in sporadic papers. Part of the difficulty was with Ramanujan’s vague definition of a mock theta function. In fact, he never defined them. Rather, he listed 17 protypical examples of these new functions and formulated general conjectures concerning them. Many mathematicians tried to prove these conjectures without a proper theory in place. To a large extent, they succeeded in proving most of Ramanujan’s conjectures. However, the unifying conceptual framework was missing. This framework was discovered only recently in 2002 in the doctoral thesis of S. Zwegers, written under the direction of D. Zagier. This thesis laid the groundwork for a new theory of mock modular forms.

We now understand Ramanujan’s theory of mock theta functions as a special case of a larger theory of mock modular forms. These objects are generalisations of modular forms and thus include the classical theory of Hecke as a special case. Already, the richer theory of mock modular forms is bearing new mathematical fruit, as is evidenced by some recent breakthrough works of J. Bruinier, J. Funke, K. Bringman, and K. Ono. For instance, Bruinier and Ono recently derived an algebraic formula for the partition function using the theory of mock modular forms. M. Dewar and R. Murty noticed that this Bruinier-Ono formula can be used to derive the Hardy-Ramanujan formula for the partition function and thereby avoid the complicated circle method. These new viewpoints are definitely the tip of the iceberg, concealing a larger mass of mathematical truth.

In 1987, the famous physicist, Freeman Dyson, predicted: “The mock theta functions give us tantalising hints of a grand synthesis still to be discovered. It should be possible to build them into a coherent group-theoretical structure, analogous to the structure of modular forms which Hecke built around the old theta functions of Jacobi. This remains the challenge for the future.”

Foreshadow

Indeed, Dyson’s prediction is right on target. The recent advances in the theory are just a foreshadow of greater things to come. Once the theory of mock modular forms is in place, it is only a question of time to marry the theory to the larger program of Langlands. This may be delicate, and one should not go too fast lest we miss the scenic beauty along the route. Nevertheless, it is the direction of the future. Thus, Ramanujan’s work has had a fundamental role in the development of 20th century mathematics and his final writings are serving as an inspiration for the mathematics of this century.

We do not know how Ramanujan discovered his theorems. On this point, Hardy wrote: “It was his insight into algebraic formulae, transformations of infinite series and so forth, that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler or Jacobi. He worked far more than the majority of modern mathematicians, by induction from numerical examples; all his congruence properties of partitions, for example, were discovered in this way. But with his memory, his patience and his power of calculation, he combined a power of generalisation, a feeling for form, a capacity for rapid modification of his hypothesis, that were often really startling, and made him, in his own peculiar field, without a rival in his day.”

Cultural legacy

But beyond the mathematical legacy, Ramanujan left behind a cultural legacy. He appeared in the midst of the British colonial rule of India and now stands as an iconic symbol of an India that was rediscovering itself, an India that was rising up to take its place in the 20th century. This meant that science and education were to be revived and energised to meet the challenges of the new, independent India. Ramanujan’s role in such a revival is best described in the words of Nobel laureate Subramanyam Chandrasekhar who, on the occasion of Ramanujan’s birth centenary in 1987, wrote: “It must have been a day in April 1920, when I was not quite ten years old, when my mother told me of an item in the newspaper of the day that a famous Indian mathematician, Ramanujan by name, had died the preceding day; and she told me further that Ramanujan had gone to England some years earlier, had collaborated with some famous English mathematicians and that he had returned only very recently, and was well-known internationally for what he had achieved. Though I had no idea at that time of what kind of a mathematician Ramanujan was, or indeed what scientific achievement meant, I can still recall the gladness I felt at the assurance that one brought up under circumstances similar to my own, could have achieved what I could not grasp. I am sure that others were equally gladdened. I hope that it is not hard for you to imagine what the example of Ramanujan could have provided for young men and women of those times, beginning to look at the world with increasingly different perceptions. The fact that Ramanujan’s early years were spent in a scientifically sterile atmosphere, that his life in India was not without hardships, that under circumstances that appeared to most Indians as nothing short of miraculous, he had gone to Cambridge, supported by eminent mathematicians, and had returned to India with every assurance that he would be considered, in time, as one of the most original mathematicians of the century — these facts were enough, more than enough, for aspiring young Indian students to break their bonds of intellectual confinement and perhaps soar the way that Ramanujan did.”

In these words of Chandrasekhar, we see the remarkable legacy left behind by Ramanujan. For the life of Chandrasekhar was equally full of hardships. Born in the same village surroundings as Ramanujan, he went to study at Cambridge and became a leading astrophysicist of the 20th century, finally being awarded the Nobel Prize in 1983. Indeed, he soared the way Ramanujan did.

But a scientist belongs to no nation. Many scientists from around the world have testified that they gained inspiration from the life story of Ramanujan. For Ramanujan embodies that marvellous miracle of the human mind to frame concepts and to use formulas and symbols as tools of thought to probe deeper into the mysteries of the universe, and the mysteries of one’s own being. As long as the spirit of inquiry is alive, his legacy will pass from one generation to the next.

(M. Ram Murty is Professor and Head of the Department of Mathematics at Queen’s University in Kingston, Ontario, Canada. V. Kumar Murty is Professor and Head of the Department of Mathematics at University of Toronto, Toronto, Ontario, Canada.)

M.Ram Murty / V. Kumar Murty

 

Girl Frozen For 500 years


Girl Frozen For 500 years

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Girl who was killed as an offering to the Inca gods sometime between 1450 and 1480, at approximately 11–15 years old.best-preserved mummy ever found, with internal organs intact, blood still present in the heart and lungs, and skin and facial features mostly unscathed. No special effort had been made to preserve her and 500 years later still looked like sleeping children

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