American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


London, December 30: American researchers claim to have solved a cryptic formula that renowned mathematician Srinivasa Ramanujan believed came to him in dreams while on his deathbed, the Daily Mail reported on Saturday.

The formula was contained in a letter he wrote to his mentor, the English mathematician G.H. Hardy, from his deathbed in 1920 outlining several new mathematical functions that had never been heard of before, together with a theory about how they worked. It had baffled mathematicians for more than 90 years, but new findings — presented at a conference at the University of Florida last month — reportedly show that Ramanujan's “hunch” about his formula was right — that it could explain the behaviour of black holes.

“We've solved the problems from his last mysterious letters,” said the well-known American mathematician Ken Ono of Emory University.

“For people who work in this area of math, the problem has been open for 90 years … Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died.”

He said the so-called “deathbed puzzle” which, according to Ramanujan, was revealed to him by the goddess Namagiri, may unlock secrets about black holes. “We proved that Ramanujan was right. We found the formula explaining one of the visions that he believed came from his goddess. No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,” said Professor Ono.

The Mail said that Ramanujan's letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.

“Functions are equations that can be drawn as graphs on an axis, like a sine wave, and produce an output when computed for any chosen input or value. Ramanujan conjectured that his mock modular forms corresponded to the ordinary modular forms earlier identified by Carl Jacobi, and that both would wind up with similar outputs for roots of 1,” it said. Nobody at the time understood what the Indian mathematical genius was talking about.

“It wasn't until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,” Prof. Ono said.

His team, which used modern mathematical tools to solve the puzzle, was “stunned” to find the function could be used even today.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
June 24,2020

Islamabad, Jun 24: A plane crash which killed 97 people in Pakistan last month was because of human error by the pilot and air traffic control, according to an initial report into the disaster released Wednesday.

The Pakistan International Airlines (PIA) plane came down among houses on May 22 after both engines failed as it approached Karachi airport, killing all but two people on board.

"The pilot as well as the controller didn't follow the standard rules," the country's aviation minister Ghulam Sarwar Khan said, announcing the findings in parliament.

He said the pilots had been discussing the coronavirus pandemic as they attempted to land the Airbus A320.

"The pilot and co-pilot were not focused and throughout the conversation was about coronavirus," Khan said.

The Pakistani investigation team, which included officials from the French government and the aviation industry, analysed data and voice recorders.

The minister said the plane was "100 percent fit for flying, there was no technical fault".

The county's deadliest aviation accident in eight years came days after domestic commercial flights resumed following a two-month coronavirus lockdown.

Many passengers were on their way to spend the Muslim holiday of Eid al-Fitr with loved ones.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
Agencies
January 15,2020

Washington, Jan 15: The historic impeachment trial of US President Donald Trump will begin on Tuesday next week, Mitch McConnell, the leader of the Senate's Republican majority, has announced.

Earlier on Tuesday (January 14), Speaker Nancy Pelosi ended the standoff between the Senate and the Democratic-controlled House of Representatives saying that it would vote on next Tuesday to send the impeachment documents to the upper house so it can hold the trial on charges that Trump obstructed Congress and abused presidential powers.

This will be only the third time in the nation's history that a US president is tried after impeachment and Trump can expect to be acquitted like his two predecessors - Bill Clinton in 1998 and Andrew Johnson in 1868 - because there won't be a two-thirds majority to convict and remove him from office.

McConnel told reporters on Tuesday that preparations like swearing in the Senators as jurors for the trial could begin this week ahead of the formal start on next Tuesday.

"This Impeachment Hoax is an outrage," Trump tweeted, repeating his longstanding complaint about it, when the move to hold the trial finally appeared to gain traction.

"The American people deserve the truth and the Constitution demands a trial," Pelosi said.

She had held on to the Articles of Impeachment - the chargesheet against Trump - that the House voted on December 18 in a bid to pressure McConnell to accept her terms for holding the trial and in an attempt to get some Republican senators to break ranks on procedural matters.

But she has agreed to let the process move forward, without an agreement on the main Democratic demand to call in their witnesses at the trial and to introduce new evidence.

The House Intelligence Committee, which conducted the investigation against the president, on Tuesday released what it said was new evidence from Lev Parnas, a former associate of Trump's personal lawyer Rudy Giuliani. Parnas is facing criminal charges.

Pelosi said that starting the trial without witnesses or documents "a pure political cover-up."

The impeachment process is only an investigation by the House and the framing of the chargesheet for the Senate trial that will be presided over by Chief Justice John Roberts with the Senators as jurors and nominees of the House as prosecutors.

While there is no chance for removal of Trump from office, Democrats see the Senate trial as a propaganda mechanism ahead of the elections in November by giving the charges against Trump another public airing and turning voter opinion against Republican senators facing re-election.

Trump called for an outright dismissal of the impeachment by the Senate, but McConnell said, "There is little or no sentiment in the Republican conference for a motion to dismiss."

He added, "Our members feel that we have an obligation to listen to the arguments."

Trump tweeted that by not dismissing the impeachment out of hand, the Senate trial was giving "credence to a trial based on the no evidence, no crime" and "the partisan Democrat Witch Hunt credibility."

Pelosi had hoped to make some Republican senators break ranks with the leaders on the procedures for the trial and has partially succeeded in this as at least four of them appear open to witnesses being called.

While Trump's conviction and ouster from office is virtually impossible because of the two-thirds vote requirement in the 100-member Senate, only a simple majority is required on procedural matters. The Republicans have 53 members and four of them shifting positions could make a difference here.

McConnell appeared confident that he would have a hold on his party senators to set the rules for the trial.

Whether witnesses would be called to testify is still open as the Republicans have said that it would be decided when the trial starts.

The main sticking point is the Democrats demand to call their witnesses to testify at the trial.

The Democrats did not allow the Republicans to call their own witnesses to testify during the impeachment proceeding in the House and Republicans did not seem inclined to oblige them in the Senate.

Trump tweeted, "'We demand fairness' shouts Pelosi and the Do Nothing Democrats, yet the Dems in the House wouldn't let us have 1 witness, no lawyers or even ask questions."

The charges against Trump stem from a July phone call he had with Ukraine's President Volodymyr Zelensky in which he asked him as a "favour" to investigate former Vice President Joe Biden and his son Hunter.

Democrats say that this was an abuse power and amounted to inviting foreign interference in US elections as Biden is the leading candidate for the Democratic nomination to run against Trump in this year's election.

They also say that he withheld crucial military aid to Ukraine, a US ally against Russia, to pressure Zelensky and this endangered US national security. Trump said he delayed the aid to make sure the new government stomped out corruption.

Hunter Biden, who was made to leave the Navy because of alleged drug use and had no experience in the energy industry or in Ukrainian businesses was appointed a director of a gas company there and received monthly payments of $83,000, according to Republicans.

The former vice president, who was looking after Ukrainians affairs, had a prosecutor looking into gas company removed.

He and the Democrats say that it was because the prosecutor was corrupt, while Republicans see it as a conflict of interest.

The obstruction of Congress resulted from Trump's refusal to provide documents that the House demanded and allow some administration officials to testify at the House hearings.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
April 26,2020

Apr 26: The remarkable story of an airman who overcame prejudice to become one of only a handful of Indian fighter pilots in the First World War has emerged in newly-released archive files by the UK's Commonwealth War Graves Commission (CWGC).

Lieutenant Shri Krishna Chanda Welinkar is one of the thousands of moving stories from the war preserved in family correspondence and being brought alive as part of a digitisation project.

The never-before-published files contain thousands of letters, pictures and other papers sent between the Commission and the next of the kin of First World War dead.

Among them is the story of Welinkar, who hailed from Bombay in colonial India. After much hardship and discrimination, he eventually became a pilot and went missing while on patrol over the skies above the Western Front in June 1918.

His family had to wait nearly three years before they finally knew for certain that he had died, and his grave was located.

“For everyone who died in the First World War, there was inevitably a partner, parent or child back home who had questions. The heartbreaking letters in CWGC's archive give us an insight into what it was like for those families trying to come to terms with their loss,” said Andrew Fetherston, chief archivist for CWGC.

“They are stories that show desperate searches for closure, former enemies uniting and, on many occasions, the sad realisation that a missing loved one would always remain so. We are pleased to be able to make this invaluable piece of World War history accessible to a new generation and help deepen our understanding of how the First World War impacted those who were left behind,” he said.

Welinkar was one of the 1.3 million Indians who answered the call to fight for the British Empire. Nearly 74,000 never saw their homeland again and are remembered today in cemeteries and memorials throughout the world, including France, Belgium, the Middle East and Africa.

Welinkar was a well-educated man studying at Cambridge University. He trained to become an aviator in Middlesex and wished to join the Royal Flying Corps, later known as the Royal Air Force.

Upon attempting to enlist, Welinkar encountered the same prejudices as his other fellow Indian airmen and was encouraged to become an air mechanic instead.

He was eventually given a commission in the Royal Flying Corps as an Officer. In 1918, he was posted to France and patrolled the skies above the Western Front.

In June 1918, Lieutenant Welinkar embarked on what would be his final patrol; he did not return and was reported missing. His fate remained unknown for many months afterwards.

The newly-released e-files chronicle the remarkable discovery of Welinkar and his final resting place long after the war had ended. Colonel Barton, who knew Welinkar, acted on behalf of his mother and helped find her missing son. They spoke to former enemies and honed their search to the grave of an unidentified man, buried by the Germans as “Oberleutnant S.C. Wumkar” in a grave in Rouvroy, Belgium.

The body was later moved and reinterred in Hangard Communal Cemetery Extension but it wasn't until the vital clue, found in the original German burial records in February 1921, that it was confirmed beyond doubt this grave was of Welinkar's.

In May 1921, Colonel Barton, on behalf of Welinkar's mother, requested that a Commission headstone be placed on the grave with the following personal inscription: “To the Honoured Memory of One of the Empire's Bravest Sons”.

This records – known as Enquiry Files – are part of a collection of nearly 3,000 files which have never been made available to the public before. Nearly half have been digitised so far, alongside a previously unreleased collection of more than 16,000 photographs held in negatives in the Commission's archive.

The files, internally referred to simply as E-Files, contain correspondence between the CWGC and the next of kin of the war dead. They often contain letters, typed memos between Commission staff and on occasion photos, maps and diagrams.

CWGC only holds an enquiry file for a small proportion of the 1.7 million people it commemorates from the Commonwealth. Today it is only possible to release those surviving records from the First World War because correspondence with families of Second World War casualties often involves people still alive today and cannot be made public for many years, due to the UK's data protection rules.

To date, more than 1,300 of the surviving 3,000 First World War enquiry files have been digitised.

The CWGC commemorates the 1.7 million Commonwealth servicemen and women who died during the two World Wars. It also holds and updates an extensive and accessible records archive, while operating over 23,000 locations in more than 150 countries and territories.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.