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.
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
January 19,2020

President Donald Trump gave a new justification for killing Qassim Suleimani, telling a gathering of Republican donors that the top Iranian general was "saying bad things about our country" before the strike, which led to his decision to authorise his killing. "How much are we going to listen to?" Trump said on Friday, according to remarks from a fundraiser obtained by CNN.

With his typical dramatic flourish, Trump recounted the scene as he monitored the strikes from the White House Situation Room when Suleimani was killed. The president spoke in a ballroom at his Mar-a-Lago club in Palm Beach, Florida, at a Republican event that raised $10 million for Trump's 2020 campaign.

The January 3 killing of Suleimani prompted Iran to retaliate with missile strikes against US forces in Iraq days later and almost triggered a broad war between the two countries. "They're together sir," Trump said military officials told him. "Sir, they have two minutes and 11 seconds. No emotion. Two minutes and 11 seconds to live, sir. They're in the car, they're in an armoured vehicle. Sir, they have approximately one minute to live, sir. Thirty seconds. Ten, 9, 8 ...'"

"Then all of a sudden, boom," he said. "They're gone, sir. Cutting off, I said, where is this guy?" Trump continued. "That was the last I heard from him". It was the most detailed account that Trump has given of the drone strike, which has drawn criticism from some US lawmakers because neither the president nor his advisers have provided public information to back up their statements that Suleimani presented an "imminent" threat to US.

Trump's comments came a day after he warned Iran's supreme leader Ayatollah Ali Khamenei to be "very careful with his words". According to Trump, Khamenei's speech on Friday, in which he attacked the "vicious" US and described UK, France and Germany as "America's lackeys", was a mistake.

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
January 2,2020

Washington, Jan 2: The number of people killed in large commercial airplane crashes fell by more than 50% in 2019 despite a high-profile Boeing 737 MAX crash in Ethiopia in March, a Dutch consulting firm said on Wednesday. Aviation consulting firm To70 said there were 86 accidents involving large commercial planes - including eight fatal incidents - resulting in 257 fatalities last year. In 2018, there were 160 accidents, including 13 fatal ones, resulting in 534 deaths, the firm said.

To70 said the fatal accident rate for large airplanes in commercial passenger air transport was just 0.18 fatal accident per million flights in 2019, or an average one fatal accident every 5.58 million flights, a significant improvement over 2018. The fatality numbers include passengers, air crew such as flight attendants and any people on the ground killed in a plane accident

Large passenger airplanes in the study are aircraft used by nearly all travelers on airlines worldwide but excludes small commuter airplanes in service, including the Cessna Caravan and some smaller turboprop airplanes, according to To70.

On Dec. 23, Boeing's board said it had fired Chief Executive Dennis Muilenburg after a pair of fatal crashes involving the 737 MAX forced it to announce it was halting output of its best-selling jetliner. The 737 MAX has been grounded since March after an October 2018 crash in Indonesia and the crash of a MAX in Ethiopia in March killed a total of 346 people.

To70 said the aviation industry spent significant effort in 2019 "focusing on so-called 'future threats' such as drones." But the MAX crashes "are a reminder that we need to retain our focus on the basics that make civil aviation so safe: well-designed and well-built aircraft flown by fully informed and well-trained crews."

The Aviation Safety Network said on Wednesday that, despite the MAX crash, 2019 "was one of the safest years ever for commercial aviation." The 157 people killed in March on Ethiopian Airlines Flight 302 accounted for more than half of all deaths last year worldwide in passenger airline crashes.

Over the last two decades, aviation deaths around the world have been falling dramatically even as travel has increased. As recently as 2005, there were 1,015 deaths aboard commercial passenger flights worldwide, the Aviation Safety Network said.

Last week, 12 people were killed when a Fokker 100 operated by Kazakh carrier Bek Air crashed near Almaty after takeoff. In May, a Russian Sukhoi Superjet 100 aircraft caught fire as it made an emergency landing at Moscow’s Sheremetyevo airport, killing 41 people.

The figures do not include accidents involving military flights, training flights, private flights, cargo operations and helicopters.

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.