American mathematicians solve Ramanujan's “deathbed” puzzle

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

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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.

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News Network
June 2,2020

Oakland, Jun 2: Facebook employees are using Twitter to register their frustration over CEO Mark Zuckerberg's decision to leave up posts by President Donald Trump that suggested protesters in Minneapolis could be shot.

While Twitter demoted and placed a warning on a tweet about the protests that read, in part, that “when the looting starts the shooting starts,” Facebook has let it stand, with Zuckerberg laying out his reasoning in a Facebook post Friday.

“I know many people are upset that we've left the President's posts up, but our position is that we should enable as much expression as possible unless it will cause imminent risk of specific harms or dangers spelled out in clear policies,” Zuckerberg wrote.

Trump's comment evoked the civil-rights era by borrowing a phrase used in 1967 by Miami's police chief to warn of an aggressive police response to unrest in black neighborhoods.

On Monday, Facebook employees staged a virtual “walkout” to protest the company's decision not to touch the Trump posts according to a report in the New York Times, which cited anonymous senior employees at Facebook.

The Times report says “dozens” of Facebook workers “took the day off by logging into Facebook's systems and requesting time off to support protesters across the country." “I work at Facebook and I am not proud of how we're showing up.

The majority of coworkers I've spoken to feel the same way. We are making our voice heard,” tweeted Jason Toff, a director of product management at Facebook who's been at the company for a year.

Toff, who has a verified Twitter account, had 131,400 “likes” and thousands of retweets of his comment. He did not immediately respond to a message seeking comment on Monday.

“I don't know what to do, but I know doing nothing is not acceptable. I'm a FB employee that completely disagrees with Mark's decision to do nothing about Trump's recent posts, which clearly incite violence. I'm not alone inside of FB.

There isn't a neutral position on racism,” tweeted another employee, design manager Jason Stirman.

Stirman did not immediately respond to a request for comment on Monday. Sara Zhang, a product designer at the company, tweeted that Facebook's “decision to not act on posts that incite violence ignores other options to keep our community safe.

The policy pigeon holes us into addressing harmful user-facing content in two ways: keep content up or take it down.” “I believe that this is a self-imposed constraint and implore leadership to revisit the solution,” she continued. Zhang declined to comment to The Associated Press.

Representatives for Facebook did not immediately respond to messages for comment.

Twitter has historically taken stronger stances than its larger rival, including a complete ban on political advertisements that the company announced last November.

That's partly because Facebook, a much larger company with a broader audience,targeted by regulators over its size and power, has more to lose. And partly because the companies' CEOs don't always see eye to eye on their role in society.

Over the weekend, Twitter changed the background and logo if its main Twitter account to black from its usual blue in support of the Black Lives Matter protesters and added a #blacklivesmatter hashtag. Facebook did the same with its own logo on its site, though without the hashtag.

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News Network
April 26,2020

Islamabad, Apr 26: Pakistan Prime Minister Imran Khan has been trumped by the country's powerful military yet again, this time over his government's inadequate steps and its poor response in curbing the coronavirus outbreak in the country, even as cases soared over 12,500.

In his address to the nation on March 22, Khan explained the reasons for not imposing a countrywide lockdown, asserting that millions would lose their jobs and affect families, who are below the poverty line, struggling to find enough food to eat. However, less than 24 hours later, Pakistan Army spokesperson Major General Babar Iftikhar announced the implementation of lockdown in the country having a population of over 200 million, contradicting the statements made by Imran Khan.

As lockdown was imposed, the military has deployed troops across Pakistan and is orchestrating the COVID-19 response through the National Core Committee, a body set up to coordinate policy between the national and provincial governments.

"The government left a big gap in its handling of the coronavirus. The army has tried to fill that gap, there was no choice," an unnamed retired general was quoted by Financial Times as saying.

The virus crisis in Pakistan has once again made things crystal clear about who is calling the shots -- the military, widely believed to bring Imran Khan to power in 2018.

The armymen have taken over the COVID-19 crisis as an opportunity to prove their competency in contrast to Imran Khan, who was mocked after urging youth to come forward and join Corona Relief Tigers Force, a volunteer body to wage "jihad" against the virus.

According to analysts, the military's seizure of the coronavirus response marks yet another policy failure for Imran Khan in the eyes of the generals, as per the Financial Times report.

The 67-year-old cricketer-turned-politician has repeatedly failed to gain international traction over the Kashmir issue and has struggled to convince the Financial Action Task Force (FATF) in getting his country removed from 'grey list' for terror funding.

In times of emergency, one has to take clear decisions and take them through. You can't dither. The whole world is advising strong lockdown. If the prime minister does not show that he is decisive, somebody else will," said Nafisa Shah, a Member of Parliament from the opposition Pakistan Peoples Party (PPP).

Even after the lockdown was imposed, Imran Khan continued to question the need for its implementation, raising eyebrows over the country's response in tackling the virus, as cases continue to rise. This comes even as such drastic measures are in place in many countries across the world, including neighbouring India.

According to The Dawn, the country has 12,657 confirmed cases of COVID-19, which includes 2,755 recoveries and 265 deaths. Punjab has the highest number of cases -- 5,326 --, followed by 4,232 in Sindh.

However, experts suggest that the actual numbers could be more given the low testing rates and inadequate supply of testing kits.

Doctors and nurses across the country have staged protests over the lack of personal protective equipment, as increasing numbers of health workers contract COVID-19.

"Because of the lack of resources, there is chaos among the doctors and healthcare workers. They know people are dying, they know the severity of the illness and they have to work without PPE," Shoaib Hasan Tarar, a doctor working in Rawalpindi, was quoted as saying.

As the coronavirus crisis continues to ravage Pakistan, the country's overwhelming health infrastructure has put a toll on its already floundering economy. The IMF said that the GDP will shrink 1.5 per cent in 2020. The cash-strapped nation is set to be the first major emerging economy to apply to a G-20 initiative to request debt repayment relief, according to Financial Times.

In early March, Pakistan saw a surge in coronavirus cases, when infected pilgrims and workers crossed the border from Qom, a religious city in Iran, which is a hotspot.

Pakistan's limited resources were exposed when quarantined pilgrims agitated against unhealthy conditions at Taftan camp on Pakistan-Iran border, where five people were living in a tent with no access to toilets.

While the lockdown is in place, authorities have been confronted by hardline clerics who have defied social distancing terms and downplayed the threat of the virus. During Friday prayers every week, worshippers violate the restrictions by gathering at various mosques.

Last week, Islamabad inked an agreement allowing mosques to stay open for Ramzan. It stipulated that people should follow 20 rules, including maintaining a six feet distance from each other.

"There is little consistency in terms of how the lockdown is being approached. Coronavirus has shown the disconnect between the national government, regional governments and the military. Imran Khan has been left behind as the cheerleader for keeping Pakistan's morale high. I think people are starting to ask, 'How long is he going to last?'", said Sajjan Gohel, South Asia expert and guest teacher at the London School of Economics.

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News Network
April 18,2020

Washington, Apr 18: The United States on Friday passed 700,000 confirmed coronavirus cases, according to a tally maintained by Johns Hopkins University.

With the highest number of cases and deaths of any country in the world, the US had recorded 700,282 cases of COVID-19 and 36,773 deaths as of 8:30 pm (0030 GMT Friday), according to the Baltimore-based university.

That marked an increase of 3,856 deaths in the past 24 hours, but that figure likely includes "probable" virus-linked deaths, which had not previously been counted.

This week, New York City said it would add 3,778 "probable" virus deaths to its official count.

The US Centers for Disease Control and Prevention gave a toll Friday night of 33,049 dead, including 4,226 probable virus-linked deaths.

The United States has seen the highest death toll in the world in the coronavirus pandemic, ahead of Italy (22,745 deaths) although its population is just a fifth of that of the US.

Spain has recorded 19,478 deaths, followed by France with 18,681.

Trump announces $19 billion relief for farmers amid COVID-19 epidemic

President Donald Trump on Friday announced a $19 billion financial rescue package to help the agriculture industry weather the staggering economic downturn sparked by measures to defeat the coronavirus.

Trump told a press conference the government "will be implementing a $19 billion relief program for our great farmers and ranchers as they cope with the fallout of the global pandemic."

The program will include direct payments to farmers, ranchers and producers who Trump said have experienced "unprecedented losses during this pandemic."

Agriculture Secretary Sonny Perdue said US farmers have been hit hard by a sharp shift in demand, as schools and restaurants close and more Americans eat at home.

That has disrupted the food supply chain, forcing farmers in many places to destroy dairy output and plow under crops that no longer have buyers.

"Having to dump milk and plow under vegetables ready to market is not only financially distressing, but it's heartbreaking as well to those who produce them," Perdue said.

Perdue said some $3 billion of the money would go to buying produce and milk from such farmers, and redistribute it to community food banks.

Millions of Americans have recently turned to food pantries for meals and groceries after losing their jobs.

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