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.

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News Network
May 20,2020

Kensington (United States), May 20: The world cut its daily carbon dioxide emissions by 17% at the peak of the pandemic shutdown last month, a new study found.

But with life and heat-trapping gas levels inching back toward normal, the brief pollution break will likely be “a drop in the ocean" when it comes to climate change, scientists said.

In their study of carbon dioxide emissions during the coronavirus pandemic, an international team of scientists calculated that pollution levels are heading back up — and for the year will end up between 4% and 7% lower than 2019 levels.

That's still the biggest annual drop in carbon emissions since World War II.

It'll be 7% if the strictest lockdown rules remain all year long across much of the globe, 4% if they are lifted soon.

For a week in April, the United States cut its carbon dioxide levels by about one-third.

China, the world's biggest emitter of heat-trapping gases, sliced its carbon pollution by nearly a quarter in February, according to a study Tuesday in the journal Nature Climate Change. India and Europe cut emissions by 26% and 27% respectively.

The biggest global drop was from April 4 through 9 when the world was spewing 18.7 million tons (17 million metric tons) of carbon pollution a day less than it was doing on New Year's Day.

Such low global emission levels haven't been recorded since 2006. But if the world returns to its slowly increasing pollution levels next year, the temporary reduction amounts to ''a drop in the ocean," said study lead author Corinne LeQuere, a climate scientist at the University of East Anglia.

“It's like you have a bath filled with water and you're turning off the tap for 10 seconds," she said.

By April 30, the world carbon pollution levels had grown by 3.3 million tons (3 million metric tons) a day from its low point earlier in the month. Carbon dioxide stays in the air for about a century.

Outside experts praised the study as the most comprehensive yet, saying it shows how much effort is needed to prevent dangerous levels of further global warming.

“That underscores a simple truth: Individual behavior alone ... won't get us there,” Pennsylvania State University climate scientist Michael Mann, who wasn't part of the study, said in an email.

“We need fundamental structural change.”

If the world could keep up annual emission cuts like this without a pandemic for a couple decades, there's a decent chance Earth can avoid warming another 1.8 degrees (1 degree Celsius) of warming from now, study authors said. But getting the type of yearly cuts to reach that international goal is unlikely, they said.

If next year returns to 2019 pollution levels, it means the world has only bought about a year's delay in hitting the extra 1.8 degrees (1 degree Celsius) of warming that leaders are trying to avoid, LeQuere said. That level could still occur anywhere from 2050 to 2070, the authors said.

The study was carried out by Global Carbon Project, a consortium of international scientists that produces the authoritative annual estimate of carbon dioxide emissions. They looked at 450 databases showing daily energy use and introduced a measurement scale for pandemic-related societal “confinement” in its estimates.

Nearly half the emission reductions came from less transportation pollution, mostly involving cars and trucks, the authors said. By contrast, the study found that drastic reductions in air travel only accounted for 10% of the overall pollution drop.

In the US, the biggest pollution declines were seen in California and Washington with plunges of more than 40%.

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News Network
April 30,2020

London, Apr 30: The coronavirus is roiling global job markets, but the picture is not all gloomy. Finance, technology and consumer goods firms are hiring tens of thousands in the United States and other countries, according to data from Microsoft Corp's professional networking site LinkedIn.

Across seven countries in North America, Europe and Asia, healthcare providers are among the busiest recruiters given the ongoing battle against the novel coronavirus, which has killed over 200,000 people and infected over 3 million people worldwide, LinkedIn said. But lifestyle changes during lockdown are also driving demand for financial consultants, factory workers, animators and game designers, and delivery workers.

Overall, the hiring rate has plunged in the first quarter from the year-ago period, and in late April remains lower than a year ago across most countries surveyed by the platform. But the data offer a glimmer of hope with a gradual uptick in China, where the coronavirus emerged last year and which leads the world in surfacing from a months-long lockdown.

LinkedIn, with over 690 million users worldwide, counts new hires when people add a new employer to their profile. The rate is the number of new hires divided by the total number of LinkedIn members in a country.

The figures, tracked since mid-February, are not corroborated by official jobs data and do not represent the actual number of jobs in an economy. Government figures are usually released with a time-lag of several weeks.

"We are confident that our data is directionally correct in that there has been a huge decline in hiring in the U.S. and abroad," Guy Berger, principal economist at LinkedIn in California, told Reuters.

Hiring in China plummeted 50% during the height of its coronavirus crisis in mid-February from 12 months earlier. Since restrictions were eased in early April, the hiring rate has inched up, and for the week ending April 24 was 3% lower than the same period in 2019.

Hiring in the United States, United Kingdom, France and Italy - which lead the world in coronavirus-related deaths - remains hugely depressed, but is falling less rapidly than a few weeks ago as the countries pass the peak of their epidemics.

Retailers including Walmart Inc, Amazon.com Inc and Instacart have said they would hire a total of over 700,000 workers to meet a surge in demand for groceries and household essentials during the coronavirus outbreak.

Coronavirus state-wise India update: Total number of confirmed cases, deaths on April 30

Consumer goods manufacturers such as Unilever, whose products include soap and shampoo, confirmed on Wednesday it was hiring to fill 300 jobs globally, but declined to elaborate.

Nestle told Reuters it was looking to fill 5,000 full-time U.S. positions in "a variety of levels across corporate and frontline."

Fidelity Investments, a Boston-based financial services firm, said it had accelerated recruitment because of the pandemic and was looking to fill at least 2,000 full-time roles for financial consultants, software engineers and customer service staff in the United States in 2020.

Companies hiring in the United States and other countries also include Apple Inc; ByteDance, the Chinese parent of video-sharing social network TikTok; Takeda Pharmaceutical Co Ltd; and aerospace and defence company Lockheed Martin Corp. These companies did not immediately respond to requests for comment.

DIRE WARNINGS

The International Labour Organization warned on Wednesday that 1.6 billion workers, or nearly half of the global workforce, especially in the informal economy, could lose their livelihoods.

Record numbers of people have applied for U.S. jobless benefits since mid-March, and the unemployment rate is expected to soar to 16%, White House economic adviser Kevin Hasset said this week, from a 50-year low of 3.5% before the pandemic hit.

Both Italy and France, in lockdown for nearly two months, have seen hiring rates drop by around 70% from a year ago, according to LinkedIn.

Since China is ahead of other countries on the pandemic timeline, improvements there could suggest the same is in store elsewhere, Berger said. Several American states and European countries have begun allowing some non-essential businesses and schools to reopen in the hopes of restarting the economy and allowing a gradual return to normal life.

"It's still slightly early to call it a firm recovery," Berger said, referring to improving prospects in China. "We're not expecting a full recovery but rather it's an indication that parts of the economy will switch on as lockdowns are eased, at least relative to the worst point of the pandemic."

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March 25,2020

Wellington, Mar 25: New Zealand has declared a state of emergency as it prepares to go into an unprecedented lockdown late Wednesday for about a month.

The declaration temporarily gives police and the military extra powers. And Prime Minister Jacinda Ardern says any New Zealanders returning home from overseas who show symptoms of COVID-19 will be put in isolation at an approved facility.

“I have one simple message for New Zealanders today as we head into the next four weeks: ‘stay at home,’” Ardern said. “It will break the chain of transmission and it will save lives.”

Ardern said exceptions include people working crucial jobs, those leaving to pick up essentials like groceries, and those engaging in solitary exercise.

The country has 205 reported cases of the virus, although Ardern said that number could rise into the thousands before it begins to recede even with the strict measures being taken.

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