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
January 27,2020

Kabul, Jan 27: A passenger plane crashed on Monday in a Taliban-held area of Afghanistan's Ghazni province, local officials said.

Arif Noori, spokesman for the provincial governor, said the plane went down around 1:10 p.m. local time in Deh Yak district, which is held by the Taliban. Two provincial council members also confirmed the crash.

The number of people on board and their fate was not immediately known, nor was the cause of the crash.

Ariana Airlines, Afghanistan's national carrier, dismissed the claim that one of their planes had crashed in a statement on their website, saying all their aircraft were operational and safe.

The mountainous Ghazni province sits in the foothills of the Hindu Kush mountains and is bitterly cold in winter.

The last major commercial air crash in Afghanistan occurred in 2005 when a Kam Air flight from western Herat to the capital Kabul crashed into the mountains as it tried to land in snowy weather.

The war however has seen a number of deadly crashes of military aircraft. One of the most spectacular occurred in 2013 when an American Boeing 747 cargo jet crashed shortly after takeoff from Bagram air base north of Kabul en route to Dubai in the United Arab Emirates. All seven crew member were killed.

Afghanistan's aviation industry suffered desperately during the rule of the Taliban when its only airline Ariana was subject to punishing sanctions and allowed to fly only to Saudi Arabia for Hajj flights.

Since the overthrow of the religious regime smaller private airlines have emerged but the industry is still a nascent one.

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News Network
April 2,2020

United Nations, Apr 2: The global economy could shrink by up to one per cent in 2020 due to the coronavirus pandemic, a reversal from the previous forecast of 2.5 per cent growth, the UN has said, warning that it may contract even further if restrictions on the economic activities are extended without adequate fiscal responses.

The analysis by the UN Department of Economic and Social Affairs (DESA) said the COVID-19 pandemic is disrupting global supply chains and international trade. With nearly 100 countries closing national borders during the past month, the movement of people and tourism flows have come to a screeching halt.

"Millions of workers in these countries are facing the bleak prospect of losing their jobs. Governments are considering and rolling out large stimulus packages to avert a sharp downturn of their economies which could potentially plunge the global economy into a deep recession. In the worst-case scenario, the world economy could contract by 0.9 per cent in 2020," the DESA said, adding that the world economy had contracted by 1.7 per cent during the global financial crisis in 2009.

It added that the contraction could be even higher if governments fail to provide income support and help boost consumer spending.

The analysis noted that before the outbreak of the COVID-19, world output was expected to expand at a modest pace of 2.5 per cent in 2020, as reported in the World Economic Situation and Prospects 2020.

Taking into account rapidly changing economic conditions, the UN DESA's World Economic Forecasting Model has estimated best and worst-case scenarios for global growth in 2020.

In the best-case scenario with moderate declines in private consumption, investment and exports and offsetting increases in government spending in the G-7 countries and China global growth would fall to 1.2 per cent in 2020.

"In the worst-case scenario, the global output would contract by 0.9 per cent instead of growing by 2.5 per cent in 2020," it said, adding that the scenario is based on demand-side shocks of different magnitudes to China, Japan, South Korea, the US and the EU, as well as an oil price decline of 50 per cent against our baseline of USD 61 per barrel.

The severity of the economic impact will largely depend on two factors - the duration of restrictions on the movement of people and economic activities in major economies; and the actual size and efficacy of fiscal responses to the crisis.

A well-designed fiscal stimulus package, prioritising health spending to contain the spread of the virus and providing income support to households most affected by the pandemic would help to minimise the likelihood of a deep economic recession, it said.

According to the forecast, lockdowns in Europe and North America are hitting the service sector hard, particularly industries that involve physical interactions such as retail trade, leisure and hospitality, recreation and transportation services. Collectively, such industries account for more than a quarter of all jobs in these economies.

The DESA said as businesses lose revenue, unemployment is likely to increase sharply, transforming a supply-side shock to a wider demand-side shock for the economy.

Against this backdrop, the UN-DESA is joining a chorus of voices across the UN system calling for well-designed fiscal stimulus packages which prioritize health spending and support households most affected by the pandemic.

Urgent and bold policy measures are needed, not only to contain the pandemic and save lives, but also to protect the most vulnerable in our societies from economic ruin and to sustain economic growth and financial stability, Under-Secretary-General for Economic and Social Affairs Liu Zhenmin said.

The analysis also warns that the adverse effects of prolonged economic restrictions in developed economies will soon spill over to developing countries via trade and investment channels.

A sharp decline in consumer spending in the European Union and the United States will reduce imports of consumer goods from developing countries.

Developing countries, particularly those dependent on tourism and commodity exports, face heightened economic risks. Global manufacturing production could contract significantly, and the plummeting number of travellers is likely to hurt the tourism sector in small island developing States, which employs millions of low-skilled workers, it said.

Meanwhile, the decline in commodity-related revenues and a reversal of capital flows are increasing the likelihood of debt distress for many nations. Governments may be forced to curtail public expenditure at a time when they need to ramp up spending to contain the pandemic and support consumption and investment.

UN Chief Economist and Assistant Secretary-General for Economic Development Elliot Harris said the collective goal must be a resilient recovery which puts the planet back on a sustainable track. We must not lose sight how it is affecting the most vulnerable population and what that means for sustainable development, he said.

The alarms raised by UN-DESA echo another report, released on March 31, in which UN experts issued a broad appeal for a large-scale, coordinated, comprehensive multilateral response amounting to at least 10 per cent of global gross domestic product (GDP).

According to estimates by the Johns Hopkins University, confirmed coronavirus cases across the world now stand at over 932,600 and over 42,000 deaths.

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Agencies
July 28,2020

Sydney, Jul 28: Nearly 3 billion koalas, kangaroos and other native Australian animals were killed or displaced by bushfires in 2019 and 2020, a study by the World Wide Fund for Nature (WWF) said on Tuesday, triple the group's earlier estimates.

Some 143 million mammals, 2.46 billion reptiles, 180 million birds and 51 million frogs were impacted by the country's worst bushfires in decades, the WWF said.

When the fires were still blazing, the WWF estimated the number of affected animals at 1.25 billion. The fires destroyed more than 11 million hectares (37 million acres) across the Australian southeast, equal to about half the area of the United Kingdom.

"This ranks as one of the worst wildlife disasters in modern history," said WWF-Australia Chief Executive Officer Dermot O'Gorman in a statement.

The project leader Lily Van Eeden, from the University of Sydney, said the research was the first continent-wide analysis of animals impacted by the bushfires, and "other nations can build upon this research to improve understanding of bushfire impacts everywhere".

The total number included animals which were displaced because of destroyed habitats and now faced lack of food and shelter or the prospect of moving to habitat that was already occupied.

The main reason for raising the number of animal casualties was that researchers had now assessed the total affected area, rather than focusing on the most affected states, they said.

After years of drought made the Australian bush unusually dry, the country battled one of its worst bushfire seasons ever from September 2019 to March 2020, resulting in 34 human deaths and nearly 3,000 homes lost.

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