Century-Old Math Provides New Understanding Of Black Holes
To mark what would have been the 125th birthday of the legendary Indian mathematician Srinivasa Ramanujan, an Emory University professor has shown the math icon’s century-old writings might lead to a better understanding of the properties of black holes.
“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 Ken Ono, who led a team of mathematicians in studying the mysteriously derived theorems.
Ramanujan’s work is well-known in academic circles because of its extraordinary numerical patterns that were seemingly devised without the use of proofs or modern mathematical methods. Ramanujan said his findings were a divine gift, revealed to him from the Hindu goddess Namagiri.
“I wanted to do something special, in the spirit of Ramanujan, to mark the anniversary,” Ono said. “It’s fascinating to me to explore his writings and imagine how his brain may have worked. It’s like being a mathematical anthropologist.”
Ramanujan only lived for 32 years and while on his death-bed in 1920, he sent a letter to his mentor, the English mathematician G. H. Hardy. In the letter, Ramanujan described numerous new functions that acted differently from known modular forms, yet closely copied their behavior. Ramanujan posited his mock modular forms correlated to the ordinary modular forms identified by the previous work of Carl Jacobi.
At the time, the mock forms were not understood and probably dismissed as the ramblings of a malnourished, sickly and dying individual.
“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,” Ono said.
Building on that more recent work, Ono and his colleagues used modern mathematical tools to show a mock modular form based on Ramanujan’s writings was possible. The mock modular form shoots off into enormous numbers; however, it corresponded to Jacobi’s modular form that expands at close to the same rate.
Ono used the analogy of “magic coins” to describe how Ramanujan’s form acts alongside the ordinary modular form. He equated both Ramanujan’s and Jacobi’s forms to a coin each man spends in a shop. Each coin then travels on its own journey—from the shop, to the bank, to another shop, and so on.
“For months, the paths of the two coins look chaotic, like they aren’t doing anything in unison,” Ono says. “But eventually Ramanujan’s coin starts mocking, or trailing, Jacobi’s coin. After a year, the two coins end up very near one another: In the same town, in the same shop, in the same cash register, about four inches apart.”
The results of the team’s finding could have ramifications for computing the entropy of black holes that do not behave according to modular form models.
“We developed a theorem that shows that the bizarre methodology he used to construct his examples is correct,” Ono says. “For the first time, we can prove that the exotic functions that Ramanujan conjured in his death-bed letter behave exactly as he said they would, in every case.”
Ono recently presented his team’s work at the Ramanujan 125 conference held in November at the University of Florida.
redOrbit.com
offers Science, Space, Technology, Health news, videos, images and
reference information. For the latest science news, space news,
technology news, health news visit redOrbit.com frequently. Learn
something new every day.\”
2012-12-18 03:31:51
Source: http://www.redorbit.com/news/science/1112749970/srinivasa-ramanujan-math-model-black-holes-121712/
Source:
Anyone can join.
Anyone can contribute.
Anyone can become informed about their world.
"United We Stand" Click Here To Create Your Personal Citizen Journalist Account Today, Be Sure To Invite Your Friends.
Before It’s News® is a community of individuals who report on what’s going on around them, from all around the world. Anyone can join. Anyone can contribute. Anyone can become informed about their world. "United We Stand" Click Here To Create Your Personal Citizen Journalist Account Today, Be Sure To Invite Your Friends.
LION'S MANE PRODUCT
Try Our Lion’s Mane WHOLE MIND Nootropic Blend 60 Capsules
Mushrooms are having a moment. One fabulous fungus in particular, lion’s mane, may help improve memory, depression and anxiety symptoms. They are also an excellent source of nutrients that show promise as a therapy for dementia, and other neurodegenerative diseases. If you’re living with anxiety or depression, you may be curious about all the therapy options out there — including the natural ones.Our Lion’s Mane WHOLE MIND Nootropic Blend has been formulated to utilize the potency of Lion’s mane but also include the benefits of four other Highly Beneficial Mushrooms. Synergistically, they work together to Build your health through improving cognitive function and immunity regardless of your age. Our Nootropic not only improves your Cognitive Function and Activates your Immune System, but it benefits growth of Essential Gut Flora, further enhancing your Vitality.
Our Formula includes: Lion’s Mane Mushrooms which Increase Brain Power through nerve growth, lessen anxiety, reduce depression, and improve concentration. Its an excellent adaptogen, promotes sleep and improves immunity. Shiitake Mushrooms which Fight cancer cells and infectious disease, boost the immune system, promotes brain function, and serves as a source of B vitamins. Maitake Mushrooms which regulate blood sugar levels of diabetics, reduce hypertension and boosts the immune system. Reishi Mushrooms which Fight inflammation, liver disease, fatigue, tumor growth and cancer. They Improve skin disorders and soothes digestive problems, stomach ulcers and leaky gut syndrome. Chaga Mushrooms which have anti-aging effects, boost immune function, improve stamina and athletic performance, even act as a natural aphrodisiac, fighting diabetes and improving liver function. Try Our Lion’s Mane WHOLE MIND Nootropic Blend 60 Capsules Today. Be 100% Satisfied or Receive a Full Money Back Guarantee. Order Yours Today by Following This Link.
