100-year-old deathbed dreams of mathematician proved true

Srinivasa Ramanujan (EMORY UNIVERSITY)

While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they’ve proved he was right.

“We’ve solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years,” Emory University mathematician Ken Ono said.
Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said.

For a brief window of time, he lit the world of math on fire.’

– Emory University mathematician Ken Ono

 

But he sent mathematicians letters describing his work, and one of the most preeminent ones, English mathematician G. H. Hardy, recognized the Indian boy’s genius and invited him to Cambridge University in England to study. While there, Ramanujan published more than 30 papers and was inducted into the Royal Society.

“For a brief window of time, five years, he lit the world of math on fire,” Ono told LiveScience.

But the cold weather eventually weakened Ramanujan’s health, and when he was dying, he went home to India.

It was on his deathbed in 1920 that he described mysterious functions that mimicked theta functions, or modular forms, in a letter to Hardy. Like trigonometric functions such as sine and cosine, theta functions have a repeating pattern, but the pattern is much more complex and subtle than a simple sine curve. Theta functions are also “super-symmetric,” meaning that if a specific type of mathematical function called a Moebius transformation is applied to the functions, they turn into themselves. Because they are so symmetric these theta functions are useful in many types of mathematics and physics, including string theory.

Ramanujan believed that 17 new functions he discovered were “mock modular forms” that looked like theta functions when written out as an infinte sum (their coefficients get large in the same way), but weren’t super-symmetric. Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.

Ramanujan died before he could prove his hunch. But more than 90 years later, Ono and his team proved that these functions indeed mimicked modular forms, but don’t share their defining characteristics, such as super-symmetry.

The expansion of mock modular forms helps physicists compute the entropy, or level of disorder, of black holes.

In developing mock modular forms, Ramanujan was decades ahead of his time, Ono said; mathematicians only figured out which branch of math these equations belonged to in 2002.

“Ramanujan’s legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died,” Ono said.

The findings were presented last month at the Ramanujan 125 conference at the University of Florida, ahead of the 125th anniversary of the mathematician’s birth on Dec. 22.

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World’s Largest Super Collider: Abandoned

A super collider is a large ring designed to accelerate particles of protons and anti-protons until they collide, the purpose being to create high amounts of energy.

In the mid 1980′s, the United States wanted to construct the largest particle collider in the world. What was to be called the Superconducting Super Collider (SSC) began as an idea in 1983. By 1987 Congress had approved the $4.4 billion dollar budget for the project, and by 1991 a site had been chosen in Texas and construction began.

By 1993 the cost projection had risen to over $12 billion. With limited financial resources, the U.S. government was forced to choose between funding the International Space Station (ISS) or the super particle collider. Congress approved the ISS and on October 21, 1993, the SSCproject was cancelled. When the project was cancelled, 14 miles of tunnels and 17 shafts had already been dug, as well as all surface structures completed. Total spent: $2 billion.

After cancellation, the site was given to Ellis County, Texas. Numerous attempts to sell the property failed until 2006, when a private investment group purchased the property. It was rumored that there were plans to use the SSC as a tier III or IV data center, but today the property still sits derelict and abandoned. All of the collider equipment has been removed save for some underground generators in the tunnels.

Some might cite the Large Hadron Collider (LHC) at CERN in Switzerland as the largest particle accelerator in the world, and they would be correct if you’re using the “currently operating” caveat (the SSC is larger, but was never made operational). CERN LHC’s collision energy output of 14 TeV (Trillion electron-Volts) was dwarfed by the planned output of 40 TeV for the Superconducting Super Collider.

So why did construction of the LHC succeed where theSSC failed? Some point to LHC’s use of a property that already had tunnels. Excavating millions of tons of Earth proved to be the most expensive item during construction. Compounding the cost was the fact that the SSC was planning to be much larger than the Large Hadron Collider. The Superconducting Super Collider had to dig from scratch; the LHC did not have to dig tunnels, thus construction costs were lower (rumored to be about $5 billion USD).

The largest operating particle collider in the United States also happens to be the second largest in the world.  The Tevatron, completed in 1983 at a cost of $120 million, is located at the Fermi National Accelerator Laboratory (Fermilab) in Illinois. The Tevatron was much smaller in scale; it only produced 1 TeV at maximum output.

UPDATE 10/2011: Unfortunately due to recent budget cuts, the Tevatron has ceased operations as of October. The costs associated with operating a collider – even on a smaller scale – outweigh the benefits in today’s budget landscape. The second-largest collider in the world is now the Relativistic Heavy Ion Collider run by Brookhaven National Laboratory (BNL) in New York.

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World’s largest atom smasher gets faster

The ATLAS experiment at the Large Hadron Collider is one of the machine’s two big all-purpose detectors. (CERN)

The Large Hadron Collider is working more efficiently, physicists announced Monday, with more particles than ever before crammed into the particle accelerator’s beams.

Scientists successfully halved the space between the bunches of protons that fly through the LHC in sprays called beams. To observe unknown particles and interactions, physicists race these beams around a 17-mile-long underground ring on the border between France and Switzerland. Head-on collisions between protons give rise to short-lived, exotic particles, perhaps including the elusive Higgs Boson, the particle theorized to be responsible for bestowing mass on all other particles.

‘The accelerator delivered more than 6 million billion collisions.’

– Steve Myers, the director for accelerators and technology for CERN

 

LHC physicists think they’ve finally found the Higgs Boson. A new subatomic particle discovered this summer matches the theoretical description of the Higgs, though more analysis and data is needed to nail down the identification.

Meanwhile, CERN, the European Laboratory for Particle Physics, which runs the collider, announced the completion of its first three-year “run” Dec. 17 by trumpeting several milestones.

“The LHC’s performance has exceeded all expectations over the last three years,” Steve Myers, the director for accelerators and technology for CERN, said in a statement. “The accelerator delivered more than 6 million billion collisions and the luminosity has continuously increased. It’s a fantastic achievement, and I’m incredibly proud of my team.” [Photos: The World’s Largest Atom Smasher]

Luminosity is a measurement of the rate of particle collisions in the accelerator.

The last few days of the LHC’s run have been partially devoted to upping the efficiency of the enormous machine. Each proton beam in the LHC is divided into hundreds of bunches, each several centimeters or inches long and each containing more than a hundred billion protons. Now, scientists have halved the spaces between each bunch of protons, leaving only 25 nanoseconds of time between each proton-rich pulse. That means twice as many proton bunches can fit into each beam, increasing the rate of particle collisions, and therefore the amount of data scientists can collect.

“This new achievement augurs well for the next LHC run starting in 2015,” Myers said. “High intensity beams mean more collisions and a better chance of observing rare phenomena.”

The Higgs, if CERN physicists have found it, is indeed a rare phenomena. Of the 6 million billion collisions generated in the last three years, only about 400 produced traces of the Higgs-like particle.

As 2013 opens, the LHC will conduct experiments involving colliding protons with lead ions before a long pause in research for maintenance through 2014. In 2015, particle collisions are expected to resume with increased energy and frequency.

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“Oddball” Galaxy Contains the Biggest Black Hole Yet

Image of lenticular galaxy NGC 1277 taken with Hubble Space Telescope. (NASA/ESA/Andrew C. Fabian)

It’s thought that at the heart of most if not every spiral galaxy (as well as some dwarf galaxies) there’s a supermassive black hole, by definition containing enormous amounts of mass — hundreds of millions, even billions of times the mass of our Sun packed into an area that would fit inside the orbits of the planets. Even our own galaxy has a central SMBH — called Sgr A*, it has the equivalent of 4.1 million solar masses.

Now, astronomers using the Hobby-Eberly Telescope at The University of Texas at Austin’s McDonald Observatory have identified what appears to be the most massive SMBH ever found, a 17 billion solar mass behemoth residing at the heart of galaxy NGC 1277.

Located 220 million light-years away in the constellation Perseus, NGC 1277 is a lenticular galaxy only a tenth the size of the Milky Way. But somehow it contains the most massive black hole ever discovered, comprising a staggering 14% of the galaxy’s entire mass.

“This is a really oddball galaxy,” said Karl Gebhardt of The University of Texas at Austin, a team member on the research. “It’s almost all black hole. This could be the first object in a new class of galaxy-black hole systems.”

The study was led by Remco van den Bosch, who is now at the Max Planck Institute for Astronomy (MPIA).

It’s estimated that the size of this SMBH’s event horizon is eleven times the diameter of Neptune’s orbit — an incredible radius of over 300 AU.

How the diamater of the black hole compares with the orbit of Neptune (D. Benningfield/K. Gebhardt/StarDate)

 

Although previously imaged by the Hubble Space Telescope, NGC 1277′s monster black hole wasn’t identified until the Hobby-Eberly Telescope Massive Galaxy Survey (MGS) set its sights on it during its mission to study the relationship between galaxies and their central black holes. Using the HET data along with Hubble imaging, the survey team calculated the mass of this black hole at 17 billion solar masses.

“The mass of this black hole is much higher than expected,” said Gebhardt, “it leads us to think that very massive galaxies have a different physical process in how their black holes grow.”

To date, the HET team has observed 700 of their 800 target galaxies.

In the video below, Remco van den Bosch describes the discovery of this unusually super supermassive black hole:

Read more on the UT Austin’s McDonald Observatory press release here, or this press release from the Max Planck Institute for Astronomy.

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‘Nile river’ discovered on Saturn moon Titan — first river on another planet

Dec. 12, 2012: NASA’s Cassini spacecraft has discovered a vast river system on Saturn’s moon Titan. It is the first time images from space have revealed a river system so vast and in such high resolution anywhere other than Earth (NASA/JPL-Caltech/ASI)

The Cassini Solstice mission has discovered what appears to be a miniature version of the Nile River on Saturn’s largest moon, Titan. In comparison, the Nile is 4,132 miles long. The 250-mile long feature — from ‘headwaters’ to a large sea — is the longest extraterrestrial river ever to be discovered and imaged to such high resolution.

Using Cassini’s radar imaging instruments, mission scientists were able to deduce that the feature is indeed a river as the dark, smooth surface within the meanders and channel suggest the presence of a liquid.

ANALYSIS: The ‘Tropical’ Lakes of Saturn’s Moon Titan

 

‘The relative straightness of the river valley suggests it follows the trace of at least one fault, similar to other large rivers.’

– Jani Radebaugh, Cassini radar team associate at Brigham Young University

 

Titan is known to have vast lakes — the only other body in the solar system, apart from Earth, to possess a cycle of liquids on its surface. However, the thick Titan atmosphere is a frigid one, meaning liquid water couldn’t possibly flow. The liquids on Titan are therefore composed of hydrocarbons such as methane and ethane.

Interestingly, using this observation of a vast river system on Titan reveals not only that rivers flow, it could also trace the path of fault lines on the Saturnian moon, suggestive of fractures in Titan’s bedrock.

“Though there are some short, local meanders, the relative straightness of the river valley suggests it follows the trace of at least one fault, similar to other large rivers running into the southern margin of this same Titan sea,” said Jani Radebaugh, Cassini radar team associate at Brigham Young University.

“Such faults — fractures in Titan’s bedrock — may not imply plate tectonics, like on Earth, but still lead to the opening of basins and perhaps to the formation of the giant seas themselves.”

ANALYSIS: Need a Vacation? Visit Titan’s Exotic Ontario Lacus

The discovery of vast river systems on Titan was perhaps inevitable. Cassini has previously confirmed the presence of large masses of liquid including Ontario Lacus, a lake in the southern hemisphere composed of liquid ethane. Rainfall has also been detected in the atmosphere, hinting not of a hydrological cycle (which gives us water rain, rivers and oceans on Earth), but of a methane cycle.

It is hard not to imagine what such a river system would look like when standing next to it. But looking at this radar observation, many familiar river features such as meanders and channels can be seen.

Titan is a complex and fascinating little world laced with complex prebiotic chemistry. Apart from the Huygens probe that landed on the surface in 2005, there have been no other surface missions and plans for future missions look iffy at best.

ANALYSIS: Titan’s Hazy History and the Potential for Life

Titan might be shrouded in a cold, high pressure atmosphere that makes it difficult for our robots to explore, but it’s hard to ignore the fact that the ingredients for the basic chemistry for life is there in abundance — could there be a form of life there, perhaps taking advantage of liquid methane and ethane rather than water? We may be waiting some time to find out.
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DNA directly photographed for first time

DNA’s double-helix structure is on display for the first time in this electron microscope photograph of a small bundle of DNA strands. (Enzo Di Fabrizio)

Fifty-nine years after James Watson and Francis Crick deduced the double-helix structure of DNA, a scientist has captured the first direct photograph of the twisted ladder that props up life.

Enzo Di Fabrizio, a physics professor at the Magna Graecia University in Catanzaro, Italy, snapped the picture using an electron microscope.

Previously, scientists had only seen DNA’s structure indirectly. The double-corkscrew form was first discovered using a technique called X-ray crystallography, in which a material’s shape is reconstructed based on how X-rays bounce after they collide with it.

But Di Fabrizio and his colleagues developed a plan to bring DNA out of hiding. They built a nanoscopic landscape of extremely water-repellant silicon pillars. When they added a solution that contained strands of DNA into this scene, the water quickly evaporated and left behind cords of bare DNA that stretched like tightropes between the tiny mesas.

They then shone beams of electrons through holes in the silicon bed, and captured high-resolution images of the illuminated molecules.

Di Fabrizio’s images actually show a thread of several interwoven DNA molecules, as opposed to just two coupled strands. This is because the energy of the electrons used would be enough to destroy an isolated double helix, or a single strand from a double helix.

But with the use of more sensitive equipment and lower energy electrons, Di Fabrizio thinks that snapshots of individual double helices will soon be possible, reports New Scientist.

Molecules of DNA, or deoxyribonucleic acid, store the genetic instructions that govern all living organisms’ growth and function.

Di Fabrizio’s innovation will allow scientists to vividly observe interactions between DNA and some of life’s other essential ingredients, such as RNA (ribonucleic acid). The results of Di Fabrizio’s work were published in the journal NanoLetters.

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At far side of solar system, Voyager 1 discovers new region of space

It keeps going … and going … and going ….

NASA’s Voyager 1 spacecraft, launched in 1977 and now the most distant human-made object from the sun, at about 11 billion miles, has entered a new region at the edge of the solar system it is close to exiting forever.

Scientists have dubbed this region the “magnetic highway” and it’s the last stop before interstellar space, or the space between stars.

“Although Voyager 1 still is inside the sun’s environment, we now can taste what it’s like on the outside because the particles are zipping in and out on this magnetic highway,” said Edward Stone, Voyager project scientist based at the California Institute of Technology, Pasadena. “We believe this is the last leg of our journey to interstellar space. Our best guess is it’s likely just a few months to a couple years away.”

“The new region isn’t what we expected, but we’ve come to expect the unexpected from Voyager.”

The findings were presented Monday at a meeting of the American Geophysical Union meeting in San Francisco.

“We are in a magnetic region unlike any we’ve been in before — about 10 times more intense than before the termination shock — but the magnetic field data show no indication we’re in interstellar space,” said Leonard Burlaga, a Voyager magnetometer team member based at NASA’s Goddard Space Flight Center in Greenbelt, Md.

Voyager 1 and its twin Voyager 2 launched 35 years ago on a tour of the outer planets. Afterward, both spacecraft continued to hurtle toward the fringes of the solar system.

Mission chief scientist Ed Stone says it’s unknown when Voyager 1 will finally break through to interstellar space. Once that happens, it’ll be the first manmade object to leave the solar system.

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