Friday 20 November 2020

Aurora: The Northern lights

The northern lights, or aurora borealis, offer an entrancing, dramatic, magical display that fascinates all who see it — but just what causes this dazzling natural phenomenon? At the center of our solar system lies the sun, the yellow star that sustains life on our planet. The sun's many magnetic fields distort and twist as our parent star rotates on its axis. When these fields become knotted together, they burst and create so-called sunspots. Usually, these sunspots occur in pairs; the largest can be several times the size of Earth's diameter.At the center of the sun, the temperature is 27 million degrees Fahrenheit (15 million degrees Celsius). As the temperature on its surface rises and falls, the sun boils and bubbles. Particles escape from the star from the sunspot regions on the surface, hurtling particles of plasma, known as solar wind, into space. It takes these winds around 40 hours to reach Earth. When they do, they can cause the dramatic displays known as the aurora borealis. [Infographics: How the Northern Lights Work & Anatomy of Sun Storms & Solar Flares] Auroras occur not only on Earth, but also on other worlds in our solar system (and perhaps exoplanets as well). The gas giants in our solar system (Jupiter, Saturn, Uranus and Neptune) each have thick atmospheres and strong magnetic fields, and each have auroras — although these auroras are a little different from Earth's, given they are formed under different conditions. Venus has an aurora generated by its stretched-out magnetic field (a "magnetotail"). Mars, which has too thin an atmosphere for global auroras, experiences local auroras due to magnetic fields in the crust. NASA's MAVEN (Mars Atmosphere and Volatile Evolution) spacecraft also found widespread northern hemisphere auroras generated by energetic particles striking the Martian atmosphere. Sunspots and cycles The sunspots and solar storms that cause the most magnificent displays of the northern lights occur roughly every 11 years. The solar cycle peaked in 2013, but it was the weakest solar maximum in a century. [Photos: Amazing Auroras of 2014] "This solar cycle continues to rank among the weakest on record," Ron Turner of Analytic Services, Inc. who serves as a Senior Science Advisor to NASA's Innovative Advanced Concepts program, said in a statement. Since record-keeping of the ebb and flow of the sun's activity began in 1749, there have been 22 full cycles. Researchers monitor space weather events because they have the potential to affect spacecraft in orbit, knock out power grids and communications infrastructure on Earth, and amp up normal displays of the northern and southern lights. Scientists are also investigating how fluctuations in the sun's activity affect weather on our planet.Particles and polar attraction Earth is constantly bombarded with debris, radiation and other magnetic waves from space that could threaten the future of life as we know it. Most of the time, the planet's own magnetic field does an excellent job of deflecting these potentially harmful rays and particles, including those from the sun. Particles discharged from the sun travel 93 million miles (around 150 million km) toward Earth before they are drawn irresistibly toward the magnetic north and south poles. As the particles pass through the Earth's magnetic shield, they mingle with atoms and molecules of oxygen, nitrogen and other elements that result in the dazzling display of lights in the sky. An Expedition 30 crew member took this photo of the North Atlantic with an aurora on March 28, 2012. 

(Image credit: NASA)

The auroras in Earth's Northern Hemisphere are called the aurora borealis. Their southern counterpart, which light up the Antarctic skies in the Southern Hemisphere, are known as the aurora australis.

What causes the colors?

The colors most often associated with the aurora borealis are pink, green, yellow, blue, violet, and occasionally orange and white. Typically, when the particles collide with oxygen, yellow and green are produced. Interactions with nitrogen produce red, violet, and occasionally blue colors.

The type of collision also makes a difference to the colors that appear in the sky: atomic nitrogen causes blue displays, while molecular nitrogen results in purple. The colors are also affected by altitude. The green lights typically in areas appear up to 150 miles (241 km) high, red above 150 miles; blue usually appears at up to 60 miles (96.5 km); and purple and violet above 60 miles.

These lights may manifest as a static band of light, or, when the solar flares are particularly strong, as a dancing curtain of ever-changing color.

History of the auroral lights

For millennia, the lights have been the source of speculation, superstition and awe. Cave paintings in France thought to date back 30,000 years have illustrations of the natural phenomenon.

In more superstitious times, the northern lights were thought to be a harbinger of war or destruction, before people really understood what causes them. Many classic philosophers, authors and astronomers, including Aristotle, Descartes, Goethe and Halley, refer to the northern lights in their work.

As early as 1616, the astronomer Galileo Galilei used the name aurora borealis to describe them, taking the name of the mythical Roman goddess of the dawn, Aurora, and the Greek name for wind of the north, Boreas.

The aurora australis, or the southern lights, occur around the south polar region. But, since the South Pole is even more inhospitable than the North Pole, it is often trickier to view the southern lights

Where to see the lights

The best places to see the northern lights are Alaska and northern Canada, but visiting these vast, open expanses is not always easy. Norway, Sweden and Finland also offer excellent vantage points. During periods of particularly active solar flares, the lights can be seen as far south as the top of Scotland and even northern England. [A Guide for Watching Earth's Auroras]

On rare occasions, the lights are seen farther south. They were first observed by European settlers in New England in 1791. In "Historical Storms of New England," published in 1891, Sidney Perley wrote, "May 15, 1719, the more beautiful and brilliant aurora borealis was first observed here as far as any record or tradition of that period inform us, and it is said that in England it was first noticed only three years before this date. In December of the same year the aurora again appeared, and the people became greatly alarmed, not dreading it so much as a means of destruction but as precursor of the fires of the last great day and a sign of coming dangers."

When to see the lights

The northern lights are always present, but winter is usually the best time to see them, due to lower levels of light pollution and the clear, crisp air. September, October, March and April are some of the best months to view the aurora borealis. The lights are known to be brighter and more active for up to two days after sunspot activity is at its highest. Several agencies, such as NASA and the National Oceanic and Atmospheric Administration, also monitor solar activity and issue aurora alerts when they are expected to put on a particularly impressive show.

Additional reporting by Elizabeth Howell and Nola Taylor Redd, Space.com contributors

Monday 19 October 2020

Area 51: The aliens home on earth

 

Nearly 200K People Have Signed Up to Steal Alien Secrets from Area 51 in Late-Summer Raid 

As this sign outside of Nevada’s infamous Area 51 military base reminds would-be visitors, guards are authorized to respond to trespassers with deadly force. (Image credit: Barry King/Getty Images)

Pack your shades, your sunscreen and your coziest tinfoil hat, because the late-summer event of the season is happening in Nevada's scenic Area 51, and you're invited.

According to a tongue-in-cheek Facebook event called "Storm Area 51, They Can't Stop All of Us," a ragtag army of alien hunters will meet up near the top-secret Air Force base in the predawn hours of Sept. 20, coordinate a plan of attack, then raid the grounds in search of captive aliens. Per the event's hosts (a page that posts memes and a guy who streams video games on Twitch), the delicate operation will involve running supernaturally fast — faster than the guards' bullets can fly — but will be worth it to "see them aliens."

So far, nearly 200,000 Facebook users have signed up to attend, with another 200,000 "interested" in the affair. [15 Far-Out Facts About Area 51]

This event is, of course, a joke (please, do not raid this or any other military base). Area 51 — a massive plot of desert about 80 miles (129 kilometers) northwest of Las Vegas — is a top-secret military installation that is infamously well-guarded by fences, radars and heavily armed "camo dudes" in white trucks. After more than 60 years of operations, the base's primary purpose remains classified and its grounds restricted to the public, fomenting an aura of spooky secrecy that has intrigued all manner of skeptics and conspiracy theorists for decades.

This much is known about the base: It's huge, covering a total of 2.9 million acres (1.2 million hectares) and 5,000 square miles (12,950 square km) of restricted airspace. Officially, the base is part of the Nevada Test and Training Range (NTTR), which is affiliated with Nellis Air Force Base; according to the Air Force, it is the largest combined air and ground space for peacetime military operations in the free world.

Since the Air Force set up shop there in 1955, Area 51 has hosted hundreds of nuclear weapons tests and has served as a training-and-testing ground for all manner of top-secret stealth aircraft, Live Science previously reported. If you believe the most popular conspiracy theory about the base, one of those aircraft may be an alien saucer that crash-landed in Roswell, New Mexico, in the late 1940s.

The U.S. military claimed that the mysterious object was a weather balloon (a 1994 Air Force report confirmed this to be true — albeit, a souped-up weather balloon designed to detect far-off nuclear fallout). However, conspiracy theorists insisted that the wreck was indeed an alien spacecraft, which had been subsequently transported to Area 51 to be broken apart, studied and put back together again. This theory gained traction in the 1980s, when a man claiming to have worked at Area 51 told the news media that he had actually seen scientists reverse engineer alien saucers there.

This man, it turns out, was a liar who never set foot on the base (he also lied about the colleges he went to and other past employment); but his stories gained enough attention that Area 51 had a new, permanent reputation as that eerie place in the desert where scientists might be tinkering with aliens. Subsequent tests of experimental, top-secret aircraft at the base have only strengthened this far-out legacy. 

The allure of the mysterious desert base is undeniable. So, what happens if you do attempt to trespass into Area 51 and liberate the juicy alien secrets contained within? For starters, you'll probably be stopped at gunpoint by guards dressed in camo, as two intrepid adventurers experienced in 2016 after trying to sneak a camera through the base's back gate.

According to signs posted around the base, these infamous "camo dudes" are permitted to greet trespassers with deadly force — but, if past encounters are any indication, trespassers are more likely to be met with a hefty fine and a court date. When an SUV filled with tourists accidentally crossed into the base's restricted area a few years ago, the driver and four passengers were each cited with a $650 fine and a misdemeanor charge. The unwary passengers eventually got their charges dropped, but the driver had to pay up — and was banned from leading tours in the area for several years.

If you happen to join the joke raid proposed for this September, keep that man's story in mind. When it comes to unearthing the truth of Area 51, you may have only one shot. Choose your plan wisely.

[press release from History]

HISTORY(R) ANNOUNCES TWO NEW PREMIUM DOCUMENTARIES "SECRETS IN THE SKY: THE UNTOLD STORY OF SKUNK WORKS" AND "GAME CHANGERS: INSIDE THE VIDEO GAME WARS" AIRING JUNE 9 AND JUNE 16 AS A PART OF ITS HISTORY FILMS STRAND
Narrated by Golden Globe(R) and Emmy Award(R) Nominee Actor Dennis Quaid "Secrets In The Sky: The Untold Story of Skunk Works" Examines the Mysterious Aerospace Organization that Produced a Fleet of Elite History-Making Aircrafts
Directed by Academy Award(R) Winner Daniel Junge "Game Changers: Inside the Video Game Wars" Divulges the Ego-Driven Rivalries Between Major Gaming Companies
New York, NY - June 4, 2019 - HISTORY premieres two new two-hour documentaries "Secrets In The Sky: The Untold Story of Skunk Works" on Sunday, June 9 at 9PM ET/PT and "Game Changers: Inside the Video Game Wars" on Sunday, June 16 at 9PM ET/PT as part of its premium documentary strand HISTORY Films, which spotlights significant and gripping historical events deserving to be told. Narrated by Golden Globe(R) and Emmy Award(R) nominee Dennis Quaid and directed by Emmy Award(R) winning director Rory Karpf, "Secrets In The Sky: The Untold Story of Skunk Works" examines the top-secret organization that for decades, starting in the 1940s, clandestinely churned out the world's most advanced technology and designed highly classified aircraft. Utilizing the narration of Skunk Works team leader Kelly Johnson as inspired by his personal logbooks and meticulous diaries, viewers will be immersed in the secret Skunk Works story of the last 75 years. Directed by Academy Award(R) winner Daniel Junge, "Game Changers: Inside the Video Game Wars" looks at the multibillion-dollar gaming industry, its success and failures and the battle for control from all of the players including Atari, Nintendo, Sega and Sony. Behind the scenes and lawsuits, viewers will learn the true untold story of some of their favorite video games and the masterminds who brought them to life.
SECRETS IN THE SKY: THE UNTOLD STORY OF SKUNK WORKS
Premieres Sunday, June 9 at 9PM ET/PT

For the first time in its 75-year history, Lockheed Martin is opening their hangar doors and pulling back the veil on "Skunk Works," the secret program and subdivision long hidden from the public. Founder and leader Kelly Johnson, as voiced by actor Dennis Quaid, congregated a team comprised of innovators, rule benders and chance takers to partake in the aerospace organization responsible for creating the most innovative machines in modern history - the U-2, the SR-71 Blackbird and the first Stealth bomber to name a few. From the mysterious Area 51 test facility to the latest "spy" plane, this documentary goes deep into a world that is still shrouded in secrecy - a world where wars are won not on a battlefield but at a design table of men drafting aviation blueprints and working with their hands to create modern marvels from the ground up.
"Secrets In The Sky: The Untold Story of Skunk Works" is produced by First Row Films in association with A+E Originals. Rory Karpf serves as director. Steve Ascher, Kristy Sabat and Jessica Conway serve as executive producers for A+E Originals. Jeff Cvitkovic is co-executive producer. Zachary Behr serves as executive producer for HISTORY.
GAME CHANGERS: INSIDE THE VIDEO GAME WARS

Premieres Sunday, June 16 at 9PM ET/PT

Premieres Sunday, June 16 at 9PM ET/PT

This is the untold story of the personal battles that gave rise to the multibillion-dollar video game industry. Brought to life by Academy Award(R) winning director Daniel Junge, this documentary is a tale of brilliant innovations, colossal failures, and ego-driven rivalries on a massive scale. It is a 50-year-long, multi-generation epic featuring corporate coups, industrial espionage and the promise of unimaginable riches being just one cartridge away. Told in chronological order and featuring the sons of the brilliant inventor of the first video game console, Ralph Baer, the co-founder of Atari, Nolan Bushnell, and many more experts in the gaming industry, this documentary highlights the programmers, engineers, management and business practices they followed to compete against each other and become the gaming tycoons we know today.

"Game Changers: Inside the Video Game Wars" is produced for HISTORY by Efran Films and Stone Cottage Media. Daniel Junge serves as director. Shawn Efran, Morgan Hertzan, Jordan J. Mallari and Megan Harding are executive producers. Zachary Behr serves as executive producer for HISTORY.

A+E Networks holds worldwide distribution rights for both films.

About HISTORY(R)

HISTORY, a division of A+E Networks, is the premier destination for historical storytelling. From best-in-class documentary events, to a signature slate of industry leading nonfiction series and premium fact-based scripted programming, HISTORY serves as the most trustworthy source of informational entertainment in media. HISTORY has been named the #1 U.S. TV network in buzz for seven consecutive years by YouGov BrandIndex, and a top favorite TV network by Beta Research Corporation. For a deeper dive, visit history.com or follow @history on Instagram, Twitterand Facebook.



Saturday 25 July 2020

Prime Number Theorem

Mathematicians Will Never Stop Proving the Prime Number Theorem

Why do mathematicians enjoy proving the same results in different ways?
Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern

The amount of prime numbers, seen as yellow dots in this hexagonal spiral of positive integers, wanes as the numbers get bigger — a relationship described by the prime number theorem and proved many times over.

“You don’t have to believe in God, but you have to believe in The Book,” the Hungarian mathematician Paul Erdős once said. The Book, which only exists in theory, contains the most elegant proofs of the most important theorems. Erdős’ mandate hints at the motives of mathematicians who continue to search for new proofs of already proved theorems. One favorite is the prime number theorem — a statement that describes the distribution of prime numbers, those whose only divisors are 1 and themselves. While mathematicians never know whether a proof would merit inclusion in The Book, two strong contenders are the first, independent proofs of the prime number theorem in 1896 by Jacques Hadamard and Charles-Jean de la Vallée Poussin.

So what does this theorem actually say?

The prime number theorem provides a way to approximate the number of primes less than or equal to a given number n. This value is called π(n), where π is the “prime counting function.” For example, π(10) = 4 since there are four primes less than or equal to 10 (2, 3, 5 and 7). Similarly, π(100) = 25 , since 25 of the first 100 integers are prime. Among the first 1,000 integers, there are 168 primes, so π(1,000) = 168, and so on. Note that as we considered the first 10, 100 and 1,000 integers, the percentage of primes went from 40% to 25% to 16.8%. These examples suggest, and the prime number theorem confirms, that the density of prime numbers at or below a given number decreases as the number gets larger.

But even if you had an ordered list of positive integers up through, say, 1 trillion, who would want to determine π(1,000,000,000,000) by way of a manual count? The prime number theorem offers a shortcut.

The theorem tells us that π(n) is “asymptotically equal” to $latex \frac{n}{\ln (n)}$, where ln is the natural logarithm. (You can think of an asymptotic equality as an approximate equality, though it is technically more than that.) As an example, let’s estimate the number of primes up to 1 trillion. Instead of counting individual primes to determine π(1,000,000,000,000), you could use this theorem to learn that there are approximately $latex \frac{1,000,000,000,000}{\ln (1,000,000,000,000)}$ of them, which equals. 36,191,206,825 when rounded to a whole number. This amount is only off by about 4% from the actual answer, 37,607,912,018.

With asymptotic equality, the accuracy improves as you plug larger numbers into the formula. Basically, as you head toward infinity — which is not itself a number, but something larger than any number — the approximate equality in the theorem approaches an actual equality. This is despite the fact that the actual number of primes will always equal an integer, while on the other side of the asymptotic equality, the fraction involving the natural logarithm function could equal any value on the real number line. This connection between integers and real numbers is counterintuitive at best.

It’s mind-blowing stuff, even among mathematicians. Maddeningly, the statement of the prime number theorem does not hint at why any of this is true.

“The theorem was never about the theorem. It was always about the proof,” said Michael Bode, a mathematics professor at Queensland University of Technology in Australia.

As elegant as they were, Hadamard’s and de la Vallée Poussin’s original proofs relied on complex analysis — the study of functions with imaginary numbers — which some found unsatisfying as the statement of this theorem does not itself involve complex numbers. However, G.H. Hardy, in 1921, dubbed the prospect of a nonanalytic proof — known as an elementary proof — of the prime number theorem “extraordinarily unlikely” and claimed that if anyone should find one, it would call for “theory to be rewritten.”

Atle Selberg and Erdős himself took on the challenge, and in 1948 they each published new, independent elementary proofs of the prime number theorem using properties of logarithms. These proofs enticed other mathematicians to consider similar methods for number theory conjectures previously considered too profound for such seemingly simple methods. Many exciting results followed, including Helmut Maier’s 1985 elementary proof showing unexpected irregularities in the distribution of primes.

“So many open questions build on the prime number theorem,” said Florian Richter, a mathematician at Northwestern University who recently posted a new elementary proof of this celebrated statement. Richter found his proof while trying to prove a far-reaching extension of the prime number theorem.

Over time, number theorists helped establish a culture in which mathematicians worked on proving and re-proving theorems not just to verify statements, but also to improve their skills at proving theorems and their understanding of the math involved.

This goes beyond the prime number theorem. Paulo Ribenboim cataloged at least 7 proofs of the infinitude of primes. Steven Kifowit and Terra Stamps identified 20 proofs demonstrating that the harmonic series, 1+ $latex \frac{1}{2}$ + $latex \frac{1}{3}$ + $latex \frac{1}{4}$ + $latex \frac{1}{5}$ + $latex \frac{1}{6}$ + $latex \frac{1}{7}$ + …, does not equal a finite number, and Kifowit later followed up with 28 more. Bruce Ratner cites more than 371 different proofs of the Pythagorean theorem, including some gems provided by Euclid, Leonardo da Vinci and U.S. President James Garfield, who was a member of Congress from Ohio at the time.

This habit of re-proving things is now so ingrained, mathematicians can literally count on it. Tom Edgar and Yajun An noted that there have been 246 proofs of a statement known as the quadratic reciprocity law following Gauss’ original proof in 1796. Plotting the number of proofs over time, they extrapolated that we could expect the 300th proof of this theorem around the year 2050.

“I love new proofs of old theorems for the same reason I love new roads and shortcuts to places I’ve already been,” said Sophia Restad, a graduate student at Kansas State University. These new paths provide mathematicians with a figurative sense of place for intellectual activity.

Mathematicians may never stop searching for new and more illuminating paths to the prime number theorem and other
beloved theorems. With luck, some of them will even merit
inclusion in The Book.