Month: December, 2017

The 500-Page Proof That Only One Mathematician Can Understand

Nearly four years after Shinichi Mochizuki unveiled an imposing set of papers that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity.

Although they have made modest progress.

Some four dozen mathematicians converged last week for a rare opportunity to hear Mochizuki present his own work at a conference on his home turf, Kyoto University’s Research Institute for Mathematical Sciences (RIMS).

Mochizuki is “less isolated than he was before the process got started”, says Kiran Kedlaya, a number theorist at the University of California, San Diego.

Although at first Mochizuki’s papers, which stretch over more than 500 pages, seemed like an impenetrable jungle of formulae.




Experts have slowly discerned a strategy in the proof that the papers describe, and have been able to zero in on particular passages that seem crucial, he says.

Mochizuki’s theorem aims to prove the important abc conjecture, which dates back to 1985 and relates to prime numbers — whole numbers that cannot be evenly divided by any smaller number except by 1.

The conjecture comes in a number of different forms, but explains how the primes that divide two numbers, a and b, are related to those that divide their sum, c.

If Mochizuki’s proof is correct, it would have repercussions across the entire field, says Dimitrov.

When you work in number theory, you cannot ignore the abc conjecture,” he says.

This is why all number theorists eagerly wanted to know about Mochizuki’s approach.”

For example, Dimitrov showed in January how, assuming the correctness of Mochizuki’s proof, one might be able to derive many other important results, including a completely independent proof of the celebrated Fermat’s last theorem.

But the purported proof, which Mochizuki first posted on his webpage in August 2012, builds on more than a decade of previous work in which Mochizuki worked in virtual isolation and developed a novel and extremely abstract branch of mathematics.

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Pass it on: New Scientist

California’s Wildfires Reaches The Pacific Ocean

Firefighters tackling a fast-moving wildfire in southern California have said the blaze has jumped the main coastal highway and reached the Pacific Ocean, US media report.

The fire, which ripped through Ventura County north of Los Angeles, triggered evacuation orders for some 150,000 people and has damaged 150 buildings.

Authorities say some 12,000 structures remain threatened by the fire.

Strong winds are expected to further hinder efforts to contain the blaze.

We are still in the middle of an aggressive and active firefight on the ground,” a spokesman for the Ventura fire department, Robert Welsbie, said.




If the winds pick up, we will face quite a challenge.”

Fire officials said a quarter of a million homes were without power and they feared many more buildings would be destroyed.

It was revealed on Wednesday that the fire had crossed Highway 101, reaching the Solimar Beach area.

The road remains open but local officials have told motorists to take care.

More than 1,000 firefighters have been battling the fires in the cities of Ventura and Santa Paula, some 70 miles (115km) north of Los Angeles.

Residents of Santa Paula and Ventura received mandatory evacuation notices on their phones and from emergency workers going house to house.

The blaze, which has devastated more than 55,000 acres (22,000 ha), continues to be fanned by ferocious Santa Ana winds – which blow in from the California desert – and low humidity.

Winds are forecast reach up to 70mph (115km/h) on Wednesday and remain strong throughout the week.

The Ventura County fire is believed to have broken out close to Thomas Aquinas College in Santa Paula at some time after 18:00 on Monday (02:00 GMT Tuesday).

The authorities have warned of widespread smoke and advised people with health conditions, the elderly and children to stay indoors in affected areas.

A separate fire broke out early on Tuesday closer to Los Angeles, in Sylmar.

California has been hit hard by wildfires in recent months. At least 40 people were killed when fires ripped through parts of northern California’s wine region in October.

Some 10,000 structures were destroyed.

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Pass it on: Popular Science

Blockchain: Way More Than Just Cryptocurrency

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You’ve heard of Blockchain, mostly in reference to Cryptocurrencies. But the potential of blockchain goes way beyond that.

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Could Our Milky Way’s Many Brown And White Dwarf Stars Be Home To Alien Life?

The dead and failed stars known as white dwarfs and brown dwarfs can give off heat that can warm up worlds, but their cooling natures and harsh light make them unlikely to host life, researchers say.

Stars generally burn hydrogen to give off light and heat up nearby worlds.

However, there are other bodies in space that can shine light as well, such as the failed stars known as brown dwarfs and the dead stars known as white dwarfs.

White dwarfs are remnants of normal stars that have burned all the hydrogen in their cores. Still, they can remain hot enough to warm nearby planets for billions of years.

Planets around white dwarfs might include the rocky cores of worlds that were in orbit before the star that became the white dwarf perished; new planets might also emerge from envelopes of gas and dust around white dwarfs.

Brown dwarfs are gaseous bodies that are larger than the heaviest planets but smaller than the lightest stars.




This means they are too low in mass for their cores to squeeze hydrogen with enough pressure to support nuclear fusion like regular stars.

Still, the gravitational energy from their contractions does get converted to heat, meaning they can warm their surroundings.

NASA’s WISE spacecraft and other telescopes have recently discovered hundreds of brown dwarfs, raising the possibility of detecting exoplanets circling them; scientists have already observed protoplanetary disks around a few of them.

White dwarfs and brown dwarfs are bright enough to support habitable zones — regions around them warm enough for planets to sustain liquid water on their surfaces.

As such, worlds orbiting them might be able support alien life as we know it, as there is life virtually everywhere there is water on Earth.

An added benefit of looking for exoplanets around these dwarfs is that they might be easier to detect than ones around regular stars.

These dwarfs are relatively small and faint, meaning any worlds that pass in front of them would dim them more noticeably than planets crossing in front of normal stars.

However, unlike regular stars, white dwarfs and brown dwarfs cool as they age, meaning their habitable zones will move inward over time.

The most obvious peril of a shifting habitable zone is that it could result in a planet getting so cold all the liquid water on its surface freezes solid.

There are other dangers, however — as white dwarfs and brown dwarfs cool, the light they give off would change as well, possibly meaning they would end up sterilizing worlds with dangerous, high-energy radiation.

To be specific, extreme ultraviolet rays would break a planet’s water apart into hydrogen and oxygen. The hydrogen can escape into space, and without hydrogen to bond with oxygen, the world has no water and is not habitable.

Such exoplanets would resemble Venus, with dry atmospheres dominated by carbon dioxide.

In addition, because white dwarfs and brown dwarfs are so dim, their habitable zones already start off very near them.

About one-hundredth the distance between the sun and Earth, which is about one-thirtieth the distance between the sun and Mercury.

White dwarfs should tidally heat planets more than brown dwarfs, since white dwarfs are so massive, the researchers noted.

White dwarfs are only about the size of the Earth, but they are remarkably dense, with masses nearly two-thirds that of the sun.

All in all, the scientists found it unlikely that planets orbiting white dwarfs would ever be truly habitable.

When they are young, white dwarfs would blast planets in their habitable zones with ultraviolet rays that would strip the worlds of water.

When they grow older, their habitable zones would shift closer to them, and the amount of tidal heating might also end up desiccating any planets residing in those zones.

Although the chances for life around white dwarfs and brown dwarfs might look slim, they are not zero, the scientists cautioned.

For instance, a planet might drift into the habitable zone of a white dwarf from a more distant orbit long after the formation of that dead star.

It would still have to contend with tidal heating, but it would have avoided radiation that likely would have sterilized its surface.

More research is needed to understand how planets orbiting white dwarfs and brown dwarfs form, and “particularly the amount of water they form with,” Barnes said,  a planetary scientist and astrobiologist at the University of Washington at Seattle

We also need to understand how the high-energy radiation of brown dwarfs evolves with time. This is the energy that can remove water, but we don’t have any idea how strong it can be, and how long it lasts.”

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Pass it on: New Scientist

The Most Distant Supermassive Black Hole Ever Discovered

Scientists searching for astronomical objects in the early universe, not long after the Big Bang, have made a record-breaking, two-for-one discovery.

Using ground-based telescopes, a team of astronomers have discovered the most distant supermassive black hole ever found.

The black hole has a mass 800 million times greater than our sun, which earns it the “supermassive” classification reserved for giants like this.

Astronomers can’t see the black hole, but they know it’s there because they can see something else: A flood of light around the black hole that can outshine an entire galaxy.

This is called a quasar, and this particular quasar is the most distant one ever observed.




The light from the quasar took more than 13 billion years to reach Earth, showing us a picture of itself as it was when the universe was just 5 percent of its current age.

Back then, the universe was “just” 690 million years old. The hot soup of particles that burst into existence during the Big Bang was cooling rapidly and expanding outward.

The first stars were starting to turn on, and the first galaxies beginning to swirl into shape.

Quasars from this time are incredibly faint compared to the nearest quasars, the light from some of which takes just 600 million light years to reach the Earth.

Black holes, mysterious as they are, are among the most recognizable astronomical phenomena in popular science.

They’re pretty straightforward: Black holes are spots in space where the tug of gravity is so strong that not even light can escape.

They gobble up gas and dust and anything that comes near, growing and growing in size. A supermassive black hole sits in the center of virtually all large galaxies, including the Milky Way.

Astronomers can infer their existence by watching fast-moving stars hurtle around a seemingly empty, dark region.

Quasars, meanwhile, are a little trickier to understand, and you’d be forgiven for thinking they sound like something out of Star Trek.

A quasar is, to put it simply, the product of a binge-eating black hole. A black hole consumes nearby gas and dust inside a galaxy with intense speed, and the violent feast generates a swirling disk of material around it as it feeds.

The disk heats up to extreme temperatures on the order of 100,000 degrees Kelvin and glows brightly. The resulting light show is what we call a quasar, and what a light show it is.

The more material a black hole consumes, the bigger it becomes. Eventually, the black hole drains the surrounding area of material and has nothing to eat.

The luminous disk around it shrinks and fades, and the quasar is extinguished.

In this way, quasars—and the black holes that power them—are like volcanoes, erupting under one set of conditions and settling into dormancy under another.

Quasars were first detected in 1963 by the Dutch astronomer Maarten Schmidt with California’s Palomar Observatory.

Astronomers thought these newly discovered points of light were stars because of their extreme brightness.

But when they studied the spectrum of their light, they were stunned to find the “stars” were more than a billion light-years away.

When light travels through space, it gets stretched thanks to the constant expansion of the universe. As it moves, it shifts toward redder, longer wavelengths.

Astronomers can measure this “redshift” to figure out how long the light took to reach Earth, which indicates how far a certain object is.

Schmidt and his fellow astronomers knew that for stars to appear so luminous to Earth from such great distances was impossible. They were dealing with completely new phenomena.

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Pass it on: New Scientist

Budweiser Is Sending Barley To Space In Hopes Of Learning How To Brew Beer On Mars

Budweiser wasn’t kidding about its plans to brew “the first beer on Mars.

After announcing its initiative at the South by Southwest conference in March, Budweiser is reportedly taking its next steps toward accomplishing its out-of-this-world goal by sending beer-making grains, namely, barley — into space later this year.

According to a press release, this December, SpaceX will be delivering the shipment of barley to the International Space Station, where it will remain in orbit for a month.




Once back on Earth, the barley will be analyzed in order to determine how the grain reacts to microgravity environments.

Budweiser’s “innovation team” will also experiment with germinating the exposed barley seeds.

Budweiser is always pushing the boundaries of innovation and we are inspired by the collective American Dream to get to Mars,” said Budweiser Vice President Ricardo Marques in a statement.

“We are excited to begin our research to brew beer for the red planet.”

The company said its efforts might also provide insight on its agricultural practices here on Earth, although it maintained that its foremost goal is to one day supply “a colonized red planet the same enjoyments provided here on Earth.

Budweiser executives originally announced the company’s plans back on March 11 during SXSW in Austin, Texas, at a panel discussion that also included retired astronaut Clayton “Clay” Anderson and actress Kate Mara, of the 2015 film “The Martian.”

At the time, Budweiser also explained the challenges it faced in brewing beer in a Mars-like environment, including limited water resources, limited sunlight for growing hops and atmospheric pressure that would turn traditional beer to “foamy slop.”

Nevertheless, the company vowed to be ready to “toast on Mars” when mankind finally colonizes the planet.

With this bold, new dream Budweiser is celebrating the entrepreneurial spirit in which our iconic brand was founded upon,” said Marques in a press release issued shortly after the initial announcement.

Through our relentless focus on quality and innovation, Budweiser can today be enjoyed in every corner of the world, but we now believe it is time for the King of Beers to set its sights on its next destination.”

“When the dream of colonizing Mars becomes a reality, Budweiser will be there to toast the next great step for mankind.”

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NASA Just Found Our Solar System’s Twin By Using Artificial Intelligent

Searching the stars for unique phenomena is not an easy process.

The problem is that space is simply too big, too diverse, and too wonderful.

Locating a specific kind of anomaly among the many wondrous sights scattered throughout the cosmos is near impossible for humans, without easily-distracted brains.

With so many stars to check, the process of scanning the galaxy to find planets like our own can take a lot of time and effort.

Thankfully, artificial intelligence can help us in the process of spotting distant stars and their neighboring planets.

NASA has announced that, thanks to an AI program that was given the task of spotting cool stuff in space, the agency has been able to find a solar system that looks uncannily like our own; albeit in miniature form.




The Kepler-90 system exists a distant 2,545 light years from Earth, but has drawn attention from the astrological society after an AI noted that its series of eight planets match up well with our own.

The primary difference is that its planets orbit a lot closer to the sun than those in our solar system, with the newly discovered Kepler-90i making a full rotation around the star in a matter of just fourteen Earth days.

In order to locate Kepler-90’s planets NASA’s AI had to scan through a daunting thirty five thousand potential signals from distant stars, over a period of four years.

This is where machine learning was able to come into play to help make the process easier—the AI was fed data from around fifteen thousand signals that NASA had previously investigated.

So the AI had a pretty good idea of what it was looking for based on the kinds of readings that NASA had flagged as noteworthy among the program’s database of reference materials.

From there, it was a simple matter of letting the AI run checks for all potential star systems against its database until the program found something that matched what it was looking for, which happened to be a bunch of newly discovered planets orbiting Kepler-90.

Kepler-90 isn’t actually the most exciting solar system in the galaxy—it’s unlikely that its super hot worlds will bear life, or even any noteworthy new discoveries.

What is special, is the fact that an AI managed to identify Kepler-90 as fitting the right parameters for investigation.

This shows that there really are benefits to employing machine learning as a technique for searching the cosmos for interesting research subjects without the need for a human to slog through thousands of signals in order to find a few interesting stars that warrant a closer look.

Essentially, NASA is building a self-teaching search engine that can trawl through all of our records of the stars to find things that look interesting, based only on a vague description of what scientists are looking for.

The future of space exploration is going to be a whole lot easier if we can trust an artificial intelligence to do all the boring stuff for us.

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Pass it on: New Scientist

Dust Storms That Could Swamp Mars And Threaten Manned Missions Could Strike Within Weeks

James Shirley, a planetary scientist at NASA’s Jet Propulsion Laboratory, Pasadena, California, said: “Mars will reach the midpoint of its current dust storm season on October 29th of this year.

Based on the historical pattern we found, we believe it is very likely that a global dust storm will begin within a few weeks or months of this date.”

The dust storm could cause problems fro exploration of the Red Planet.

The NASA Curiosity rover droid is currently exploring the Martian surface, sending back detailed images of the surface for analysis by scientists and taking samples, and relies on solar power to operate and could be put out of action by severe dust contamination.

A similar dust storm in 2007 stopped two rovers on the planet at the time from working.

A NASA spokesman said: “The most recent Martian global dust storm occurred in 2007, significantly diminishing solar power available to two NASA Mars rovers – Spirit and Opportunity – then active halfway around the planet from each other.




JPL’s John Callas, project manager for Spirit and Opportunity, said: “The global dust storm in 2007 was the first major threat to the rovers since landing.

We had to take special measures to enable their survival for several weeks with little sunlight to keep them powered.”

Each rover powered up only a few minutes each day, enough to warm them up, then shut down to the next day without even communicating with Earth.”

“For many days during the worst of the storm, the rovers were completely on their own.”

There are fears dust storms on Mars could hamper planned missions to Mars by humans.

The spokesman said: “Dust storms also will present challenges for astronauts on the Red Planet.

“Although the force of the wind on Mars is not as strong as portrayed in an early scene in the movie “The Martian,” dust lofted during storms could affect electronics and health, as well as the availability of solar energy.”

Local dust storms occur frequently on Mars.

These localized storms occasionally grow or coalesce to form regional systems, particularly during the southern spring and summer, when Mars is closest to the sun.

On rare occasions, regional storms produce a dust haze that encircles the planet and obscures surface features beneath.

A few of these events may become truly global storms, as is predicted for later this year, and such as one in 1971 that greeted the first spacecraft to orbit Mars, NASA’s Mariner 9.

Discerning a predictable pattern for which Martian years will have planet-encircling or global storms has been a challenge.

But, global dust storms on Mars could soon become more predictable – which would be a boon for future astronauts there – if the next one follows a pattern suggested by those in the past.

The Red Planet has been observed shrouded by planet-encircling dust nine times since 1924, with the five most recent planetary storms detected in 1977, 1982, 1994, 2001 and 2007.

The actual number of such events is no doubt higher.

In some of the years when no orbiter was observing Mars up close, Mars was poorly positioned for Earth-based telescopic detection of dust storms during the Martian season when global storms are most likely.

Shirley’s 2015 paper in the journal Icarus reported finding a pattern in the occurrence of global dust storms when he factored in a variable linked to the orbital motion of Mars.

Other planets have an effect on the momentum of Mars as it orbits the solar system’s center of gravity.

This effect on momentum varies with a cycle time of about 2.2 years, which is longer than the time it takes Mars to complete each orbit: about 1.9 years.

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Pass it on: New Scientist

Planet Nine Could Be Our Solar System’s Missing ‘Super Earth’

Planet Nine is out there, and astronomers are determined to find it, according to a new statement from NASA. In fact, mounting evidence suggests it’s hard to imagine our solar system without the unseen world.

The hypothetical planet is believed to be about 10 times more massive than Earth and located in the dark, outer reaches of the solar system, approximately 20 times farther from the sun than Neptune is.

While the mysterious world still has yet to be found, astronomers have discovered a number of strange features of our solar system that are best explained by the presence of a ninth planet, according to the NASA statement.

There are now five different lines of observational evidence pointing to the existence of Planet Nine,” Konstantin Batygin, a planetary astrophysicist at the California Institute of Technology (Caltech) in Pasadena, said in the statement.




If you were to remove this explanation and imagine Planet Nine does not exist, then you generate more problems than you solve.”

“All of a sudden, you have five different puzzles, and you must come up with five different theories to explain them.

In 2016, Batygin and co-author Mike Brown, an astronomer at Caltech, published a study that examined the elliptical orbits of six known objects in the Kuiper Belt, a distant region of icy bodies stretching from Neptune outward toward interstellar space.

Their findings revealed that all of those Kuiper Belt objects have elliptical orbits that point in the same direction and are tilted about 30 degrees “downward” compared to the plane in which the eight official planets circle the sun.

Using computer simulations of the solar system with a Planet Nine, Batygin and Brown also showed that there should be even more objects tilted a whopping 90 degrees with respect to the solar plane.

Further investigation revealed that five such objects were already known to fit these parameters, the researchers said.

Since then, the astronomers have found new evidence that further supports the existence of Planet Nine.

With help from Elizabeth Bailey, an astrophysicist and planetary scientist at Caltech, the team showed that Planet Nine’s influence might have tilted the planets of our solar system

Which would explain why the zone in which the eight major planets orbit the sun is tilted by about 6 degrees compared to the sun’s equator.

Finally, the researchers demonstrate how Planet Nine’s presence could explain why some Kuiper Belt objects orbit in the opposite direction from everything else in the solar system.

Going forward, the researchers plan to use the Subaru Telescope at Mauna Kea Observatory in Hawaii to find Planet Nine, and then deduce where the mysterious world came from.

The most common type of planets discovered around other stars in our galaxy has been what astronomers call “super Earths” — rocky worlds that are larger than Earth but smaller than Neptune.

However, no such planet has yet been discovered in our solar system, meaning that Planet Nine could be our missing “super Earth,” the researchers said.

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Pass it on: New Scientist

The Best “Lite” Versions Of Your Favorite Android Apps

If you’re looking for a good way to speed up your phone or cut down on your data usage, there are a lot of official “lite” versions of popular apps like Facebook or YouTube.

These are generally less feature-rich than their full-powered counterparts, but they’re often a great middle ground between features and function.

What Are “Lite” Apps?

Big companies like Google, Facebook, and Twitter want as many people as possible using their services. But not all phones are powerful for their full-featured apps, and some data plans are heavily limited.

So, they’ve created “lite” versions of their apps for those audiences.

This is not to be confused with the hundreds of makeshift lite applications out there that are just containerized versions of mobile web sites, the apps on this list are official applications provided by the original developers.




This is an important and noteworthy mention, because there are a lot of “fakes” out there—we recommend using the official lite apps whenever you can.

These official “lite” versions are generally designed for use in countries with less powerful Android devices and slower mobile internet.

They keep the speed up and data usage down by omitting the superfluous features that people on slower connections wouldn’t be able to use anyway.

The Best Lite Apps

Alright, now that you know what lite apps are and why you’d want to use them, it’s time to look at the best options for the apps you’re probably already using.

Facebook Lite

Facebook is one of the most popular apps on the Play Store, but the full app is notoriously big. The primary app is nearly 65MB in size, where the much smaller lite version only tips the scale at a measly 1.6MB. That’s a huge difference.

Facebook Messenger Lite

Similar to Facebook Lite, there’s a lightweight version of Messenger available too.

It’s lacking nearly all of Messenger’s more robust features, like video chat, Facebook calls, SMS integration, and chat heads, but it’s pretty solid if all you want to do is text chat with Facebook friends.

As a result, Messenger Lite is about a fifth the size of the full Messenger app (11MB vs. 55MB).

Twitter Lite

Twitter Lite is arguably the best lite application on this list, as it’s almost as robust as its much larger counterpart.

It’s essentially a packaged version of the Twitter mobile website, which has undergone some major upgrades over the last several months—as a result, you’ll get a killer lightweight Twitter client that offers almost everything you need.

YouTube Go

Look, everyone loves YouTube. But if you’re finding the stock YouTube app to be a bit bulky and slow, YouTube Go is the answer.

It’s super fast and light, and offers some of the better features of the stock app—like the option to save videos for offline viewing.

It even asks what you want to do (save or view) each time you select a video and offers various quality levels. Very cool.

Skype Lite

There are a lot of good video chat apps out there, many of which are arguably better than Skype—but if your grandma uses Skype, you’re stuck using Skype too.

Thankfully, there’s a lite version. This app actually leverages Google Play’s testing feature, as it’s technically an “unreleased” app—at least on an official level.

Like it’s bigger brother, it offers voice and video calling, text chats, and even SMS integration.

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Pass it on: Popular Science