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Even Physics Textbooks Tend to Get Friction Slightly Wrong

Even Physics Textbooks Tend to Get Friction Slightly Wrong

Sometimes you think you have a complete understanding of something and then BOOM—a simple problem throws everything out the window. Let's consider a very basic physics problem involving pushing a block with a frictional force. These kinds of problems are common in introductory physics textbooks—but they often miss some subtle details.

I'm going to go over two fundamental ideas in physics: the momentum principle and the work-energy principle. Let's use these two ideas for some simple physics cases and see what happens. It's going to be fun.

Momentum Principle

The momentum principle says that a net force on an object is equal to the change in momentum (Δp) divided by (Δt), the change in time (the time rate of change of momentum). Oh, momentum (for most objects) can be defined as the product of mass (m) and velocity (v). I'm going to show you this with a 1-dimensional example just so that I can avoid using vector notation (this will keep it simple). Here is the momentum principle (in 1-D):

Rhett Allain

Now let's use this. Suppose I have a very low-friction cart with a constant-strength force pushing on it (in this case, it has a fan mounted on top). Since there is a force, the cart will speed up. Here's what that looks like.

Rhett Allain

We can now use the momentum principle to find the change in speed over some time interval. Here are some mostly real values for the cart above (I made some slight modifications due to measurement errors).

Cart mass = 0.85 kg Fan force = 0.15 newtons Time interval = 3.0 seconds

With the force and the time interval, I get a change in momentum (F × Δt) of 0.45 kgm/s. Dividing this change in momentum by the mass, I get a final speed (assuming it starts from rest) of 0.53 m/s. Yay.

OK, let's do it again. This time with TWO fans. Here is a cart with two equal forces pushing in opposite directions. After turning on the two fans, I give the cart a push so that it moves to the right.

Rhett Allain

In this case, the net force on the cart is zero newtons since the force pushing to the right has the same magnitude as the force pushing to the left. With zero net force, there is zero change in momentum and the cart moves along at a constant speed.

One more case. Suppose I take a box with some masses and pull it along the table at a constant speed. In this case, there is a force pulling to the right (the string) and a frictional force pulling to the left.

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Again, since the net force is zero, there is no change in momentum. Everything is fine.

Work-Energy Principle

This isn't completely new. In fact, you can derive this idea from the momentum principle. The work-energy principle says that the work (W) done on a point mass is equal to its change in kinetic energy. Work is done by a force moving a certain distance. Actually, it's only the force in the direction of motion that matters. As an equation, it looks like this.

Rhett Allain

Here θ is the angle between the force and the displacement. If the force is "pushing backwards" you can have negative work. For the kinetic energy, it depends on the mass and the velocity.

Rhett Allain

OK, let's go back to the fan cart from above. Suppose I want to look at this problem using the work-energy principle instead of the momentum principle. In that case, I need one extra thing—the distance over which the force is applied. From that same fan video, the force pushes the cart over a distance of about 0.79 meters. Now I can calculate the work (the angle is zero degrees) with a value of 0.11 joules. If I set this equal to the final kinetic energy, I can solve for the final velocity and I get 0.528 m/s. Boom. That's essentially the same thing as with the momentum principle.

What about the case with the two fans pushing in opposite directions? In this case, one fan does some work—let's just say it does 0.11 joules. The other fan has the same force for the same distance, but it is pushing in the opposite direc­tion. For the backwards-pushing force, the angle between the force and the displacement is 180 degrees. Since the cosine of 180 degrees is negative 1, the work done by this force is –0.11 joules. That makes the total work equal to zero joules and a change in kinetic energy of zero joules. The only way for that to happen is for the cart to move along at a constant speed. Great.

What about the block being pulled along the table with friction? Again, the two forces are the force from the string pulling to the right and friction pulling to the left. The total work on the block would be zero, and it would move at a constant speed.

BUT WAIT! There is a problem. What if you measure the temperature of this block before and after you pull it? Here are two thermal images—also, I put a piece of styrofoam on the bottom so you could see the temperature change.

Rhett Allain

It's not a huge increase in temperature, but it did indeed warm up. If I slide the block over a larger distance (or back and forth), you can see a bright streak on the surface. That is an area where the table increases in temperature—the block also gets hotter.

Rhett Allain

But if the block gets warmer, that means it increases in energy. In this case, it would be an increase in thermal energy. So, how can the block increase in energy if there is zero work done on the object? That is indeed a mystery. How is it possible for there to be zero work AND an increase in energy.

Here is the answer. You can see this with a different example. Suppose that I rub two brushes together instead of a block and a table. Watch what happens.

Rhett Allain

Notice that as the brush is pulled, there are two forces that do work. My hand does work (positive work), and the brushes do work (negative work). But look closely. Notice that as the brush (and my hand) move to the left a certain distance, the brushes bend. This means that the force the bottom brush exerts on the top brush moves over a shorter distance than the hand moves. Even if the force of the brush is the same magnitude as the force of my hand, the brush does less work because it moves over a shorter distance. That means the total work done on the brush is NOT zero joules but some positive amount.

Of course the brush is an analogy for friction. We like to think of friction as this nice and simple interaction, but it's not. For the block sliding on a table, the frictional force is an interaction between the surface atoms in the block and the surface atoms on the table. It's not so simple. Physics textbooks like to treat a block as a point object—but it is not a point object. It's a complicated object made of countless atoms. In the case of friction, you can't forget that and just treat a block as a point object. It doesn't work.

Work Done by Friction

Let's just be clear. If a physics textbook asks you to calculate the "work done by friction"—just say no. Just say no. You can't really calculate that. Yes, we want to make physics as simple as possible—but not so simple that it gets you into impossible situations like the one with a block sliding at a constant speed.

Oh, but wait. There are quite a few physics textbooks that actually ask about work done by friction. The first book I grabbed had an example that was something like this:

Jake pulls a box with a mass of 22 kg. The rope makes an angle of 25 degrees with respect to the horizontal. The coefficient of kinetic friction is 0.1. Find the work done by Jake and the work done by friction for the case where the box moves along the ground a distance of 144 meters.

Bad. Bad question. You could indeed calculate the force of friction, but you can't calculate the work done (unless you also know some stuff about the changes in thermal energy). If you calculated the work done by friction as the frictional force multiplied by the distance the block moves, how would you account for the increase in thermal energy of the block (and floor)? Oh, but you could do this problem with the momentum principle and it wouldn't be a problem. Remember that the momentum principle deals with forces and time, not distance. So even though the frictional force acts over a different distance, the time is the same for both the frictional force and the force pulling the string.

What Then?

Then what are we to do? If we can't do work done by friction, how are we supposed to teach physics? Well, here is the problem. The main goal in physics is to build models that agree with real-life experiences. These models could be a big idea like the work-energy principle—and that's great. Let's consider an example with another model. What about a globe? It's a model of the Earth. It even shows the location of the continents and everything. But what if I want to use this globe and measure its mass and volume so I can determine the density of the real (full-sized) Earth? That wouldn't work, because the globe isn't actually Earth. The same is true with the work-energy principle. It's great for some things, but you can't just use it wherever you like.

Finally, let me point out that I only know about these problems with work and friction because of my good colleagues Bruce Sherwood and Ruth Chabay (yes, the authors of my favorite physics textbook, Matter and Interactions). It was during an informal side conversation at the recent meeting of the American Association of Physics Teachers (AAPT). Honestly, there are so many educators at this conference that have a huge impact on the way that I think about physics. It's always great to see them.

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Original author: Rhett Allain
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The Smart Prison Initiative Pairing Inmates With Rescue Dogs

The Smart Prison Initiative Pairing Inmates With Rescue Dogs

In 2016, the California City Correctional Facility in the western edge of the state's Mojave Desert launched a pilot program that paired inmates, many of them convicted of violent offenses, with rescue dogs. Under the supervision of volunteers from Marley's Mutts, a California dog rescue group, the inmates worked together to train the dogs so that, at the end of the two- to three-month program, they could be adopted by forever homes. The pilot, known as Pawsitive Change, proved wildly successful and has since expanded to other prisons around the Golden State.

"The inmates want so badly to get into the program," says LA-based photographer Shayan Asgharnia, who spent several months documenting the training sessions in 2017. "It gives them a sense of purpose." Asgharnia, best known for his psychologically acute celebrity portraits, maintains a sideline in photographing rescue dogs, which is how he first heard about Pawsitive Change. After receiving permission to shoot inside the prison, he began driving two hours to and from California City every Tuesday.

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Inside the prison walls, he witnessed a series of remarkable transformations. "When the dogs come in, they're like some of the inmates," Asgharnia says. "I remember one that was just terrified of everything—super skittish, wasn't able to cope with any kind of human. It went in there, and with patient training and love, those inmates were able to turn the situation around." Training the dogs allows—in fact, requires—the men to express their emotions in ways normally discouraged behind bars.

Some of Asgharnia's most powerful photographs were taken after the "graduation" ceremony in which the inmates had to say goodbye to their dogs. "These guys are living with them for 10 weeks, 12 weeks, and have to let them go," he says. "It's heartbreaking." Although most dogs come from high-kill shelters in the US, some have been rescued, via Marley's Mutts, from as far away as China and Asgharnia's native Iran. When it comes to inmates selected for the program, the only disqualifying factors are convictions for sex offenses or violence against animals.

In addition to improving their interpersonal skills, Pawsitive Change provides inmates with valuable career skills—a number of participants go on to work as professional dog trainers after their release. "I do believe people have the capacity to change," Asgharnia says. "The prison system is deeply flawed, but I'm thankful this program is giving people a second chance. Because nobody else is doing that."

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Original author: Michael Hardy
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Apple Puts the AR in 'Art' (and in 'Transparent Sky-Being')

Apple Puts the AR in 'Art' (and in 'Transparent Sky-Being')

Thanks to a hot desert air mass stalling over San Francisco, the sky was a fogless blue, which made the words stand out even more as they floated upwards past St. Patrick Church in downtown San Francisco. White and uppercase, they rose in perfectly justified blocks, the voice of artist and poet John Giorno intoning them in my headphones: "A vast dome of blue sky / and your mind / is an iron nail in between." On and on, the uppermost words breaking up and floating away, a Star Wars crawl of Buddhist introspection.

It was breathtaking for its scale—each word was dozens of feet high—yet the lunchtime crowds in Yerba Buena Gardens didn't even notice. The only people who seemed as rapt as I was, in fact, were the three who were pointing an iPhone XS Plus in the same direction I was and wearing Beats headphones identical to mine. All that Apple was no coincidence: Giorno's piece, Now at the Dawn of My Life, was one of six pieces in the company's [AR]T Walk, an augmented-reality public art walking tour that launched this week.

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AR, in which virtual objects are integrated into your real-world surroundings, has been embraced by museums and artists (conventional and guerrilla) dating back nearly a decade, and AR- and VR-specific exhibits have been popping up with ever more regularity. Much of that is because AR is easier to build and implement than ever before: Android and iOS feature AR development toolkits that have improved significantly since their 2017 introductions, and Facebook turned its Camera Effects platform into a similar toolkit called Spark AR.

But while all three of those systems—along with wearables like Microsoft HoloLens and the Magic Leap One—have been used to create virtual art in real-world galleries, moving outside those confines and into public spaces has been a more difficult proposition, in no small part because of the challenge of presenting a consistent experience for all users. (More on that in a bit.) The two-hour [AR]T Walks, developed in partnership with the New Museum in New York City, may only be available at six of the more than 500 Apple Stores around the globe, but in scope and scale they're wildly ambitious, a deployment of AR that's all but unprecedented outside the world of games.

Each of the walks features the same six pieces, which artists developed with New Museum over the course of a year; the only difference is the cityscapes housing them. For the Walk leaving from San Francisco's Union Square store, groups venture first down car-free Maiden Lane, where they experience a piece from Chicago artist Nick Cave. (No, not that Nick Cave.) Known for his wearable "soundsuits" that shroud their wearers' identifying characteristics, Cave uses AR to refashion the idea completely. On the phone screen, you're presented with a swirling virtual soundsuit that you follow down the street, tapping and swiping at it to see how it reacts. It's cute, if not mindbending—until you reach the end of the street to find an enormous transparent being perched atop a building, hoovering up those soundsuits to clothe itself in their patterns.

The finale of Nick Cave's Soundsuits, as seen from inside New York's Central Park.


The result, as with the best of the pieces in the process, hinges on some painstaking procedural hygiene. Two employees from Apple's in-store events staff—Today At Apple, as it's known—lead each group. One carries an iPad that controls the private [AR]T Walk app on the Apple-furnished XS Pluses attendees use; the other acts as a behavioral model, demonstrating at each location exactly how to trigger the AR experience.

About that: If you're going to create a good shared persistent AR experience—shared meaning it's visible to anyone in that specific location, and persistent meaning it can be seen on multiple visits to that location—you need a coordinate system so that the AR elements always show up in the same place. Think of it as a three-dimensional version of the origin point in a Cartesian plane, where the X and Y axes cross. Once your phone registers that it's looking at the anchor, it can then layer in all the AR elements in their proper places based on that starting position.

Even then, things can go wrong. Take this unrelated AR piece of the late Jeffrey Epstein hovering over the site of a President Trump rally in New Hampshire, which artist Nancy Baker Cahill unveiled this week.

As a piece of political trollery, it's undeniable; as a convincing illusion, less so. It jitters visibly, and seems to have trouble staying anchored to the arena—both immersion-breakers of the highest order.

The [AR]T Walk largely avoids such pitfalls by relying on a preparatory dance at each location. You walk to a very specific area, hold up your phone while facing away from the anchor—usually a sign, which features enough unique high-contrast patterns to be quickly recognizable—and then rotate a full 180 degrees until you face the anchor. The whole thing feels very Apple: incredibly polished and incredibly stable, as long as you did things exactly the way Apple told you to.

The other pieces, distributed throughout three locations covering about a mile and a half of walking, range from the whimsical to the bleak. In Cao Fei's Trade Eden, a labyrinthine series of conveyor belts ferrying unmarked boxes appears in a plaza, distilling global trade into a fantastical display of futility. Nathalie Djurberg and Hans Berg's This Is It uses a series of midair speech balloons to beckon attendees through a grove of trees, until finally unveiling a cautionary tale seemingly hidden inside a tree.

Peter Rubin writes about media, culture, and virtual reality for WIRED.

Meanwhile, over the course of the walk, an entirely different form of art emerges. A half-dozen people walking through public places, clustering around seeming nothingness and staring at their phones? It might have been commonplace when Pokémon Go first swept the outdoors in 2016, but it still attracts attention. Apple has made no secret of its AR aspirations, but its slow-drip approach has always targeted users inside the home: placing furniture, playing with Legos. The [AR]T Walks are still a drip—small groups, close supervision, very few locations—but they're also an unmistakably public drip, one that's much closer to a stream than ever before.

Besides, any new technology trying to catch a current into the mainstream needs to feel familiar, or at the very least not alienating—and part of that is acclimating people to unexpected new behaviors. Like selfies. Or taking phone calls in public on near-invisible earbuds. Or even walking through the middle of a crowded park during lunch hour, following a winding path no one else can see.

If you don't happen to live in San Francisco—or New York, Tokyo, Hong Kong, Paris, or London, the other five cities with walks—you're not totally ARsed. All Apple Stores are currently hosting an additional Nick Cave augmented-reality installation, Amass, as well as free sessions where you can learn to build AR experiences using an iPad app.

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Original author: Peter Rubin
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How to Land a Busted Airliner in a Russian Cornfield

How to Land a Busted Airliner in a Russian Cornfield

An airliner crash-landed in a Russian cornfield after a bird strike took out both engines on Thursday afternoon, leaving some of the 233 people aboard with minor injuries, but killing no one (apart from a number of seagulls). The Ural Airlines Airbus A321-100 had just taken off from Moscow’s Zhukovsky International Airport, bound for Simferopol in Crimea, and landed a mere 3.2 miles from the runway.

After the plane landed, the flight attendants deployed the emergency slides and passengers evacuated the cabin. Fifty-five people, including 17 children, were hurt, according to the Russian Health Ministry, but just six required hospitalization for “moderate” injuries.

Ural's flight 178 has already been dubbed the “Miracle on the Ramenskoe,” for the part of Moscow where the plane came down—echoing the 2009 “Miracle on the Hudson,” when a US Airways Airbus A320 lost both engines after taking off from LaGuardia Airport in New York City and landed safely on the river nearby.

Chesley “Sully” Sullenberger and Jeffrey Skiles were at about 2,800 feet when a flock of geese wiped out their power. By contrast, the Ural pilots, Damir Yusupov and Georgy Muruzin, found themselves without working engines at just 750 feet. Rather then try to turn around and get back to the runway, they shut the engines and coasted straight ahead, aiming for the open fields southeast of the airport, which is itself just southeast of Moscow.

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“The best thing is to find a flat spot,” says Pete Field, an aviation consultant and former Navy test pilot. When a jet loses power, the altimeter becomes the fuel gauge, and even in an airliner that’s built to glide, 750 feet is pretty close to empty. Turning around is costly in terms of time and altitude, Field adds, and the pilots were lucky to have an open surface straight ahead, with no tree lines or trenches to worry about. (The Moskva River was to their right, but its winding path wouldn’t have made for an easy touchdown.) Field also says the pilots were wise to leave the landing gear up. On an unpaved surface, the wheels could have sunk into the ground and risked flipping the aircraft.

The Kremlin plans to nominate both pilots for state awards, according to The New York Times, and the Ministry of Agriculture will assess the damage to the cornfield.

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Original author: Alex Davies
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Disney Is Finally Taking On Account Sharers

Disney Is Finally Taking On Account Sharers

Disney and Charter Communications are teaming up to fight account sharing in an attempt to prevent multiple people from using a single account to access streaming video services.

The battle against account sharing was announced as Disney and the nation's second-biggest cable company struck a new distribution agreement involving Disney's Hulu, ESPN+, and the forthcoming Disney+. Customers could still buy those online services directly from Disney, but the new deal would also let them make those purchases through Charter's Spectrum TV service.


This story originally appeared on Ars Technica, a trusted source for technology news, tech policy analysis, reviews, and more. Ars is owned by WIRED's parent company, Condé Nast.

If you buy a Disney service through Charter, be aware that the companies will work together to prevent you from sharing a login with friends. Disney and Charter said in their announcement Wednesday that they have "agreed to work together on piracy mitigation. The two companies will work together to implement business rules and techniques to address such issues as unauthorized access and password sharing."

In addition to streaming services, the deal will let Charter continue carrying Disney-owned TV channels on its cable service. That includes ABC, the various Disney and ESPN channels, FX, National Geographic, and more.

"This agreement will allow Spectrum to continue delivering to its customers popular Disney content, makes possible future distribution by Spectrum of Disney streaming services, and will begin an important collaborative effort to address the significant issue of piracy mitigation," Charter Executive VP Tom Montemagno said.

The announcement didn't say exactly how the companies will fight account sharing. We asked Charter for technical details on how it'll work and about whether this will result in more personal customer data being shared between Charter and Disney. Charter did not answer any of our questions, saying, "we don't have details to share at this time."

We sent the same questions to Disney and will update this article if we get any answers.

Charter CEO complained about account sharing

The crackdown could target people who use Charter TV account logins to sign into Disney services online. Charter CEO Tom Rutledge has complained about account sharing several times over the past few years while criticizing TV networks for not fully locking down their content.

"There's lots of extra streams, there's lots of extra passwords, there's lots of people who could get free service," Rutledge said at an industry conference in 2017. He argues that password sharing has helped people avoid buying cable TV. ESPN has also complained about account sharing, calling it piracy.


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Another possibility is that Charter could monitor usage of its broadband network to help Disney fight account sharing. For example, Disney could track the IP addresses of users signing in to its services, and Charter could match those IP addresses to those of its broadband customers. Charter has plenty of leeway to share its customers' private browsing data because the Republican-controlled Congress eliminated broadband privacy rules in 2017.

Customers could use VPN services to attempt to avoid detection, though.

Charter has 15.8 million residential TV customers nationwide, making it the second-biggest cable TV service after Comcast. But it lost 400,000 video customers in the past year. Charter's broadband service has gone in the other direction, rising from 23.1 million to 24.2 million residential customers in the past year.

In contrast to Charter and Disney, Netflix and HBO haven't cared as much about account sharing.

Netflix and HBO take less strict approach

Sharing a Netflix account "with individuals beyond your household" does violate Netflix's terms of use, but the restriction isn't heavily enforced. "Password sharing is something you have to learn to live with, because there's so much legitimate password sharing, like you sharing with your spouse, with your kids," Netflix CEO Reed Hastings said in 2016.

Now-former HBO CEO Richard Plepler once said that password sharing is a "terrific marketing vehicle for the next generation of viewers" and that "we're in the business of creating addicts." (Plepler left HBO in February, less than a year after AT&T bought HBO owner Time Warner.)

Netflix, HBO, and the Disney-owned Hulu all limit the number of concurrent streams on each account, however. That doesn't prevent account sharing entirely, but such a policy can make it inconvenient to share an account with a bunch of friends.

This story originally appeared on Ars Technica.

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Original author: Jon Brodkin, Ars Technica
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What Does Amazon's 'Top Brand' Badge Actually Mean?

What Does Amazon's 'Top Brand' Badge Actually Mean?

Amazon’s biggest asset can also be a headache for its customers. The so-called “everything store” really does sell almost any item consumers might want, but it’s often cumbersome and time-consuming to sort through them all. To avoid “choice overload,” the retail giant has come up with certain signals designed to help people distinguish high-quality products from the rest. They include star ratings and product reviews, as well as “Amazon’s Choice,” a mysterious badge bestowed on some individual items, which has recently become the subject of scrutiny from lawmakers. Now Amazon is testing a new signifier, called “Top Brand.” But no one seems to know what, exactly, a “Top Brand” is, and Amazon won’t say.

Amazon has long given customers the ability to search by “Top Brands,” but the products previously weren’t distinguished by a special badge in search results. Now, if you search for “swimming goggles,” for instance, Amazon may return several pairs from Speedo whose photos bear a “Top Brand” badge. Here’s the weird part: The longstanding “Top Brands” search filter isn’t quite the same thing as the newer “Top Brand” badge. Here’s an example: If you look up “women’s belts” on Amazon, and filter for “Top Brands,” you may notice that not all of the results actually receive the Top Brand badge. How can a company be a Top Brand in one sense, but not in another?

Louise Matsakis via Amazon

Amazon says the discrepancy exists because the Top Brand badge is only a feature within Amazon Fashion, the part of its website dedicated to clothes, accessories, and luggage, while the Top Brands search filter is available across the entire marketplace. It makes sense for Amazon to try out this new badge feature specifically for fashion, since consumers are generally brand-conscious when shopping for things like handbags and shoes. But since not all women’s belts are within the fashion category, they’re not eligible for the Top Brand badge, even though Amazon might consider them to be Top Brands generally. Confusing, right?

Louise Matsakis via Amazon

At this point in the story, you may be wondering: What even is a Top Brand? Are Top Brands selected by humans? Or is the metric controlled by an algorithm? Amazon, for its part, says the Top Brand badge simply highlights brands that customers love, but did not go into any further detail about how that's determined.

WIRED reached out to four Amazon experts to ask about the logic behind the preexisting Top Brands filter, including two former employees, and they each had different explanations. Fred Dimyan, the CEO of Potoo Solutions, a firm that consultants with ecommerce companies, says Amazon takes two factors into consideration when awarding the honor: the amount of products a brand sells and how many different products they offer in the first place. In other words, companies that make a narrow range of goods, but sell a lot of them, are likely to be Top Brands. Dave Bryant, an Amazon seller and blogger, thinks the distinction might be related to customers’ overall purchase satisfaction, which can include metrics like how often people returned items.

Louise Matsakis covers Amazon, internet law, and online culture for WIRED.

James Thomson, a former Amazon employee and a partner at Buy Box Experts, a firm that consults with independent Amazon sellers, says Top Brands likely have high sales volumes and high conversion rates, meaning a lot of people who look at their product listings ultimately choose to buy from them. Chris McCabe, another former Amazon employee who now consults with Amazon sellers at eCommerceChris.com, says Top Brands are the highest revenue-earning items in a certain category. Every expert agreed that “Top Brand” is not a promotional title companies can pay to display on their Amazon product listings.

At least anecdotally, Top Brands look to encompass household names you might find in a mall, like Steve Madden, Oakley, Under Armour, and IZOD. That might be the point: to flag the names you’re already familiar with from shopping in brick-and-mortar stores, so it’s easier to purchase something quickly from a trusted company. “I wouldn’t be surprised if the idea is to make this function like being verified on social platforms,” says Juozas Kaziukénas, founder of the ecommerce intelligence firm Marketplace Pulse, who first alerted WIRED to the Top Brand badge. But there are also lots of unknown companies with the Top Brand distinction, and every one of Amazon’s in-house labels appears to be designated a Top Brand, too.

After WIRED reached out to Amazon for this story, something strange happened. Many of the Top Brand badges that had been present in search results WIRED conducted disappeared, including in an incognito browsing window on several different computers, browsers, and phones. Amazon says because the feature is a test, it may not always be visible.

US lawmakers have begun scrutinizing how Amazon evaluates the goods for sale in its sprawling marketplace using signals like Top Brand. On Monday, Senator Bob Menendez and Senator Richard Blumenthal, both Democrats, sent a letter to Amazon CEO Jeff Bezos asking for a “detailed explanation” about how the Amazon’s Choice badge is awarded, after a Buzzfeed investigation found it was sometimes given to what appeared to poor-quality items. Democratic presidential candidate and Massachusetts senator Elizabeth Warren has also expressed concern that Amazon may favor items from its own house brands over those from competitors. And the Department of Justice and Federal Trade Commission each recently announced they are looking at the business practices of online marketplaces, including Amazon specifically.

In a statement, a spokesperson for Amazon didn’t respond directly to the senators’ letter. The company instead highlighted its efforts to detect fake product reviews, and said it believes that 90 percent of inauthentic reviews are computer-generated.

Opaque features like “Top Brand” serve as a reminder that Amazon isn’t a traditional retailer, despite the fact that it often wants to look like one to consumers. It’s an enormous marketplace where millions of independent merchants from around the world sell their goods. Amazon needs not just to combat bad actors but also steer customers toward the brands it knows they’re likely to be happy with, or risk them getting overwhelmed and going somewhere else. The hard part for Amazon, like every online platform, is figuring out how to manage the chaos without taking full responsibility for the consequences of its management choices.

Is there something about Amazon you think we should know? Contact the author at This email address is being protected from spambots. You need JavaScript enabled to view it. or via Signal at 347-966-3806.

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Original author: Louise Matsakis
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The Serious Money Is Warming to Bitcoin

The Serious Money Is Warming to Bitcoin

There’s an arms race afoot over who can store cryptocurrency safest. Perhaps you’d like your bitcoin buried in a vault under a mountain in the Swiss Alps? Xapo has offered that as a service to wealthy investors, for free. Coinbase, best known for its popular cryptocurrency exchange, prefers elaborate key-printing rituals along with a Faraday cage. Anchorage, an Andreessen Horowitz-backed startup, promises easy-access digital storage with some cryptographic voodoo. And now old-school firms like Fidelity and Bakkt, which shares an owner with the New York Stock Exchange, are jumping into the fray with storage solutions of their own.

The aim behind all these sophisticated security arrangements: wooing Wall Street.

Gregory Barber covers cryptocurrency, blockchain, and artificial intelligence for WIRED.

A key property of crypto is that it’s proven a pretty dang easy target for thieves. Whether it’s North Korea hammering crypto businesses around the world or an exchange founder absconding with cash, vulnerabilities are abundant. For the crypto industry, that’s not a good look, especially when it comes to institutional investors—pensions and hedge funds and university endowments—for whom there are major consequences when breaches occur. For them, it’s not just a good idea to nail down the furniture, it’s the law.

This week, the still-fringe world of crypto custody saw a spike in activity. Late Thursday, Coinbase’s custody arm purchased the institutional business of rival Xapo for a reported $55 million. The deal wasn’t a surprise, following reports this spring that Coinbase had outbid Fidelity Digital Assets, which started offering custody to clients in March. Then on Friday, Bakkt announced that it had received approval to offer bitcoin futures in September, following months of regulatory delays.

So is crypto the next big thing in institutional investment, or is this fighting over scraps? For now, crypto custody still involves a relatively small pool of money. Coinbase got a boost earlier this month when Grayscale Investments moved its $2.7 billion worth of crypto funds from Xapo to Coinbase, more than doubling the company’s assets under custody. That’s tiny compared with the trillions under management for a company like Fidelity. Custody competitors like Palo Alto, California-based BitGo have reportedly been circling for Xapo’s other clients.

Still, companies like Coinbase and Fidelity think there’s room for growth. In May, Fidelity released a survey of more than 400 institutional investors that found 22 percent already held cryptocurrency, and another quarter saw potential to do so.


The Serious Money Is Warming to Bitcoin

The WIRED Guide to Bitcoin

The companies point to the recent surge in bitcoin’s price as a sign that investors are warming up to crypto. Fundamentally, nothing has changed since late 2017, when the price of bitcoin spiked to nearly $20,000, driven mainly by hysteria. It’s still backed by nothing and managed by no government; it’s still dominated by a select set of mining pools, based mainly in China. Now, though, there’s a more sophisticated economy being built around crypto, says John Sedunov, a professor of finance at Villanova University. In February, JP Morgan announced it would start a coin of its own. Then in June, Facebook announced its Libra cryptocurrency with the backing of large consumer tech companies like Uber and Spotify. New vehicles like futures contracts offer investors, who might’ve balked at an asset with price shocks that come out of nowhere, more of a buffer.

Another interpretation is that bitcoin is increasingly seen as a way to hedge against uncertainty, notes Sedunov. While volatility means that it’s not a safe harbor, like gold or the Swiss franc, it is a potential hedge when nations take up arms in a global trade war. “There’s uncertainty in where we’re heading, and that makes cryptocurrency more attractive,” he says. The better custody arrangements are another draw, he suggests, making it more appealing for institutional investors who could potentially store hundreds of millions of dollars worth of digital assets.

Original author: Gregory Barber
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Back-to-School Sales for 2019: Best Tech Deals We Could Find

Back-to-School Sales for 2019: Best Tech Deals We Could Find

The air is cooling, the days are getting shorter, and the school-goers among us are returning to their desks and carrels kicking and screaming. Don't fight the inevitable—instead, get prepared with our favorite weekend deals on laptops, phones, and more to keep you, or your kids, connected and productive. And when you find yourself with downtime while you ignore your homework? Don't worry, we have a few picks for you there, too.

Note: When you buy something using the retail links in our stories, we may earn a small affiliate commission. Read more about how this works.

Laptops, Phones, and Accessories Deals

LG G8 ThinQ


TI-84 Plus Graphing Calculator for $88 ($28 off): If a class requires you to have a graphing calculator, it's because you're really going to need it. Let this deal be a little bit of a balm for your initial sticker shock. (And don't worry, you can totally play games on it.)

LG G8 ThinQ 128 GB Unlocked for $500 ($350 off): This is a great phone, and even better at a low price. It's also got fancy gesture controls, if you're into that. Just make sure to get a case with it. It can be a little slippery.

Microsoft Surface Laptop 2 (Intel i5, 8 GB RAM, 128 GB) for $799 ($200 off)): We like the keyboard and battery life of this ultralight laptop, but thought it was a tad on the expensive side. Now's a great chance to get it for a more reasonable price.

Lenovo Yoga 730 15.6-Inch Touchscreen Laptop for $650 ($200 off): We really like this bendy laptop's big sibling, the C930. This is a more middle-of-the-road option, but the $200 price cut makes it a solid bargain. Just make sure you get one that has an actual keyboard.

SanDisk 1 TB Portable USB SSD for $167 ($150 off): If you need external storage, chances are you need it to be portable, too. This slim solid state driver has a ton of space and can fit right in your pocket.

Apple iPad 128 GB for $329 ($100 off): It can be tricky to figure out which iPad you should actually buy, but the extra storage on this one makes it a great pick. Apple Pencil support and long battery life make this a decent laptop substitute.

Audio, Home, and Camera Deals

Bose QC35 II


Bose QC35 II Wireless Noise-Canceling Headphones for $299 ($50 off): Whether you're riding the bus or trying to get some much needed shut-eye in a dorm, it's nice to be able to drown out the sound of everything but what you want to hear. These are some of our absolute favorite wireless headphones, even if they are a little bulky.

JBL Charge 4 Portable Speaker for $120 ($30 off): Sometimes you want to blast your music for everyone else to hear, too. With 20 hours of battery life and a waterproofed exterior, the Charge 4 prepares you for that underwater dance party you've been wanting to throw. It isn't on our list of Best Bluetooth Speakers, but we've used it and like it a lot, especially its ability to network with other JBL speakers.

Digital Microscope with Flexible Arm Observation Stand for $34 ($6 off): Get a closeup view of the micro universe with this handy digital microscope. It works with Windows, Mac, and Linux. Make sure to check the coupon box below the price in order to get the discount.

Sceptre 50-Inch 4K TV or $210 ($190 off): Upgrade from your high-def to ultra-high-def on the cheap with this 4K TV. The sound might not be the best, but it's about on par with other modern TVs. Luckily, a good soundbar is pretty affordable.

Ampulla Bedside Lamp, Bluetooth Speaker, Wireless Charger for $90 ($50 off): Here's a strange one. We haven't tried this lamp, but we want to now. This hybrid bedside table is supposed to charge your phone, dim your lights, and blast your music. Just maybe don't balance a glass of water on there. It's available at Amazon, as well.

Fujifilm Instax Mini 70 Instant Camera for $50 ($13 off): This is our pick for the best value in instant cameras. On sale, it's a no-brainer, and available in several colors, all of them rad.

Canon Pixma iP110 Portable Photo Printer for $149 ($100 off): It's all about the form factor here. This slim color printer will be a slick fit in a dorm or classroom. It's also on sale at Amazon.

Back-to-School Sales Around The Web

Don't see something you need? Check our back-to-school sales from a few of our favorite retailers:

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Original author: WIRED Staff
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A Heroic Plane Landing, Instagram's New Fact Checkers, and More News

A Heroic Plane Landing, Instagram's New Fact Checkers, and More News

A gull strike forced a Russian airliner to land in a cornfield, Instagram is getting into the fact-checking game, and new technology is catching lightning from afar. Here's the news you need to know, in two minutes or less.

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Today's Headlines

A pilot landed a busted airliner in a Russian cornfield

After a flock of seagulls took out both engines of a Russian airliner at a mere 750 feet on Thursday, the pilots crash-landed it in a cornfield. Call 'em Russian-Sullys. What is now being dubbed the “Miracle on the Ramenskoe" left 55 of the 233 people on board with minor injuries, but no fatalities.

Instagram now fact-checks, but who will do the checking?

Instagram users in the US can now report content they believe is false, which sounds great in theory, but what's not actually clear is how the process will work. After all, parent company Facebook has already struggled with fact checking on its main site. The company hopes to use human fact checkers to train AI to do the process in the future, but those solutions are still a long way off.

Fast Fact: 6,000 miles

That's how far away new triangulation technology can be and still pinpoint a lightning storm, like the rare one that happened in the North Pole this past weekend. The technology is relatively new, but it gives weather experts brand new information on how lightning works in earth's rarest-seen corners.

WIRED Recommends: Adobe Fresco

iPad Artists: Don't brush off Adobe's new product—Fresco—just yet. Maybe you've been hoping for more capabilities from your iPad, or maybe you haven't dusted that thing off in awhile. Either way, here's how to get back in touch with your creative side with this new app.

News You Can Use

Here's how to share and store all your photos in the cloud.

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Original author: Alex Baker-Whitcomb
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Best Gaming Mouse for 2019 (WIRED Tested, Wireless, Cheap)

Best Gaming Mouse for 2019 (WIRED Tested, Wireless, Cheap)

Whether you're into esports or casual fragging, these are the greatest gaming mice we've tested.

Picking a gaming mouse is a very personal endeavor. Everyone's hands are different, everyone's preferences and needs are different, and we all play different games. That's why we're lucky to live in the golden age of gaming mice, with major manufacturers pouring engineering muscle into one-upping each other. The result is a market loaded with high-quality, yet relatively inexpensive, gaming mice. I've tested most of them. While I can't tell you which mouse is right for you, I can give you a few recommendations. So, here they are: The best gaming mice for every kind of gamer. Be sure to also read up on our favorite gaming headsets and keyboards.

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Ryan King/Getty Images

Original author: Jess Grey
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When Tech Moguls Act Like Galactic Overlords

When Tech Moguls Act Like Galactic Overlords
In Max Gladstone's new novel *Empress of Forever*, technology controls everyone.
Original author: Geek's Guide to the Galaxy
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VW's ID Buggy Is an Electric Dune Dominator

VW's ID Buggy Is an Electric Dune Dominator

In the race toward electrification, some car companies are more motivated than others. Take Volkswagen: Still reeling from the fallout of its Dieselgate scandal, the German giant’s various arms are announcing, developing, and trying to sell EVs at a dizzying pace, from Audi’s E-Tron SUV to Porsche’s Taycan, to a slew of VWs in the pipeline. And funnily enough, VW’s rush to the future has put me a bit back in time, and into a dune buggy.

This swoopy green sand machine, called the ID Buggy, isn’t destined for production, unlike VW’s revived-as-electric Microbus. The concept’s mission is to prove the flexibility of VW’s Modularer E-Antriebs-Baukasten, or MEB, or modular electric car platform. The idea is to that, like the old Beetles enthusiasts turned into dune buggies, today’s electrics can become just about anything.

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A few months after showing the concept at the Geneva Motor Show, VW brought the ID Buggy to Monterey Car Week, perhaps the year’s greatest event for automotive enthusiasts. Sadly, my drive was short, speed-limited, and restricted to pavement, due to the Monterey’s anti-fun ordinances and the fact that this is still a concept car and not quite ready for full-on dune bashing. But it was nevertheless revealing about the potential—and limits—of future EV manufacturing.

“We wanted to know how make electromobility more popular, and one of those solutions became allowing third-party manufacturers to license the platform,” says Jochen Tekotte, VW’s communication director for its electrified models. “In the 1960s people took the Beetle and built onto it, including most famously dune buggies like the Meyers Manx.”

The ID Buggy's 228 pound-feet of torque and 201 horsepower are plenty to spin up some dirt—or sand.

Eric Adams

The Manx, created by Bruce Meyers, saw high-profile action in Steve McQueen and Elvis Presley films, and became a staple of California car and beach culture. Volkswagen recently commissioned a new one for themselves from Meyers. The small, gas-powered, open-top ride had a four-speed manual transmission directing power from the Beetle engine to the rear wheels. Driving it up and down 17-Mile Drive in Monterey was a thrill. Steering was mushy at best, the transmission felt suicidal, and the wipers didn’t so much move a molecule of mist from the windshield. But it was light and small and quick, and it felt magnetically drawn to the nearby, woefully off-limits dunes. Then it was time to drive VW’s electric version.

The ID Buggy pulls away smoothly and silently, and rips briskly up to 25 mph. That was enough to motor down the road at a comfortable casual pace, and the 228 lb-ft of torque from the 150 kW, 201-hp motor was enough to spin up some dirt when mashing the pedal from a stop. Steering felt precise and silky, aided by the car’s powerful electric motors. The waterproof interior is roomy and comfortable, the controls an exercise in minimalism. The foot pedals have familiar digital-media symbols representing their respective functions—press “play” to go, “pause” to stop. It’s also fully weather-sealed and ready to go splashing through the surf.

The connection to the Manx is mostly in spirit. The original buggy is a high-riding off-roader that weighs around 1,500 pounds, built on the cheap using the chassis, engines, and other components from the Beetle. Agile and durable, they’re renowned for their fun, energetic vibes. The ID Buggy weighs around 4,400 pounds, thanks to its battery and all the structural hardware required to make modern cars safe. Still, it can shoot up to 62 mph in a respectable-enough 7.2 seconds and drive for a full 155 miles on a single charge. A production version matching these specs could top out at 99 mph.

But that spirit of fun remained, thanks to the smoothness, the open-air aura, a suspension engineered for off-roading, and its responsiveness. The ID Buggy more or less looks the part, and anyway, the only one who can build a true electric Manx is probably Meyers Manx Inc., itself.

Which is fine, because the point of this exercise isn’t to rebirth the Manx but to show that that the MEB electric platform on which this concept is built can fit any number of applications, including a slightly bloated but still fun dune buggy. Want to replicate the looseness of rear-wheel-drive? Flip a switch. Want to bail yourself out of trouble on the trail? Hit all-wheel-drive. Ultimately, there might be a day when electrics become as heavily customized as similarly versatile cars were in the ’60s and ’70s.

So while VW has no immediate intention to produce the ID Buggy itself, it is hoping aftermarket builders might take on the challenge of customizing the MEB Platform. It’s already gaining some traction in this respect: Ford just licensed the platform to build a small EV for its European market. No word yet on whether it’ll be any fun.

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Original author: Eric Adams
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Facebook's Voice Transcripts Were More Invasive Than Amazon's

Facebook's Voice Transcripts Were More Invasive Than Amazon's

The tail end of the Defcon hacking conference this week saw a remote car-start dongle and app that could have been hacked to steal cars, along with a drone hacking a smart TV. Oh, also, researchers have found a way to decrypt ubiquitous GSM calls. And common devices all around us can have their speakers manipulated to become acoustic cyber-weapons. You know, the usual.

Meanwhile, Microsoft announced this week that it has found and patched a set of new Remote Desktop Protocol vulnerabilities, including two that could be used to spread worms worldwide, similar to the recently patched BlueKeep vulnerability. The classic massively multiplayer online game Second Life is riddled with security vulnerabilities, according to a new lawsuit. And Facebook is sharing more about an internal tool it built to hunt for bugs quickly in its 100 million line codebase.

Oh, and one more warning. Do not reserve a "NULL" vanity plate thinking you're being clever. You could end up with thousands of dollars of glitch-induced tickets.

And, of course, there’s more. Every Saturday, we round up the security and privacy stories that we didn’t break or report on in-depth but which we think you should know about nonetheless. Click on the headlines to read them, and stay safe out there.

Facebook Contractors Transcribed Audio From Messenger Chats

Facebook has been using contractors to transcribe audio clips users send each other through its Messenger communication platform. Bloomberg reported Tuesday that the third-party transcribers working on the project didn't know where the audio came from or what it was being used for. Facebook said it has paused human review of the audio, which was being used to check AI analysis of the audio messages.

For months now, revelations have emerged that every major smart assistant developer (Amazon, Apple, Google, Microsoft) uses or has used contractors to transcribe snippets of user audio for quality control and to improve the accuracy of their products. But the news about Facebook has an additional element, since the audio doesn't come from users giving commands to a smart assistant, but from actual human to human communications. On Wednesday, Facebook's main European Union regulator—the Irish Data Protection Commission—opened a probe to evaluate the legality of the practice.

Court Documents Allege Capital One Hacker Stole Data From More Than 30 Institutions

The alleged Capital One hacker, Paige A. Thompson, may have also pilfered data from more than 30 victim companies, as was previously rumored based on Thompson's publicly available online activity. "The servers seized from Thompson’s bedroom during the search of Thompson’s residence, include not only data stolen from Capital One, but also multiple terabytes of data stolen by Thompson from more than 30 other companies, educational institutions, and other entities," prosecutors wrote in court documents. "That data varies significantly in both type and amount." Most of the other stolen data doesn't seem to specifically contain people's personally identifying information. Prosecutors said that they intend to add charges based on this evidence, and that Thompson has a history of threats to harm herself and others.

Dating Apps Can Be Manipulated to Provide Users’ Locations

The popular dating apps Grindr, Romeo, Recon, and 3fun have vulnerabilities that would allow an attacker to determine a user's exact location. Researchers from the security firm Pen Test Partners published findings this week that an attacker would just need a person's username to track them. The researchers created a service that feeds made-up latitude and longitude data to the apps' public application programming interfaces, which can then be induced to return distance data about how far a user is from that random point. By triangulating these distance returns, the system can determine where the user is. Some of the services made changes in response to the Pen Test Partners findings, but some, like Grindr, did not respond to the firm. The researchers also found other data exposures in some of the apps, like photo and personal data leaks.

New Bluetooth Attack Undermines Encryption During Pairing

A new vulnerability and corresponding exploit of Bluetooth could allow an attacker to determine the encryption keys used during device pairing and let themselves in on the party. Dubbed "Key Negotiation of Bluetooth attack" or "KNOB," the hack would put attackers in a position to surveil or manipulate data moving between paired devices. The issue was announced through a coordinated disclosure by a large consortium of tech companies and industry groups. The Bluetooth and Bluetooth Low Energy standards have been criticized for introducing potential security issues as a result of their complexity.

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Original author: Lily Hay Newman
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A Brief History of Vanity License Plates Gone Wrong

A Brief History of Vanity License Plates Gone Wrong

This week, WIRED looked into the plight of Joseph Tartaro, a security researcher whose NULL vanity license plate at one point had him on the hook for $12,049 in fines. The problem? Apparently every time a traffic cop wrote a ticket and left the license plate blank, those citations headed straight for Tartaro’s mailbox, regardless of the actual culprit.

Tartaro has since worked to clear his name; a quick check of the Citation Processing Center’s public online database shows no tickets currently linked to NULL. But while his ordeal was agonizing, it was also far from unique. In fact, Tartaro joins a long lineage of people whose vanity plates backfired in spectacular fashion.

In a way, it’s surprising that this could happen at all. States actively police what vanity plates get approved; Utah alone has rejected around 1,000 plates over the years, and that’s not even counting those turned down for being duplicates of existing plates. Each state handles things a little differently, but Wisconsin’s lawmakers captured the prevailing ethos pretty well: “The department may refuse to issue any combination of letters or numbers, or both, which may carry connotations offensive to good taste or decency, or which would be misleading, or in conflict with the issuance of any other registration plates.”

That’s plenty broad. But too many times, it seems, states have focused too much on decency and not enough on practical outcomes. A POOPHED plate might offend sensibilities, but NULL broke an entire system.

The following examples, like Tartaro’s, might sound unbelievable. But they’re all real—and hopefully a cautionary tale for anyone who wants to get a little clever at the DMV.


The oldest entry on our list—which owes a major debt to Snopes—comes from Los Angeles, circa 1979. As the LA Times reported a few years later, the state at that time let you give your top three choices for a personalized license plate. An avid maritime sportsman named Robert G. Barbour put in SAILING and BOATING as his top two picks. He didn’t have a third, so he wrote NO PLATE in that slot, assuming it would revert him to a regular random alphanumeric. Instead, he got NO PLATE. It took a month before the first citation came through. Seven months later, he was up to 2,500 notices. Perhaps surprisingly, Barbour never relented; he kept his plate for years, sending a form letter to the issuing authority every time a new ticket arrived. Eventually, according to the LA Times, the DMV told ticket-issuing authorities to stop writing “no plate” on citations, and to switch to “none” instead. Problem solved.


NOTAG has struck multiple motorists. As also reported by Snopes, the Associated Press relayed the story of Jim Cara in 2004, whose Suzuki motorcycle racked up over 200 citations as Delaware’s computer system linked his personal info to any ticket without a plate. And the same gag landed Florida's Carol Schroeder with 135 tickets tallying over $8,000 in 2012.


In a slight variation on the theme, Washington, DC's Danny White opted for a NO TAGS plate nearly 30 years ago. Since then, he told his local NBC affiliate in 2012, he had received over $20,000 in tickets. That whole time, he said, he would go to the courthouse every few months to clear his name. Eventually, city officials told ticket writers to say “none” instead of “no tags” when they ran into a vehicle without plates, presumably alleviating the problem.


Another Snopes find: In 2008, Alabama resident Scottie Roberson chose a vanity plate that would pay homage both to his nickname (Racer X) and his favorite number (seven). The result, as the Birmingham News reported at the time: XXXXXXX. Seems innocuous enough, but what Roberson didn’t realize, at least at first, was that Birmingham, Alabama, officers used Xs to indicate a vehicle with missing or expired plates. And so the citations came like summer rain. Roberson said he got as many as 10 tickets in a single day, hitting $19,000 in total fines before the city adjusted the system to accommodate him.


When Nick Vautier moved to California around 2004, he got a new Miata convertible and personalized plates with his initials to go with it. So far, so good. What he soon figured out, though, is that NV also stands for “not visible,” at least to California traffic cops. At first, he wrote in a blog post detailing the situation, the tickets would trickle in, and he’d deal with them one at a time with a phone call to city administrators. But before long, something changed in Oakland’s computer system, Vautier said, that led to dozens of tickets across seven different counties landing in his mailbox, totaling over $3,000.


This one’s not even a traffic joke. In 2015, New York City resident Brigitta Wareham encountered an unexpected problem: Her car had been booted four times in less than two years. Yet she didn’t owe any money for fines. As the local CBS affiliate reported at the time, the issue turned out to be that New York allowed residents to have the same vanity plate as long as they owned different types of vehicles. Which meant that Wareham was paying for the sins of a 1HONEY truck, perhaps the cruelest indignity of all.

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Original author: Brian Barrett
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Space Photos of the Week: Sun Spotting

Space Photos of the Week: Sun Spotting

Much of how the Sun works remains a mystery: It has its own weather cycles, which we are just beginning to understand, for starters, and scientists are unsure how the solar wind—a major component in solar weather—exactly works. Good thing NASA recently launched a mission toward the center of our solar system to take a look at how this furnace functions.

Launched in 2018, NASA’s Parker Solar Probe will take years to swoop into orbit around the Sun, but once it’s there, its main goal is to figure out exactly what drives the solar wind, the constant stream of highly charged particles that are spit out from the openings in the surface. The probe will also study the Sun’s magnetic field. Solar weather is important to understand because those particles and blasts of radiation can affect our satellites, causing communication delays or even blackouts.

The Parker Solar Probe is on an epic journey to study our Sun, which is one of the most challenging places to visit in the entire solar system. Because it’s hot, of course, but because gravitationally it’s a challenge as well, since the pull from the Sun has a goal of destroying spacecraft. What's more, once a craft gets closer, it has to contend with highly charged particles called the solar wind, which can damage it. This image from Parker, a composite of several photos, shows the solar wind passing by its instruments. At the closest approach to the Sun, Parker will be traveling an astounding 430,000 miles per hour. While it is not going quite that fast yet, between its speed and the streaks of solar wind whooshing by, the NASA probe appears to be on a space roller coaster. Oh, and that small white sphere at upper left? Say hello to planet Mercury.

NASA/Naval Research Laboratory/Parker Solar Probe

Before the Parker Solar Probe launched into space nearly a year ago, it was built in something called a clean room. This image shows the spacecraft being tested there by NASA engineers. The spacecraft will not only revolutionize our understanding of the Sun and its, um, climate, but the spacecraft itself is a transformative innovation. Outfitted with a high-tech carbon foam heat shield, Parker is able to withstand temperatures up to 2,500 degrees Fahrenheit. However, on the other side of the heat shield, the spacecraft will remain a comfortable 70 degrees.

Leif Heimbold/NASA

The European Space Agency’s star mapping satellite called Gaia has been keeping an eye on the events closer to Earth—particularly near potential asteroids. This image shows a representation of the paths of 14,000 known asteroids. The streaks in orange and red are mostly objects located in the main asteroid belt between Mars and Jupiter. And while Gaia mostly spots asteroids we already know about, it also found three near-Earth asteroids that we’d never seen before, shown here as the light gray rings. It’s always good to have an idea of exactly how many near-Earth asteroids are out there at any given time, not only to be able to track and study them, but also because we could then try to redirect one if we were worried it was going to strike the planet.


Talk about boudoir photography: Here's Gaia in its own clean room prior to launch. The large circular feature is its sun shield, built to cast a permanent shadow over the spacecraft. It regulates the temperature of Gaia and shields it from the radiation found in space.

Manuel Pédoussuat/ESA

It’s not pumpkin season yet, but this image of the Sun is pretty orange and plump. NASA’s Solar Dynamics Observatory is always studying our star, observing it through different wavelength filters to get the full picture of what’s happening. This UV filter highlights the Sun's corona, which you can see is sort of a cloud-like feature puffing out from the edges. The darker regions are called coronal holes; these are regions with less radiation, but the openings release the highly charged particles that make up the solar wind.


Sun still in your eyes? Gaze upon WIRED’s full collection of space photos here.

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Original author: Shannon Stirone
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Robot Coffee Tastes Great, But at What Cost? (About $5)

Robot Coffee Tastes Great, But at What Cost? (About $5)

Airports have robot coffee now.

But first, consider that moment—you’ve experienced this—where your multiply delayed flight finally lands, maybe at the airport you expected and maybe not. Then you realize, taxiing across the tarmac, that it is in fact the middle of the night. So picture the terminal, the one in which you are alone. The Hermès shop is not open. The massage place is kneadless. The food court is no longer in session. Should airports also be shopping malls? I don’t know. Right now this one, which usually is, isn’t.

Let’s say you’re at San Francisco International Airport, Terminal 3, across from the Yankee Pier fish place. There’s a signpost, up ahead. A glowing beacon in the night. Since early August, a touchscreen has offered lonely travelers a mug o’ mud—exuded by the sleek, cargo-container-sized structure looming next to it. This is a “Coffee Haus,” brown, horizontal window on one side, big touchscreen on the other, and in the middle, a white-framed presentation space. As the great architect and known caffeine abuser Le Corbusier would definitely have said, “a Coffee Haus is a machine for coffee.”

A hundred times an hour, it can make a coffee drink. Kevin Nater, CEO of Briggo, the company that builds Coffee Hauses (Häussen?), says a fully staffed Starbucks can only do one coffee drink a minute. Sixty an hour—and that’s with human people! All that stuff about “third places” and interpersonal interactions, the thing where hey, you wanna get a coffee, the Coffee Haus burns all that away.

Adam Rogers is the author of Proof: The Science of Booze. He writes about science and miscellaneous geekery for WIRED.

This is San Francisco, so the Coffee Haus isn’t even first to market. Before Briggo, there was Cafe X, a more compact, more theatrical iteration with a six-degree-of-freedom robot arm, like the ones that build cars or have swordfights, making the drinks. That company (with venture funding from Silicon Valley puffer fish including Khosla Ventures and the Thiel Foundation) has three baristabots hashtag-disrupting coffee around the city. Cafe X competed for the SFO contract, but Austin-based Briggo’s bigger, more industrial assembly line-like droid (and $20 million in series-A funding from S3 Ventures) muscled them out. Briggo has nine other machines in operation now—at Austin’s airport and a few corporate campuses among other places, as well as a contract for dozens more to come at airports and train stations across North America. In the roughly $26 billion US specialty coffee market, every marginal advantage makes a difference.

Coffee Haus coffee is pretty good. At SFO, the beans are a choice between Briggo’s blend or Sightglass, a beloved San Francisco coffeeteer—with Verge, another SF third-wave choice, to come. Of course the company will carry local favorites as it expands; every town has a coffee now. The various milks stay in a refrigerator unit, subject to public health laws stricter than the ones non-robot emporia follow, before they hit the “milk reactor” for steaming. Finished drinks, 16 at a time, sit on a carousel inside the Coffee Haus holding cell. It’ll text you when it’s ready. You walk up to the big touchscreen, type in your code, and the door opens. Here’s your coffee, master.

Caffeine Machine

All day long, all night long, if you ask the robot to make you a coffee drink, it will. It has to. That is its function.

You can order from the touchscreen, but of course you can also download an app—no duh, you guessed there was an app. It uses location services to guess which Coffee Haus is closest. Choose between coffees and espresso drinks, choose your milk. And then you can watch a cardboard cup migrate past dispenser tubes like cyborg udders. A tiny little moving arm passes the cups along, places the finished drinks under a stack of tops leveled by laser beams, their red targeting dots visible through the window. The Coffee Haus can’t be reasoned with. It doesn't feel pity, or remorse, or fear. And it absolutely will not stop until you have a cup of coffee.

Slightly hard to see through the window on the Coffee Haus are bean hoppers and grinders, precisely weighing and compacting the grind. A sort of instahot system brings water up to a coffee-nerd approved temperature before steaming or pouring over. Most of that’s invisible, happening inside ducts. Sensors throughout monitor the temperature of the water and the milk, how much coffee there is, whether the lids are stacked … and all that information goes back to a Briggo Network Operating Center in Austin, monitoring all 10 Coffee Haus kiosks. They hardly ever clog or break, a tech tells me. This kind of machinery actually works better at high volume.

But Can It Make Latte Art?

Given the right software, maybe loyal subjects of the coffee robot will be able to email high-fives to the people who grew the beans, a continent away. If you have the app and you know your partner’s going to be passing a Coffee Haus, you can buy them a coffee, and the robot will text them. “We’re connected coffee,” Nater says.

As the Coffee Hausroboter spread across the world, presumably while emitting some sort of lockstep chugging sound, they will learn more about the coffee habits of everyone who uses the app. They will add our human biological and technological distinctiveness to their own. It looks like you’re trying to order a latte? Would you like some help? Or maybe, since it has your cell phone number, it’ll just text you around 3:30. Hey, Adam. Wanna get a coffee? Click here.


The WIRED Guide to Robots

You think I’m being paranoid? “We have all that data,” Nater adds. “We’re a data platform.” Which, wow, all I wanted was a latte. I’m already chasing the caffeine dragon so hard I can calculate my journalistic output in words per milligram. I’m in no hurry to be a machine thrall.

And yet, standing in line at an airport Peets at 6:30 AM, that’s no way to live, either. Hoping that the not-overly-happy-to-be-there human staff will turn around everyone else’s order fast enough for you to make your flight? That’s not convenience. In the restaurant world, baristas are famous for their inconveniently artistic temperaments. At the fastest-food versions of coffee outlets, humans are already mostly just pushing buttons on a compact coffee robot.

Maybe the world of espresso will be better for a robotic invasion. No false pleasantries at the counter, no drink errors, no transliterations of your name into … what is that, Cyrillic? Just a decent cup of joe, a gleamingly automated dispensation. The robots—they’re just here to serve.

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Original author: Adam Rogers
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Form Swim Goggles Review: Fitness Tracking at the Pool

Form Swim Goggles Review: Fitness Tracking at the Pool

When my mother uses an elliptical machine, she covers the screen with a towel. She says she doesn’t want to “become obsessed” with when it will end. For me, numbers are everything.

I have to count down the minutes, seconds, and fractions of a mile as I go. Obsessing over my pace and stats is how I keep my brain busy while I work out. There isn't much opportunity to do that while swimming, which is why I leapt at the chance to try the Form Swim Goggles, which have a screen built right into them. Boy, are they fun.

The goggles automatically detect the type of stroke, stroke rate, and split times (the times for each lap in a multi-lap interval), while the see-through augmented reality (AR) display in the lens shows you any combination of these metrics you want, in real time. There are several watches on the market that can also measure all this kind of data automatically, but the novelty of not having to wait until the end of my lap or awkwardly glance at my wrist mid-stroke to get information is hard to overstate.

On top of that, their $199 price is surprisingly competitive with wrist-based trackers.

Just Keep Swimming

To start a workout, you select Swim in the Goggles' menu, enter the length of the pool you're in, and push off! That's about it. You’ll notice a delay as the accelerometer and gyroscope start recording and the computer starts analyzing. After a second, the timer retroactively compensates, showing the correct time you started in your field of vision. (You can display the data in either of your eyes.)

The company used machine learning to train the computer, looking at data recorded from a large sample of swimmers of all levels. The onboard processor recognizes the accelerometer signals as backstrokes or breaststrokes, and can tell if you’re turning around or taking a rest.

I found the stroke detection to be bang-on, but the lap detection was overly sensitive. If I looked behind me to glare at the swimmer basically tickling my feet with their lane-tailgating, the goggles would sometimes split one length into two, calculating my speed to be twice as fast as it was in reality. In a crowded pool, that guy nonchalantly cruising on a kickboard who drastically changed my pace also muddied up my time and speed. Form says it has implemented post-processing to detect and correct for this automatically, though it's tough to account for every situation.

The goggles are perfectly comfortable, with dense lenses and smooth, strong, adjustable rubber straps. They come with multiple nose bridge sizing options, too.

Having numbers float in your field of vision does somewhat impair your spatial awareness. I invaded some personal bubbles and did some lane-drifting before I swapped the display to my non-dominant eye. After wearing it for a while, you get used to switching your focus. There is, however, little to be done about the lack of peripheral vision on the side with all the tech in it.


The onboard computer is in a small black box firmly attached to the side of one lens. It's easy to ignore while swimming, and doesn't look too odd or out of place, though the asymmetry can't be missed. It has a two-button control setup: the front button is held down to power on or off, and is used to select options, while the back button is used to toggle between those options. The buttons are a little difficult to press, though that may be to prevent accidental presses. The tech is waterproof up to 32 feet.

The display is fairly customizable. You can choose to display any two of the following metrics at a given time: total distance swum, length distance per stroke, length stroke rate, length stroke count, length counter, total calories, length pace per 100m, length/split time, or total time.

You can also see different information while you swim, rest, and each time you turn to do another lap. If you don't want to see metrics the whole time you're swimming, you can disable the swim screen, though you’ll still see numbers pop up when you turn and pause to rest. You can adjust the brightness as well, which is handy when switching between indoor and outdoor pools.

The goggles can hold a charge for 16 hours according to Form. I didn't use them for quite that long, but the rate of battery decrease for how long I used them seems to be on track. Should you lose the unique magnetic USB charger cable, you will probably have to order a replacement from Form.

The goggles use Bluetooth sync with an Android or iOS app, which you can use to analyze data or customize the goggles' settings. Form only supports Android 8.0 (Oreo) and up, which is unfortunate for my 4-year-old LG G4, but I was still able to pair it with the goggles outside of the app—an effective workaround.



The app looks pretty slick. Swim data can be put into a list or table, colorfully plotted by time or distance, or placed in a SWOLF ("swim golf"?) plot that calculates your efficiency using speed and distance per stroke.

The app connects to Strava, TrainingPeaks, and Garmin Connect. It also has a social aspect to it, where users follow one another, trading "likes" and comments on workouts. Every workout can be tagged with a location and have a custom label. For those who prefer their swimdata not be made available to the world, there are privacy settings for accounts or workouts.

It would be nice if you could manually edit workout entries. Being able to combine lengths in the app seems like a useful feature, especially depending on how effective their post-processing ends up being. For now, your stats are what they are. If you want a better time, try again.

Good Form

As someone who loves to play with timing and pace as I exercise, I really enjoyed the Form Swim Goggles and what they offer: unfettered real-time access to my workout times and stats. It was a novel and efficient way to obsess over my numbers. For the kind of professional athletes that treat their lap times like treasure, I imagine the benefits would be even greater.

Original author: Meredith Fore
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Amazon Says It Can Detect Fear on Your Face. You Scared?

Amazon Says It Can Detect Fear on Your Face. You Scared?

Amazon announced a breakthrough from its AI experts Monday: Their algorithms can now read fear on your face, at a cost of $0.001 per image—or less if you process more than 1 million images.

Tom Simonite covers artificial intelligence for WIRED.

The news sparked interest because Amazon is at the center of a political tussle over the accuracy and regulation of facial recognition. Amazon sells a facial-recognition service, part of a suite of image-analysis features called Rekognition, to customers that include police departments. Another Rekognition service tries to discern the gender of faces in photos. The company said Monday that the gender feature had been improved—apparently a response to research showing it was much less accurate for people with darker skin.

Rekognition has been assessing emotions in faces along a sliding scale for seven categories: “happy,” “sad,” “angry,” “surprised,” “disgusted,” “calm,” and “confused.” Fear, added Monday, is the eighth.

Amazon isn't the first company to offer developers access to algorithms that claim to detect emotions. Microsoft has had similar offerings since 2015; its service looks for a similar list of emotions, adding “contempt” but deleting confusion. Google has offered its own similar service since 2016.

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The latest on artificial intelligence, from machine learning to computer vision and more

Amazon declined to detail how customers are using emotion recognition. Online documentation for Rekognition warns that the service “is not a determination of the person’s internal emotional state and should not be used in such a way." But on its Rekognition website, Amazon, whose ecommerce business has squeezed brick-and-mortar retailers in part via deep data on consumers, suggests that stores could feed live images of shoppers into its face-analysis tools to track emotional and demographic trends at different retail locations over time.

Even as Amazon, Google, and Microsoft charge ahead with algorithms that intuit feelings, psychologists warn that trying to read emotions from facial expressions is fundamentally misguided.

A study published in February by UC Berkeley researchers found that for a person to accurately read someone else’s emotions in a video requires paying attention to not just their face but also their body language and surroundings. Software offered by tech companies generally analyzes each face in isolation.

Another study, published last month, took more direct and devastating aim at emotion-detection software. Psychologists reviewed more than 1,000 published findings about facial expressions and emotion and concluded there was no evidence that facial expressions reliably communicate emotion on their own, undermining the core assumption of emotion-detection software.

“It is not possible to confidently infer happiness from a smile, anger from a scowl, or sadness from a frown, as much of current technology tries to do when applying what are mistakenly believed to be the scientific facts,” the authors wrote.

An online demo of Google's cloud-image analysis service shows how its AI software attempts to identify objects in photos and read facial expressions to discern emotions.

Getty Images; Google

Rumman Chowdhury, who leads work on responsible AI at Accenture, says the situation is an example of the industry not pausing to think through the limitations of its technology. Even if software could read faces accurately, the idea of collapsing the richness of human feeling into a handful of categories for all people and contexts doesn’t make much sense, she says. But hype about the power of AI has led many people inside and outside the tech industry to be overconfident about what computers can do.

“To most programmers, as long as the output is something reasonable and the accuracy looks OK on some measure, it’s considered to be fine,” she says. Customers told that AI is more powerful than ever are unlikely to check the foundation of the claims, Chowdhury says.

As with facial recognition, easier access to emotion-recognition algorithms seems to be causing the technology to spread more widely, including into law enforcement.

In July, Oxygen Forensics, which sells software that the FBI and others use to extract data from smartphones, added facial recognition and emotion detection to its product. Lee Reiber, Oxygen’s chief operating officer, says the features were added to help investigators sort through the hundreds or thousands of images that often turn up during digital evidence gathering.

Officers can now search for a specific face in an evidence trove, or cluster images of the same person together. They can also filter faces by race or age group, and emotions such as “joy” and “anger.” Reiber says visual tools can help investigators do their work more quickly, even if they are less than perfect, and that the investigative process means leads are always checked multiple ways. “I want to take as many pieces as possible and put them together to paint a picture,” he says

The number of commercial emotion-detection programs is growing, but they don’t appear to be very widely used. Oxygen Forensics added facial recognition and emotion detection using software from Rank One, a startup that has contracts with law enforcement. But when WIRED contacted Rank One CEO Brendan Klare, he was unaware that Oxygen Forensics had implemented emotion detection in addition to facial recognition.

Klare says the emotion detector has so far not proved popular. “The market’s pretty limited at the moment, and it’s not clear to us if it will ever pay off as a feature,” he says. “It’s not something that is that big right now.”

The changing focus of emotion-recognition startup Affectiva illustrates the challenge. The company emerged in 2009 from an MIT project trying to help people with autism understand people around them. It won funding from investors that include advertising giant WPP and launched products to help marketers measure audience reaction to commercials and other content. More recently, the company has focused on improving car safety, for example, through technology to spot when drivers are sleepy or angry. Affectiva announced $26 million in funding earlier this year, with auto parts manufacturer Aptiv as lead investor. The company declined to comment.

At least one big tech company appears to have decided that emotion recognition isn’t worth the effort. IBM competes with Amazon and Microsoft in cloud computing and facial recognition but does not offer emotion detection. An IBM spokesperson said the company does not plan to offer such a service.

Google does not offer facial recognition, a decision it says resulted from an internal ethical review raising concerns that the technology could be used to infringe privacy. But the company’s AI cloud services will detect and analyze faces in photos, estimating age, gender, and four emotions: joy, sorrow, anger, and surprise.

Google says its emotion-detection features passed through the same review process that nixed facial recognition. The company has also decided that it’s OK to apply the technology to personal photos of its users.

Searching for “happiness,” “surprise,” or “anger” in Google’s Photos app will surface images with appropriate facial expressions. It will also look for “fear.”

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Original author: Tom Simonite
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A Major Proof Shows How to Approximate Numbers Like Pi

A Major Proof Shows How to Approximate Numbers Like Pi

The deep recesses of the number line are not as forbidding as they might seem. That’s one consequence of a major new proof about how complicated numbers yield to simple approximations.

Quanta Magazine

author photo

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: Under what circumstances is it possible to represent irrational numbers that go on forever—like pi—with simple fractions, like 22/7? The proof establishes that the answer to this very general question turns on the outcome of a single calculation.

“There’s a simple criterion for whether you can approximate virtually every number or virtually no numbers,” said James Maynard of the University of Oxford, co-author of the proof with Dimitris Koukoulopoulos of the University of Montreal.

Mathematicians had suspected for decades that this simple criterion was the key to understanding when good approximations are available, but they were never able to prove it. Koukoulopoulos and Maynard were able to do so only after they reimagined this problem about numbers in terms of connections between points and lines in a graph—a dramatic shift in perspective.

“They had what I’d say was a great deal of self-confidence, which was obviously justified, to go down the path they went down,” said Jeffrey Vaaler of the University of Texas, Austin, who contributed important earlier results on the Duffin-Schaeffer conjecture. “It’s a beautiful piece of work.”

The Ether of Arithmetic

Rational numbers are the easy numbers. They include the counting numbers and all other numbers that can be written as fractions.

This amenability to being written down makes rational numbers the ones we know best. But rational numbers are actually rare among all numbers. The vast majority are irrational numbers, never-ending decimals that cannot be written as fractions. A select few are important enough to have earned symbolic representations, such as pi, e and the square root of 2. The rest can’t even be named. They are everywhere but untouchable, the ether of arithmetic.

So maybe it’s natural to wonder—if we can’t express irrational numbers exactly, how close can we get? This is the business of rational approximation. Ancient mathematicians, for instance, recognized that the elusive ratio of a circle’s circumference to its diameter can be well approximated by the fraction 22/7. Later mathematicians discovered an even better and nearly as concise approximation for pi: 355/113.

“It’s hard to write down what pi is,” said Ben Green of Oxford. “What people have tried to do is to find explicit approximations to pi, and one common way of doing that is with rationals.”

Lucy Reading-Ikkanda/Quanta Magazine

In 1837 the mathematician Gustav Lejeune Dirichlet found a rule for how well irrational numbers can be approximated by rational ones. It’s easy to find approximations so long as you’re not too particular about the error. But Dirichlet proved a straightforward relationship between fractions, irrational numbers and the errors separating the two.

He proved that for every irrational number, there exist infinitely many fractions that approximate the number evermore closely. Specifically, the error of each fraction is no more than 1 divided by the square of the denominator. So the fraction 22/7, for example, approximates pi to within 1/72, or 1/49. The fraction 355/113 gets within 1/1132, or 1/12,769. Dirichlet proved that there is an infinite number of fractions that draw closer and closer to pi as the denominator of the fraction increases.

“It’s a rather beautiful and remarkable thing that you can always approximate a real number by a fraction and the error is no more than 1 over [the denominator squared],” said Andrew Granville of the University of Montreal.

In a 1913 manuscript, the mathematician Srinivasa Ramanujan used the fraction 355/113 as a rational approximation for pi.


Dirichlet’s discovery was, in a sense, a narrow statement about rational approximation. It said that you can find infinitely many approximating fractions for each irrational number if your denominators can be any whole number, and if you’re willing to accept an error that’s 1 over the denominator squared. But what if you want your denominators to be drawn from some (still infinite) subset of the whole numbers, like all prime numbers, or all perfect squares? And what if you want your approximation error to be 0.00001, or any other values you might choose? Will you succeed at producing infinitely many approximating fractions under such specific conditions?

The Duffin-Schaeffer conjecture is an attempt to provide the most general possible framework for thinking about rational approximation. In 1941 the mathematicians R.J. Duffin and A.C. Schaeffer imagined the following scenario. First, choose an infinitely long list of denominators. This could be anything you want: all odd numbers, all numbers that are multiples of 10, or the infinite list of prime numbers.

Second, for each of the numbers in your list, choose how closely you’d like to approximate an irrational number. Intuition tells you that if you give yourself very generous error allowances, you’re more likely to be able to pull off the approximation. If you give yourself less leeway, it will be harder. “Any sequence can work provided you leave enough room,” Koukoulopoulos said.

Now, given the parameters you’ve set up — the numbers in your sequence and the defined error terms — you want to know: Can I find infinitely many fractions that approximate all irrational numbers?

The conjecture provides a mathematical function to evaluate this question. Your parameters go in as inputs. Its outcome could go one of two ways. Duffin and Schaeffer conjectured that those two outcomes correspond exactly to whether your sequence can approximate virtually all irrational numbers with the demanded precision, or virtually none. (It’s “virtually” all or none because for any set of denominators, there will always be a negligible number of outlier irrational numbers that can or can’t be well approximated.)

“You get virtually everything or you get virtually nothing. There’s no middle ground at all,” Maynard said.

It was an extremely general statement that tried to characterize the warp and weft of rational approximation. The criterion that Duffin and Schaeffer proposed felt correct to mathematicians. Yet proving that the binary outcome of this function is all you need to know whether your approximations work — that was much harder.

Double Counting

Proving the Duffin-Schaeffer conjecture is really about understanding exactly how much mileage you’re getting out of each of your available denominators. To see this, it’s useful to think about a scaled-down version of the problem.

Imagine that you want to approximate all irrational numbers between 0 and 1. And imagine that your available denominators are the counting numbers 1 to 10. The list of possible fractions is pretty long: First 1/1, then 1/2 and 2/2, then 1/3, 2/3, 3/3 and so on up to 9/10 and 10/10. Yet not all of these fractions are useful.

The fraction 2/10 is the same as 1/5, for example, and 5/10 covers the same ground as 1/2, 2/4, 3/6 and 4/8. Prior to the Duffin-Schaeffer conjecture, a mathematician named Aleksandr Khinchin had formulated a similarly sweeping statement about rational approximation. But his theorem didn’t account for the fact that equivalent fractions should only count once.

Dimitris Koukoulopoulos (left) and James Maynard announced their proof of the Duffin-Schaeffer conjecture in July in a talk at a conference in Italy.

Kevin Ford

“Usually something that’s first-grade mathematics shouldn’t make a difference to the solution,” Granville said. “But in this case surprisingly it did make a difference.”

So the Duffin-Schaeffer conjecture includes a term that calculates the number of unique fractions (also called reduced fractions) you get from each denominator. This term is called the Euler phi function after its inventor, the 18th-century mathematician Leonhard Euler. The Euler phi function of 10 is 4, since there are only four reduced fractions between 0 and 1 with 10 as a denominator: 1/10, 3/10, 7/10, and 9/10.

The next step is to figure out how many irrational numbers you can approximate with each of the reduced fractions. This depends on how much error you’re willing to accept. The Duffin-Schaeffer conjecture lets you choose an error for each of your denominators. So for fractions with denominator 7 you might set the allowable error to 0.02. With denominator 10 you might expect more and set it to 0.01.

Once you’ve identified your fractions and set your error terms, it’s time to go trawling for irrationals. Plot your fractions on the number line between 0 and 1 and picture the error terms as nets extending from either side of the fractions. You can say that all irrationals caught in the nets have been “well approximated” given the terms you set. The question — the big question — is: Just how many irrationals have you caught?

Lucy Reading-Ikkanda/Quanta Magazine

There are infinitely many irrational numbers contained in any interval on the number line, so the captured irrationals can’t be expressed as an exact number. Instead, mathematicians ask about the proportion of the total number of irrationals corralled by each fraction. They quantify these proportions using a concept called the “measure” of a set of numbers — which is like quantifying a catch of fish by total weight rather than number of fish.

The Duffin-Schaeffer conjecture has you add up the measures of the sets of irrational numbers captured by each approximating fraction. It represents this number as a large arithmetic sum. Then it makes its key prediction: If that sum goes off to infinity, then you have approximated virtually all irrational numbers; if that sum instead stops at a finite value, no matter how many measures you sum together, then you’ve approximated virtually no irrational numbers.

This question, of whether an infinite sum “diverges” to infinity or “converges” to a finite value, comes up in many areas of mathematics. The Duffin-Schaeffer conjecture’s main claim is that if you want to figure out whether you can approximate nearly all irrational numbers given a set of denominators and allowable error terms, this is the only feature you need to know: whether that infinite sum of measures diverges to infinity or converges to a finite value.

“At the end of the day, no matter how you’ve decided the degree of approximation for [each denominator], whether or not you’ve succeeded purely depends on whether the associated infinite sequence diverges or not,” Vaaler said.

Plotting a Solution

You may be wondering: What if the numbers approximated by one fraction overlap with the numbers approximated by another fraction? In that case aren’t you double-counting when you add up the measures?

For some approximation sequences the double-counting problem isn’t significant. Mathematicians proved decades ago, for example, that the conjecture is true for approximation sequences composed of all prime numbers. But for many other approximation sequences the double-counting challenge is formidable. It’s why mathematicians were unable to solve the conjecture for 80 years.

The extent to which different denominators capture overlapping sets of irrational numbers is reflected in the number of prime factors the denominators have in common. Consider the numbers 12 and 35. The prime factors of 12 are 2 and 3. The prime factors of 35 are 5 and 7. In other words, 12 and 35 have no prime factors in common — and as a result, there isn’t much overlap in the irrational numbers that can be well approximated by fractions with 12 and 35 in the denominator.

But what about the denominators 12 and 20? The prime factors of 20 are 2 and 5, which overlap with the prime factors of 12. Likewise, the irrational numbers that can be approximated by fractions with denominator 20 overlap with the ones that can be approximated by fractions with denominator 12. The Duffin-Schaeffer conjecture is hardest to prove in situations like these — where the numbers in the approximating sequence have many small prime factors in common and there’s a lot of overlap between the sets of numbers each denominator approximates.

“When a lot of the denominators you have to choose from have a lot of small prime factors then they start to get in the way of each other,” said Sam Chow of Oxford.

The key to solving the conjecture has been to find a way to precisely quantify the overlap in the sets of irrational numbers approximated by denominators with many small prime factors in common. For 80 years no one could do it. Koukoulopoulos and Maynard got there by finding a completely different way to look at the problem.

Lucy Reading-Ikkanda/Quanta Magazine

In their new proof, they create a graph out of their denominators — plotting them as points and connecting the points with a line if they share a lot of prime factors. The structure of this graph encodes the overlap between the irrational numbers approximated by each denominator. And while that overlap is hard to assay directly, Koukoulopoulos and Maynard found a way to analyze the structure of the graph using techniques from graph theory — and the information they cared about fell out from there.

“The graph is a visual aid, it’s a very beautiful language in which to think about the problem,” Koukoulopoulos said.
Koukoulopoulos and Maynard proved that the Duffin-Schaeffer conjecture is indeed true: If you’re handed a list of denominators with allowable error terms, you can determine whether you can approximate virtually all irrational numbers or virtually none just by checking whether the corresponding sum of the measures around each fraction diverges to infinity or converges to a finite value.

It’s an elegant test that takes a vast question about the nature of rational approximation and boils it down to a single calculable value. By proving that the test holds universally, Koukoulopoulos and Maynard have achieved one of the rarest feats in mathematics: They’ve given a final answer to a foundational concern in their field.

“Their proof is a necessary and sufficient result,” Green said. “I suppose this marks the end of a chapter.”

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

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Original author: Kevin Hartnett
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The Poem on the Statue of Liberty Tops This Week's Internet News Roundup

The Poem on the Statue of Liberty Tops This Week's Internet News Roundup

The last week of internet madness started, of course, with the death of Jeffrey Epstein, and the numerous resultant conspiracy theories that followed—including one shared on Twitter by the President of the United States. Of course, it didn't help that Epstein was removed from suicide watch for mysterious reasons before his death, or that two of the guards and the warden of the jail Epstein died in were removed after the fact, because they reportedly slept through his death and falsified records. It's a story that was built for the age of QAnon and paranoia politics, so it's no surprise that it's the story that's provided the quiet but ever-present heartbeat to the last week.

But this last week also shined a surprising spotlight on CNN anchor Chris Cuomo, who threatened a man on video after being taunted in public. The week also brought even more warnings that the global economy is about to collapse again. Oh, and we also discovered that President Trump wants to buy Greenland. Which sounds like a joke, but somehow isn't. What, you may wonder, is actually happening in the world? Glad you asked. This is what the internet has been talking about for the last week.

The New 'New Colossus'

What Happened: If "The New Colossus"—the poem on the Statue of Liberty—has shaped your understanding of the American Dream, this week might have come as quite a shock to you, with the current administration seeking to rework that sonnet (and the US' immigration policy as a whole) a little bit.

What Really Happened: What with everything that's been happening lately—see above, but also, gestures vaguely in the direction of the entire world—you're possibly wondering just where the Trump administration is on the subject of immigration these days. The answer is this.

No, wait; we didn't mean that whole thing where the president uses undocumented workers on his properties. We mean the new policy suggestion that would deny green cards to poor people, effectively limiting legal immigration to the wealthy.

That last part is, tragically, not hyperbole. The acting director of US Citizenship and Immigration Services, Ken Cuccinelli did, indeed tell NPR that "The New Colossus," Emma Lazarus' poem on the Statue of Liberty was, in his mind, ripe for a rewrite.

But surely, you think, he doesn't actually mean that; it's one of the cornerstones of how the world—including America—views America. But, oh yes he does. And then he doubled down.

Of course, there are those who will be fighting the proposed changes.

If anyone needed reminding that 2019 is actually the Upside Down, however, consider this: In literally any other presidential administration, making the kind of public statements that Cuccinelli made would mean that a story like this would end with something along the lines of, "He was immediately reprimanded for his remarks." In the world that actually exists, however, this happened.

The Takeaway: Let's go with this.

Twitter Diplomacy

What Happened: Since the arrival in office of Donald Trump, the idea of Twitter Diplomacy has been an actual reality. Last week, however, that became more true than ever—and that's not a good thing.

Original author: Graeme McMillan
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About Terminal Madness

Terminal Madness started out as a Computer Bulletin Board, ( BBS ) back in the early 90's. Fascinated that one could get all the information they ever wanted "on line", for FREE, the "BBS" was named Terminal Madness.

Now, about 22 years later, that fascination with computers and information continues.

From the USA, to the Dominican Republic, to Curacao and back to the USA.

© 2016 Terminal Madness. All Rights Reserved. Designed By Terminal Madness