Math is weird. Take, for example, Zipf's law, which io9 wrote about on Monday. Linguist George Zipf discovered, back in the 1940s, that if he ranked words by their popular usage, a surprising pattern appeared. The most popular word was used twice as frequently as the next most popular, and that word was used twice as frequently as the next most popular, and so on. Zipf called this the rank vs. frequency rule, though it's now known as Zipf's law. And Zipf's law doesn't just apply to words. It applies to the sizes of cities, too.

Strangely, the population distribution among cities in many countries follows the pattern of Zipf's law. It doesn't work 100 percent of the time, but Zipf's law is surprisingly accurate when applied to cities over 100,000 population.

"Just take a look at the top ranked cities in the United States by population," io9 writes. "In the 2010 census, the biggest city in the U.S., New York, had a population of 8,175,133. Los Angeles, ranked number 2, had a population of 3,792,621. And the cities in the next three ranks, Chicago, Houston and Philadelphia, clock in at 2,695,598, 2,100,263 and 1,526,006 respectively. You can see that obviously the numbers aren't exact, but looked at statistically, they are remarkably consistent with Zipf's predictions."

Photo credit: Flickr user c1ssou via Creative Commons.

Economist Xavier Gabaix wrote a paper titled "Zipf's Law for Cities: An Explanation" that showed cities graphed very closely to a line representing Zipf's law. Gabaix writes that Zipf's law applies to countries like the US and China and India, even though their backgrounds differ enormously. He concludes that "cities in the upper tail follow similar growth processes," referencing Gibrat's law.

Perhaps the most interesting thing about Zipf's law, though, is how it applies to what, exactly, constitutes a city. The urban sprawl surrounding a city may not technically be considered part of the city itself, but colloquially, it certainly would. New York city, for example, has a population of about 8.3 million. But the New York metropolitan area has a population of 23.3 million.

Turns out, Zipf's law still applies.

The Lotus effect is one of those elements of nature science has envied, and attempted to copy, for many years. The surface of the lotus leaf is incredibly water repellant, and hydrophobic coatings are based on studies of the lotus leaf and other elements in nature that demonstrate a similar effect. And now science has discovered an even more impressive hydrophobic surface in nature: a butterfly's wings.

And not just any butterfly, those butterflies do, in general, have hydrophobic wings that can help them survive a downpour. Smithsonian Mag writes that the blue morpho butterfly of South America's rainforests has special ridged patterns on the surface of its wings. Their wings are even more adept at staying dry than the lotus leaf.

How does the lotus effect work, anyway? In both the blue morpho butterfly and the lotus leaf, a ridged surface is responsible for casting off unwanted water droplets. Ask Nature offers a deeper explanation:

"Lotus leaves, for example, exhibit extensive folding (i.e., papillose epidermal cells) and epicuticular wax crystals jutting out from the plant's surface, resulting in a roughened microscale surface. As water and air adhere less well than water and solids, roughened surfaces tend to reduce adhesive force on water droplets, as trapped air in the interstitial spaces of the roughened surface result in a reduced liquid-to-solid contact area. This allows the self-attraction of the polar molecule of water to express more fully, causing it to form spheres. Dirt particles on the leaf's surface stick to these droplets, both due to natural adhesion between water and solids and because contact with the leaf surface is reduced by over 95% from the leaf's micro-topography. The slightest angle in the surface of the leaf (e.g., caused by a passing breeze) then causes the balls of water to roll off due to gravity, taking the attached dirt particles with them and cleaning the leaf without using detergent or expending energy."

MIT engineering professor Kripa Varanasi, whose research team developed LiquiGlide--known for helping ketchup ooze freely out of a bottle--has written about the potential of making even more hydrophobic surfaces by reducing the contact time between water droplet and surface. His latest paper explains how a greater number of tiny surface ridges will cause droplets to break into smaller droplets, which bounce off a surface more quickly. That minimizes surface contact and makes for a dryer pair of Dockers. Or airplane wings that won't build up dangerous frost, or perhaps windshields that clean themselves.

Varanasi's latest study reduced the surface contact time by about 40 percent. He's shooting for a 70 - 80 percent reduction.

What separates a technology from an assistive technology? We use computers and smartphones every day to interact with others, make ourselves more knowledgeable and more productive. The wheel is instrumental in getting us, and our things, from one place to another. But assistive technologies usually fit into a narrower category: Crutches and wheelchairs and hearing aids, which assist the disabled. The Atlantic ran an interview on Tuesday with Sara Hendren, who runs the website Abler, challenging that notion.

Hendren argues that all technology is, in fact, assistive technology, which is something some scholars have argued in disability studies. Hendren's goal is to bring that point of view into the tech world.

What kind of technology is Google Glass?

" 'Assistive technologies' have largely taken their points of departure from medical aids, primarily because in industrialized cultures, people with atypical bodies and minds have been thought of as medical 'cases,' not as people with an expanded set of both capacities and needs," she says. "So a lot of the design attention to things like crutches, wheelchairs, hearing aids, and the like have followed the material look and structure of hospital gear. And accordingly, designers and people working in tech have 'read' them as a branch of medical technologies and, usually, uninteresting."

Hendren points out there's a big acceptance/interest gap between technologies viewed as assistive, and technologies viewed as, more or less, normal. Glasses are a prime example. "Eyeglasses have moved culturally from being a medical aid to a fashion accessory," she says. "People who use them are getting 'assistance' in a very dependent way, but their cultural register has no stigma attached to it, the way that hearing aids still do."

The technology behind hearing aids may be advancing all the time, making them better and smaller, but they're still not viewed as normal in the same way that glasses are. There aren't fashion designers building thousands of varieties of attractive hearing aids, either.

Of course, there are plenty of explanations for glasses' mainstream acceptance. They've been around far longer than hearing aids, for example. But Hendren makes a good point about their design, and the segregated field of assistive technologies could likely benefit enormously from an influx of great technology designers.

That's what Hendren is hoping for. "What I’m interested in is seeing technologies that have thus far been labeled for 'special needs' get the kind of design attention that mainstream technologies do; I’m also interested in designers and technology developers seeing needs—interdependence—as a fundamentally human social state on a universal continuum."

If you want to find new species of plant life in the world, you have to get out and look for it. That means trekking slowly through jungles and forests--and spending a lot of time staring through binoculars at leaves, fruits, and flowers. New York Botanical Garden curator of Amazonian botany, Doug Daly, specializes in plants of the Amazon region. Specifically he spends a lot of time in Brazil and, most recently, Colombia. He chatted with us about what it’s like to identify new plant species in regions of the world that aren’t always so friendly to humans.

Photo courtesy Doug Daly.

Why do you study forests?

Most people wouldn’t understand the thrill you get from being a taxonomist. I can’t separate it from the motive for becoming one. There’s a mindset for people who do systematics. As one of my old professors once said: “There are two kinds of people. Those who ask: ‘How does it work?’ And those who ask: ‘What is it?’”

"Figuring out what things are is a complicated process. We don’t separate that from how things are related to each other."

Figuring out what things are is a complicated process. We don’t separate that from how things are related to each other. The reason I go to places I go, to the tropics, is that’s where the species are. You’re looking for quantity and amazing mega-diversity, so traveling to those areas is kind of decided for you.

What I’m doing right now is working on two big projects in the Brazilian Amazon that involve forest management. There’s been progress made in sustainable logging and there’s also a national forest inventory going on in Brazil. Although loggers might follow the correct procedures in practice, between 50 and 70 percent of the species are misidentified. So people have no clue about what we’re actually cutting down.

There are practices where you can minimize the impacts on the forest, but if you don’t know what the trees are you’re kind of hamstrung.

Far back in Tested's history, Will and Norm undertook a bold experiment: Harness the power of the potato. Many raw potatoes were wired together into a battery, providing a medium for the current to travel from one electrode to the other. The acidity of the potato turns it into a rudimentary battery cell. Alas, the Tested potato battery never came to life. It couldn't power an LED or a digital clock. Turns out, the Tested potato battery had one fatal flaw: Its potatoes weren't boiled.

Researchers at the Hebrew University of Jerusalem discovered that potatoes boiled for eight minutes can produce a battery that's ten times more powerful than a plain old raw potato. Of course, raw potatoes have worked in science experiments for years. The Tested battery could've functioned without boiled potatoes. But boy, would it have been better.

Photo credit: Flickr user arselectronica via Creative Commons

Good enough to serve as a substitute battery to those who can't afford the real thing, even. Smithsonian Mag writes:

"Using small units comprised of a quarter-slice of potato sandwiched between a copper cathode and a zinc anode that’s connected by a wire, agricultural science professor Haim Rabinowitch and his team wanted to prove that a system that can be used to provide rooms with LED-powered lighting for as long as 40 days. At around one-tenth the cost of a typical AA battery, a potato could supply power for cell phone and other personal electronics in poor, underdeveloped and remote regions without access to a power grid."

As the fourth most abundant crop in the world, potatoes could be a virtually limitless, dirt cheap energy source. Limitless in the sense that they'd be easily replaceable, that is--we're not going to be launching rockets into space or powering Teslas with potato batteries. "Compared to kerosene lamps used in many developing parts of the world, the system can provide equivalent lighting at one-sixth the cost; it’s estimated to be somewhere around $9 per kilowatt hour and a D cell battery, for another point of comparison, can run as much as $84 per kilowatt hour," writes Smithsonian Mag.

Of course, the power of the boiled potato isn't a cure-all. Potato batteries will only be effective when they won't eat into a critical food supply, and the places where potatoes are grown aren't necessarily the places that need potato power. Still, if you could light a room for 40 days with a few potatoes, that could have an enormous impact on places where power is a rare commodity.

CubeSats, the small, square, inexpensive satellites loved by startups and academics, are changing how we study the Earth and space. For example, Skybox Imaging wants to massively increase the satellite coverage of Earth's surface with a fleet of CubeSats. Once the small satellites hitch a ride with an outgoing spacecraft, they can relax in Earth's orbit and collect data. But what if they could leave Earth's orbit and journey to Mars, or beyond? Wouldn't that require them to be far more expensive? Not according to Benjamin Longmier, Ph.D., who's heading up the CAT project. His solution: Propel CubeSats with water.

CAT stands for the CubeSat Ambipolar Thruster. Longmier and a team at the University of Michigan’s Plasmadynamics and Electric Propulsion Laboratory are developing a thruster that converts water into a plasma propellant, which will help CubeSats break free from Earth's orbit and head out to parts unknown. Solar panels provide CAT with a constant renewable energy source.

Image credit: University of Michigan

It all sounds great, but CAT isn't a reality yet. The project has some private funding, but a crowdfunding drive in July failed to bring in the $200,000 Longmier. Now the team has relaunched its Kickstarter with a more conservative $50,000 goal. That $50,000 will supposedly be enough to get the project started, using the traditional propellant of xenon gas in place of water for early engine testing. If CAT hits its stretch goals, or brings in more money, the team hopes to bring it to NASA's Technology Readiness Level 8, making it worthy for a jaunt out into the solar system.

The Kickstarter page claims CAT could propel an 11 pound CubeSat the 80,000,000 miles to Mars using 5.5 pounds of fuel. It explains the technology, stating "Just like a normal rocket that produces thrust from the burning and expansion of hot gases, CAT produces thrust from the expansion of a super-heated 350,000 °C plasma stream. Plasma is an ionized gas that can be accelerated to produce thrust (F=ma). The force generated by this thruster will be very low (micro-newtons) but very efficient. The engine will be turned on for long durations, accelerating the spacecraft to much higher velocities than a typical chemical rocket."

The project page also lists out some of the many possible uses for mobile, exploratory CubeSats. They could easily move around the Earth, providing Internet coverage or gathering weather information. They could give us the same kind of weather readings in orbit around other planets. Given how much we've learned from each individual probe sent to Mars, imagine how much more we could learn from a fleet of CubeSats orbiting the planet. $50,000 is just a small step in that direction--the stretch goals estimate needing $1,750,000 to get a CubeSat on its way to Mars--but that's still remarkably cheap compared to just about everything else in the field of space exploration.

Even if you really, really like beer, you've probably never compared drinking a brew to the dramatic impact of a nuclear bomb. That would just be...excessive, right? Pure exaggeration. Or not.

While the act of drinking a beer doesn't have much to do with a nuclear explosion, the act of tapping a beer bottle on its top, hard and fast, does. If you've ever been the victim of a beer-tapping prank, you know the beer will basically explode out of the bottle, turning most of its contents into foam and fizzling away. Physicists say the effect is not so different from a nuclear explosion. Minus the nuclear part.

Photo credit: NPR

NPR writes that physicist Javier Rodriguez Rodriguez and his team at Carlos III University in Madrid "have figured out that a stiff hit on the bottle's top sets off miniature explosions inside the beer. These tiny blasts create mushroom clouds similar to those generated in the air by an atomic bomb."

Rodriguez said that " the laws of physics that control the development of these beer mushroom clouds are the same as [those that drive] the development of the cloud in an atomic bomb."

Rodriguez and his team filmed beers with high speed cameras to crack the case of the beer tap. Eventually, they broke down the chain reaction that was happening.

A tap to the top of a beer bottle sends a wave traveling through the beer. The glass bottle can also compress, compounding those waves. Very small bubbles in the beer pulsate as they're hammered by the waves. Eventually, they can't take the impact, so the little pockets of gas collapse into clouds of smaller bubble fragments.

Then things get exciting. Rodriguez says "The carbon dioxide has an easier time to get into the bubbles because of the increase in surface area. So they grow very, very fast." As the bubbles grow, they become lighter, so they float to the surface of the beer. "The faster the bubbles rise, the faster they grow, because the mixing with carbon dioxide is more efficient," Rodriguez says. And so the bubbles feed on their own energy, becoming an unstoppable foamsplosion. Once tapped, there's no way to stop the reaction.

Earlier this year we wrote about the revival of Buckminster Fuller's Dymaxion map, which has long been a favorite of triangle-loving cartographers. The Buckminster Fuller Institute held a contest for map lovers to submit a Dymax Redux design, reinterpreting the classic shape of the Dymaxion with a new visual appearance. The Dymaxion unfolds the globe into a series of triangles, designed to preserve the size and shape of the Earth's landmasses. The winner of the contest was the Dymaxion Woodocean World, a gorgeous woodcut Fuller map.

The Dymaxion competition has also revived a bit of a cartographer competition, as Wired describes in Projection Smackdown: Cahill's Butterfly vs. the Dymaxion Map. The Dymaxion map is presented as a more accurate competitor to the popular Mercator projection, which distorts the sizes of continents. But the lesser-known Cahill Butterfly may be more accurate still.

Cahill "proposed skinning the globe into eight triangular lobes, a method invented by Leonardo Da Vinci," Wired writes. "Rather than arrange them into a clover, as Da Vinci did, Cahill made a butterfly shape. He was interested in balance, and obsessed with his projection’s aesthetic. And his math was not too shabby either. The lobes – also called gores – are each exactly 90 degrees wide and run 10,000 km along the edge. There is practically no distortion along the edges of each lobe. The lines of latitude and longitude shrink towards the middle of each lobe. The overall effect is a map that can be scaled to any size, and errors that are easy to calculate and correct."

Image via geographer-at-large.blogspot.com.

Fuller's Dymaxion map presents the world from an uncommon vantage point. There's no "right" way to look at the map, nothing that suggests North America should be "above" South America, and so on. Wired points out one problem that the Dymaxion map has that Cahill's butterfly avoids, however.

"Take a look at the United States on the Fuller map," Wired writes. "See the diagonal line that bisects the country? Notice the graticules? They run away from the seam at different angles, a pattern that repeats itself across the entire map. Every facet of the Dymaxion map has a different pattern of longitude and latitude. There isn’t a single large landmass on the planet that’s free from bent meridians and broken parallels."

Neither map is exactly great for navigation, but the butterfly map at least preserves longitude and latitude. The Dymaxion Redux competition helped a new audience appreciate Fuller's map; maybe someday, someone will do the same for Cahill's butterfly.

Take away Darth Vader and Yoda, lightsabers and R2-D2, and the most famous thing about Star Wars may be its sound. Some people prefer to call Star Wars fantasy or space opera rather than science fiction, and sound is an effective tool in that argument. Star Wars definitely isn't hard sci-fi thanks to the blasts of turbolasers, exploding ships and roaring engines in the vacuum of space. There's no sound in space!

The explanation for that sound is simple, of course: Lucas knew those sounds would make the movie more exciting, more imaginative, more fun. Fighters would move like World War II fighter planes, and larger ships would engage in combat much like World War II era ships in naval battles. Today, Star Wars' sound effects are iconic. They make the movies better, even if they're not realistic. But the authors of Make It So: Interaction Design Lessons From Science Fiction have come up with a fascinating alternate way to interpret Star Wars' sound effects. What if the sounds in Star Wars were a type of user interface?

Image credit: 20th Century Fox

When we think of user interfaces, we usually think of surfaces we touch. More recently, we've thought more and more about gestures in front of cameras or other motion sensing devices. But sound can be an interface element, too. 99% Invisible talked to the authors of Make It So and offered an explanation focused on the shootout in Star Wars, when the Millenium Falcon escapes from the Death Star.

"Is there an explanation that can warrant hearing ships exploding in space?" asks 99% Invisible. "Well, what if the sound is the interface? Audio is a much more efficient gauge of surroundings, since it spans 360 degrees, whereas vision only covers 120 degrees. It might be that there are sensors on the outside of the Millennium Falcon that provide 3D sound inside the gunner seat. So when we hear ships blow up, we’re actually hearing an augmented reality interface that Luke and Han hear. Maybe?"

Suddenly, sound isn't a tool for the audience that makes the movie more fun and easier to understand. It's a tool for the characters that makes space easier to understand. Sensors outside the ship track the positioning and trajectory of the TIE fighters and convert that information into sound that Han and Luke can understand as useful sensory data. Fantasy becomes science, if you read the scene that way.

Of course, the theory falls apart outside the context of the gun battle. There's little justification for the sound created by Star Destroyers and other ships, which are often shown making sound in external space shots--with no internal POV to explain that sound. Ships make sound in Star Wars because that makes for a better movie. But it's still cool to think of sound as an element of interface design instead of the usual glowing buttons and touchscreens.

The loose skin around a cat's neck makes for a perfect hand-or-mouth grip, as evidenced by mother cats--from house cats to lionesses--carrying their cubs around in a gentle neck grip. After some impressive research, io9 discovered why that grip is so effective. The answer has to do a myth about cats called clipnosis, which io9 describes as " the phenomenon whereby a cat is rendered suddenly immobile by a gentle squeezing of the loose skin on the back of its neck." Despite the term sounding sketchy--anything invoking hypnosis is going to be a little suspect--it turns out that clipnosis is a very real effect.

Scientists have studied clipnosis by placing a few binder clips along the loose skin of cats' necks. And then, bam, the cats are immobile. Clipnosis sounds like a myth, but it's actually true.

Photo credit: Flickr user williamspictures via Creative Commons

"Led by Tony Buffington, a professor of Veterinary Clinical Sciences at Ohio State University, the study examined the effectiveness of clipnosis by placing – what else? – standard 2-inch binder clips along the neck-skin of 31 cats," io9 explains. "Much to my relief, Buffington and his colleagues referred to the phenomenon not as 'clipnosis' but as 'pinch-induced behavioral inhibition,' or 'PIBI.' "

PIBI, then, is a better way to refer to clipnosis. There's no hypnosis involved, but the pinching is creating a very real response in cats. They become passive and their tails curl up between their legs. And it's not like their bodies are frozen while their minds are freaking out. "The cats' pupils did not dilate – a physiological response often seen in fearful animals– and their heart rates did not increase," io9 writes. "Nor did their breathing quicken. The cats also remained responsive, in contrast with cats seen to exhibit what is called 'tonic immobility,' whereby the animal will freeze and become entirely unresponsive in the face of highly threatening stimuli."

Buffington's conclusion was that the response was meant to make it easier for mother cats to pick up and carry their cubs. Young cats are easier to pick up and carry when they go limp. Buffington's study didn't answer why PIBI works, but other studies have found that the response isn't just present in cats. Similar responses happen in dogs, rabbits, mice, even humans. Researchers have found a number of systems contribute to the physiological response in mammals. We have evolved to experience a calming effect from being held by our mothers.

Want to know more about PIBI? Check out this paper by zoologist Stephen C. Gammie.

After the audience Q&A, Adam finished his conversation with retired-astronaut Chris Hadfield by asking an important question: "Why do we need a space program?" This is the reasoning Colonel Hadfield gave, an explanation we should also remember and a message we are all deputized to spread:

"If anybody asks, or if you're just thinking about it in your own mind. It's a question you ought to ask all the time. 'Why do we spend money on space exploration.' It's a valid question. You ought to ask it. We're not spending our own money, we're spending the money of the whole country. We're spending someone else's money. So why is it worthwhile? I've asked myself that right from the beginning. I don't want to waste other people's money just so I can go for a ride. As much fun as it is, that's not the point.

So, number one. The direct benefit. What did we learn from doing it? There's understanding the Earth itself. All the ways we observe our planet, though the observatories that we've built, through the long-term looking of the changes of the atmosphere--the changes in the surface, measuring the temperature. All of the satellites that we've launched, whether unmanned, launched from the Shuttle, or things that are on the outside of space station. We have 200 experiments running inside--that teach us about things like fundamental fluid physics and how flame propagates.

We invented a box about this big that is a flow cytometer that you can do blood analysis in a machine in ten minutes. It's called Microflow. We recognize the need on the space station for it, and brought the right people together to build it. Because when you have the common enemy of complexity and cost, you bring together people who would never talk to each other otherwise. So that box is being tested in Canada, with experiments being done in Ghana right now. There's a whole suite of direct applications that come back. That's one.

Two, is that it's absolutely fundamental to our nature. Right from the earliest of history. The only reason that there are people in North America is that each successive generation has taken the best of their technology and carried it as far as they could go. And 30,000 years ago, people starting coming to this continent, and pushing us [forward]. Every dissatisfied teenager is an emissary for taking the best of technology and seeing what's over the next hill. And as we invented the next level--canoes, sailboats, and watches so we could figure out longitude. As we invented steamboats and locomotives and airplanes and spaceships, we have always taken the very best of our technology to take us as far as we could go, so that we could better understand the universe around us.

Colonel Chris Hadfield wasn't the first astronaut to tweet from space, but his engagement with fans and the people who followed him on social media was unprecedented. One attendee at his conversation with Adam last week at NASA Ames asked how he felt about the reception of his social media presence, and whether that kind of interaction was planned from the start. His response is transcribed below.

"Social media is a really interesting new invention. It's not just what it seems to be. It is kind of a changer of behavior and human communication. I'm really impressed with it. And the word that is important is 'social.' The big difference for me is this. A lot of media is a broadcast. 'This is our product, this is what we've done, and we are now sending it to you.' Like all of the news you watch on television, all of the advertisements. All of the media that exists is a prepared message that is broadcast at you.

The wonder of social media, when it's used properly, is that it is an invitation to come aboard into my world. If you want. And that's a real difference. And at first I had no interest in social media. Even Twitter--I thought 'what a stupid name.' Twitter sounds like two eleven year olds talking to each other--why would I have anything to do with that? But the first time I used it was when I was living at the bottom of the ocean. And they said, 'we want you to tweet.' And as commander of that mission, I explained to everybody [at the Aquarious underwater laboratory] what it was supposed to be.

I watched--and the beauty of it was--the guys who would never ever tell you a cool thing they had seen, or a transient emotion they had, or some insight that had occurred to them, suddenly had an outlet with which to share those things. Not only with the whole world, but with the members of the crew. And as the commander, I would go through and read what the guys had tweeted during the day and be delighted! It was like they had invited me into their emotions, thoughts, and observations that they would never have, otherwise. So then I thought 'ah, I understand this. This is really interesting." This is a whole different way to share something personal and honest at an almost effortless and instantaneous level. I was converted, then.