24 Photographs Taken at the Exact Same Moment All Around the World



3:29 PM Sept. 22, Midway Atoll Eric Dale



3:29 PM Sept. 22, Midway Atoll


Eric Dale



4:29 PM Sept. 22, Honolulu, Hawaii Linny Morris



4:29 PM Sept. 22, Honolulu, Hawaii


Linny Morris



5:29 PM Sept. 22, Adak, Alaska Calvin Kashevarof



5:29 PM Sept. 22, Adak, Alaska


Calvin Kashevarof



6:29 PM Sept. 22, Anchorage, Alaska Brian Adams



6:29 PM Sept. 22, Anchorage, Alaska


Brian Adams



7:29 PM Sept. 22, Gray Whale Cove Beach, California Ian Allen



7:29 PM Sept. 22, Gray Whale Cove Beach, California


Ian Allen



8:29 PM Sept. 22, Edmonton, Alberta, Canada Grant Harder



8:29 PM Sept. 22, Edmonton, Alberta, Canada


Grant Harder



9:29 PM Sept. 22, Mexico City, Mexico Jorge Dávalos



9:29 PM Sept. 22, Mexico City, Mexico


Jorge Dávalos



10:29 PM Sept. 22, New York, New York Floto & Warner



10:29 PM Sept. 22, New York, New York


Floto & Warner



11:29 PM Sept. 22, Rio de Janeiro, Brazil Tuca Reinés



11:29 PM Sept. 22, Rio de Janeiro, Brazil


Tuca Reinés



12:29 AM Sept. 23, Nuuk, Greenland Mads Pihl



12:29 AM Sept. 23, Nuuk, Greenland


Mads Pihl



1:29 AM Sept. 23, Praia, Cape Verde Daniel Reyes



1:29 AM Sept. 23, Praia, Cape Verde


Daniel Reyes



2:29 AM Sept. 23, Reykjavík, Iceland Bernhard Kristinn



2:29 AM Sept. 23, Reykjavík, Iceland


Bernhard Kristinn



3:29 AM Sept. 23, London, England Ben Anders



3:29 AM Sept. 23, London, England


Ben Anders



4:29 AM Sept. 23, Johannesburg, South Africa Reney Warrington



4:29 AM Sept. 23, Johannesburg, South Africa


Reney Warrington



5:29 AM Sept. 23, Istanbul, Turkey Serkan Taycan



5:29 AM Sept. 23, Istanbul, Turkey


Serkan Taycan



6:29 AM Sept. 23, Moscow, Russia Anastasia Rudenko



6:29 AM Sept. 23, Moscow, Russia


Anastasia Rudenko



7:59 AM Sept. 23, New Delhi, India Akshay Mahajan



7:59 AM Sept. 23, New Delhi, India


Akshay Mahajan



8:29 AM Sept. 23, Dhaka, Bangladesh Saiful Huq



8:29 AM Sept. 23, Dhaka, Bangladesh


Saiful Huq



9:29 AM Sept. 23, Bangkok, Thailand Noah Sheldon



9:29 AM Sept. 23, Bangkok, Thailand


Noah Sheldon



10:29 AM Sept. 23, Beijing, China Peng & Chen



10:29 AM Sept. 23, Beijing, China


Peng & Chen



11:29 AM Sept. 23, Tokyo, Japan Takashi Kikuchi



11:29 AM Sept. 23, Tokyo, Japan


Takashi Kikuchi



12:29 PM Sept. 23, Sydney, Australia Sean Fennessy



12:29 PM Sept. 23, Sydney, Australia


Sean Fennessy



1:29 PM Sept. 23, Honiara, Solomon Islands Kim Litera



1:29 PM Sept. 23, Honiara, Solomon Islands


Kim Litera



2:29 PM Sept. 23, Auckland, New Zealand Shaun Pettigrew



2:29 PM Sept. 23, Auckland, New Zealand


Shaun Pettigrew



The Baffling and Beautiful Wormhole Between Branches of Math



Onformative


Math Geeks extol its beauty, even finding in it hints of a mysterious connectedness in the universe. It’s on tank tops and coffee mugs. Aliens, apparently, carve it into crop circles (in 8-bit binary code). It’s appeared on The Simpsons. Twice.


What’s the deal with Euler’s identity? Basically, it’s an equation about numbers—specifically, those elusive constants π and e. Both are “transcendental” quantities; in decimal form, their digits unspool into infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect symmetry and closure of the circle; it’s in planetary orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore’s law. It’s used to model everything that grows.


What Leonhard Euler showed in 1748 is that π and e are deeply related, but in a very weird way: They’re connected in a dimension perpendicular to the world of real things, a place measured in units of i, the square root of -1, which doesn’t actually … exist. Mathematicians call it an imaginary number.


Courage, pilgrim! Imagine a graph with real numbers on the horizontal axis and, well, imaginary ones on the vertical. Now, remember the exponential function, f(x) = ex , from high school math? Ordinarily it graphs as an upward swooping curve—the very paradigm of progress. But in this “complex” space, eix traces a circle around the origin—an endless wheel of samsara intercepting reality at -1 and +1. Add a dimension for time and it’s a helix winding into the future; viewed from the side, that helix is a sine wave. That’s the alchemy of Euler’s formula: It equates disruptive, exponential change (the land of e) and infinite repetition (π). You might think you’re getting ahead in the world, but from this astral perch, you’re just running laps.



Onformative



The rest is easy: Take that function f(x) = eix, set x = π, and you get e = –1. Rearrange terms and you have the famous identity: e + 1 = 0.


That’s the essence of Euler’s alchemy: By venturing off the real number line into this empyrean dimension, he showed that disruptive, exponential change (the land of e) reduces to infinite repetition (π). You might think you’re getting ahead in the world, but from this astral perch you’re just running laps.


Now, maybe you’ve never thought of math equations as “beautiful,” but look at that result: It combines the five most fundamental numbers in math—0, 1, e, i, and π—in a relation of irreducible simplicity. (Even more astonishing if you slog through the proof, which involves infinite sums, factorials, and fractions nested within fractions within fractions like matryoshka dolls.) And remember, e and π are infinitely long decimals with seemingly nothing in common; they’re the ultimate jigsaw puzzle pieces. Yet they fit together perfectly—not to a few places, or a hundred, or a million, but all the way to forever.


You can take this farther, too. If you write that function above in more general form as f(x) = e(zx), where z = (a + bi), what you get is no longer a circle but a logarithmic spiral, combining rotation with a reawakened impetus of exponential growth. Log spirals are also found everywhere in nature, from the whorls in a nautilus shell to the arms of our galaxy. And they’re related, in turn, to the golden ratio (another infinite decimal, 1.61803 …) and the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …), which neatly describes the arrangement of leaves and petals in plants.


But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digitize music, and it tames all manner of wavy things in quantum mechanics, electronics, and signal processing; without it, computers might not exist.


The takeaway? Those crop-circle aliens were trying to tell us something.



A Guide to Flatland: What It’s Like to Live in Two Dimensions



Valero Doval


Mathematician Ian Stewart wants us to see what he sees. Which is kind of a problem, because he’s accustomed to envisioning some pretty impossible shapes: snowflakes in fractional dimensions, hypercubes in 4-D, 11-dimensional superstrings. So when the University of Warwick professor and author writes about these freaky geometries, he relies on an analogy—a way for us blockheads to understand realities above, below, and in between our three dimensions. His guide is a little mathematical fantasy he read over half a century ago: the cult classic Flatland .


Written in the early 1880s by Edwin A. Abbott, the story follows A. Square, a regular quadrilateral who lives on a 2-D plane. He can’t conceive of depth, but his perspective expands when a sphere visits him from 3-D Spaceland. Though Square can’t experience all three of the sphere’s dimensions, he can see it in cross-section as a circle of various sizes. That’s the trick Stewart uses: By describing what it’s like for a flat object to imagine a solid one, he can help us imagine an object in four dimensions. For instance, a crazy 4-D sphere (called a glome) might appear to us as expanding and contracting spherical cross-sections. “Starting with Flatland‘s point of view,” he says, “you find a way in.”


Stewart considers Flatland one of the earliest works of popular science, a genre he’s been writing in for decades (his latest book came out in October). In addition to an annotated Flatland and a trippy follow-up (Flatterland , natch), he has collaborated on four educational books about the science of Terry Pratchett’s Discworld, in which wizards ponder the strange technology of Earth from a separate (magical) dimension.


In Flatland and Discworld, the act of removing yourself from your own reality allows you to understand it. And Stewart wants his readers to push that concept as far as they can. “How does the fourth dimension relate to the 11th?” Stewart asks. “We can crank up the analogy.” Whatever you say, Professor—we’ll keep an eye out for Stringland.



The Impact of Borges, Brazil, and MC Escher on Interstellar



Chart: Thomas Porostocky Blade Runner; 007: Everett Collection


Christopher Nolan owes a lot to 1977: Star Wars, Close Encounters of the Third Kind, and The Spy Who Loved Me—three movies he often cites as major influences. But more important, 1977 was the year his dad took him to the theater to see 2001: A Space Odyssey. The precocious kid instantly fell in love, and a career was born. “Movies become indistinguishable from our own memories,” Nolan says. “You file them away and they become very personal.” Those memories burrow through time and erupt in his films, so we journeyed back to see which works and artists have incepted him.



Interstellar Was So Big It Almost Broke IMAX



Christopher Griffith


When it comes to Interstellar, the spaceship Endurance isn't the only thing going where no one has gone before—so is the movie itself. At 2 hours, 47 minutes, and 7 seconds, Interstellar is the longest Imax presentation ever. To screen it, all that film is wound up and placed on a 72-inch-diameter platter; fully loaded it weighs 600 pounds and takes a forklift to move. Director Christopher Nolan thinks it’s worth it: 70-mm Imax film means higher resolution and crisper, clearer colors. But for years the limit on Imax running time was 2 hours, 30 minutes. “The diameter of the Imax platter dictates how long films can be,” says David Keighley, chief quality officer at Imax. Then in 2009, when director James Cameron was producing a special-edition release of Avatar, he demanded more. So the company’s engineers moved the clamp system that keeps the film on the platter from the top to the bottom, allowing more film to wrap around the outermost edge without flying off. The result? Cameron’s cut came in at 2 hours, 46 minutes, and 54 seconds. Now Interstellar is topping that record by 13 seconds, including more than an hour of ultrasharp space footage shot with Imax cameras. Bigger isn't always better, but when it comes to Imax movies, we think it is.



An App That Helps Retailers Steal Each Other’s Customers


Cash Dash feature on Find&Save app

Cash Dash, the new feature from Find&Save. Wanderful Media



Holiday shopping, that happy American pastime, seems to get a little more cutthroat with each passing year.


Those already insane 4 a.m. door-buster deals have now given way to retailers opening up on Thanksgiving night. And the price-gouging war between retailers has become so extreme that even Walmart, with its bargain basement prices, is vowing to match Amazon’s prices so it won’t lose customers to its e-commerce adversary.


But this was just a prelude. Thanks to Ben Smith, things are about to get even nastier.


Smith is the CEO of Wanderful Media, the company behind a couponing app called Find&Save. The app was originally designed to serve you coupons for nearby stores—and it still does. But on Wednesday, Smith and company announced that they’ve added a new wrinkle. It’s called Cash Dash, and basically, it lets retailers push you promotions the minute you walk into a competitor’s store—or merely past it.


In other words, when you’re at Walmart, Target could offer you $25 to visit one of its stores within the next 24 hours. Yes, the goal is to help retailers steal shoppers away from the competition. “When you’re walking into a Home Depot on Saturday morning, your intent is clear,” Smith says. “You’re in home repair mode. That would be a very valuable audience for Lowe’s.”


The smartphone has become the smart shopper’s best friend in the last few years. According to a recent survey by Accenture, 68 percent of consumers say they are likely to check out prices in-store and then search for lower prices online, a phenomenon now commonly referred to as “showrooming.” But retailers are now catching onto the trend and looking for ways to use the proliferation of mobile technology to their advantage.


In other words, when you’re at Walmart, Target could offer you $25 to visit one of its stores within the next 24 hours.


In many cases, they’re using geolocation technology to pitch deals at shoppers who are near their stores. But Cash Dash inverts that model.


It too uses GPS to track your location, but instead of offering better deals at the store where you are, it tries to send you somewhere else. Once you accept the deal and complete the purchase, you submit a photo of your receipt using the Find&Save app, and the cash reward gets sent to your PayPal account. Smith says the next version of the app will connect to users’ credit cards, and subtract the dollar amount automatically.


The Dash for Cash Dash


Cash Dash has only been live for three weeks, and already, some 50 retailers, from Walgreens to Macy’s, are paying Find&Save to send these notifications. About 100,000 alerts have been sent out every day since the feature launched, and Smith says about 30 percent of shoppers who receive an alert actually click through and accept it.


What’s more, Cash Dash has completely changed how users feel about allowing the app to track their location. Before it launched, only 20 percent of users opted into geolocation. Afterward, 80 percent did.


In many ways, experts say, this is an evolution of what Amazon has been doing all along, enabling users to do online price checks. Now, brick and mortar retailers can play that game as well. But this doesn’t mean Amazon is no longer a threat. It still offers shoppers all the convenience that physical stores can’t.


“There’s a travel cost for consumers to go from one store to the other,” says Raj Venkatesan, a professor of business administration at Georgetown’s Darden School of business, “but if you’re on Amazon it’s on your phone.”


The Power of Discounts


The Cash Dash promotions become less appealing if, say, you’re standing in Walmart, and the nearest Target is 15 miles away. That’s why Venkatesan says the deals work best in densely populated shopping areas. They will also have to be substantial enough to compel people to get in their cars and drive to another store.


But that doesn’t mean the deals can’t work. In that Accenture survey, a whopping 96 percent of respondents said discounts would be important to their purchasing decisions this season.


Meanwhile, Venkatesan points to research that’s been done on traditional coupon circulars, which has found that the right deal will, in fact, drive shoppers to different stores. “If you think about that fact, then, yes, this app could have the potential to switch consumers to another store,” he says.


Smith, however, admits his biggest competitors are the retailers themselves, many of which have built apps that already push promotions directly to shoppers. And yet, he says, even those promotions can’t reach competitors’ audiences. “For Walgreens to do what we’re doing, they would have to get everybody to install their app, including people who aren’t Walgreens customers,” he says. “They can’t do that. I can do that.”


Disclaimer: Wanderful Media is backed by Advance Publications, WIRED’s parent company, which has no editorial input.