In casinos, the odds always favor the house; it’s just math. But every once in a while, ambitious gamblers will try to skew those odds to break the system. We’ve hunted down ten stories of hustlers who managed to bring down the house in ways that would make Hollywood proud. Some used science, some used skill, and some straight-up cheated, but they all walked away with tons of cash in their pockets.
Stanford student (and World Cube Association member) Ravi Fernando uploaded this video of his famous rubix's cube juggling feat from a first-person perspective. The cubes are solved at the 1:38, 4:15, and 5:55 marks. There's even a near drop!
If math is the only universal language, as the saying goes, then it's a language more or less like any other. And approaching it like a language makes us think about elements of mathematics that we normally take for granted. For example: When and how did the symbols for addition and subtraction come from? Astrophysicist Mario Livio was curious and decided to find out the answers for himself, and the resulting blog post is an interesting mathematics history lesson.
Though mathematics has been around for more than two thousand years--famous mathematician Pythagoras lived in the 6th century BC--Livio traced the + sign back to the 1300s.
"There is little doubt that our + sign has its roots in one of the forms of the word 'et,' meaning 'and' in Latin," writes Livio. "The first person who may have used the + sign as an abbreviation for et was the astronomer Nicole d’Oresme (author of The Book of the Sky and the World) at the middle of the fourteenth century. A manuscript from 1417 also has the + symbol (although the downward stroke is not quite vertical) as a descendent of one of the forms of et."
The - sign, meanwhile, hasn't been around as long--Livio writes that it first appeared in 1481 in a German algebra manuscript. Neither the + or - symbol appeared in English writing on math until 1551. And, like any other language, the writing of mathematics has evolved over the years. Livio notes a few examples of how the symbols have changed into the forms we now know:
Mirrors are old. Thousands of years old. They don't exactly seem like the trickiest bit of technology to invent--once you've spotted your reflection in a shiny piece of stone or metal, you're going to figure it out pretty quickly. And once glassmaking came around, well, the leap to glass mirrors seems only natural. The silvered-glass mirrors that we know and love today are relatively young, comparatively--they were invented in the early 1800s. Since then, inventors have discovered convex glass can provide a wider field of view of the world, and glass surfaces with both concave and convex segments (aka carnival mirrors) can create crazy distorted reflections of reality.
The work of mathematics professor R. Andrew Hicks may represent the most significant evolution in mirror technology since...well, glass. Hicks has been using math for years to design mirrors that reflect light in just the right ways--they're essentially finely-tuned versions of the carnival mirrors that make everything look all wacky--and has come up with some impressive reflective surfaces.
For example, he's developed a curved mirror that reflects the world without reversing its image. It's one smooth piece of glass, not a pair of mirrors connected at a 90-degree angle like a traditional non-reversing mirror. As you'd expect from a mathematics professor, algorithms made it all possible--Hicks worked out equations to represent the kind of reflection he wanted to create, then used those to develop the coordinates for thousands of tilted points on the mirror's surface.
Hicks has invented and patented a driver-side mirror for cars that eliminates blind spots.
When those coordinates are fed to a machine and ground away with a diamond, they can create all sorts of mirror variations--another example, which Hicks calls the vampire mirror, doesn't even create a true mirror image. If you look into the mirror and wave your left hand around, it'll look like you're actually moving you right.
More importantly, Hicks has invented and patented a driver-side mirror for cars that eliminates blind spots. Here's how it works.
You stand poised for action in the lobby, eyes darting back and forth between the doors in front of you. Any moment now one of them will open. But which one? You wait to hear that wonderful Ding! that means arrival, doors opening, salvation from the interminable boredom of a 30 second wait. When you hear it you'll spring into action, rushing into the elevator and jamming on the button for your floor. The doors close. And then you wait again.
It's a ritual we all know by heart, but it's amazing how much math and planning go into the 18 billion elevator rides taken annually in the United States alone. When everything goes right, you won't even have to wait 30 seconds for the doors to open. According to Theresa Christy, a mathematician and researcher at Otis Elevator Company, 20 seconds is the magic number for an elevator wait. And that number hasn't changed in about 50 years.
You'd think we'd have faster elevators five decades after 20 seconds became the target waiting time, but speed isn't really the issue. It's all about the number of stops elevators have to make and juggling the wait times for people on every floor of a building. A recent profile of Christy in the Wall Street Journal reveals just how much math goes into every imaginable elevator use scenario.
When Christy programs elevators, she has to take into account the size and weight of elevators and how many people can fit in them. Building owners want to install as few elevators as possible, since they take up a great deal of space. Passengers in various countries prefer different amounts of personal space. So, for example, more Japanese riders will crowd into elevators than Americans, but they want to know in advance which elevator they'll be getting into, so they can line up in front of the right set of doors.
The elevator code has to strike a balance between convenience for riders and convenience for waiters. If an elevator has already made three stops, should it make a third to pick up someone who's been waiting for 30 seconds and inconvenience its current passengers? Christy runs simulations to analyze the decisions elevators make according to their programming, then tweaks that programming to better her score.
She compares it to a video game; we hope she's never played Mass Effect. NPR's Marketplace calls her work an art. We think either label works--it's an underappreciated, endlessly challenging job that will never have a perfect solution. Christy's short Marketplace interview is an interesting look into a job that most of us would never think about, despite how much it affects our daily lives.
What do we know about coins? They're legal tender, they usually depict dead men on one side, and they're the go-to tiebreakers for problems big and small. Thing is, coins aren't perfectly suited to that role. A study on coin tosses reveals that the "randomness" of a toss is actually weighted ever so slightly towards the side of the coin that's facing upwards when a flip begins. "For natural flips, the chance of coming up as started is about .51," the study concludes.
The paper, written by statistics and math professors from Stanford and UC Santa Cruz, also points out that a perfect coin toss can reproduce the same result 100 percent of the time. Of course, the perfect flip was performed by a machine, not a person. And the results that lean ever-so-slightly in favor of flipped-side-up don't take into account flipping a coin after catching it or letting it bounce around on a floor or table. In practical usage, the .51 bias is so slight that you'll never notice.
If, like me, you'd always heard that coins tend to land tails-up because the heads side is heavier, there's some science available for you, too. Spinning, rather than flipping, an old penny will land on heads something like 80 percent of the time. Lincoln's head is heavier than the Lincoln memorial on the reverse, which leaves tails facing up more often than not. Unless the penny has accrued enough dirt or oil to throw the weight off.
And let's be honest--how often do you come across an old, clean penny?
With the help of a high-speed camera, Will and Norm test the theory that cracking a leather bullwhip breaks the speed of sound and creates a mini sonic boom. Take note--slow motion silliness, maths, and bath towels within.
When it comes to high-speed data transfers, most of the technological breakthroughs we catch wind of use some specialized, experimental hardware. We'd all love to be able to send friends HD video files at 26 terabits per second, but who has the equipment lying around to encode data into 300 beams of light? Researchers at MIT (who else?) have worked out an alternative that apparently has real potential--companies have already licensed their technology, which increased Internet bandwidth from one to 16 megabits per second in a recent test.
How's it work? With math, naturally. Specifically, algebra, which the researchers hope to use to eliminate or drastically reduce packet loss. When packets are dropped due to interference or clogged airwaves, devices have to re-request the missing information, and that information has to be sent again, contributing to the congestion problem.
The researchers want to replace packets with equations. How does that help? Something like this, according to MIT professor Muriel Medard:
The technology transforms the way packets of data are sent. Instead of sending packets, it sends algebraic equations that describe series of packets. So if a packet goes missing, instead of asking the network to resend it, the receiving device can solve for the missing one itself. Since the equations involved are simple and linear, the processing load on a phone, router, or base station is negligible.
Coded TCP, as it's called, has already increased bandwidth of sluggish 1mbps and .5mbps connections to 16mbps and 13.5 mbps. Those were lab tests, so it's hard to judge how well Coded TCP would work in real-world situations. But it's currently operating with a proxy server stashed in Amazon's cloud, which makes the technology especially exciting. You may need to download an app for your phone to turn algebraic equations into bits of usable data, but you won't need new hardware to make use of Coded TCP.
New hardware could help, as well: the researchers claim Coded TCP can seamlessly merge data from Wi-Fi and cellular connections without switching between the two.
Want to read a whole lot more about a technology that could be driving faster network throughput in a few years? Dig into this Coded TCP white paper.
Watch this video and you'll never think about notebook doodles and parabolas the same way again.
Webcomic xkcd regularly revolves around jokes that require a degree in math or physics to appreciate--which makes sense, because author Randall Munroe has an undergraduate degree in physics. He recently started up a weekly blog called What If? that answers reader questions by putting his past career as a physicist to use. And the first one is awesome: "What would happen if you tried to hit a baseball pitched at 90% the speed of light?"
As Munroe explains, things wouldn't go well for the batter. Or the pitcher. Or anyone within a square mile, really.
At 90 percent the speed of light, or 604,000,000 miles per hour, the ball would be traveling so much faster than the air particles around it that it would collide with the particles in front of it. That collision would release gamma rays and tear apart air molocules, creating an expanding bubble of plasma that arrives at the plate before the ball itself.
Well, the ball doesn't even get there at all, really: in the 70 nanoseconds it takes to arrive, it's turned into a cloud of debris. That's about the time the batter is swept backwards into the backstop and disintegrates, even though he hasn't even seen the pitcher release the ball yet. Within a microsecond everything else disintegrates, too.
The whole thing's more fun with Munroe's illustrations, so check out the original post. Still, the lesson's pretty clear: steer clear of lightspeed baseballs.
Cats. The Internet is full of them. Researchers at Google X, the Goog's in-house skunkworks, has created a neural network out of a massive cluster of computers to detect patterns in YouTube videos. What patterns did the cluster detect? Cat faces. Somehow, I bet you aren't surprised.
It's important to understand exactly what's happened here, because it's simultaneously very exciting and kind of mundane. Detecting patterns in images is something that the human brain is so exceptionally good at that you don't realize how difficult a task it actually is. The fact that you can not only recognize that those shiny things in the carpark are in fact, automobiles is amazing. The fact that you can pick your car out from a group of hundreds is damn near miraculous.
If your brain is atop the leaderboard for pattern recognition, computers are near the bottom, somewhere below brine shrimp and some forms of protozoa. Anyone who has used facial recognition software in popular photo managers knows exactly how bad computers are at detecting faces. Conversely, studies have shown that parts of the human brain actually specialize in detecting faces. This is why the Thatcher Effect optical illusion works. You can thank the neural network in your brain for that.
Computer-based neural networks have much greater success at recognizing patterns in data than traditional computational models. They do this by mimicing the massively connected nature of neurons. The simulated neurons are arranged in layers, with each neuron in a layer connected to all the neurons in the layer above and below it. This is a gross oversimplification, but data enters the input layer of the network, which triggers a series of signals. Those signals propogate through the network and eventually exit the output side of the network. That output contains the information that the neural network uncovered.
Typically, before you can use a neural network to detect a pattern in data, you need to seed it with examples of the pattern you want to find. This trains the network to look for specific patterns. If you want to find pictures of cats, you seed the network with bunches of pictures of cats.
The Google X team did something a little different. They ran millions of images culled from YouTube videos through the neural network, but they didn't seed the network with patterns first. Instead they just let the algorithm find patterns in the data--all of the patterns. They reported that the network found human faces, human bodies, and cats. The top-performing networks were almost twice as accurate at detection as previous efforts.
The big news here isn't that the Internet is full of cats. We knew that. Proof of concept that neural networks can still work when they're scaled up to massive clusters of machines and equally massive data sets is a huge step forward. Google X processed 10,000,000 images using a 16,000 CPU cluster in about 3 days, and the images were significantly larger than normal.
However, that doesn't mean that this type of processing will be coming to your Android phone anytime soon. And your computer still doesn't understand the philosophical implications of Magritte paintings--it doesn't understand the metaphysical difference between a picture of a cat and a cat. Even the fanciest neural network built is nothing more than a pattern recognizer.
Inside North Carolina State's Constructed Facilities Laboratory, engineers test their designs to see how they function in the real world. Maggie Koerth-Baker toured the lab earlier this year. Her videos are an interesting look into a side of engineering we don't often see.
Ion Luchin, a designer in Spain, creatively animates a simple sphere as an experiment to explore different ways of morphing the shape. Great score by Brand X Music, too.
In the science-fiction film Primer, garage scientists building engineering experiments in their spare time create a box to intended reduce the weight of objects. Closer observation into the box revealed an unintended consequence: it was also a time machine. The researchers at the Australian National University's Center of Excellence for Quantum Computation and Communication Technology (say that ten times fast) also have a seemingly empty box that has surprising utility. Though it's not as wild as time travel, the box is able to generate what the researchers are claiming to be truly random numbers, and at a very high rate. From the project's website:
The random numbers are generated in real-time in our lab by measuring the quantum fluctuations of the vacuum. The vacuum is described very differently in the quantum mechanical context than in the classical context. Traditionally, a vacuum is considered as a space that is empty of matter or photons. Quantum mechanically, however, that same space resembles a sea of virtual particles appearing and disappearing all the time. This results in the fact that the vacuum does not possess a zero-point energy, and consequently the electo-magnetic field describing this vacuum possesses random fluctuations in phase and amplitude at all frequencies. By carefully measuring these fluctuations, we are able to generate ultra-high bandwidth random numbers.
Basically, the scientists have monitored the vacuum noise--subatomic particles spontaneously appearing and disappearing--and used converted that data in random strings. This is a physical method random number generation, as opposed the computational methods like processing a seed number through a complex algorithm. Vacuum noise, as one of the researchers explains, is intrinsically one of the ultimate sources of randomness, and the rate at which their device can generate random strings is only limited by how closely they can monitor the quantum activity. Currently, the machine can generation billions of random numbers every second--or, if just measuring in bits, an approximate rate of 5.7Gbits per second.
Random numbers are serious business, as software engineers use them in a wide range of applications, such as modelling weather simulations and developing strong software encryption. A random number generator that succumbs to patterns in the long run may generate encryption keys that are easier to crack. To gauge the effectiveness random numbers generators, computer scientists have devised numerous statistical tests of randomness, checking for repeating patterns and uniform distribution of output. The Quantum Random Number Generator's creators claim that their device has produced results that, through testing, are shown to be consistent with true randomness.
You can sample a live stream of random strings from the device at the ANU website. In addition to sequences of hex and binary strings, the site also generates visualizations of randomness, in the form of scatter plots, white noise generators, and even Matrix code.
Two maths enthusiasts walk you through the process of imagining Graham's Number, a theoretical number so big that successfully comprehending it would collapse your head into a small black hole.
At the end of Martin Scorsese's movie Casino, Robert De Niro's character laments the modern commercialization of Las Vegas--the transition from a romanticized notion of smokey Old Vegas to the glamorous family-friendly resorts which he disdainfully compares with Disneyland. But while De Niro's Ace Rothstein scoffed at casinos turning into tourist attractions, it's actually very good business. As Jonah Lehrer writes in a profile for The New Yorker (and excerpted in Wired), modern casino design is a very calculated business, crafted by interior designers that not only understand aesthetic appeal, but the psychology of the players gambling there.
The subject of Lehrer's profile, Roger Thomas, is the brains behind the Bellagio and Wynn resorts, lavishly designed casinos which violated all previous rules in casino design--and making more money as a result. It's not just about keeping patrons clueless about what time is it (casinos never have clocks) or designing labyrinth-like floorplans so players are constantly being funneled back to the casino floor, it's also about subtly creating a pleasant atmosphere to reduce stress and convey a "playground" environment. University of Guelph professor Karen Finlay conducted a study testing various casino designs:
“The data is clear. Gamblers in a playground casino will stay longer, feel better, and bet more. Although they come away with bigger losses, they’re eager to return.”
Finlay notes that the effectiveness of such designs comes at the expense of the guests, who have been persuaded by flowers and nice furniture to squander money on games that are rigged in favor of the house. According to her findings, Thomas’s designs have a particularly marked efect on those guests who normally don’t gamble. The seduction of his décor, perhaps, is that it doesn’t feel like a gambling environment. The beauty is a kind of anesthesia, distracting people from the pain of their inevitable losses.
[Interesting aside: Finlay conducted her experiments using a Panoscope--360-degree environmental simulator not unlike a personal holodeck.]
This got me thinking about how the psychology of design applies to the digital equivalent of slot machines--micro-transaction-based mobile games. And make no mistake, Angry Birds and Tiny Tower are very much analogues to casino games. They all exploit the same behavioral traits and tendencies that we're all susceptible to. David Caolo's piece on the behavioral exploitation in Angry Birds explains clearly how the game is a very traditional Skinner Machine, offering just enough positive reinforcement to keep players hooked. And often, players can't control themselves, which has led to lawsuits over the issue of who's to blame when people's habits are exploited.
The advantage of mobile games is that the designers don't have to spend hundreds of billions creating a comfortable and welcoming environment for you to play--you're already playing in the places that are comfortable and convenient for you, like at home or during a commute. Instead of spending design efforts on set dressing, they can focus on making their money machines look and play as much like a game as possible. The cute 8-bit graphics of Tiny Tower is the mobile gaming equivalent of the Bellagio's granite floors and marble statues--expertly designed distractions. Like casino designers, game designers never want you to think about the way your wallet is being drained. You're not losing money, you're spending it. And just as Las Vegas has slowly become more like Disneyland, our mobile games are becoming more like blackjack and slot machines.
The good news is that you can beat the system. The casinos don't always win. That's perhaps best exemplified by Don Johnson, the man who took Atlantic City for over $15 million, not by card counting, but by evening the odds and exploiting the casinos' accommodations though negotiation. Johnson knew that the only way to win was by understanding the system and playing the math. But with mobile games, the math isn't so easy. $10 spent in Tiny Tower may equate to a hundred hours otherwise spent grinding through game. The only winning move may be to take a cue from another movie, and not play at all.
This isn't particularly new, but gave me a chuckle when I saw it linked on Makezine's blog and adafruit. Last December, programmers on Stackoverflow (think Quora, but just about coding) had a serious discussion about the best way to use Wolfram's image-processing in Mathematica software to find the eponymous character in Where's Waldo books. The thread was even picked up by NPR's Wait Wait... Don't Tell Me game show. Mathematica has a been a pretty power tool for researchers since its release in the late 80s (Steve Jobs is actually credited for naming it), but it's also been used for fun side projects.
Hat tip to adafruit for finding the link.
The story so far: Roughly in the middle of the Pacific Ocean lies a vortex created by the North Pacific Gyre. The Gyre is made up of several ocean currents that carry warm water to the poles and cold water back to the tropics. The interesting thing about the North Pacific Gyre is that the vortex in the center of the gyre contains relatively calm water and has collected a massive quantity of floating trash, dubbed the Great Pacific Garbage Patch.
The trash floats in the same area as neustonic organisms--floating on or just under the water’s surface. The trash is largely invisible, it’s made of up many tiny particles of broken down plastic and bits of mono filament fishing line. How small are the particles? According to a 2001 study, the average size of pieces is 5mm x 5mm, making them essentially invisible from the surface. Unfortunately, the plastic does significant damage to the marine ecosystem, harming or killing animals that ingest it and emitting damaging chemicals that impact.
Because of the size of the particles involved and the fact that the garbage patch is in the middle of the Pacific Ocean, cleaning the mess is a bit of a sticky wicket. However, the designers of the Plastic Fish Tower, an entry into this year’s eVolo Skyscraper competition by a team from South Korea, aims to fix that. The Plastic Fish Tower is a spherical floating structure attached to a 1km diameter ring. The ring filters the floating plastic from the ocean, then pulls it into a central floating spherical tower, where it’s recycled into plastic fences for fish farms. Also in the tower are laboratories, residential areas, and leisure space, all beneath the sea.
Obviously, the Plastic Fish Tower won’t be built anytime soon. But with similar garbage patches being discovered in ocean vortexes around the world, we’ll need to find a solution for the floating plastic pellet problem sooner rather than later.
Image via eVolo
