What’s the News: In the long-running debate over the differences between men and women, one mental skill has emerged as being perhaps more biologically rooted than any other: the ability to solve problems involving physical spaces, shapes, or forms. Many studies have concluded that men simply seem to have an inherent advantage in this area. But a new study of two tribes in Northern India is suggesting that the gender gap we see in spatial skills may be partially due to culture rather than raw biology. This finding may affect the way researchers look at gender differences, but it will surely not settle the question, considering that it’s one study of a small group of people living in one limited environment.
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What’s the News: Most of us need everyone to stop talking when we perform mental math. But for children trained to do math visually with a “mental abacus,” verbal disturbances roll off their backs, prompting psychologists to posit that unlike the rest of us, they aren’t routing their calculations through words.
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What’s the News: Adults and school-age children may understand some basic principles of geometry even without formal math training at all, according to a study published online yesterday by the Proceedings of the National Academy of Sciences. Thirty members of the Mundurucú, an indigenous Amazonian group, could intuitively grasp geometric concepts about angles, lines, and points, the researchers found.
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What’s the News: Cool new apps come out every day, but not every app comes with its own car service. Starting in San Francisco, one company lets pedestrians hail a car using their iPhone or Android phone (or any old text-messaging clunker), providing a more expensive, yet faster alternative to cabs. To make this possible, computer scientists had to find a way to make driving routes as efficient as possible, which is actually quite complicated when you’re dealing with a city-ful of car-hailing people. As Uber CEO Travis Kalanick told Wired, “It’s really fun, sexy math.”
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How we talk about numbers plays a big role in how we think about numbers—that much is clear. But this week, new research makes the case that language is not a key part of thinking about numbers, but the key part, overriding other influences like cultural ones.
The study in the Proceedings of the National Academy of Sciences by psychologist Elizabet Spaepen focuses on a group of deaf Nicaraguans called the homesigners, who invented their own form of sign language—a form that lacks a numerical vocabulary.
That’s a common trait in many hunter-gatherer societies, where the numbering system is often one-two-three-many. For example, the Munduruku Amazonian people in rural Brazil don’t have any words for exact numbers larger than five. Their neighbors, the Piraha, no exact number words at all. [USA Today]
There are two things that make the homesigners extremely scientifically interesting. One is the fact that they spontaneously invented this language when brought together at a home for the deaf in the 1970s. And the other—the one that’s important for this study—is that they’re not an isolated tribe in which nobody uses numbers. They live within Nicaragua, surrounding by a Spanish-speaking society that’s as number-dependent as any other country. Thus, Spaepen’s team reasoned, if the homesigners struggle to conceptualize larger numbers, the reason would have to be linguistic and not cultural.
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New neuroscience research is not only adding to our understanding of math and number processing in the brain, it’s also suggesting a way to improve learning in the math-deficient.
A small new study published in Current Biology involved electrical stimulation of the parietal lobe, a part of the brain involved in math learning and understanding. When this area was stimulated, students performed better on a math problem test. Said study leader Cohen Kadosh:
“We’ve shown before that we can induce discalculia [an inability to do math], and now it seems we might be able to make someone better at maths, so we really want to see if we can help people with dyscalculia…. Electrical stimulation is unlikely to turn you into the next Einstein, but if we’re lucky it might be able to help some people to cope better with maths.” [BBC News]
Dyscalculia is a learning disability similar to dyslexia, in which a person has an innate difficulty with learning or understanding math. People with this condition can have trouble with daily arithmetic, telling left from right, and telling time on analog clocks. Some studies estimate up to five percent of the population suffers from dyscalculia, and about 20 percent have less severe troubles with math.
For the experiment, 15 students were hooked up to a transcranial direct current stimulation (tDCS) machine, which stimulates the brain through the skull with 1 milliamp of electricity, and were given either a positive (right to left) zap to their parietal lobe for 20 minutes, a positive zap for 30 seconds, or a negative (left to right) zap for 20 minutes (five students per group). The current produced a tingling sensation in the scalp, but it didn’t hurt. Then the students were trained to learn the assigned number values of made-up symbols.
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About two-fifths of marathon runners “hit the wall” on the big day. That means they completely deplete their body’s stash of readily available energy, which makes them feel wiped out and severely limits their running pace; it sometimes forces people out of the run completely.
Marathoner and biomedical engineer Benjamin Rapoport has been physically and mentally struggling with this phenomenon for years, and had the bright idea to turn it into a research project. He published a mathematical theory in the journal PLoS Computational Biology describing how and why runners hit the wall–and how they can avoid it.
By taking into account the energy it takes to run a marathon, the body’s energy storage capacity and the runner’s power, the researchers were able to accurately calculate how many energy-rich carbohydrates a runner needed to eat before race day and how fast to run to complete all 26.2 miles (42 kilometers). [LiveScience]
Rapoport’s studies of marathoners were prompted by his desire to run in the Boston Marathon in 2005, and his teacher’s desire for him to be in class. In return for missing class, Rapoport was tasked with giving a class lecture on the physiology of the marathoner. That same year, Rapoport himself hit the wall while running the New York Marathon.
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The world is not smooth, made of perfect spheres and unbroken lines. Its edges are tattered and torn, ragged yet recognizable. Last week the world lost the man whose mathematics helped to explain those patterns we see all the time in nature.
On Thursday, Benoît Mandelbrot died. His great book The Fractal Geometry of Nature appeared in 1982, and its fascinating notion rests on the idea of a shape becoming more and more complicated the further in one zooms.
“Fractals are easy to explain, it’s like a romanesco cauliflower, which is to say that each small part of it is exactly the same as the entire cauliflower itself,” Catherine Hill, a Gustave Roussy Institute statistician, [says]. “It’s a curve that reproduces itself to infinity. Every time you zoom in further, you find the same curve.” [PC World]
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After analyzing light coming from distant quasars, some researchers have asked a physical constant a blunt question: Are you really constant at all? And since the “fine structure constant” that they’re interrogating is important for how physicists understand things like electrons’ behavior in atoms and fusion in stars, other physicists are asking their own question: Are your measurements correct?
The paper, which appeared last month in arXiv, argues that the constant might vary depending on location. This controversial claim is a new twist on a previous controversial claim–made over the past decade by some of the same physicists–which said that the constant varied with time.
Craig Hogan of the University of Chicago and the Fermi National Accelerator Laboratory in Batavia, Ill., acknowledges that “it’s a competent team and a thorough analysis.” But because the work has such profound implications for physics and requires such a high level of precision measurements, “it needs more proof before we’ll believe it.” [Science News]
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Scientists have cranked through the numbers and determined that no matter how you mangle a Rubik’s Cube, if you’re doing it right you can theoretically solve the puzzle in 20 moves or fewer. By doing it right, we mean doing it like a supercomputer: Researchers tapped Google’s spare computing power to burn through the Cube’s 43,252,003,274,489,856,000 starting positions.
Even given Google’s processing power, the team–which included a mathematician, a Google engineer, a math teacher, and a programmer–could not solve the problem using brute force alone. They had to take all the starting positions and divide them into more manageable chunks, 2.2 billion smaller groups called “corsets,” which Google’s computers could solve simultaneously.
“The primary breakthrough was figuring out a way to solve so many positions, all at once, at such a fast rate,” says Tomas Rokicki, a programmer from Palo Alto, California, who has spent 15 years searching for the minimum number of moves guaranteed to solve any configuration of the Rubik’s cube. [New Scientist]
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P is not equal to NP. Seems simple enough. But if it’s true, it could be the answer to a problem computer scientists have wrestled for decades.
Vinay Deolalikar, who is with Hewlett-Packard Labs, has sent to peers copies of a proof he did stating that P is not equal to NP. Mathematicians are reviewing his work now—a task that could go on for a long time. If he’s correct, Deolalikar will have figured out one of the Clay Mathematics Institute’s seven Millennium Prize Problems, for which they give $1 million prizes. (Grigory Perelman won one of the seven for solving the Poincaré conjecture, but turned down the money last month.)
What’s all the hubbub? First, an explainer:
The P versus NP question concerns the speed at which a computer can accomplish a task such as factorising a number. Some tasks can be completed reasonably quickly – in technical terms, the running time is proportional to a polynomial function of the input size – and these tasks are in class P. If the answer to a task can be checked quickly then it is in class NP [New Scientist].
That definition is pretty abstract, so here’s a more concrete example:
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To test the basics of quantum theory, physicists recently pulled out an antique. In a paper published today in Science, they confirmed a staple of quantum mechanics, using a test derived from a classic nineteenth century light experiment.
In particular, the researchers questioned how particles move through three slits, something previously too difficult to measure. They found that the particles behaved just like quantum theory–or more specifically the Born Rule–would have predicted.
As physicist Chad Orzel describes in his blog, that’s bad news for theorists hoping to tweak this rule to solve Nobel Prize-worthy problems related to quantum gravity or Grand Unifying Theories.
[The study is good news if] you’re the ghost of Max Born, or the author of an introductory quantum book…. This was disappointing news for some theorists, though, as there are a number of ways to approach problems … that would require some modification of the Born rule. [Uncertain Principles]
But how did they do it?
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Though the wing-flapping contraptions of early human flight haven’t quite caught on, researchers think birds may still have something to teach us about navigating the air: how to land. MIT researchers have made a system that can bring a modified glider to an elegant bird-like stop, causing it to set down on its tail.
Russ Tedrake of MIT’s Computer Science and Artificial Intelligence Laboratory and his student Rick Cory developed the computer model to bring a basic foam glider to a unique landing. The principle behind the plane’s stop is the same one used by stunt planes–stall. When its wings tilt back, the plane loses lift and falls from the sky. Traditional planes don’t use this method to land because the airflow is chaotic (see smoke visualization above) making it hard to predict how the plane will behave.
Birds come to a stop by tilting their wings back at sharp angles. This creates turbulence and large, unpredictable whirlwinds behind the wings. If an airplane pointed its wings up in this way, it would lose lift and fall out of the sky. But MIT researchers wanted to take advantage of stall–specifically, post-stall drag–to help a plane come to a controlled landing. [Popular Science]
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Grigori Perelman isn’t much for prizes. This week Perelman, one of the world best and strangest mathematicians, proved it again by turning down a $1 million dollar prize from the Clay Mathematics Institute Millennium Prize for solving one of the most troubling math problems of the last century.
The Poincaré conjecture, named after prominent French mathematician Henri Poincaré, involves a complex problem in the field of topology — an important area of math that studies the enduring properties of objects that are stretched or otherwise deformed, but not torn or otherwise reconstituted. Scores of prominent mathematicians tried to solve it over decades but failed, leading to its characterization as the Mount Everest of math [Washington Post].
In 2003 Perelman put forth his solution to the conjecture, but not in the traditional way of putting it through the peer review process. Instead, he simply emerged from the shadows and threw his work up on the Internet with in a rebellious, “ta-da,” and waited for the world to catch up.
After a brief barnstorming tour in the United States, during which he refused interviews, Dr. Perelman returned to Russia, leaving the world’s mathematicians to pick up the pieces and decide whether he had really done it. A worldwide race to retrace, explicate and check Dr. Perelman’s proof ensued. In the meantime, Dr. Perelman quit his post at the Steklov Mathematical Institute, moved in with his mother and ceased communicating with the outside world [The New York Times].
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This week, the FBI arrested 11 alleged Russian spies living in New Jersey. How did they catch them? By digging through their photos.
These weren’t snapshots of covert meetings or secret handshakes, but–more likely–the quotidian: kittens and ice cream cones. They weren’t hidden in some obscure drop location, but viewable to the public, online. The pictures’ real importance was tucked inside, in encoded messages detailing secret meetings.
We aren’t talking Magic Eye–no mater how long you cross your eyes, staring at these pictures wouldn’t tell you where to drop off money or who to call. The alleged spies reportedly encoded the messages at the pixel level.
Every color on your computer screen is a combination of red, blue, and green–digitally represented as three numeric values. By making subtle changes to these numbers, the Russians hid binary code that someone–with the right software–could recombine into a message.
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