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Tomorrow are the semi-final and final rounds of the 2013 Scripps National Spelling Bee. Talented orthographers aged 8 to 14 will be tasked with spelling difficult words such as last year’s winner, guetapens, or the winner from 2012, cymotrichous.
However, many of us still have difficulty spelling even the simplest of words. We asked our followers on Twitter and fellow Reverbers what kinds of words still trip them up. MORE
Some cities have a litter problem, some suffer from high crime rates and others might have a lack of affordable housing. And then you have Dubai, which for the last several years has been facing the unusual problem of high end sports cars being abandoned and left to gather thick layers of dust at airport car parks and on the roadside across the city.
Above: (c) Nigel S, Below: (c) Didi Paterno
If you’ve ever been to Dubai or anywhere in the United Arab Emirates, you will have noticed they have a serious car culture out there, with a particular preference for the latest and greatest in high-end super cars. MORE
by Jason Marlin – May 23 2013
“Sir, look at me—did you have any shoes on?” asked the emergency medical tech. “Were you wearing shoes when you were struck?”
“Huh?” I wondered, a little dazed. “What’s with the shoe obsession?”
Let me back up. My family and I moved from Chicago to Asheville, North Carolina last autumn, ostensibly to get closer to nature. Mostly, this has been great. We still have an urban center we can walk to, but the woodland behind my house hosts all manner of flora and fauna. We’ve traded rat-infested dumpsters for trash bins overturned by bears; instead of skyscrapers, we now have mountains. Unfortunately, mountains don’t have lightning rods.
Yesterday, I was sitting in my studio office—basically a converted garage—while a thunderstorm brewed outside. After wrapping up a conference call with some of Ars’ finest, I was getting ready to dive back into work when the storm really picked up. “Ahhhh,” I thought as I leaned back in my chair to stare out at the strange greenish light against a purple-clouded backdrop. “So beautiful!”
At that moment—and this part is a little foggy—a bright arc of electricity shot through the window and directly into my chest. I’m not sure whether the arc originated from the sky or the ground, but it knocked me out of my chair. I hit the concrete floor and bounced back up to my feet, which were shuffling at top speed into a bookshelf. I remember thinking, “OK, going to die now. Do not fall down. Do not pass out.”
I’ve read that being struck by lightning is akin to a being hit by a huge defibrillator. I’m not sure about that—but it did feel magnitudes worse than the time I touched an electric fence as a kid.
I stumbled out of the studio and toward the house where my wife and children were staring out at me in horror. They had seen the flash and heard the tremendous crack that comes with a nearby lightning strike. My son Felix said the flash was so bright that he thought it had gone through the kitchen. As I staggered into the house looking like a wide-eyed psychopath, everyone knew something had happened. “I, I, I… think we need to call 911!” I stuttered.
At this point, I still couldn’t sit down, so I paced the house like a coked-out fratboy, clutching my heart while my wife Kris spoke with 911. “I’m sorry, did you ask if he had shoes on?” she said, then directed the question to me. It turns out there’s something of an obsession with shoes and lightning, the predominant belief being that rubber soles offer some insulating protection against the current. But as Kyle Hill writes in a blog post, “If lightning has burned its way through a mile or more of air (which is a superb insulator), it is hardly logical to believe that a few millimeters of any insulating material will be protective… I tend to believe that there would be little effect from whatever is on the bottom of your feet.”
By the time EMTs arrived in a siren-wailing ambulance (to the significant delight of my two-year-old), I was feeling much better. Still soaked in adrenaline, I felt no pain. The EMTs took my vitals and urged me to go to the hospital for testing. I declined, promising to call my doctor if anything weird started to happen. I mean, my grandmother was struck by lightning twice—how bad can it be? I didn’t have any burn marks, nor did I end up with a badass Lichtenburg scar. I was like a pirate with no peg leg or eyepatch.
I spent the rest of the day in a state of foggy confusion and realized that I may have developed a bona fide new phobia. As more thunderstorms rolled into the area last night, I gathered groggy children to the center-most area of the house and created a makeshift pillow raft to sleep on. I even woke a sleeping toddler; only a madman does this.
Neighbors blocks away later told my wife they heard the enormous boom and knew it was very close. “That would be my husband,” she replied.
To describe the experience as surreal is an understatement. I’m not sure how things worked out the way they did. I was on a concrete floor surrounded by electronics, which was something like a worst-case scenario. Remarkably, even the laptop and monitors just a few feet away from me survived.
Today, my whole body is sore—even my organs ache in a hard-to-describe way—but I feel lucky to have walked away unscathed. There’s a fine line between awe and terror. I have now been inextricably nudged to the right of it.
And no… I was not wearing shoes.
If you want to see which kids will grow up to be the most successful adults, visit their second-grade classroom, new research suggests.
A study by researchers at the University of Edinburgh in Scotland discovered that math and reading ability at age 7 are linked with socioeconomic status several decades later. The researchers found that such childhood abilities predict socioeconomic status in adulthood over and above associations with intelligence, education and socioeconomic status in childhood.
The study was based on data
from the National Child Development Study, a nationally representative study that followed more 17,000 people in England, Scotland and Wales over a span of about 50 years, from when they were born in 1958 to present-day. MORE
On April 17, a paper arrived in the inbox of Annals of Mathematics, one of the discipline’s preeminent journals. Written by a mathematician virtually unknown to the experts in his field — a 50-something lecturer at the University of New Hampshire named Yitang Zhang — the paper claimed to have taken a huge step forward in understanding one of mathematics’ oldest problems, the twin primes conjecture.
Editors of prominent mathematics journals are used to fielding grandiose claims from obscure authors, but this paper was different. Written with crystalline clarity and a total command of the topic’s current state of the art, it was evidently a serious piece of work, and the Annals editors decided to put it on the fast track.
Yitang Zhang (Photo: University of New Hampshire)
Just three weeks later — a blink of an eye compared to the usual pace of mathematics journals — Zhang received the referee report on his paper.
“The main results are of the first rank,” one of the referees wrote. The author had proved “a landmark theorem in the distribution of prime numbers.”
Rumors swept through the mathematics community that a great advance had been made by a researcher no one seemed to know — someone whose talents had been so overlooked after he earned his doctorate in 1992 that he had found it difficult to get an academic job, working for several years as an accountant and even in a Subway sandwich shop.
“Basically, no one knows him,” said Andrew Granville, a number theorist at the Université de Montréal. “Now, suddenly, he has proved one of the great results in the history of number theory.”
Mathematicians at Harvard University hastily arranged for Zhang to present his work to a packed audience there on May 13. As details of his work have emerged, it has become clear that Zhang achieved his result not via a radically new approach to the problem, but by applying existing methods with great perseverance.
“The big experts in the field had already tried to make this approach work,” Granville said. “He’s not a known expert, but he succeeded where all the experts had failed.”
The Problem of Pairs
Prime numbers — those that have no factors other than 1 and themselves — are the atoms of arithmetic and have fascinated mathematicians since the time of Euclid, who proved more than 2,000 years ago that there are infinitely many of them.
Because prime numbers are fundamentally connected with multiplication, understanding their additive properties can be tricky. Some of the oldest unsolved problems in mathematics concern basic questions about primes and addition, such as the twin primes conjecture, which proposes that there are infinitely many pairs of primes that differ by only 2, and the Goldbach conjecture, which proposes that every even number is the sum of two primes. (By an astonishing coincidence, a weaker version of this latter question was settled in a paper posted online by Harald Helfgott of École Normale Supérieure in Paris while Zhang was delivering his Harvard lecture.)
Prime numbers are abundant at the beginning of the number line, but they grow much sparser among large numbers. Of the first 10 numbers, for example, 40 percent are prime — 2, 3, 5 and 7 — but among 10-digit numbers, only about 4 percent are prime. For over a century, mathematicians have understood how the primes taper off on average: Among large numbers, the expected gap between prime numbers is approximately 2.3 times the number of digits; so, for example, among 100-digit numbers, the expected gap between primes is about 230.
But that’s just on average. Primes are often much closer together than the average predicts, or much farther apart. In particular, “twin” primes often crop up — pairs such as 3 and 5, or 11 and 13, that differ by only 2. And while such pairs get rarer among larger numbers, twin primes never seem to disappear completely (the largest pair discovered so far is 3,756,801,695,685 x 2666,669 – 1 and 3,756,801,695,685 x 2666,669 + 1).
For hundreds of years, mathematicians have speculated that there are infinitely many twin prime pairs. In 1849, French mathematician Alphonse de Polignac extended this conjecture to the idea that there should be infinitely many prime pairs for any possible finite gap, not just 2.
Since that time, the intrinsic appeal of these conjectures has given them the status of a mathematical holy grail, even though they have no known applications. But despite many efforts at proving them, mathematicians weren’t able to rule out the possibility that the gaps between primes grow and grow, eventually exceeding any particular bound.
Now Zhang has broken through this barrier. His paper shows that there is some number N smaller than 70 million such that there are infinitely many pairs of primes that differ by N. No matter how far you go into the deserts of the truly gargantuan prime numbers — no matter how sparse the primes become — you will keep finding prime pairs that differ by less than 70 million.
The result is “astounding,” said Daniel Goldston, a number theorist at San Jose State University. “It’s one of those problems you weren’t sure people would ever be able to solve.”
A Prime Sieve
The seeds of Zhang’s result lie in a paper from eight years ago that number theorists refer to as GPY, after its three authors — Goldston, János Pintz of the Alfréd Rényi Institute of Mathematics in Budapest, and Cem Y?ld?r?m of Bo?aziçi University in Istanbul. That paper came tantalizingly close but was ultimately unable to prove that there are infinitely many pairs of primes with some finite gap.
Instead, it showed that there will always be pairs of primes much closer together than the average spacing predicts. More precisely, GPY showed that for any fraction you choose, no matter how tiny, there will always be a pair of primes closer together than that fraction of the average gap, if you go out far enough along the number line. But the researchers couldn’t prove that the gaps between these prime pairs are always less than some particular finite number.
GPY uses a method called “sieving” to filter out pairs of primes that are closer together than average. Sieves have long been used in the study of prime numbers, starting with the 2,000-year-old Sieve of Eratosthenes, a technique for finding prime numbers.
To use the Sieve of Eratosthenes to find, say, all the primes up to 100, start with the number two, and cross out any higher number on the list that is divisible by two. Next move on to three, and cross out all the numbers divisible by three. Four is already crossed out, so you move on to five, and cross out all the numbers divisible by five, and so on. The numbers that survive this crossing-out process are the primes.
The Sieve of Eratosthenes This procedure, which dates back to the ancient Greeks, identifies all the primes less than a given number, in this case 121. It starts with the first prime — two, colored bright red — and eliminates all numbers divisible by two (colored dull red). Then it moves on to three (bright green) and eliminates all multiples of three (dull green). Four has already been eliminated, so next comes five (bright blue); the sieve eliminates all multiples of five (dull blue). It moves on to the next uncolored number, seven, and eliminates its multiples (dull yellow). The sieve would go on to 11 — the square root of 121 — but it can stop here, because all the non-primes bigger than 11 have already been filtered out. All the remaining numbers (colored purple) are primes. (Illustration: Sebastian Koppehel)
The Sieve of Eratosthenes works perfectly to identify primes, but it is too cumbersome and inefficient to be used to answer theoretical questions. Over the past century, number theorists have developed a collection of methods that provide useful approximate answers to such questions.
“The Sieve of Eratosthenes does too good a job,” Goldston said. “Modern sieve methods give up on trying to sieve perfectly.”
GPY developed a sieve that filters out lists of numbers that are plausible candidates for having prime pairs in them. To get from there to actual prime pairs, the researchers combined their sieving tool with a function whose effectiveness is based on a parameter called the level of distribution that measures how quickly the prime numbers start to display certain regularities.
The level of distribution is known to be at least ½. This is exactly the right value to prove the GPY result, but it falls just short of proving that there are always pairs of primes with a bounded gap. The sieve in GPY could establish that result, the researchers showed, but only if the level of distribution of the primes could be shown to be more than ½. Any amount more would be enough.
The theorem in GPY “would appear to be within a hair’s breadth of obtaining this result,” the researchers wrote.
But the more researchers tried to overcome this obstacle, the thicker the hair seemed to become. During the late 1980s, three researchers — Enrico Bombieri, a Fields medalist at the Institute for Advanced Study in Princeton, John Friedlander of the University of Toronto, and Henryk Iwaniec of Rutgers University — had developed a way to tweak the definition of the level of distribution to bring the value of this adjusted parameter up to 4/7. After the GPY paper was circulated in 2005, researchers worked feverishly to incorporate this tweaked level of distribution into GPY’s sieving framework, but to no avail.
“The big experts in the area tried and failed,” Granville said. “I personally didn’t think anyone was going to be able to do it any time soon.”
Closing the Gap
Meanwhile, Zhang was working in solitude to try to bridge the gap between the GPY result and the bounded prime gaps conjecture. A Chinese immigrant who received his doctorate from Purdue University, he had always been interested in number theory, even though it wasn’t the subject of his dissertation. During the difficult years in which he was unable to get an academic job, he continued to follow developments in the field.
“There are a lot of chances in your career, but the important thing is to keep thinking,” he said.
Zhang read the GPY paper, and in particular the sentence referring to the hair’s breadth between GPY and bounded prime gaps. “That sentence impressed me so much,” he said.
Without communicating with the field’s experts, Zhang started thinking about the problem. After three years, however, he had made no progress. “I was so tired,” he said.
To take a break, Zhang visited a friend in Colorado last summer. There, on July 3, during a half-hour lull in his friend’s backyard before leaving for a concert, the solution suddenly came to him. “I immediately realized that it would work,” he said.
Zhang’s idea was to use not the GPY sieve but a modified version of it, in which the sieve filters not by every number, but only by numbers that have no large prime factors.
“His sieve doesn’t do as good a job because you’re not using everything you can sieve with,” Goldston said. “But it turns out that while it’s a little less effective, it gives him the flexibility that allows the argument to work.”
While the new sieve allowed Zhang to prove that there are infinitely many prime pairs closer together than 70 million, it is unlikely that his methods can be pushed as far as the twin primes conjecture, Goldston said. Even with the strongest possible assumptions about the value of the level of distribution, he said, the best result likely to emerge from the GPY method would be that there are infinitely many prime pairs that differ by 16 or less.
But Granville said that mathematicians shouldn’t prematurely rule out the possibility of reaching the twin primes conjecture by these methods.
“This work is a game changer, and sometimes after a new proof, what had previously appeared to be much harder turns out to be just a tiny extension,” he said. “For now, we need to study the paper and see what’s what.”
It took Zhang several months to work through all the details, but the resulting paper is a model of clear exposition, Granville said. “He nailed down every detail so no one will doubt him. There’s no waffling.”
Once Zhang received the referee report, events unfolded with dizzying speed. Invitations to speak on his work poured in. “I think people are pretty thrilled that someone out of nowhere did this,” Granville said.
For Zhang, who calls himself shy, the glare of the spotlight has been somewhat uncomfortable. “I said, ‘Why is this so quick?’” he said. “It was confusing, sometimes.”
Zhang was not shy, though, during his Harvard talk, which attendees praised for its clarity. “When I’m giving a talk and concentrating on the math, I forget my shyness,” he said.
Zhang said he feels no resentment about the relative obscurity of his career thus far. “My mind is very peaceful. I don’t care so much about the money, or the honor,” he said. “I like to be very quiet and keep working by myself.”
Meanwhile, Zhang has already started work on his next project, which he declined to describe. “Hopefully it will be a good result,” he said.
Simons Science News is an editorially independent division of SimonsFoundation.org. Its 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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Authorities have arrested three people following allegations of prostitution and drug use at a senior citizen housing complex in northern New Jersey. GO HERE
If you haven’t settled on a career yet, this interactive chart from Rasmussen College can help you find the best options. It organizes occupations into four quadrants based on salary, expected job growth, and number of opportunities available.
