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Sunday, November 18, 2018

Amateur Mathematician Finds Smallest Universal Cover | Mathematics - Quanta Magazine

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape, argues Kevin Hartnett, senior writer at Quanta Magazine covering mathematics and computer science.

A universal cover such as the hexagon can cover up any shape.
Photo: DVDP for Quanta Magazine

Philip Gibbs is not a professional mathematician. So when he wanted a problem to chew on, he looked for one where even an amateur could make a difference. What he found was a challenge that could drive even the most exacting minds mad. In a paper completed earlier this year, Gibbs achieved a major advance on a 100-year-old question that hinges on the ability to accurately measure area down to the atomic scale.

Amateur mathematician Philip Gibbs reduced the size of the smallest known universal cover using techniques inspired by a compass and protractor.
Photo: Courtesy of Philip Gibbs

The problem was first proposed by Henri Lebesgue, a French mathematician, in a 1914 letter to his friend Julius Pál. Lebesgue asked: What is the shape with the smallest area that can completely cover a host of other shapes (which all share a certain trait in common)?

In the century since, Lebesgue’s “universal covering” problem has turned out to be a mousetrap: Progress, when it’s come at all, has been astonishingly incremental. Gibbs’ improvement is dramatic by comparison, though you still have to squint to see it.

Picture a dozen paper cutouts of different sizes and shapes lying on your floor. Now imagine being asked to design another shape that is just big enough to cover any of those dozen shapes. Through experimentation — by overlaying the shapes and rotating them — you could feel your way to a solution. But once you’d found a “universal” cover, how would you know if you’d found the smallest one? You could imagine returning to your cover throughout the day and finding places to trim a little more here or a little more there.

That is the spirit of Lebesgue’s universal covering problem. Instead of paper cutouts, it considers shapes where no two points are farther than one unit apart...

Over the next 80 years, two other mathematicians shaved slivers from Pál’s universal cover. In 1936 Roland Sprague removed a section near one of the corners; in 1992 H. C. Hansen removed two vanishingly small wedges from the lower right and left corners. Illustrations of Hansen’s area savings would convey something about the locations but inevitably mislead about the size: They had an area of 0.00000000004 units.

“You can’t really draw them in scale because they’d be atom-sized pieces,” said John Baez, a mathematician at the University of California, Riverside.

Baez lifted Lebesgue’s universal covering problem out of obscurity when he wrote about it in 2013 on his popular math blog. He confessed he was attracted to the problem the way you might be attracted to watching an insect drown...

Atomic Scissors 
Early in his life, Gibbs thought he might become a scientist. He received an undergraduate degree in mathematics from the University of Cambridge and a Ph.D. in theoretical physics from the University of Glasgow. But he soon lost his enthusiasm for academic research and instead became a software engineer. He worked on systems for ship design, air traffic control and finance, before retiring in 2006...

In 2014 Gibbs ran computer simulations on 200 randomly generated shapes with diameter 1. Those simulations suggested he might be able to trim some area around the top corner of the previous smallest cover. He turned that lead into a proof that the new cover worked for all possible diameter-1 shapes. Gibbs sent the proof to Baez, who worked with one of his undergraduate students, Karine Bagdasaryan, to help Gibbs revise the proof into a more formal mathematical style.

The three of them posted the paper online in February 2015. It reduced the area of the smallest universal covering from 0.8441377 to 0.8441153 units. The savings — just 0.0000224 units — was almost one million times larger than the savings that Hansen had found in 1992.

Gibbs was confident he could do better. In a paper posted online in October, he lopped another relatively gargantuan slice from the universal cover, bringing its area down to 0.84409359 units...

In 2014 Gibbs ran computer simulations on 200 randomly generated shapes with diameter 1. Those simulations suggested he might be able to trim some area around the top corner of the previous smallest cover. He turned that lead into a proof that the new cover worked for all possible diameter-1 shapes. Gibbs sent the proof to Baez, who worked with one of his undergraduate students, Karine Bagdasaryan, to help Gibbs revise the proof into a more formal mathematical style.

The three of them posted the paper online in February 2015. It reduced the area of the smallest universal covering from 0.8441377 to 0.8441153 units. The savings — just 0.0000224 units — was almost one million times larger than the savings that Hansen had found in 1992.

Gibbs was confident he could do better. In a paper posted online in October, he lopped another relatively gargantuan slice from the universal cover, bringing its area down to 0.84409359 units.
Read more... 

Source: Quanta Magazine


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Twelve philosophy books everyone should read: from Plato to Foucault [slideshow] | Arts & Humanities - OUPblog

Panumas King, marketing executive for philosophy at Oxford University Press inform, This month, to mark World Philosophy Day, we’ve curated a reading list of historical texts by philosophers that shaped the modern world and who had important things to say about the issues that we wrestle with today such as freedom, authority, equality, sexuality, and the meaning of life.

Photo: Book-covered walls by Eugenio Mazzone. Public Domain via Unsplash.

Every year the third Thursday in November marks World Philosophy Day, UNESCO’s collaborative “initiative towards building inclusive societies, tolerance and peace.” To celebrate, we’ve curated a reading list of historical texts by great philosophers that shaped the modern world and who had important things to say about the issues that we wrestle with today such as freedom, authority, equality, sexuality, and the meaning of life.
Read more...

Source: OUPblog


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What Do Our Oldest Books Say About Us? | Culture - The New Republic

On the ineffable magic of four little manuscripts of Old English poetry, according to Josephine Livingstone, culture staff writer at The New Republic.

Codex Amiatinus, the earliest surviving complete Christian Bible in Latin.
Photo: British Library Board

There are four original manuscripts containing poetry in Old English—the now-defunct language of the medieval Anglo-Saxons—that have survived to the present day. No more, no less. They are: the Vercelli Book, which contains six poems, including the hallucinatory “Dream of the Rood”; the Junius Manuscript, which comprises four long religious poems; the Exeter Book, crammed with riddles and elegies; and the Beowulf Manuscript, whose name says it all. There is no way of knowing how many more poetic codices (the special term for these books) might have existed once upon a time, but have since been destroyed.

Until last week, I had seen two of these manuscripts in person and turned the pages of one. But then I visited “Anglo-Saxon Kingdoms: Art, Word, War,” a new show of artifacts at the British Library in London. It’s a vast exhibition, covering the art, literature, and history of the people whose kingdoms spread across Britain between the sixth and the eleventh centuries. The impetus for the show came from the library’s 2012 acquisition of the St Cuthbert Gospel, the “earliest intact European book,” in the words of the show’s catalog...

In 2018, we are in a much more elaborate and abstracted phase of Benjamin’s reproduction theory. We are accustomed to reading without reference to any physical object specific to the act of reading. We might have a romantic association with libraries, or prefer to turn real pages rather than electronic ones, but those are tastes borne of nostalgia. They have no real meaning for our experience of literature’s power.

This is why the reunion of the Old English poetic codices is so overwhelming. We have no mental equipment—or, at best, a very rusty apparatus—to process the existence of a physical original. Even our encounters with paintings in a museum are ultimately filtered through mass media and the devices with which we read the written word. It is difficult even to summon in our minds the circumstances of Benjamin’s 1936 essay; the technology has simply moved too quickly.
Read more... 

Source: The New Republic


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The 10 Best Fiction Books of 2018 | Books - TIME

Lucy Feldman, Books & Special Projects Editor at Time Magazine summarizes, From 'There There' to 'The Mars Room'. 


The best of this year’s fiction deals with prisons of all kinds — literal ones, but also dead-end jobs, luxury apartments and uncomfortable home states. Vibrant protagonists struggle against the confines of their worlds in novels by the likes of Rachel Kushner, Tayari Jones, Ottessa Moshfegh and more. But as with all great stories, there’s hope to be found in these pages. There’s resilience to be gained and hard-earned escapes to be savored. 

Here, the best fiction books of 2018.
Read more... 

Source: TIME


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For Keeps, a shop for rare and classic black books, opens on Auburn Avenue | News & Culture - Atlanta Magazine

For Keeps is open Thursdays through Sundays from 10 a.m.-5 p.m at 171 Auburn Avenue. This weekend, on November 17, they are open 9 a.m.-2 p.m. and closed Sunday the 18th. Follow their Instagram for updates.


Rosa Duffy designed the shop and reading room to be a place for people to interact with history that is often overlooked, says Jewel Wicker, entertainment reporter.

Inside For Keeps
Photo: courtesy of Rosa Duffy

There is, perhaps, no street in Atlanta more fitting than Auburn Avenue to house For Keeps bookstore.

Located in the historically black Sweet Auburn District, Rosa Duffy, 28, has opened a place she hopes will invite everyone, but especially black people, to come in and stay awhile. Inside the space, located at 171 Auburn Avenue, Duffy adjusts the books on display, wearing a caramel turtleneck, wide-legged blue jeans, and patent leather boots. A Kanga cloth from Tanzania that reads “Hongera Barack Obama,” (Swahili for “congratulations”) with a monochrome photo of the former president, hangs on display on one wall. Duffy’s own prints, sourced from old magazines and newspapers, including the Atlanta Daily World, are on display on the opposite wall.

For Keeps Bookstore is more than a place for visitors to purchase rare and classic black books. Duffy designed it to also be a reading room where people can stop in and interact with history that is often overlooked or placed in the bottom of the dollar bins at other bookstores.

Although the space has only been open for about a week, Rosa Duffy’s desire to open a bookstore was sparked over a decade ago by her introduction to Soulbook, a black periodical published in the 1960s and ’70s. She first encountered copies in her father’s personal literature collection and, around the age of 18, she began using scans of them for her art. (Duffy, who recently worked for Atlanta artist Radcliffe Bailey, mostly works with sculpture and paper.)...

Duffy says she’s hoping For Keeps will help dispel the myth that black people aren’t interested in learning about their history.

“The reality is, [some of] this stuff is in other spaces,” she says. “Some of the books that I have out here right now are in an exhibit at Emory [University], but it’s not inviting. It’s an atmosphere where you feel like you have to be a certain type of person to go in there and look at stuff.”
Read more...

Source: Atlanta Magazine  


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4 New Books We Recommend This Week | Book Review - New York Times

Follow on Twitter as @GregoryCowles
Suggested reading from critics and editors at The New York Times by Gregory Cowles, Senior Editor, Books.
 

Last week we offered you 12 new books to read — ambitious, I know, even for people who love books the way we do. So consider this the hangover edition, or the self-care edition, or what have you: four titles on an array of subjects, from historical fiction out of Italy (“The Novel of Ferrara”) to essays about Asian-American identity and other topics (“The Souls of Yellow Folk”) to the fraught evolution of particularly American catchphrases (“Behold, America”) to the book you were probably going to buy anyway, if only to keep up with your neighbors (Michelle Obama’s memoir, “Becoming”). If you have time left over, you can turn back to last week’s recommendations for a little hair of the dog.
Read more...

Source: New York Time   


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Saturday, November 17, 2018

UCCI set to unveil new degree program for working adults | Education - Cayman Compass

University College of the Cayman Islands President Roy Bodden believes the country’s adult population is an untapped resource for college study, inform Mark Muckenfuss, Journalist. 

Photo: University College of the Cayman Islands
“I was always interested in growing the numbers of the institution,” Mr. Bodden said, noting that enrollment in recent years has plateaued at about 1,200 students, almost all of whom are in their late teens or early 20s.

Recently, he said, he was at a conference when he heard Goldie Blumenstyk, a senior writer at the Chronicle of Higher Education, talking about adult learning.
“I said, ‘Voilà!’” Mr. Bodden said.

Ms. Blumenstyk will be the keynote speaker on Nov. 29, when UCCI hosts a “soft launch” of its Prior Learning Assessment program. Mr. Bodden said he expects the school will soon begin evaluating and accepting students for the program, with the first courses beginning in fall 2019.

The new program is designed to give adults with experience in the working world a leg up on pursuing or completing a college degree. Program administrators will grant prospective students with appropriate work experience course credit toward a degree, thus shortening the time it takes to graduate...

The initial course offerings are expected to be limited to business studies. Mr. Bodden said students will be assessed individually.
Read more...

Source: Cayman Compass


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How do mathematicians think? | The London Mathematical Society

This 60 minute documentary film features nine UK-based mathematicians offering insights into their mathematical thinking across a broad range of mathematical research fields.

Watch the Video - Vimeo

Through explorations of their various thought processes, the film portrays mathematicians who are grappling with advanced mathematical ideas. We are presented with the concepts of imagination, intuition, and wonder, as well as rigorous mathematical deduction.

The film features Kevin Buzzard, Peter Donnelly, Tim Gowers, Martin Hairer, Roger Penrose, Caroline Series, Richard Thomas, Reidun Twarock, and Karen Vogtmann.

Thinking Space is directed and produced by Heidi Morstang. The interviews were conducted and selected by Martin Hyland.

Source: The London Mathematical Society and Vimeo


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Adventures in Memory - The Science and Secrets of Remembering and Forgetting | Books - greystone books

Novelist Hilde Østby and neuroscientist Ylva Østby uncover the secrets of human memory.
 

Adventures in Memory
The Science and Secrets
of Remembering and Forgetting

What makes us remember? Why do we forget? And what, exactly, is a memory? Forgetting things is a positive sign. A new book by a Scandinavian neuropsychologist and her sister concludes that forgetfulness is essential for a healthy brain.

With playfulness and intelligence, Adventures in Memory answers these questions and more, offering an illuminating look at one of our most fascinating faculties. The authors—two Norwegian sisters, one a neuropsychologist and the other an acclaimed writer—skillfully interweave history, research, and exceptional personal stories, taking readers on a captivating exploration of the evolving understanding of the science of memory from the Renaissance discovery of the hippocampus—named after the seahorse it resembles—up to the present day. Mixing metaphor with meta-analysis, they embark on an incredible journey: “diving for seahorses” for a memory experiment in Oslo fjord, racing taxis through London, and “time-traveling” to the future to reveal thought-provoking insights into remembering and forgetting.
Read more... 

Source: greystone books


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11 Things You Need to Know About Generation Z | Hunt Scanlon Media

Contributed by Scott A. Scanlon, Editor-in-Chief; Dale M. Zupsansky, Managing Editor; Stephen Sawicki, Managing Editor; and Andrew W. Mitchell, Managing Editor – Hunt Scanlon Media.


Photo: Kevin Sheridan
Kevin Sheridan, a renowned talent consultant, provides 11 traits you should know about this digital native generation, along with insights from expert recruiters from Bridge Partners and Executives Unlimited. - They have known the digital world since birth, and now they are entering the workforce.
 
Photo: Hunt Scanlon Media

Generation Z. It is the first generation to know only a digital world. Its members grew up playing on their parents’ mobile devices, and many had their own smartphone as early as elementary school. Now that they’re on the brink of entering the job market, older workers are wondering how these ‘digital natives’ will impact the workforce.
There are many other monikers given to this generation, including Digital Natives, Globals, Post-Millennials, Millennials-On-Steroids, iGeneration, Plurals, the Homeland Generation, Centennials, and Delta Generation, or Deltas. That the generation has such an array of names in many ways illustrates the general lack of understanding about them, says a new report by talent consultant Kevin Sheridan.

Mr. Sheridan is an internationally-recognized keynote speaker, a New York Times bestselling author and a sought-after voice on the subject of employee engagement. Having spent 30 years as a human capital management consultant, he has helped some of the world’s largest corporations rebuild cultures that foster productive engagement, earning him several distinctive awards and honors.
Read more...

Source: Hunt Scanlon Media


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